Subgroups — C₁₃×#62818 #15749157

Order 3328.

8042 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3542	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3537	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3536	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3534	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3519	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3496	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3494	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3492	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3490	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3484	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3484	C₂	1	4	yes	maximal, complemented
14	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
21	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#562	C₂²	1	16	yes	complemented
23	C₁₃×#560	C₂²	1	16	yes	complemented
24	C₁₃×#555	C₂²	1	8	yes	complemented
25	C₁₃×#554	C₂²	1	8	yes	complemented
26	C₁₃×#553	C₂²	1	8	yes	complemented
27	C₁₃×#553	C₂²	1	16	yes	complemented
28	C₁₃×#553	C₂²	1	8	yes	complemented
29	C₁₃×#553	C₂²	1	8	yes	complemented
30	C₁₃×#552	C₂²	1	8	yes	complemented
31	C₁₃×#551	C₂²	1	16	yes	complemented
32	C₁₃×#551	C₂²	1	16	yes	complemented
33	C₁₃×#550	C₂²	1	8	yes	complemented
34	C₁₃×#548	C₂²	1	8	yes	complemented
35	C₁₃×#547	C₂²	1	8	yes	complemented
36	C₁₃×#547	C₂²	1	8	yes	complemented
37	C₁₃×#546	C₂²	1	16	yes	complemented
38	C₁₃×#546	C₂²	1	8	yes	complemented
39	C₁₃×#546	C₂²	1	16	yes	complemented
40	C₁₃×#546	C₂²	1	8	yes	complemented
41	C₁₃×#546	C₂²	1	16	yes	complemented
42	C₁₃×#546	C₂²	1	16	yes	complemented
43	C₁₃×#546	C₂²	1	16	yes	complemented
44	C₁₃×#546	C₂²	1	8	yes	complemented
45	D₄²×C₁₃	C₂²	1	8	yes	complemented
46	D₄²×C₁₃	C₂²	1	16	yes	complemented
47	D₄²×C₁₃	C₂²	1	16	yes	complemented
48	D₄²×C₁₃	C₂²	1	8	yes	complemented
49	D₄²×C₁₃	C₂²	1	8	yes	complemented
50	C₁₃×#544	C₂²	1	2	yes	complemented
51	C₁₃×#543	C₂²	1	4	yes	complemented
52	C₁₃×#542	C₂²	1	8	yes	complemented
53	C₁₃×#540	C₂²	1	16	yes	complemented
54	C₁₃×#540	C₂²	1	8	yes	complemented
55	C₁₃×#539	C₂²	1	8	yes	complemented
56	C₁₃×#539	C₂²	1	8	yes	complemented
57	C₁₃×#538	C₂²	1	8	yes	complemented
58	C₁₃×#538	C₂²	1	8	yes	complemented
59	C₁₃×#538	C₂²	1	16	yes	complemented
60	C₁₃×#538	C₂²	1	8	yes	complemented
61	C₁₃×#537	C₂²	1	2	yes	complemented
62	C₁₃×#537	C₂²	1	8	yes	complemented
63	C₁₃×#537	C₂²	1	8	yes	complemented
64	C₁₃×#535	C₂²	1	8	yes	complemented
65	C₁₃×#535	C₂²	1	4	yes	complemented
66	C₁₃×#535	C₂²	1	8	yes	complemented
67	C₁₃×#534	C₂²	1	8	yes	complemented
68	C₁₃×#534	C₂²	1	8	yes	complemented
69	C₁₃×#534	C₂²	1	8	yes	complemented
70	C₁₃×#534	C₂²	1	4	yes	complemented
71	C₁₃×#534	C₂²	1	8	yes	complemented
72	C₁₃×#532	C₂²	1	8	yes	complemented
73	C₁₃×#529	C₂²	1	8	yes	complemented
74	C₁₃×#525	C₂²	1	4	yes	complemented
75	C₁₃×#525	C₂²	1	4	yes	complemented
76	C₁₃×#525	C₂²	1	8	yes	complemented
77	C₁₃×#525	C₂²	1	4	yes	complemented
78	C₁₃×#525	C₂²	1	4	yes	complemented
79	C₁₃×#525	C₂²	1	4	yes	complemented
80	C₁₃×#525	C₂²	1	4	yes	complemented
81	C₁₃×#525	C₂²	1	4	yes	complemented
82	C₁₃×#525	C₂²	1	4	yes	complemented
83	C₁₃×#525	C₂²	1	8	yes	complemented
84	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
85	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
86	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
87	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
88	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
89	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
90	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
93	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
94	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
95	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
96	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
97	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
98	C₁₃×#520	C₂²	1	4	yes	complemented
99	C₁₃×#518	C₂²	1	2	yes	complemented
100	C₁₃×#518	C₂²	1	4	yes	complemented
101	C₁₃×#518	C₂²	1	8	yes	complemented
102	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
103	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
104	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
105	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂⁵×C₁₃	C₂³	1	2	yes	—
109	C₁₃×H(5,𝔽₂)	—	4	16	no	—
110	C₁₃×H(5,𝔽₂)	—	4	8	no	—
111	C₂×C₁₃×#41	—	4	8	no	—
112	C₂×C₁₃×#41	C₂³	1	4	yes	—
113	C₂×C₁₃×#41	C₂³	1	4	yes	—
114	C₂×C₁₃×#41	C₂³	1	8	yes	—
115	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
116	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
117	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
118	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
119	C₂²×Q₈×C₁₃	C₂³	1	2	yes	complemented
120	C₂²×D₄×C₁₃	—	4	4	no	—
121	C₂²×D₄×C₁₃	—	4	8	no	—
122	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
123	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
129	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
130	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
132	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
133	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
134	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
137	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
138	C₂²×D₄×C₁₃	C₂³	1	8	yes	complemented
139	C₂³×C₄×C₁₃	—	4	4	no	—
140	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
150	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
151	C₁₃×#127	C₂³	1	8	yes	complemented
152	C₁₃×#127	C₂³	1	16	yes	complemented
153	C₁₃×#126	C₂³	1	16	yes	complemented
154	C₁₃×#126	C₂³	1	16	yes	complemented
155	C₁₃×#126	C₂³	1	16	yes	complemented
156	C₁₃×#125	C₂³	1	8	yes	complemented
157	C₁₃×#125	C₂³	1	16	yes	complemented
158	C₁₃×#124	C₂³	1	8	yes	complemented
159	C₁₃×#124	C₂³	1	16	yes	complemented
160	C₁₃×#124	C₂³	1	16	yes	complemented
161	C₁₃×#124	C₂³	1	16	yes	complemented
162	C₁₃×#123	C₂³	1	8	yes	—
163	C₁₃×#123	C₂³	1	8	yes	—
164	C₁₃×#123	C₂³	1	16	yes	—
165	C₁₃×#123	C₂³	1	8	yes	complemented
166	C₁₃×#123	C₂³	1	8	yes	complemented
167	C₁₃×#123	C₂³	1	16	yes	complemented
168	C₁₃×#123	C₂³	1	16	yes	complemented
169	C₁₃×#123	C₂³	1	16	yes	complemented
170	C₁₃×#123	C₂³	1	16	yes	complemented
171	C₁₃×#123	C₂³	1	16	yes	complemented
172	C₁₃×#123	C₂³	1	16	yes	complemented
173	C₁₃×#123	C₂³	1	16	yes	complemented
174	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
181	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
182	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
183	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
184	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
185	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
186	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
187	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
188	C₁₃×#121	C₂³	1	8	yes	—
189	C₁₃×#121	C₂³	1	8	yes	—
190	C₁₃×#121	C₂³	1	8	yes	—
191	C₁₃×#121	C₂³	1	8	yes	—
192	C₁₃×#121	C₂³	1	8	yes	—
193	C₁₃×#121	C₂³	1	8	yes	—
194	C₁₃×#121	C₂³	1	8	yes	—
195	C₁₃×#121	C₂³	1	8	yes	—
196	C₁₃×#121	C₂³	1	4	yes	—
197	C₁₃×#121	C₂³	1	4	yes	—
198	C₁₃×#121	C₂³	1	4	yes	—
199	C₁₃×#121	C₂³	1	4	yes	—
200	C₁₃×#121	C₂³	1	8	yes	—
201	C₁₃×#121	C₂³	1	8	yes	—
202	C₁₃×#121	C₂³	1	4	yes	complemented
203	C₁₃×#121	C₂³	1	4	yes	complemented
204	C₁₃×#121	C₂³	1	4	yes	complemented
205	C₁₃×#121	C₂³	1	4	yes	complemented
206	C₁₃×#121	C₂³	1	16	yes	complemented
207	C₁₃×#121	C₂³	1	8	yes	complemented
208	C₁₃×#121	C₂³	1	8	yes	complemented
209	C₁₃×#121	C₂³	1	16	yes	complemented
210	C₁₃×#121	C₂³	1	8	yes	complemented
211	C₁₃×#121	C₂³	1	16	yes	complemented
212	C₁₃×#121	C₂³	1	16	yes	complemented
213	C₁₃×#121	C₂³	1	16	yes	complemented
214	C₁₃×#121	C₂³	1	16	yes	complemented
215	C₁₃×#121	C₂³	1	16	yes	complemented
216	C₁₃×#121	C₂³	1	16	yes	complemented
217	C₁₃×#121	C₂³	1	16	yes	complemented
218	C₁₃×#121	C₂³	1	16	yes	complemented
219	C₁₃×#120	C₂³	1	8	yes	—
220	C₁₃×#120	C₂³	1	8	yes	—
221	C₁₃×#120	C₂³	1	8	yes	—
222	C₁₃×#120	C₂³	1	8	yes	—
223	C₁₃×#120	C₂³	1	16	yes	—
224	C₁₃×#120	C₂³	1	16	yes	—
225	C₁₃×#120	C₂³	1	16	yes	—
226	C₁₃×#120	C₂³	1	16	yes	complemented
227	C₁₃×#120	C₂³	1	16	yes	complemented
228	C₁₃×#120	C₂³	1	16	yes	complemented
229	C₁₃×#120	C₂³	1	16	yes	complemented
230	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
231	C₄×D₄×C₁₃	C₂³	1	8	yes	—
232	C₄×D₄×C₁₃	C₂³	1	8	yes	—
233	C₄×D₄×C₁₃	C₂³	1	8	yes	—
234	C₄×D₄×C₁₃	C₂³	1	8	yes	—
235	C₄×D₄×C₁₃	C₂³	1	16	yes	—
236	C₄×D₄×C₁₃	C₂³	1	16	yes	—
237	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
238	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
239	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
240	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
241	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
242	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
243	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
244	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
245	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
246	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
247	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
248	C₁₃×#117	C₂³	1	4	yes	—
249	C₁₃×#117	C₂³	1	4	yes	—
250	C₁₃×#117	C₂³	1	8	yes	—
251	C₁₃×#117	C₂³	1	4	yes	complemented
252	C₁₃×#117	C₂³	1	4	yes	complemented
253	C₁₃×#117	C₂³	1	16	yes	complemented
254	C₁₃×#117	C₂³	1	8	yes	complemented
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
264	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
265	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
266	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
267	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
269	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
270	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
271	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
273	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
274	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
275	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
276	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
277	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
278	#62818	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂⁴×C₁₃	—	2	4	no	—
280	C₂⁴×C₁₃	—	4	2	no	—
281	C₂⁴×C₁₃	—	4	2	no	—
282	C₂⁴×C₁₃	—	4	4	no	—
283	C₂⁴×C₁₃	—	4	4	no	—
284	C₂⁴×C₁₃	—	4	4	no	—
285	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
287	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
288	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
289	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
290	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
291	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
292	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
294	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₁₃×#41	—	2	16	no	—
296	C₁₃×#41	—	4	8	no	—
297	C₁₃×#41	—	4	8	no	—
298	C₁₃×#41	—	4	16	no	—
299	C₁₃×#41	—	4	32	no	—
300	C₁₃×#41	—	4	8	no	—
301	C₁₃×#41	—	4	16	no	—
302	C₂×Q₈×C₁₃	—	4	4	no	—
303	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
304	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
305	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
306	C₂×D₄×C₁₃	—	2	16	no	—
307	C₂×D₄×C₁₃	—	2	16	no	—
308	C₂×D₄×C₁₃	—	2	8	no	—
309	C₂×D₄×C₁₃	—	4	8	no	—
310	C₂×D₄×C₁₃	—	4	8	no	—
311	C₂×D₄×C₁₃	—	4	4	no	—
312	C₂×D₄×C₁₃	—	4	16	no	—
313	C₂×D₄×C₁₃	—	4	4	no	—
314	C₂×D₄×C₁₃	—	4	8	no	—
315	C₂×D₄×C₁₃	—	4	16	no	—
316	C₂×D₄×C₁₃	—	4	16	no	—
317	C₂×D₄×C₁₃	—	4	8	no	—
318	C₂×D₄×C₁₃	—	4	16	no	—
319	C₂×D₄×C₁₃	—	4	8	no	—
320	C₂×D₄×C₁₃	—	4	16	no	—
321	C₂×D₄×C₁₃	—	4	16	no	—
322	C₂×D₄×C₁₃	—	4	32	no	—
323	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
324	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
325	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
326	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
327	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
328	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
329	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
330	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
331	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
332	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
333	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
334	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
336	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
337	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
338	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
339	C₂²×C₄×C₁₃	—	2	4	no	—
340	C₂²×C₄×C₁₃	—	2	8	no	—
341	C₂²×C₄×C₁₃	—	4	4	no	—
342	C₂²×C₄×C₁₃	—	4	4	no	—
343	C₂²×C₄×C₁₃	—	4	4	no	—
344	C₂²×C₄×C₁₃	—	4	4	no	—
345	C₂²×C₄×C₁₃	—	4	8	no	—
346	C₂²×C₄×C₁₃	—	4	4	no	—
347	C₂²×C₄×C₁₃	—	4	2	no	—
348	C₂²×C₄×C₁₃	—	4	4	no	—
349	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
353	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
365	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
369	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
370	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
373	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
374	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
379	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
380	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
381	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
382	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
383	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
386	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
387	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
388	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
390	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
391	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
392	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
393	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
394	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
395	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
396	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
397	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
398	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
400	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
401	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
404	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
405	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
406	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
407	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
408	C₄²×C₁₃	C₂⁴	1	8	yes	—
409	C₄²×C₁₃	C₂⁴	1	8	yes	—
410	C₄²×C₁₃	C₂⁴	1	16	yes	—
411	#3542	C₂×C₁₃	1	8	yes	complemented
412	#3537	C₂×C₁₃	1	4	yes	complemented
413	#3536	C₂×C₁₃	1	4	yes	complemented
414	#3534	C₂×C₁₃	1	8	yes	complemented
415	#3519	C₂×C₁₃	1	8	yes	complemented
416	#3505	C₂×C₁₃	1	4	yes	complemented
417	#3496	C₂×C₁₃	1	4	yes	complemented
418	#3494	C₂×C₁₃	1	4	yes	complemented
419	#3492	C₂×C₁₃	1	2	yes	complemented
420	#3490	C₂×C₁₃	1	4	yes	complemented
421	#3488	C₂×C₁₃	1	4	yes	complemented
422	#3484	C₂×C₁₃	1	2	yes	complemented
423	#3484	C₂×C₁₃	1	4	yes	complemented
424	C₂×#525	C₂×C₁₃	1	2	yes	complemented
425	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
426	C₂³×C₁₃	—	2	2	no	—
427	C₂³×C₁₃	—	2	2	no	—
428	C₂³×C₁₃	—	2	2	no	—
429	C₂³×C₁₃	—	2	4	no	—
430	C₂³×C₁₃	—	2	4	no	—
431	C₂³×C₁₃	—	2	4	no	—
432	C₂³×C₁₃	—	2	2	no	—
433	C₂³×C₁₃	—	2	4	no	—
434	C₂³×C₁₃	—	2	8	no	—
435	C₂³×C₁₃	—	2	8	no	—
436	C₂³×C₁₃	—	2	8	no	—
437	C₂³×C₁₃	—	2	8	no	—
438	C₂³×C₁₃	—	4	1	no	—
439	C₂³×C₁₃	—	4	2	no	—
440	C₂³×C₁₃	—	4	1	no	—
441	C₂³×C₁₃	—	4	1	no	—
442	C₂³×C₁₃	—	4	2	no	—
443	C₂³×C₁₃	—	4	1	no	—
444	C₂³×C₁₃	—	4	4	no	—
445	C₂³×C₁₃	—	4	4	no	—
446	C₂³×C₁₃	—	4	4	no	—
447	C₂³×C₁₃	—	4	4	no	—
448	C₂³×C₁₃	—	4	4	no	—
449	C₂³×C₁₃	—	4	4	no	—
450	C₂³×C₁₃	—	4	4	no	—
451	C₂³×C₁₃	—	4	4	no	—
452	C₂³×C₁₃	—	4	8	no	—
453	C₂³×C₁₃	—	4	8	no	—
454	C₂³×C₁₃	—	4	8	no	—
455	C₂³×C₁₃	—	4	16	no	—
456	C₂³×C₁₃	—	8	16	no	—
457	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
458	C₂³×C₁₃	C₂⁵	1	8	yes	—
459	C₂³×C₁₃	C₂⁵	1	2	yes	—
460	C₂³×C₁₃	C₂⁵	1	8	yes	—
461	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
462	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
463	C₂³×C₁₃	C₂⁵	1	2	yes	—
464	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
465	Q₈×C₁₃	—	2	8	no	—
466	Q₈×C₁₃	—	4	4	no	—
467	Q₈×C₁₃	—	4	8	no	—
468	D₄×C₁₃	—	2	32	no	—
469	D₄×C₁₃	—	2	16	no	—
470	D₄×C₁₃	—	2	16	no	—
471	D₄×C₁₃	—	2	16	no	—
472	D₄×C₁₃	—	2	16	no	—
473	D₄×C₁₃	—	2	16	no	—
474	D₄×C₁₃	—	2	8	no	—
475	D₄×C₁₃	—	4	8	no	—
476	D₄×C₁₃	—	4	16	no	—
477	D₄×C₁₃	—	4	8	no	—
478	D₄×C₁₃	—	4	16	no	—
479	D₄×C₁₃	—	4	16	no	—
480	D₄×C₁₃	—	4	16	no	—
481	D₄×C₁₃	—	4	8	no	—
482	D₄×C₁₃	—	4	4	no	—
483	D₄×C₁₃	—	4	8	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	4	no	—
486	C₂×C₄×C₁₃	—	2	8	no	—
487	C₂×C₄×C₁₃	—	2	8	no	—
488	C₂×C₄×C₁₃	—	2	4	no	—
489	C₂×C₄×C₁₃	—	2	4	no	—
490	C₂×C₄×C₁₃	—	2	4	no	—
491	C₂×C₄×C₁₃	—	2	4	no	—
492	C₂×C₄×C₁₃	—	2	4	no	—
493	C₂×C₄×C₁₃	—	2	4	no	—
494	C₂×C₄×C₁₃	—	2	16	no	—
495	C₂×C₄×C₁₃	—	4	1	no	—
496	C₂×C₄×C₁₃	—	4	2	no	—
497	C₂×C₄×C₁₃	—	4	2	no	—
498	C₂×C₄×C₁₃	—	4	2	no	—
499	C₂×C₄×C₁₃	—	4	2	no	—
500	C₂×C₄×C₁₃	—	4	2	no	—
501	C₂×C₄×C₁₃	—	4	1	no	—
502	C₂×C₄×C₁₃	—	4	4	no	—
503	C₂×C₄×C₁₃	—	4	4	no	—
504	C₂×C₄×C₁₃	—	4	4	no	—
505	C₂×C₄×C₁₃	—	4	8	no	—
506	C₂×C₄×C₁₃	—	4	4	no	—
507	C₂×C₄×C₁₃	—	4	8	no	—
508	C₂×C₄×C₁₃	—	4	16	no	—
509	C₂×C₄×C₁₃	—	4	8	no	—
510	C₂×C₄×C₁₃	—	4	8	no	—
511	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
512	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
513	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
514	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
515	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
516	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
517	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
518	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
519	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
520	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
521	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
522	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
523	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
525	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
526	#562	C₂²×C₁₃	1	16	yes	complemented
527	#560	C₂²×C₁₃	1	16	yes	complemented
528	#555	C₂²×C₁₃	1	8	yes	complemented
529	#554	C₂²×C₁₃	1	8	yes	complemented
530	#553	C₂²×C₁₃	1	8	yes	complemented
531	#553	C₂²×C₁₃	1	8	yes	complemented
532	#553	C₂²×C₁₃	1	8	yes	complemented
533	#553	C₂²×C₁₃	1	16	yes	complemented
534	#552	C₂²×C₁₃	1	8	yes	complemented
535	#551	C₂²×C₁₃	1	16	yes	complemented
536	#551	C₂²×C₁₃	1	16	yes	complemented
537	#550	C₂²×C₁₃	1	8	yes	complemented
538	#548	C₂²×C₁₃	1	8	yes	complemented
539	#547	C₂²×C₁₃	1	8	yes	complemented
540	#547	C₂²×C₁₃	1	8	yes	complemented
541	#546	C₂²×C₁₃	1	16	yes	complemented
542	#546	C₂²×C₁₃	1	8	yes	complemented
543	#546	C₂²×C₁₃	1	16	yes	complemented
544	#546	C₂²×C₁₃	1	8	yes	complemented
545	#546	C₂²×C₁₃	1	16	yes	complemented
546	#546	C₂²×C₁₃	1	16	yes	complemented
547	#546	C₂²×C₁₃	1	8	yes	complemented
548	#546	C₂²×C₁₃	1	16	yes	complemented
549	D₄²	C₂²×C₁₃	1	16	yes	complemented
550	D₄²	C₂²×C₁₃	1	8	yes	complemented
551	D₄²	C₂²×C₁₃	1	8	yes	complemented
552	D₄²	C₂²×C₁₃	1	16	yes	complemented
553	D₄²	C₂²×C₁₃	1	8	yes	complemented
554	#544	C₂²×C₁₃	1	2	yes	complemented
555	#543	C₂²×C₁₃	1	4	yes	complemented
556	#542	C₂²×C₁₃	1	8	yes	complemented
557	#540	C₂²×C₁₃	1	8	yes	complemented
558	#540	C₂²×C₁₃	1	16	yes	complemented
559	#539	C₂²×C₁₃	1	8	yes	complemented
560	#539	C₂²×C₁₃	1	8	yes	complemented
561	#538	C₂²×C₁₃	1	8	yes	complemented
562	#538	C₂²×C₁₃	1	8	yes	complemented
563	#538	C₂²×C₁₃	1	8	yes	complemented
564	#538	C₂²×C₁₃	1	16	yes	complemented
565	#537	C₂²×C₁₃	1	2	yes	complemented
566	#537	C₂²×C₁₃	1	8	yes	complemented
567	#537	C₂²×C₁₃	1	8	yes	complemented
568	#535	C₂²×C₁₃	1	4	yes	complemented
569	#535	C₂²×C₁₃	1	8	yes	complemented
570	#535	C₂²×C₁₃	1	8	yes	complemented
571	#534	C₂²×C₁₃	1	8	yes	complemented
572	#534	C₂²×C₁₃	1	8	yes	complemented
573	#534	C₂²×C₁₃	1	8	yes	complemented
574	#534	C₂²×C₁₃	1	4	yes	complemented
575	#534	C₂²×C₁₃	1	8	yes	complemented
576	#532	C₂²×C₁₃	1	8	yes	complemented
577	#529	C₂²×C₁₃	1	8	yes	complemented
578	#525	C₂²×C₁₃	1	4	yes	complemented
579	#525	C₂²×C₁₃	1	4	yes	complemented
580	#525	C₂²×C₁₃	1	8	yes	complemented
581	#525	C₂²×C₁₃	1	4	yes	complemented
582	#525	C₂²×C₁₃	1	4	yes	complemented
583	#525	C₂²×C₁₃	1	4	yes	complemented
584	#525	C₂²×C₁₃	1	4	yes	complemented
585	#525	C₂²×C₁₃	1	4	yes	complemented
586	#525	C₂²×C₁₃	1	4	yes	complemented
587	#525	C₂²×C₁₃	1	8	yes	complemented
588	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
589	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
590	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
591	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
592	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
593	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
594	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
595	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
596	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
597	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
598	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
599	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
600	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
601	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
602	#520	C₂²×C₁₃	1	4	yes	complemented
603	#518	C₂²×C₁₃	1	2	yes	complemented
604	#518	C₂²×C₁₃	1	4	yes	complemented
605	#518	C₂²×C₁₃	1	8	yes	complemented
606	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
607	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
608	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
609	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
611	C₂²×C₁₃	—	2	8	no	—
612	C₂²×C₁₃	—	2	2	no	—
613	C₂²×C₁₃	—	2	1	no	—
614	C₂²×C₁₃	—	2	1	no	—
615	C₂²×C₁₃	—	2	1	no	—
616	C₂²×C₁₃	—	2	1	no	—
617	C₂²×C₁₃	—	2	2	no	—
618	C₂²×C₁₃	—	2	1	no	—
619	C₂²×C₁₃	—	2	1	no	—
620	C₂²×C₁₃	—	2	2	no	—
621	C₂²×C₁₃	—	2	8	no	—
622	C₂²×C₁₃	—	2	8	no	—
623	C₂²×C₁₃	—	2	8	no	—
624	C₂²×C₁₃	—	2	8	no	—
625	C₂²×C₁₃	—	2	2	no	—
626	C₂²×C₁₃	—	2	8	no	—
627	C₂²×C₁₃	—	2	8	no	—
628	C₂²×C₁₃	—	2	2	no	—
629	C₂²×C₁₃	—	4	4	no	—
630	C₂²×C₁₃	—	4	8	no	—
631	C₂²×C₁₃	—	4	8	no	—
632	C₂²×C₁₃	—	4	4	no	—
633	C₂²×C₁₃	—	8	8	no	—
634	C₂²×C₁₃	—	8	8	no	—
635	C₂²×C₁₃	—	8	8	no	—
636	C₂²×C₁₃	—	8	8	no	—
637	C₂²×C₁₃	—	16	8	no	—
638	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
639	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
640	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
641	C₂²×C₁₃	#585	1	2	yes	—
642	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
643	C₄×C₁₃	—	2	2	no	—
644	C₄×C₁₃	—	2	2	no	—
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	—	2	8	no	—
647	C₄×C₁₃	—	2	8	no	—
648	C₄×C₁₃	—	2	8	no	—
649	C₄×C₁₃	—	2	8	no	—
650	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
651	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
652	C₂⁵	C₂³×C₁₃	1	2	yes	—
653	H(5,𝔽₂)	—	4	16	no	—
654	H(5,𝔽₂)	—	4	8	no	—
655	C₂×#41	—	4	8	no	—
656	C₂×#41	C₂³×C₁₃	1	4	yes	—
657	C₂×#41	C₂³×C₁₃	1	4	yes	—
658	C₂×#41	C₂³×C₁₃	1	8	yes	—
659	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
660	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
661	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
662	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
663	C₂²×Q₈	C₂³×C₁₃	1	2	yes	complemented
664	C₂²×D₄	—	4	4	no	—
665	C₂²×D₄	—	4	8	no	—
666	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
667	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
668	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
669	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
670	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
671	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
672	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
673	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
674	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
675	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
676	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
677	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
678	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
679	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
680	C₂²×D₄	C₂³×C₁₃	1	2	yes	complemented
681	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
682	C₂²×D₄	C₂³×C₁₃	1	8	yes	complemented
683	C₂³×C₄	—	4	4	no	—
684	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
685	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
686	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
687	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
688	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
689	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
690	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
691	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
692	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
693	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
694	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
695	#127	C₂³×C₁₃	1	8	yes	complemented
696	#127	C₂³×C₁₃	1	16	yes	complemented
697	#126	C₂³×C₁₃	1	16	yes	complemented
698	#126	C₂³×C₁₃	1	16	yes	complemented
699	#126	C₂³×C₁₃	1	16	yes	complemented
700	#125	C₂³×C₁₃	1	8	yes	complemented
701	#125	C₂³×C₁₃	1	16	yes	complemented
702	#124	C₂³×C₁₃	1	8	yes	complemented
703	#124	C₂³×C₁₃	1	16	yes	complemented
704	#124	C₂³×C₁₃	1	16	yes	complemented
705	#124	C₂³×C₁₃	1	16	yes	complemented
706	#123	C₂³×C₁₃	1	8	yes	—
707	#123	C₂³×C₁₃	1	8	yes	—
708	#123	C₂³×C₁₃	1	16	yes	—
709	#123	C₂³×C₁₃	1	8	yes	complemented
710	#123	C₂³×C₁₃	1	8	yes	complemented
711	#123	C₂³×C₁₃	1	16	yes	complemented
712	#123	C₂³×C₁₃	1	16	yes	complemented
713	#123	C₂³×C₁₃	1	16	yes	complemented
714	#123	C₂³×C₁₃	1	16	yes	complemented
715	#123	C₂³×C₁₃	1	16	yes	complemented
716	#123	C₂³×C₁₃	1	16	yes	complemented
717	#123	C₂³×C₁₃	1	16	yes	complemented
718	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
719	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
720	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
721	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
722	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
723	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
724	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
725	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
726	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
727	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
728	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
729	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
730	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
731	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
732	#121	C₂³×C₁₃	1	8	yes	—
733	#121	C₂³×C₁₃	1	8	yes	—
734	#121	C₂³×C₁₃	1	8	yes	—
735	#121	C₂³×C₁₃	1	8	yes	—
736	#121	C₂³×C₁₃	1	8	yes	—
737	#121	C₂³×C₁₃	1	8	yes	—
738	#121	C₂³×C₁₃	1	8	yes	—
739	#121	C₂³×C₁₃	1	8	yes	—
740	#121	C₂³×C₁₃	1	4	yes	—
741	#121	C₂³×C₁₃	1	4	yes	—
742	#121	C₂³×C₁₃	1	4	yes	—
743	#121	C₂³×C₁₃	1	4	yes	—
744	#121	C₂³×C₁₃	1	8	yes	—
745	#121	C₂³×C₁₃	1	8	yes	—
746	#121	C₂³×C₁₃	1	4	yes	complemented
747	#121	C₂³×C₁₃	1	4	yes	complemented
748	#121	C₂³×C₁₃	1	4	yes	complemented
749	#121	C₂³×C₁₃	1	4	yes	complemented
750	#121	C₂³×C₁₃	1	16	yes	complemented
751	#121	C₂³×C₁₃	1	8	yes	complemented
752	#121	C₂³×C₁₃	1	8	yes	complemented
753	#121	C₂³×C₁₃	1	16	yes	complemented
754	#121	C₂³×C₁₃	1	8	yes	complemented
755	#121	C₂³×C₁₃	1	16	yes	complemented
756	#121	C₂³×C₁₃	1	16	yes	complemented
757	#121	C₂³×C₁₃	1	16	yes	complemented
758	#121	C₂³×C₁₃	1	16	yes	complemented
759	#121	C₂³×C₁₃	1	16	yes	complemented
760	#121	C₂³×C₁₃	1	16	yes	complemented
761	#121	C₂³×C₁₃	1	16	yes	complemented
762	#121	C₂³×C₁₃	1	16	yes	complemented
763	#120	C₂³×C₁₃	1	8	yes	—
764	#120	C₂³×C₁₃	1	8	yes	—
765	#120	C₂³×C₁₃	1	8	yes	—
766	#120	C₂³×C₁₃	1	8	yes	—
767	#120	C₂³×C₁₃	1	16	yes	—
768	#120	C₂³×C₁₃	1	16	yes	—
769	#120	C₂³×C₁₃	1	16	yes	—
770	#120	C₂³×C₁₃	1	16	yes	complemented
771	#120	C₂³×C₁₃	1	16	yes	complemented
772	#120	C₂³×C₁₃	1	16	yes	complemented
773	#120	C₂³×C₁₃	1	16	yes	complemented
774	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
775	C₄×D₄	C₂³×C₁₃	1	8	yes	—
776	C₄×D₄	C₂³×C₁₃	1	8	yes	—
777	C₄×D₄	C₂³×C₁₃	1	8	yes	—
778	C₄×D₄	C₂³×C₁₃	1	8	yes	—
779	C₄×D₄	C₂³×C₁₃	1	16	yes	—
780	C₄×D₄	C₂³×C₁₃	1	16	yes	—
781	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
782	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
783	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
784	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
785	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
786	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
787	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
788	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
789	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
790	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
791	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
792	#117	C₂³×C₁₃	1	4	yes	—
793	#117	C₂³×C₁₃	1	4	yes	—
794	#117	C₂³×C₁₃	1	8	yes	—
795	#117	C₂³×C₁₃	1	4	yes	complemented
796	#117	C₂³×C₁₃	1	4	yes	complemented
797	#117	C₂³×C₁₃	1	16	yes	complemented
798	#117	C₂³×C₁₃	1	8	yes	complemented
799	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
800	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
802	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
803	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
804	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
805	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
806	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
807	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
808	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
819	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
820	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
821	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
822	C₂×C₁₃	—	2	2	no	—
823	C₂×C₁₃	—	2	2	no	—
824	C₂×C₁₃	—	2	2	no	—
825	C₂×C₁₃	—	2	4	no	—
826	C₂×C₁₃	—	4	2	no	—
827	C₂×C₁₃	—	4	8	no	—
828	C₂×C₁₃	—	4	8	no	—
829	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
832	C₂⁴	—	2	4	no	—
833	C₂⁴	—	4	2	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	4	no	—
836	C₂⁴	—	4	4	no	—
837	C₂⁴	—	4	4	no	—
838	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
839	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
840	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
841	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
842	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
843	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
844	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
845	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
847	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
848	#41	—	2	16	no	—
849	#41	—	4	8	no	—
850	#41	—	4	8	no	—
851	#41	—	4	16	no	—
852	#41	—	4	32	no	—
853	#41	—	4	8	no	—
854	#41	—	4	16	no	—
855	C₂×Q₈	—	4	4	no	—
856	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
857	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
858	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
859	C₂×D₄	—	2	16	no	—
860	C₂×D₄	—	2	16	no	—
861	C₂×D₄	—	2	8	no	—
862	C₂×D₄	—	4	8	no	—
863	C₂×D₄	—	4	8	no	—
864	C₂×D₄	—	4	4	no	—
865	C₂×D₄	—	4	16	no	—
866	C₂×D₄	—	4	4	no	—
867	C₂×D₄	—	4	8	no	—
868	C₂×D₄	—	4	16	no	—
869	C₂×D₄	—	4	16	no	—
870	C₂×D₄	—	4	8	no	—
871	C₂×D₄	—	4	16	no	—
872	C₂×D₄	—	4	16	no	—
873	C₂×D₄	—	4	8	no	—
874	C₂×D₄	—	4	16	no	—
875	C₂×D₄	—	4	32	no	—
876	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
877	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
878	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
879	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
880	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
881	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
882	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
883	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
884	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
885	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
886	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
887	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
888	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
889	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
890	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
891	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
892	C₂²×C₄	—	2	4	no	—
893	C₂²×C₄	—	2	8	no	—
894	C₂²×C₄	—	4	4	no	—
895	C₂²×C₄	—	4	4	no	—
896	C₂²×C₄	—	4	4	no	—
897	C₂²×C₄	—	4	4	no	—
898	C₂²×C₄	—	4	8	no	—
899	C₂²×C₄	—	4	4	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	—	4	4	no	—
902	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
904	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
906	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
911	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
914	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
916	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
918	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
919	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
920	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
921	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
922	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
923	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
926	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
927	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
931	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
933	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
934	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
935	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
936	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
937	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
938	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
939	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
941	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
942	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
943	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
944	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
945	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
949	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
950	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
951	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
953	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
954	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
955	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
956	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
957	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
958	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
961	C₄²	C₂⁴×C₁₃	1	8	yes	—
962	C₄²	C₂⁴×C₁₃	1	8	yes	—
963	C₄²	C₂⁴×C₁₃	1	16	yes	—
964	C₁₃	#62818	1	1	yes	characteristic, direct product factor, Sylow
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	4	no	—
969	C₂³	—	2	4	no	—
970	C₂³	—	2	4	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	4	no	—
973	C₂³	—	2	8	no	—
974	C₂³	—	2	8	no	—
975	C₂³	—	2	8	no	—
976	C₂³	—	2	8	no	—
977	C₂³	—	4	1	no	—
978	C₂³	—	4	2	no	—
979	C₂³	—	4	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	2	no	—
982	C₂³	—	4	1	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	4	4	no	—
985	C₂³	—	4	4	no	—
986	C₂³	—	4	4	no	—
987	C₂³	—	4	4	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	4	4	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	8	no	—
994	C₂³	—	4	16	no	—
995	C₂³	—	8	16	no	—
996	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
997	C₂³	C₂⁵×C₁₃	1	8	yes	—
998	C₂³	C₂⁵×C₁₃	1	2	yes	—
999	C₂³	C₂⁵×C₁₃	1	8	yes	—
1000	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1001	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1002	C₂³	C₂⁵×C₁₃	1	2	yes	—
1003	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1004	Q₈	—	2	8	no	—
1005	Q₈	—	4	4	no	—
1006	Q₈	—	4	8	no	—
1007	D₄	—	2	32	no	—
1008	D₄	—	2	16	no	—
1009	D₄	—	2	16	no	—
1010	D₄	—	2	16	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	16	no	—
1013	D₄	—	2	8	no	—
1014	D₄	—	4	8	no	—
1015	D₄	—	4	16	no	—
1016	D₄	—	4	8	no	—
1017	D₄	—	4	16	no	—
1018	D₄	—	4	16	no	—
1019	D₄	—	4	16	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	8	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	4	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	4	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	4	no	—
1031	C₂×C₄	—	2	4	no	—
1032	C₂×C₄	—	2	4	no	—
1033	C₂×C₄	—	2	16	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	8	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	8	no	—
1047	C₂×C₄	—	4	16	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
1051	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1052	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1053	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1054	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1055	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1056	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1057	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1058	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1059	C₂²	—	2	8	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	8	no	—
1070	C₂²	—	2	8	no	—
1071	C₂²	—	2	8	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	8	no	—
1075	C₂²	—	2	8	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	4	no	—
1078	C₂²	—	4	8	no	—
1079	C₂²	—	4	8	no	—
1080	C₂²	—	4	4	no	—
1081	C₂²	—	8	8	no	—
1082	C₂²	—	8	8	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	8	8	no	—
1085	C₂²	—	16	8	no	—
1086	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1087	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1088	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1089	C₂²	C₁₃×#585	1	2	yes	—
1090	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	8	no	—
1096	C₄	—	2	8	no	—
1097	C₄	—	2	8	no	—
1098	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1099	C₂	—	2	2	no	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	2	no	—
1102	C₂	—	2	4	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	8	no	—
1105	C₂	—	4	8	no	—
1106	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1107	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3542	C₂	semidirect
2. C₁₃×#3537	C₂	semidirect
3. C₁₃×#3536	C₂	semidirect
4. C₁₃×#3534	C₂	semidirect
5. C₁₃×#3519	C₂	semidirect
6. C₁₃×#3505	C₂	semidirect
7. C₁₃×#3496	C₂	semidirect
8. C₁₃×#3494	C₂	semidirect
9. C₁₃×#3492	C₂	semidirect
10. C₁₃×#3490	C₂	semidirect
11. C₁₃×#3488	C₂	semidirect
12. C₁₃×#3484	C₂	semidirect
13. C₁₃×#3484	C₂	semidirect
14. C₂×C₁₃×#525	C₂	semidirect
15. C₂²×C₁₃×#121	C₂	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
19. C₂³×D₄×C₁₃	C₂²	semidirect
20. C₂³×D₄×C₁₃	C₂²	semidirect
21. C₂⁴×C₄×C₁₃	C₂²	semidirect
22. C₁₃×#562	C₂²	semidirect
23. C₁₃×#560	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
27. C₁₃×#553	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
30. C₁₃×#552	C₂²	semidirect
31. C₁₃×#551	C₂²	semidirect
32. C₁₃×#551	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
34. C₁₃×#548	C₂²	semidirect
35. C₁₃×#547	C₂²	semidirect
36. C₁₃×#547	C₂²	semidirect
37. C₁₃×#546	C₂²	semidirect
38. C₁₃×#546	C₂²	semidirect
39. C₁₃×#546	C₂²	semidirect
40. C₁₃×#546	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
43. C₁₃×#546	C₂²	semidirect
44. C₁₃×#546	C₂²	semidirect
45. D₄²×C₁₃	C₂²	semidirect
46. D₄²×C₁₃	C₂²	semidirect
47. D₄²×C₁₃	C₂²	semidirect
48. D₄²×C₁₃	C₂²	semidirect
49. D₄²×C₁₃	C₂²	semidirect
50. C₁₃×#544	C₂²	semidirect
51. C₁₃×#543	C₂²	semidirect
52. C₁₃×#542	C₂²	semidirect
53. C₁₃×#540	C₂²	semidirect
54. C₁₃×#540	C₂²	semidirect
55. C₁₃×#539	C₂²	semidirect
56. C₁₃×#539	C₂²	semidirect
57. C₁₃×#538	C₂²	semidirect
58. C₁₃×#538	C₂²	semidirect
59. C₁₃×#538	C₂²	semidirect
60. C₁₃×#538	C₂²	semidirect
61. C₁₃×#537	C₂²	semidirect
62. C₁₃×#537	C₂²	semidirect
63. C₁₃×#537	C₂²	semidirect
64. C₁₃×#535	C₂²	semidirect
65. C₁₃×#535	C₂²	semidirect
66. C₁₃×#535	C₂²	semidirect
67. C₁₃×#534	C₂²	semidirect
68. C₁₃×#534	C₂²	semidirect
69. C₁₃×#534	C₂²	semidirect
70. C₁₃×#534	C₂²	semidirect
71. C₁₃×#534	C₂²	semidirect
72. C₁₃×#532	C₂²	semidirect
73. C₁₃×#529	C₂²	semidirect
74. C₁₃×#525	C₂²	semidirect
75. C₁₃×#525	C₂²	semidirect
76. C₁₃×#525	C₂²	semidirect
77. C₁₃×#525	C₂²	semidirect
78. C₁₃×#525	C₂²	semidirect
79. C₁₃×#525	C₂²	semidirect
80. C₁₃×#525	C₂²	semidirect
81. C₁₃×#525	C₂²	semidirect
82. C₁₃×#525	C₂²	semidirect
83. C₁₃×#525	C₂²	semidirect
84. C₂×C₁₃×#123	C₂²	semidirect
85. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₁₃×#121	C₂²	semidirect
88. C₂×C₁₃×#121	C₂²	semidirect
89. C₂×C₁₃×#121	C₂²	semidirect
90. C₂×C₁₃×#121	C₂²	semidirect
91. C₂×C₁₃×#121	C₂²	semidirect
92. C₂×C₁₃×#121	C₂²	semidirect
93. C₂×C₁₃×#121	C₂²	semidirect
94. C₂×C₁₃×#121	C₂²	semidirect
95. C₂×C₁₃×#121	C₂²	semidirect
96. C₂×C₁₃×#120	C₂²	semidirect
97. C₂×C₁₃×#120	C₂²	semidirect
98. C₁₃×#520	C₂²	semidirect
99. C₁₃×#518	C₂²	semidirect
100. C₁₃×#518	C₂²	semidirect
101. C₁₃×#518	C₂²	semidirect
102. C₂×C₄×D₄×C₁₃	C₂²	semidirect
103. C₂×C₄×D₄×C₁₃	C₂²	semidirect
104. C₂×C₁₃×#117	C₂²	semidirect
105. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
106. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
115. C₂×C₁₃×#41	C₂³	semidirect
116. C₂×C₁₃×#41	C₂³	semidirect
117. C₂×C₁₃×#41	C₂³	semidirect
118. C₂×C₁₃×#41	C₂³	semidirect
119. C₂²×Q₈×C₁₃	C₂³	semidirect
136. C₂²×D₄×C₁₃	C₂³	semidirect
137. C₂²×D₄×C₁₃	C₂³	semidirect
138. C₂²×D₄×C₁₃	C₂³	semidirect
149. C₂³×C₄×C₁₃	C₂³	semidirect
150. C₁₃×C₄⋊Q₈	C₂³	semidirect
151. C₁₃×#127	C₂³	semidirect
152. C₁₃×#127	C₂³	semidirect
153. C₁₃×#126	C₂³	semidirect
154. C₁₃×#126	C₂³	semidirect
155. C₁₃×#126	C₂³	semidirect
156. C₁₃×#125	C₂³	semidirect
157. C₁₃×#125	C₂³	semidirect
158. C₁₃×#124	C₂³	semidirect
159. C₁₃×#124	C₂³	semidirect
160. C₁₃×#124	C₂³	semidirect
161. C₁₃×#124	C₂³	semidirect
165. C₁₃×#123	C₂³	semidirect
166. C₁₃×#123	C₂³	semidirect
167. C₁₃×#123	C₂³	semidirect
168. C₁₃×#123	C₂³	semidirect
169. C₁₃×#123	C₂³	semidirect
170. C₁₃×#123	C₂³	semidirect
171. C₁₃×#123	C₂³	semidirect
172. C₁₃×#123	C₂³	semidirect
173. C₁₃×#123	C₂³	semidirect
180. C₁₃×C₂²⋊Q₈	C₂³	semidirect
181. C₁₃×C₂²⋊Q₈	C₂³	semidirect
182. C₁₃×C₂²⋊Q₈	C₂³	semidirect
183. C₁₃×C₂²⋊Q₈	C₂³	semidirect
184. C₁₃×C₂²⋊Q₈	C₂³	semidirect
185. C₁₃×C₂²⋊Q₈	C₂³	semidirect
186. C₁₃×C₂²⋊Q₈	C₂³	semidirect
187. C₁₃×C₂²⋊Q₈	C₂³	semidirect
202. C₁₃×#121	C₂³	semidirect
203. C₁₃×#121	C₂³	semidirect
204. C₁₃×#121	C₂³	semidirect
205. C₁₃×#121	C₂³	semidirect
206. C₁₃×#121	C₂³	semidirect
207. C₁₃×#121	C₂³	semidirect
208. C₁₃×#121	C₂³	semidirect
209. C₁₃×#121	C₂³	semidirect
210. C₁₃×#121	C₂³	semidirect
211. C₁₃×#121	C₂³	semidirect
212. C₁₃×#121	C₂³	semidirect
213. C₁₃×#121	C₂³	semidirect
214. C₁₃×#121	C₂³	semidirect
215. C₁₃×#121	C₂³	semidirect
216. C₁₃×#121	C₂³	semidirect
217. C₁₃×#121	C₂³	semidirect
218. C₁₃×#121	C₂³	semidirect
226. C₁₃×#120	C₂³	semidirect
227. C₁₃×#120	C₂³	semidirect
228. C₁₃×#120	C₂³	semidirect
229. C₁₃×#120	C₂³	semidirect
230. C₄×Q₈×C₁₃	C₂³	semidirect
237. C₄×D₄×C₁₃	C₂³	semidirect
238. C₄×D₄×C₁₃	C₂³	semidirect
239. C₄×D₄×C₁₃	C₂³	semidirect
240. C₄×D₄×C₁₃	C₂³	semidirect
241. C₄×D₄×C₁₃	C₂³	semidirect
242. C₄×D₄×C₁₃	C₂³	semidirect
243. C₄×D₄×C₁₃	C₂³	semidirect
244. C₄×D₄×C₁₃	C₂³	semidirect
245. C₄×D₄×C₁₃	C₂³	semidirect
246. C₄×D₄×C₁₃	C₂³	semidirect
247. C₄×D₄×C₁₃	C₂³	semidirect
251. C₁₃×#117	C₂³	semidirect
252. C₁₃×#117	C₂³	semidirect
253. C₁₃×#117	C₂³	semidirect
254. C₁₃×#117	C₂³	semidirect
259. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
260. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
261. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
262. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
263. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
274. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
275. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
276. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
277. C₂×C₄²×C₁₃	C₂³	semidirect
278. #62818	C₁₃	direct (N × H)
411. #3542	C₂×C₁₃	semidirect
412. #3537	C₂×C₁₃	semidirect
413. #3536	C₂×C₁₃	semidirect
414. #3534	C₂×C₁₃	semidirect
415. #3519	C₂×C₁₃	semidirect
416. #3505	C₂×C₁₃	semidirect
417. #3496	C₂×C₁₃	semidirect
418. #3494	C₂×C₁₃	semidirect
419. #3492	C₂×C₁₃	semidirect
420. #3490	C₂×C₁₃	semidirect
421. #3488	C₂×C₁₃	semidirect
422. #3484	C₂×C₁₃	semidirect
423. #3484	C₂×C₁₃	semidirect
424. C₂×#525	C₂×C₁₃	semidirect
425. C₂²×#121	C₂×C₁₃	semidirect
457. C₂³×C₁₃	H(5,𝔽₂)	semidirect
511. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
520. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
521. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
522. C₂²×#41	C₂²×C₁₃	semidirect
523. C₂³×D₄	C₂²×C₁₃	semidirect
524. C₂³×D₄	C₂²×C₁₃	semidirect
525. C₂⁴×C₄	C₂²×C₁₃	semidirect
526. #562	C₂²×C₁₃	semidirect
527. #560	C₂²×C₁₃	semidirect
528. #555	C₂²×C₁₃	semidirect
529. #554	C₂²×C₁₃	semidirect
530. #553	C₂²×C₁₃	semidirect
531. #553	C₂²×C₁₃	semidirect
532. #553	C₂²×C₁₃	semidirect
533. #553	C₂²×C₁₃	semidirect
534. #552	C₂²×C₁₃	semidirect
535. #551	C₂²×C₁₃	semidirect
536. #551	C₂²×C₁₃	semidirect
537. #550	C₂²×C₁₃	semidirect
538. #548	C₂²×C₁₃	semidirect
539. #547	C₂²×C₁₃	semidirect
540. #547	C₂²×C₁₃	semidirect
541. #546	C₂²×C₁₃	semidirect
542. #546	C₂²×C₁₃	semidirect
543. #546	C₂²×C₁₃	semidirect
544. #546	C₂²×C₁₃	semidirect
545. #546	C₂²×C₁₃	semidirect
546. #546	C₂²×C₁₃	semidirect
547. #546	C₂²×C₁₃	semidirect
548. #546	C₂²×C₁₃	semidirect
549. D₄²	C₂²×C₁₃	semidirect
550. D₄²	C₂²×C₁₃	semidirect
551. D₄²	C₂²×C₁₃	semidirect
552. D₄²	C₂²×C₁₃	semidirect
553. D₄²	C₂²×C₁₃	semidirect
554. #544	C₂²×C₁₃	semidirect
555. #543	C₂²×C₁₃	semidirect
556. #542	C₂²×C₁₃	semidirect
557. #540	C₂²×C₁₃	semidirect
558. #540	C₂²×C₁₃	semidirect
559. #539	C₂²×C₁₃	semidirect
560. #539	C₂²×C₁₃	semidirect
561. #538	C₂²×C₁₃	semidirect
562. #538	C₂²×C₁₃	semidirect
563. #538	C₂²×C₁₃	semidirect
564. #538	C₂²×C₁₃	semidirect
565. #537	C₂²×C₁₃	semidirect
566. #537	C₂²×C₁₃	semidirect
567. #537	C₂²×C₁₃	semidirect
568. #535	C₂²×C₁₃	semidirect
569. #535	C₂²×C₁₃	semidirect
570. #535	C₂²×C₁₃	semidirect
571. #534	C₂²×C₁₃	semidirect
572. #534	C₂²×C₁₃	semidirect
573. #534	C₂²×C₁₃	semidirect
574. #534	C₂²×C₁₃	semidirect
575. #534	C₂²×C₁₃	semidirect
576. #532	C₂²×C₁₃	semidirect
577. #529	C₂²×C₁₃	semidirect
578. #525	C₂²×C₁₃	semidirect
579. #525	C₂²×C₁₃	semidirect
580. #525	C₂²×C₁₃	semidirect
581. #525	C₂²×C₁₃	semidirect
582. #525	C₂²×C₁₃	semidirect
583. #525	C₂²×C₁₃	semidirect
584. #525	C₂²×C₁₃	semidirect
585. #525	C₂²×C₁₃	semidirect
586. #525	C₂²×C₁₃	semidirect
587. #525	C₂²×C₁₃	semidirect
588. C₂×#123	C₂²×C₁₃	semidirect
589. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
590. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
591. C₂×#121	C₂²×C₁₃	semidirect
592. C₂×#121	C₂²×C₁₃	semidirect
593. C₂×#121	C₂²×C₁₃	semidirect
594. C₂×#121	C₂²×C₁₃	semidirect
595. C₂×#121	C₂²×C₁₃	semidirect
596. C₂×#121	C₂²×C₁₃	semidirect
597. C₂×#121	C₂²×C₁₃	semidirect
598. C₂×#121	C₂²×C₁₃	semidirect
599. C₂×#121	C₂²×C₁₃	semidirect
600. C₂×#120	C₂²×C₁₃	semidirect
601. C₂×#120	C₂²×C₁₃	semidirect
602. #520	C₂²×C₁₃	semidirect
603. #518	C₂²×C₁₃	semidirect
604. #518	C₂²×C₁₃	semidirect
605. #518	C₂²×C₁₃	semidirect
606. C₂×C₄×D₄	C₂²×C₁₃	semidirect
607. C₂×C₄×D₄	C₂²×C₁₃	semidirect
608. C₂×#117	C₂²×C₁₃	semidirect
609. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
610. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
659. C₂×#41	C₂³×C₁₃	semidirect
660. C₂×#41	C₂³×C₁₃	semidirect
661. C₂×#41	C₂³×C₁₃	semidirect
662. C₂×#41	C₂³×C₁₃	semidirect
663. C₂²×Q₈	C₂³×C₁₃	semidirect
680. C₂²×D₄	C₂³×C₁₃	semidirect
681. C₂²×D₄	C₂³×C₁₃	semidirect
682. C₂²×D₄	C₂³×C₁₃	semidirect
693. C₂³×C₄	C₂³×C₁₃	semidirect
694. C₄⋊Q₈	C₂³×C₁₃	semidirect
695. #127	C₂³×C₁₃	semidirect
696. #127	C₂³×C₁₃	semidirect
697. #126	C₂³×C₁₃	semidirect
698. #126	C₂³×C₁₃	semidirect
699. #126	C₂³×C₁₃	semidirect
700. #125	C₂³×C₁₃	semidirect
701. #125	C₂³×C₁₃	semidirect
702. #124	C₂³×C₁₃	semidirect
703. #124	C₂³×C₁₃	semidirect
704. #124	C₂³×C₁₃	semidirect
705. #124	C₂³×C₁₃	semidirect
709. #123	C₂³×C₁₃	semidirect
710. #123	C₂³×C₁₃	semidirect
711. #123	C₂³×C₁₃	semidirect
712. #123	C₂³×C₁₃	semidirect
713. #123	C₂³×C₁₃	semidirect
714. #123	C₂³×C₁₃	semidirect
715. #123	C₂³×C₁₃	semidirect
716. #123	C₂³×C₁₃	semidirect
717. #123	C₂³×C₁₃	semidirect
724. C₂²⋊Q₈	C₂³×C₁₃	semidirect
725. C₂²⋊Q₈	C₂³×C₁₃	semidirect
726. C₂²⋊Q₈	C₂³×C₁₃	semidirect
727. C₂²⋊Q₈	C₂³×C₁₃	semidirect
728. C₂²⋊Q₈	C₂³×C₁₃	semidirect
729. C₂²⋊Q₈	C₂³×C₁₃	semidirect
730. C₂²⋊Q₈	C₂³×C₁₃	semidirect
731. C₂²⋊Q₈	C₂³×C₁₃	semidirect
746. #121	C₂³×C₁₃	semidirect
747. #121	C₂³×C₁₃	semidirect
748. #121	C₂³×C₁₃	semidirect
749. #121	C₂³×C₁₃	semidirect
750. #121	C₂³×C₁₃	semidirect
751. #121	C₂³×C₁₃	semidirect
752. #121	C₂³×C₁₃	semidirect
753. #121	C₂³×C₁₃	semidirect
754. #121	C₂³×C₁₃	semidirect
755. #121	C₂³×C₁₃	semidirect
756. #121	C₂³×C₁₃	semidirect
757. #121	C₂³×C₁₃	semidirect
758. #121	C₂³×C₁₃	semidirect
759. #121	C₂³×C₁₃	semidirect
760. #121	C₂³×C₁₃	semidirect
761. #121	C₂³×C₁₃	semidirect
762. #121	C₂³×C₁₃	semidirect
770. #120	C₂³×C₁₃	semidirect
771. #120	C₂³×C₁₃	semidirect
772. #120	C₂³×C₁₃	semidirect
773. #120	C₂³×C₁₃	semidirect
774. C₄×Q₈	C₂³×C₁₃	semidirect
781. C₄×D₄	C₂³×C₁₃	semidirect
782. C₄×D₄	C₂³×C₁₃	semidirect
783. C₄×D₄	C₂³×C₁₃	semidirect
784. C₄×D₄	C₂³×C₁₃	semidirect
785. C₄×D₄	C₂³×C₁₃	semidirect
786. C₄×D₄	C₂³×C₁₃	semidirect
787. C₄×D₄	C₂³×C₁₃	semidirect
788. C₄×D₄	C₂³×C₁₃	semidirect
789. C₄×D₄	C₂³×C₁₃	semidirect
790. C₄×D₄	C₂³×C₁₃	semidirect
791. C₄×D₄	C₂³×C₁₃	semidirect
795. #117	C₂³×C₁₃	semidirect
796. #117	C₂³×C₁₃	semidirect
797. #117	C₂³×C₁₃	semidirect
798. #117	C₂³×C₁₃	semidirect
803. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
804. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
805. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
806. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
807. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
818. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
819. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
820. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
821. C₂×C₄²	C₂³×C₁₃	semidirect
964. C₁₃	#62818	direct (N × H)
996. C₂³	C₁₃×H(5,𝔽₂)	semidirect
1050. C₂×C₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3542	2
C₁₃×#3537	2
C₁₃×#3536	2
C₁₃×#3534	2
C₁₃×#3519	2
C₁₃×#3505	2
C₁₃×#3496	2
C₁₃×#3494	2
C₁₃×#3492	2
C₁₃×#3490	2
C₁₃×#3488	2
C₁₃×#3484	2
C₂×C₁₃×#525	2
C₂²×C₁₃×#121	2
#62818	13

Subgroups — C13×#62818 #15749157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62818 #15749157