Subgroups — C₁₃×#62819 #15749158

Order 3328.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3541	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3538	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3536	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3535	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3520	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3501	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3495	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3492	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3492	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3490	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3489	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3486	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#563	C₂²	1	16	yes	complemented
21	C₁₃×#562	C₂²	1	16	yes	complemented
22	C₁₃×#556	C₂²	1	8	yes	complemented
23	C₁₃×#554	C₂²	1	16	yes	complemented
24	C₁₃×#554	C₂²	1	8	yes	complemented
25	C₁₃×#554	C₂²	1	8	yes	complemented
26	C₁₃×#554	C₂²	1	16	yes	complemented
27	C₁₃×#553	C₂²	1	8	yes	complemented
28	C₁₃×#553	C₂²	1	16	yes	complemented
29	C₁₃×#552	C₂²	1	8	yes	complemented
30	C₁₃×#552	C₂²	1	16	yes	complemented
31	C₁₃×#552	C₂²	1	8	yes	complemented
32	C₁₃×#552	C₂²	1	8	yes	complemented
33	C₁₃×#551	C₂²	1	16	yes	complemented
34	C₁₃×#551	C₂²	1	16	yes	complemented
35	C₁₃×#551	C₂²	1	16	yes	complemented
36	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
37	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
38	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
39	C₁₃×#548	C₂²	1	8	yes	complemented
40	C₁₃×#548	C₂²	1	8	yes	complemented
41	C₁₃×#548	C₂²	1	8	yes	complemented
42	C₁₃×#547	C₂²	1	8	yes	complemented
43	C₁₃×#547	C₂²	1	16	yes	complemented
44	C₁₃×#547	C₂²	1	8	yes	complemented
45	C₁₃×#546	C₂²	1	16	yes	complemented
46	C₁₃×#546	C₂²	1	16	yes	complemented
47	C₁₃×#546	C₂²	1	8	yes	complemented
48	C₁₃×#544	C₂²	1	8	yes	complemented
49	C₁₃×#544	C₂²	1	4	yes	complemented
50	C₁₃×#544	C₂²	1	2	yes	complemented
51	C₁₃×#543	C₂²	1	4	yes	—
52	C₁₃×#543	C₂²	1	8	yes	complemented
53	C₁₃×#542	C₂²	1	8	yes	complemented
54	C₁₃×#542	C₂²	1	16	yes	complemented
55	C₁₃×#541	C₂²	1	8	yes	complemented
56	C₁₃×#539	C₂²	1	8	yes	complemented
57	C₁₃×#539	C₂²	1	8	yes	complemented
58	C₁₃×#539	C₂²	1	8	yes	complemented
59	C₁₃×#539	C₂²	1	8	yes	complemented
60	C₁₃×#539	C₂²	1	16	yes	complemented
61	C₁₃×#538	C₂²	1	8	yes	complemented
62	C₁₃×#538	C₂²	1	8	yes	complemented
63	C₁₃×#538	C₂²	1	8	yes	complemented
64	C₁₃×#537	C₂²	1	4	yes	complemented
65	C₁₃×#537	C₂²	1	2	yes	complemented
66	C₁₃×#537	C₂²	1	8	yes	complemented
67	C₁₃×#536	C₂²	1	8	yes	complemented
68	C₁₃×#536	C₂²	1	4	yes	complemented
69	C₁₃×#536	C₂²	1	8	yes	complemented
70	C₁₃×#534	C₂²	1	4	yes	—
71	C₁₃×#533	C₂²	1	8	yes	complemented
72	C₁₃×#529	C₂²	1	8	yes	complemented
73	C₁₃×#525	C₂²	1	4	yes	—
74	C₁₃×#525	C₂²	1	4	yes	—
75	C₁₃×#525	C₂²	1	4	yes	—
76	C₁₃×#525	C₂²	1	4	yes	—
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	8	yes	complemented
82	C₁₃×#525	C₂²	1	8	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	4	yes	—
86	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
87	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
88	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
89	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
90	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
91	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
92	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
93	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
94	C₂×C₁₃×#121	C₂²	1	2	yes	—
95	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
96	C₂×C₁₃×#120	C₂²	1	4	yes	—
97	C₁₃×#520	C₂²	1	8	yes	complemented
98	C₁₃×#520	C₂²	1	4	yes	complemented
99	C₁₃×#519	C₂²	1	2	yes	complemented
100	C₁₃×#518	C₂²	1	8	yes	—
101	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
102	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
103	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
104	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
106	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×2₋¹⁺⁴	—	4	8	no	—
109	C₂×C₁₃×#41	—	4	8	no	—
110	C₂×C₁₃×#41	C₂³	1	4	yes	—
111	C₂×C₁₃×#41	C₂³	1	8	yes	—
112	C₂×C₁₃×#41	C₂³	1	4	yes	—
113	C₂×C₁₃×#41	C₂³	1	4	yes	—
114	C₂×C₁₃×#41	C₂³	1	4	yes	—
115	C₂×C₁₃×#41	C₂³	1	8	yes	—
116	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
117	C₂²×Q₈×C₁₃	—	4	4	no	—
118	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
120	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
123	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
124	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	—	4	4	no	—
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
136	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
141	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
142	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
143	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
144	C₁₃×#126	C₂³	1	16	yes	—
145	C₁₃×#126	C₂³	1	16	yes	—
146	C₁₃×#126	C₂³	1	16	yes	complemented
147	C₁₃×#126	C₂³	1	16	yes	complemented
148	C₁₃×#126	C₂³	1	16	yes	complemented
149	C₁₃×#125	C₂³	1	8	yes	complemented
150	C₁₃×#125	C₂³	1	16	yes	complemented
151	C₁₃×#125	C₂³	1	16	yes	complemented
152	C₁₃×#125	C₂³	1	16	yes	complemented
153	C₁₃×#125	C₂³	1	16	yes	complemented
154	C₁₃×#124	C₂³	1	16	yes	—
155	C₁₃×#124	C₂³	1	16	yes	—
156	C₁₃×#124	C₂³	1	8	yes	complemented
157	C₁₃×#124	C₂³	1	16	yes	complemented
158	C₁₃×#123	C₂³	1	8	yes	—
159	C₁₃×#123	C₂³	1	8	yes	—
160	C₁₃×#123	C₂³	1	8	yes	—
161	C₁₃×#123	C₂³	1	8	yes	—
162	C₁₃×#123	C₂³	1	16	yes	—
163	C₁₃×#123	C₂³	1	16	yes	—
164	C₁₃×#123	C₂³	1	16	yes	—
165	C₁₃×#123	C₂³	1	16	yes	—
166	C₁₃×#123	C₂³	1	16	yes	—
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×C₂²⋊Q₈	C₂³	1	8	yes	—
171	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	8	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	8	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
193	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
194	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
195	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
196	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
197	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
200	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
201	C₁₃×#121	C₂³	1	4	yes	—
202	C₁₃×#121	C₂³	1	4	yes	—
203	C₁₃×#121	C₂³	1	4	yes	—
204	C₁₃×#121	C₂³	1	4	yes	—
205	C₁₃×#121	C₂³	1	4	yes	—
206	C₁₃×#121	C₂³	1	4	yes	—
207	C₁₃×#121	C₂³	1	4	yes	—
208	C₁₃×#121	C₂³	1	4	yes	—
209	C₁₃×#121	C₂³	1	8	yes	—
210	C₁₃×#121	C₂³	1	8	yes	—
211	C₁₃×#121	C₂³	1	8	yes	—
212	C₁₃×#121	C₂³	1	8	yes	—
213	C₁₃×#121	C₂³	1	16	yes	—
214	C₁₃×#121	C₂³	1	16	yes	—
215	C₁₃×#121	C₂³	1	8	yes	complemented
216	C₁₃×#121	C₂³	1	16	yes	complemented
217	C₁₃×#120	C₂³	1	8	yes	—
218	C₁₃×#120	C₂³	1	8	yes	—
219	C₁₃×#120	C₂³	1	8	yes	—
220	C₁₃×#120	C₂³	1	8	yes	—
221	C₁₃×#120	C₂³	1	16	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
223	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
224	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
225	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
226	C₄×D₄×C₁₃	C₂³	1	8	yes	—
227	C₄×D₄×C₁₃	C₂³	1	8	yes	—
228	C₄×D₄×C₁₃	C₂³	1	8	yes	—
229	C₄×D₄×C₁₃	C₂³	1	8	yes	—
230	C₄×D₄×C₁₃	C₂³	1	8	yes	—
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	16	yes	—
235	C₄×D₄×C₁₃	C₂³	1	16	yes	—
236	C₄×D₄×C₁₃	C₂³	1	16	yes	—
237	C₄×D₄×C₁₃	C₂³	1	16	yes	—
238	C₄×D₄×C₁₃	C₂³	1	16	yes	—
239	C₄×D₄×C₁₃	C₂³	1	16	yes	—
240	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
241	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
242	C₁₃×#117	C₂³	1	4	yes	—
243	C₁₃×#117	C₂³	1	4	yes	—
244	C₁₃×#117	C₂³	1	4	yes	—
245	C₁₃×#117	C₂³	1	4	yes	—
246	C₁₃×#117	C₂³	1	16	yes	—
247	C₁₃×#117	C₂³	1	8	yes	—
248	C₁₃×#117	C₂³	1	8	yes	—
249	C₁₃×#117	C₂³	1	8	yes	complemented
250	C₁₃×#117	C₂³	1	16	yes	complemented
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	8	yes	—
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
265	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
266	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
267	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	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	4	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
273	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
274	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
275	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
276	#62819	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂⁴×C₁₃	—	2	4	no	—
278	C₂⁴×C₁₃	—	4	2	no	—
279	C₂⁴×C₁₃	—	4	2	no	—
280	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
282	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
283	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
284	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₁₃×#41	—	2	16	no	—
287	C₁₃×#41	—	4	8	no	—
288	C₁₃×#41	—	4	8	no	—
289	C₁₃×#41	—	4	16	no	—
290	C₁₃×#41	—	4	16	no	—
291	C₁₃×#41	—	4	8	no	—
292	C₁₃×#41	—	4	16	no	—
293	C₂×Q₈×C₁₃	—	2	8	no	—
294	C₂×Q₈×C₁₃	—	4	4	no	—
295	C₂×Q₈×C₁₃	—	4	8	no	—
296	C₂×Q₈×C₁₃	—	4	8	no	—
297	C₂×Q₈×C₁₃	—	4	4	no	—
298	C₂×Q₈×C₁₃	—	4	16	no	—
299	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
300	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
301	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
302	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
303	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
304	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
305	C₂×D₄×C₁₃	—	2	16	no	—
306	C₂×D₄×C₁₃	—	4	4	no	—
307	C₂×D₄×C₁₃	—	4	8	no	—
308	C₂×D₄×C₁₃	—	4	8	no	—
309	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
310	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
311	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
312	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
314	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
315	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
316	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
317	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
318	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
319	C₂²×C₄×C₁₃	—	2	4	no	—
320	C₂²×C₄×C₁₃	—	2	8	no	—
321	C₂²×C₄×C₁₃	—	4	4	no	—
322	C₂²×C₄×C₁₃	—	4	4	no	—
323	C₂²×C₄×C₁₃	—	4	4	no	—
324	C₂²×C₄×C₁₃	—	4	4	no	—
325	C₂²×C₄×C₁₃	—	4	8	no	—
326	C₂²×C₄×C₁₃	—	4	4	no	—
327	C₂²×C₄×C₁₃	—	4	2	no	—
328	C₂²×C₄×C₁₃	—	4	4	no	—
329	C₂²×C₄×C₁₃	—	4	4	no	—
330	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
340	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
373	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
374	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
375	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
376	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
385	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
386	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
387	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
388	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
389	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
390	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
391	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
392	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
393	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
394	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
395	C₄²×C₁₃	C₂⁴	1	8	yes	—
396	C₄²×C₁₃	C₂⁴	1	8	yes	—
397	C₄²×C₁₃	C₂⁴	1	16	yes	—
398	C₄²×C₁₃	C₂⁴	1	16	yes	—
399	#3541	C₂×C₁₃	1	8	yes	complemented
400	#3538	C₂×C₁₃	1	4	yes	complemented
401	#3536	C₂×C₁₃	1	4	yes	complemented
402	#3535	C₂×C₁₃	1	8	yes	complemented
403	#3520	C₂×C₁₃	1	8	yes	complemented
404	#3505	C₂×C₁₃	1	4	yes	complemented
405	#3501	C₂×C₁₃	1	4	yes	complemented
406	#3495	C₂×C₁₃	1	4	yes	complemented
407	#3492	C₂×C₁₃	1	2	yes	complemented
408	#3492	C₂×C₁₃	1	4	yes	complemented
409	#3490	C₂×C₁₃	1	4	yes	complemented
410	#3489	C₂×C₁₃	1	4	yes	complemented
411	#3486	C₂×C₁₃	1	2	yes	complemented
412	C₂×#525	C₂×C₁₃	1	2	yes	complemented
413	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
414	C₂³×C₁₃	—	2	2	no	—
415	C₂³×C₁₃	—	2	2	no	—
416	C₂³×C₁₃	—	2	2	no	—
417	C₂³×C₁₃	—	2	4	no	—
418	C₂³×C₁₃	—	2	4	no	—
419	C₂³×C₁₃	—	2	4	no	—
420	C₂³×C₁₃	—	2	2	no	—
421	C₂³×C₁₃	—	2	4	no	—
422	C₂³×C₁₃	—	2	8	no	—
423	C₂³×C₁₃	—	4	1	no	—
424	C₂³×C₁₃	—	4	2	no	—
425	C₂³×C₁₃	—	4	1	no	—
426	C₂³×C₁₃	—	4	1	no	—
427	C₂³×C₁₃	—	4	2	no	—
428	C₂³×C₁₃	—	4	1	no	—
429	C₂³×C₁₃	—	4	4	no	—
430	C₂³×C₁₃	—	4	4	no	—
431	C₂³×C₁₃	—	4	16	no	—
432	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	complemented
433	C₂³×C₁₃	C₂⁵	1	2	yes	—
434	C₂³×C₁₃	C₂⁵	1	8	yes	—
435	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
436	C₂³×C₁₃	C₂⁵	1	2	yes	—
437	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
438	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
439	Q₈×C₁₃	—	2	16	no	—
440	Q₈×C₁₃	—	2	8	no	—
441	Q₈×C₁₃	—	4	8	no	—
442	Q₈×C₁₃	—	4	8	no	—
443	Q₈×C₁₃	—	4	4	no	—
444	Q₈×C₁₃	—	4	8	no	—
445	D₄×C₁₃	—	2	16	no	—
446	D₄×C₁₃	—	2	16	no	—
447	D₄×C₁₃	—	2	16	no	—
448	D₄×C₁₃	—	2	16	no	—
449	D₄×C₁₃	—	2	8	no	—
450	D₄×C₁₃	—	4	8	no	—
451	D₄×C₁₃	—	4	4	no	—
452	D₄×C₁₃	—	4	8	no	—
453	D₄×C₁₃	—	4	8	no	—
454	D₄×C₁₃	—	4	8	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	4	no	—
457	C₂×C₄×C₁₃	—	2	8	no	—
458	C₂×C₄×C₁₃	—	2	8	no	—
459	C₂×C₄×C₁₃	—	2	8	no	—
460	C₂×C₄×C₁₃	—	2	4	no	—
461	C₂×C₄×C₁₃	—	2	4	no	—
462	C₂×C₄×C₁₃	—	2	4	no	—
463	C₂×C₄×C₁₃	—	2	4	no	—
464	C₂×C₄×C₁₃	—	2	4	no	—
465	C₂×C₄×C₁₃	—	2	4	no	—
466	C₂×C₄×C₁₃	—	2	16	no	—
467	C₂×C₄×C₁₃	—	4	1	no	—
468	C₂×C₄×C₁₃	—	4	2	no	—
469	C₂×C₄×C₁₃	—	4	2	no	—
470	C₂×C₄×C₁₃	—	4	2	no	—
471	C₂×C₄×C₁₃	—	4	1	no	—
472	C₂×C₄×C₁₃	—	4	2	no	—
473	C₂×C₄×C₁₃	—	4	2	no	—
474	C₂×C₄×C₁₃	—	4	4	no	—
475	C₂×C₄×C₁₃	—	4	4	no	—
476	C₂×C₄×C₁₃	—	4	4	no	—
477	C₂×C₄×C₁₃	—	4	4	no	—
478	C₂×C₄×C₁₃	—	4	4	no	—
479	C₂×C₄×C₁₃	—	4	8	no	—
480	C₂×C₄×C₁₃	—	4	4	no	—
481	C₂×C₄×C₁₃	—	4	16	no	—
482	C₂×C₄×C₁₃	—	4	16	no	—
483	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
484	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
485	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
486	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
487	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
488	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
489	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
490	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
491	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
492	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
493	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
494	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
495	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
497	#563	C₂²×C₁₃	1	16	yes	complemented
498	#562	C₂²×C₁₃	1	16	yes	complemented
499	#556	C₂²×C₁₃	1	8	yes	complemented
500	#554	C₂²×C₁₃	1	8	yes	complemented
501	#554	C₂²×C₁₃	1	16	yes	complemented
502	#554	C₂²×C₁₃	1	8	yes	complemented
503	#554	C₂²×C₁₃	1	16	yes	complemented
504	#553	C₂²×C₁₃	1	8	yes	complemented
505	#553	C₂²×C₁₃	1	16	yes	complemented
506	#552	C₂²×C₁₃	1	16	yes	complemented
507	#552	C₂²×C₁₃	1	8	yes	complemented
508	#552	C₂²×C₁₃	1	8	yes	complemented
509	#552	C₂²×C₁₃	1	8	yes	complemented
510	#551	C₂²×C₁₃	1	16	yes	complemented
511	#551	C₂²×C₁₃	1	16	yes	complemented
512	#551	C₂²×C₁₃	1	16	yes	complemented
513	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
514	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
515	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
516	#548	C₂²×C₁₃	1	8	yes	complemented
517	#548	C₂²×C₁₃	1	8	yes	complemented
518	#548	C₂²×C₁₃	1	8	yes	complemented
519	#547	C₂²×C₁₃	1	16	yes	complemented
520	#547	C₂²×C₁₃	1	8	yes	complemented
521	#547	C₂²×C₁₃	1	8	yes	complemented
522	#546	C₂²×C₁₃	1	16	yes	complemented
523	#546	C₂²×C₁₃	1	16	yes	complemented
524	#546	C₂²×C₁₃	1	8	yes	complemented
525	#544	C₂²×C₁₃	1	2	yes	complemented
526	#544	C₂²×C₁₃	1	4	yes	complemented
527	#544	C₂²×C₁₃	1	8	yes	complemented
528	#543	C₂²×C₁₃	1	4	yes	—
529	#543	C₂²×C₁₃	1	8	yes	complemented
530	#542	C₂²×C₁₃	1	8	yes	complemented
531	#542	C₂²×C₁₃	1	16	yes	complemented
532	#541	C₂²×C₁₃	1	8	yes	complemented
533	#539	C₂²×C₁₃	1	8	yes	complemented
534	#539	C₂²×C₁₃	1	8	yes	complemented
535	#539	C₂²×C₁₃	1	8	yes	complemented
536	#539	C₂²×C₁₃	1	8	yes	complemented
537	#539	C₂²×C₁₃	1	16	yes	complemented
538	#538	C₂²×C₁₃	1	8	yes	complemented
539	#538	C₂²×C₁₃	1	8	yes	complemented
540	#538	C₂²×C₁₃	1	8	yes	complemented
541	#537	C₂²×C₁₃	1	2	yes	complemented
542	#537	C₂²×C₁₃	1	4	yes	complemented
543	#537	C₂²×C₁₃	1	8	yes	complemented
544	#536	C₂²×C₁₃	1	4	yes	complemented
545	#536	C₂²×C₁₃	1	8	yes	complemented
546	#536	C₂²×C₁₃	1	8	yes	complemented
547	#534	C₂²×C₁₃	1	4	yes	—
548	#533	C₂²×C₁₃	1	8	yes	complemented
549	#529	C₂²×C₁₃	1	8	yes	complemented
550	#525	C₂²×C₁₃	1	4	yes	—
551	#525	C₂²×C₁₃	1	4	yes	—
552	#525	C₂²×C₁₃	1	4	yes	—
553	#525	C₂²×C₁₃	1	4	yes	—
554	#525	C₂²×C₁₃	1	4	yes	complemented
555	#525	C₂²×C₁₃	1	4	yes	complemented
556	#525	C₂²×C₁₃	1	4	yes	complemented
557	#525	C₂²×C₁₃	1	4	yes	complemented
558	#525	C₂²×C₁₃	1	8	yes	complemented
559	#525	C₂²×C₁₃	1	8	yes	complemented
560	#525	C₂²×C₁₃	1	8	yes	complemented
561	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
562	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
563	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
564	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
565	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
566	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
567	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
568	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
569	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
570	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
571	C₂×#121	C₂²×C₁₃	1	2	yes	—
572	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
573	C₂×#120	C₂²×C₁₃	1	4	yes	—
574	#520	C₂²×C₁₃	1	4	yes	complemented
575	#520	C₂²×C₁₃	1	8	yes	complemented
576	#519	C₂²×C₁₃	1	2	yes	complemented
577	#518	C₂²×C₁₃	1	8	yes	—
578	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
579	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
580	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
581	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
583	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
584	C₂²×C₁₃	—	2	8	no	—
585	C₂²×C₁₃	—	2	1	no	—
586	C₂²×C₁₃	—	2	1	no	—
587	C₂²×C₁₃	—	2	2	no	—
588	C₂²×C₁₃	—	2	1	no	—
589	C₂²×C₁₃	—	2	1	no	—
590	C₂²×C₁₃	—	2	1	no	—
591	C₂²×C₁₃	—	2	1	no	—
592	C₂²×C₁₃	—	2	2	no	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	2	8	no	—
595	C₂²×C₁₃	—	2	8	no	—
596	C₂²×C₁₃	—	2	2	no	—
597	C₂²×C₁₃	—	2	8	no	—
598	C₂²×C₁₃	—	2	2	no	—
599	C₂²×C₁₃	—	4	4	no	—
600	C₂²×C₁₃	—	4	8	no	—
601	C₂²×C₁₃	—	4	8	no	—
602	C₂²×C₁₃	—	4	4	no	—
603	C₂²×C₁₃	—	8	8	no	—
604	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
605	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
606	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
607	C₂²×C₁₃	#585	1	2	yes	—
608	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
609	C₄×C₁₃	—	2	2	no	—
610	C₄×C₁₃	—	2	2	no	—
611	C₄×C₁₃	—	2	2	no	—
612	C₄×C₁₃	—	2	8	no	—
613	C₄×C₁₃	—	2	8	no	—
614	C₄×C₁₃	—	2	8	no	—
615	C₄×C₁₃	—	2	8	no	—
616	C₄×C₁₃	—	2	8	no	—
617	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
618	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
619	2₋¹⁺⁴	—	4	8	no	—
620	C₂×#41	—	4	8	no	—
621	C₂×#41	C₂³×C₁₃	1	4	yes	—
622	C₂×#41	C₂³×C₁₃	1	8	yes	—
623	C₂×#41	C₂³×C₁₃	1	4	yes	—
624	C₂×#41	C₂³×C₁₃	1	4	yes	—
625	C₂×#41	C₂³×C₁₃	1	4	yes	—
626	C₂×#41	C₂³×C₁₃	1	8	yes	—
627	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
628	C₂²×Q₈	—	4	4	no	—
629	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
630	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
631	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
632	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
633	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
634	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
635	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
636	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
637	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
638	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
639	C₂³×C₄	—	4	4	no	—
640	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
642	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
643	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
644	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
646	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
647	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
648	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
649	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
650	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
651	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
652	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
653	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
654	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
655	#126	C₂³×C₁₃	1	16	yes	—
656	#126	C₂³×C₁₃	1	16	yes	—
657	#126	C₂³×C₁₃	1	16	yes	complemented
658	#126	C₂³×C₁₃	1	16	yes	complemented
659	#126	C₂³×C₁₃	1	16	yes	complemented
660	#125	C₂³×C₁₃	1	8	yes	complemented
661	#125	C₂³×C₁₃	1	16	yes	complemented
662	#125	C₂³×C₁₃	1	16	yes	complemented
663	#125	C₂³×C₁₃	1	16	yes	complemented
664	#125	C₂³×C₁₃	1	16	yes	complemented
665	#124	C₂³×C₁₃	1	16	yes	—
666	#124	C₂³×C₁₃	1	16	yes	—
667	#124	C₂³×C₁₃	1	8	yes	complemented
668	#124	C₂³×C₁₃	1	16	yes	complemented
669	#123	C₂³×C₁₃	1	8	yes	—
670	#123	C₂³×C₁₃	1	8	yes	—
671	#123	C₂³×C₁₃	1	8	yes	—
672	#123	C₂³×C₁₃	1	8	yes	—
673	#123	C₂³×C₁₃	1	16	yes	—
674	#123	C₂³×C₁₃	1	16	yes	—
675	#123	C₂³×C₁₃	1	16	yes	—
676	#123	C₂³×C₁₃	1	16	yes	—
677	#123	C₂³×C₁₃	1	16	yes	—
678	#123	C₂³×C₁₃	1	16	yes	complemented
679	#123	C₂³×C₁₃	1	16	yes	complemented
680	#123	C₂³×C₁₃	1	16	yes	complemented
681	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
682	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
683	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
684	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
685	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
686	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
687	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
688	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
689	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
690	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
693	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
694	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
696	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
698	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
699	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
700	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
701	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
702	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
703	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
704	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
705	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
706	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
707	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
708	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
709	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
710	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
711	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
712	#121	C₂³×C₁₃	1	4	yes	—
713	#121	C₂³×C₁₃	1	4	yes	—
714	#121	C₂³×C₁₃	1	4	yes	—
715	#121	C₂³×C₁₃	1	4	yes	—
716	#121	C₂³×C₁₃	1	4	yes	—
717	#121	C₂³×C₁₃	1	4	yes	—
718	#121	C₂³×C₁₃	1	4	yes	—
719	#121	C₂³×C₁₃	1	4	yes	—
720	#121	C₂³×C₁₃	1	8	yes	—
721	#121	C₂³×C₁₃	1	8	yes	—
722	#121	C₂³×C₁₃	1	8	yes	—
723	#121	C₂³×C₁₃	1	8	yes	—
724	#121	C₂³×C₁₃	1	16	yes	—
725	#121	C₂³×C₁₃	1	16	yes	—
726	#121	C₂³×C₁₃	1	8	yes	complemented
727	#121	C₂³×C₁₃	1	16	yes	complemented
728	#120	C₂³×C₁₃	1	8	yes	—
729	#120	C₂³×C₁₃	1	8	yes	—
730	#120	C₂³×C₁₃	1	8	yes	—
731	#120	C₂³×C₁₃	1	8	yes	—
732	#120	C₂³×C₁₃	1	16	yes	—
733	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
734	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
735	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
736	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
737	C₄×D₄	C₂³×C₁₃	1	8	yes	—
738	C₄×D₄	C₂³×C₁₃	1	8	yes	—
739	C₄×D₄	C₂³×C₁₃	1	8	yes	—
740	C₄×D₄	C₂³×C₁₃	1	8	yes	—
741	C₄×D₄	C₂³×C₁₃	1	8	yes	—
742	C₄×D₄	C₂³×C₁₃	1	8	yes	—
743	C₄×D₄	C₂³×C₁₃	1	8	yes	—
744	C₄×D₄	C₂³×C₁₃	1	8	yes	—
745	C₄×D₄	C₂³×C₁₃	1	16	yes	—
746	C₄×D₄	C₂³×C₁₃	1	16	yes	—
747	C₄×D₄	C₂³×C₁₃	1	16	yes	—
748	C₄×D₄	C₂³×C₁₃	1	16	yes	—
749	C₄×D₄	C₂³×C₁₃	1	16	yes	—
750	C₄×D₄	C₂³×C₁₃	1	16	yes	—
751	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
752	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
753	#117	C₂³×C₁₃	1	4	yes	—
754	#117	C₂³×C₁₃	1	4	yes	—
755	#117	C₂³×C₁₃	1	4	yes	—
756	#117	C₂³×C₁₃	1	4	yes	—
757	#117	C₂³×C₁₃	1	16	yes	—
758	#117	C₂³×C₁₃	1	8	yes	—
759	#117	C₂³×C₁₃	1	8	yes	—
760	#117	C₂³×C₁₃	1	8	yes	complemented
761	#117	C₂³×C₁₃	1	16	yes	complemented
762	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
763	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
764	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
765	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
766	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
767	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
769	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
770	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
773	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
774	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
775	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
776	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
786	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
787	C₂×C₁₃	—	2	2	no	—
788	C₂×C₁₃	—	2	2	no	—
789	C₂×C₁₃	—	2	2	no	—
790	C₂×C₁₃	—	2	4	no	—
791	C₂×C₁₃	—	4	2	no	—
792	C₂×C₁₃	—	4	8	no	—
793	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
794	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
795	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
796	C₂⁴	—	2	4	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
801	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
802	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
803	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
805	#41	—	2	16	no	—
806	#41	—	4	8	no	—
807	#41	—	4	8	no	—
808	#41	—	4	16	no	—
809	#41	—	4	16	no	—
810	#41	—	4	8	no	—
811	#41	—	4	16	no	—
812	C₂×Q₈	—	2	8	no	—
813	C₂×Q₈	—	4	4	no	—
814	C₂×Q₈	—	4	8	no	—
815	C₂×Q₈	—	4	8	no	—
816	C₂×Q₈	—	4	4	no	—
817	C₂×Q₈	—	4	16	no	—
818	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
819	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
820	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
821	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
822	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
823	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
824	C₂×D₄	—	2	16	no	—
825	C₂×D₄	—	4	4	no	—
826	C₂×D₄	—	4	8	no	—
827	C₂×D₄	—	4	8	no	—
828	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
829	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
830	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
831	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
832	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
833	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
834	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
835	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
836	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
837	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	8	no	—
840	C₂²×C₄	—	4	4	no	—
841	C₂²×C₄	—	4	4	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	—	4	4	no	—
844	C₂²×C₄	—	4	8	no	—
845	C₂²×C₄	—	4	4	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	4	no	—
848	C₂²×C₄	—	4	4	no	—
849	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
851	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
852	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
859	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
862	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
863	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
864	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
866	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
867	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
868	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
869	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
870	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
871	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
875	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
879	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
880	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
881	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
882	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
883	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
884	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
885	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
886	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
887	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
888	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
889	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
891	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
892	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
893	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
894	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
895	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
896	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
897	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
899	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
900	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
901	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
902	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
905	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
907	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
908	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
909	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
910	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
911	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
913	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
914	C₄²	C₂⁴×C₁₃	1	8	yes	—
915	C₄²	C₂⁴×C₁₃	1	8	yes	—
916	C₄²	C₂⁴×C₁₃	1	16	yes	—
917	C₄²	C₂⁴×C₁₃	1	16	yes	—
918	C₁₃	#62819	1	1	yes	characteristic, direct product factor, Sylow
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	4	no	—
923	C₂³	—	2	4	no	—
924	C₂³	—	2	4	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	8	no	—
928	C₂³	—	4	1	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	1	no	—
931	C₂³	—	4	1	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	4	no	—
935	C₂³	—	4	4	no	—
936	C₂³	—	4	16	no	—
937	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	complemented
938	C₂³	C₂⁵×C₁₃	1	2	yes	—
939	C₂³	C₂⁵×C₁₃	1	8	yes	—
940	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
941	C₂³	C₂⁵×C₁₃	1	2	yes	—
942	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
943	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
944	Q₈	—	2	16	no	—
945	Q₈	—	2	8	no	—
946	Q₈	—	4	8	no	—
947	Q₈	—	4	8	no	—
948	Q₈	—	4	4	no	—
949	Q₈	—	4	8	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	16	no	—
953	D₄	—	2	16	no	—
954	D₄	—	2	8	no	—
955	D₄	—	4	8	no	—
956	D₄	—	4	4	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	8	no	—
959	D₄	—	4	8	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	4	no	—
962	C₂×C₄	—	2	8	no	—
963	C₂×C₄	—	2	8	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	4	no	—
969	C₂×C₄	—	2	4	no	—
970	C₂×C₄	—	2	4	no	—
971	C₂×C₄	—	2	16	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	2	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	16	no	—
987	C₂×C₄	—	4	16	no	—
988	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
989	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
990	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
991	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
992	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
993	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
994	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
995	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
996	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
997	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
998	C₂²	—	2	8	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	8	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	8	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	8	no	—
1015	C₂²	—	4	8	no	—
1016	C₂²	—	4	4	no	—
1017	C₂²	—	8	8	no	—
1018	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1019	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
1020	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
1021	C₂²	C₁₃×#585	1	2	yes	—
1022	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	8	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	8	no	—
1029	C₄	—	2	8	no	—
1030	C₄	—	2	8	no	—
1031	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1032	C₂	—	2	2	no	—
1033	C₂	—	2	2	no	—
1034	C₂	—	2	2	no	—
1035	C₂	—	2	4	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	8	no	—
1038	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1039	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1040	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×#3541	C₂	semidirect
2. C₁₃×#3538	C₂	semidirect
3. C₁₃×#3536	C₂	semidirect
4. C₁₃×#3535	C₂	semidirect
5. C₁₃×#3520	C₂	semidirect
6. C₁₃×#3505	C₂	semidirect
7. C₁₃×#3501	C₂	semidirect
8. C₁₃×#3495	C₂	semidirect
9. C₁₃×#3492	C₂	semidirect
10. C₁₃×#3492	C₂	semidirect
11. C₁₃×#3490	C₂	semidirect
12. C₁₃×#3489	C₂	semidirect
13. C₁₃×#3486	C₂	semidirect
14. C₂×C₁₃×#525	C₂	semidirect
15. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂³×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#563	C₂²	semidirect
21. C₁₃×#562	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#553	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
30. C₁₃×#552	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
32. C₁₃×#552	C₂²	semidirect
33. C₁₃×#551	C₂²	semidirect
34. C₁₃×#551	C₂²	semidirect
35. C₁₃×#551	C₂²	semidirect
36. D₄×Q₈×C₁₃	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#548	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
41. C₁₃×#548	C₂²	semidirect
42. C₁₃×#547	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. C₁₃×#546	C₂²	semidirect
48. C₁₃×#544	C₂²	semidirect
49. C₁₃×#544	C₂²	semidirect
50. C₁₃×#544	C₂²	semidirect
52. C₁₃×#543	C₂²	semidirect
53. C₁₃×#542	C₂²	semidirect
54. C₁₃×#542	C₂²	semidirect
55. C₁₃×#541	C₂²	semidirect
56. C₁₃×#539	C₂²	semidirect
57. C₁₃×#539	C₂²	semidirect
58. C₁₃×#539	C₂²	semidirect
59. C₁₃×#539	C₂²	semidirect
60. C₁₃×#539	C₂²	semidirect
61. C₁₃×#538	C₂²	semidirect
62. C₁₃×#538	C₂²	semidirect
63. C₁₃×#538	C₂²	semidirect
64. C₁₃×#537	C₂²	semidirect
65. C₁₃×#537	C₂²	semidirect
66. C₁₃×#537	C₂²	semidirect
67. C₁₃×#536	C₂²	semidirect
68. C₁₃×#536	C₂²	semidirect
69. C₁₃×#536	C₂²	semidirect
71. C₁₃×#533	C₂²	semidirect
72. C₁₃×#529	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
87. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
91. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
92. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₁₃×#121	C₂²	semidirect
97. C₁₃×#520	C₂²	semidirect
98. C₁₃×#520	C₂²	semidirect
99. C₁₃×#519	C₂²	semidirect
102. C₂×C₄×D₄×C₁₃	C₂²	semidirect
103. C₂×C₁₃×#117	C₂²	semidirect
104. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
105. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
116. C₂×C₁₃×#41	C₂³	semidirect
123. C₂²×Q₈×C₁₃	C₂³	semidirect
140. C₁₃×C₄⋊Q₈	C₂³	semidirect
141. C₁₃×C₄⋊Q₈	C₂³	semidirect
142. C₁₃×C₄⋊Q₈	C₂³	semidirect
143. C₁₃×C₄⋊Q₈	C₂³	semidirect
146. C₁₃×#126	C₂³	semidirect
147. C₁₃×#126	C₂³	semidirect
148. C₁₃×#126	C₂³	semidirect
149. C₁₃×#125	C₂³	semidirect
150. C₁₃×#125	C₂³	semidirect
151. C₁₃×#125	C₂³	semidirect
152. C₁₃×#125	C₂³	semidirect
153. C₁₃×#125	C₂³	semidirect
156. C₁₃×#124	C₂³	semidirect
157. C₁₃×#124	C₂³	semidirect
167. C₁₃×#123	C₂³	semidirect
168. C₁₃×#123	C₂³	semidirect
169. C₁₃×#123	C₂³	semidirect
192. C₁₃×C₂²⋊Q₈	C₂³	semidirect
193. C₁₃×C₂²⋊Q₈	C₂³	semidirect
194. C₁₃×C₂²⋊Q₈	C₂³	semidirect
195. C₁₃×C₂²⋊Q₈	C₂³	semidirect
196. C₁₃×C₂²⋊Q₈	C₂³	semidirect
197. C₁₃×C₂²⋊Q₈	C₂³	semidirect
198. C₁₃×C₂²⋊Q₈	C₂³	semidirect
199. C₁₃×C₂²⋊Q₈	C₂³	semidirect
200. C₁₃×C₂²⋊Q₈	C₂³	semidirect
215. C₁₃×#121	C₂³	semidirect
216. C₁₃×#121	C₂³	semidirect
222. C₄×Q₈×C₁₃	C₂³	semidirect
223. C₄×Q₈×C₁₃	C₂³	semidirect
224. C₄×Q₈×C₁₃	C₂³	semidirect
225. C₄×Q₈×C₁₃	C₂³	semidirect
240. C₄×D₄×C₁₃	C₂³	semidirect
241. C₄×D₄×C₁₃	C₂³	semidirect
249. C₁₃×#117	C₂³	semidirect
250. C₁₃×#117	C₂³	semidirect
263. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
264. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
276. #62819	C₁₃	direct (N × H)
399. #3541	C₂×C₁₃	semidirect
400. #3538	C₂×C₁₃	semidirect
401. #3536	C₂×C₁₃	semidirect
402. #3535	C₂×C₁₃	semidirect
403. #3520	C₂×C₁₃	semidirect
404. #3505	C₂×C₁₃	semidirect
405. #3501	C₂×C₁₃	semidirect
406. #3495	C₂×C₁₃	semidirect
407. #3492	C₂×C₁₃	semidirect
408. #3492	C₂×C₁₃	semidirect
409. #3490	C₂×C₁₃	semidirect
410. #3489	C₂×C₁₃	semidirect
411. #3486	C₂×C₁₃	semidirect
412. C₂×#525	C₂×C₁₃	semidirect
413. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
432. C₂³×C₁₃	2₋¹⁺⁴	semidirect
493. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
494. C₂²×#41	C₂²×C₁₃	semidirect
495. C₂³×Q₈	C₂²×C₁₃	semidirect
497. #563	C₂²×C₁₃	semidirect
498. #562	C₂²×C₁₃	semidirect
499. #556	C₂²×C₁₃	semidirect
500. #554	C₂²×C₁₃	semidirect
501. #554	C₂²×C₁₃	semidirect
502. #554	C₂²×C₁₃	semidirect
503. #554	C₂²×C₁₃	semidirect
504. #553	C₂²×C₁₃	semidirect
505. #553	C₂²×C₁₃	semidirect
506. #552	C₂²×C₁₃	semidirect
507. #552	C₂²×C₁₃	semidirect
508. #552	C₂²×C₁₃	semidirect
509. #552	C₂²×C₁₃	semidirect
510. #551	C₂²×C₁₃	semidirect
511. #551	C₂²×C₁₃	semidirect
512. #551	C₂²×C₁₃	semidirect
513. D₄×Q₈	C₂²×C₁₃	semidirect
514. D₄×Q₈	C₂²×C₁₃	semidirect
515. D₄×Q₈	C₂²×C₁₃	semidirect
516. #548	C₂²×C₁₃	semidirect
517. #548	C₂²×C₁₃	semidirect
518. #548	C₂²×C₁₃	semidirect
519. #547	C₂²×C₁₃	semidirect
520. #547	C₂²×C₁₃	semidirect
521. #547	C₂²×C₁₃	semidirect
522. #546	C₂²×C₁₃	semidirect
523. #546	C₂²×C₁₃	semidirect
524. #546	C₂²×C₁₃	semidirect
525. #544	C₂²×C₁₃	semidirect
526. #544	C₂²×C₁₃	semidirect
527. #544	C₂²×C₁₃	semidirect
529. #543	C₂²×C₁₃	semidirect
530. #542	C₂²×C₁₃	semidirect
531. #542	C₂²×C₁₃	semidirect
532. #541	C₂²×C₁₃	semidirect
533. #539	C₂²×C₁₃	semidirect
534. #539	C₂²×C₁₃	semidirect
535. #539	C₂²×C₁₃	semidirect
536. #539	C₂²×C₁₃	semidirect
537. #539	C₂²×C₁₃	semidirect
538. #538	C₂²×C₁₃	semidirect
539. #538	C₂²×C₁₃	semidirect
540. #538	C₂²×C₁₃	semidirect
541. #537	C₂²×C₁₃	semidirect
542. #537	C₂²×C₁₃	semidirect
543. #537	C₂²×C₁₃	semidirect
544. #536	C₂²×C₁₃	semidirect
545. #536	C₂²×C₁₃	semidirect
546. #536	C₂²×C₁₃	semidirect
548. #533	C₂²×C₁₃	semidirect
549. #529	C₂²×C₁₃	semidirect
554. #525	C₂²×C₁₃	semidirect
555. #525	C₂²×C₁₃	semidirect
556. #525	C₂²×C₁₃	semidirect
557. #525	C₂²×C₁₃	semidirect
558. #525	C₂²×C₁₃	semidirect
559. #525	C₂²×C₁₃	semidirect
560. #525	C₂²×C₁₃	semidirect
561. C₂×#123	C₂²×C₁₃	semidirect
564. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
565. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
566. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
567. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
568. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
569. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
570. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
572. C₂×#121	C₂²×C₁₃	semidirect
574. #520	C₂²×C₁₃	semidirect
575. #520	C₂²×C₁₃	semidirect
576. #519	C₂²×C₁₃	semidirect
579. C₂×C₄×D₄	C₂²×C₁₃	semidirect
580. C₂×#117	C₂²×C₁₃	semidirect
581. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
582. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
627. C₂×#41	C₂³×C₁₃	semidirect
634. C₂²×Q₈	C₂³×C₁₃	semidirect
651. C₄⋊Q₈	C₂³×C₁₃	semidirect
652. C₄⋊Q₈	C₂³×C₁₃	semidirect
653. C₄⋊Q₈	C₂³×C₁₃	semidirect
654. C₄⋊Q₈	C₂³×C₁₃	semidirect
657. #126	C₂³×C₁₃	semidirect
658. #126	C₂³×C₁₃	semidirect
659. #126	C₂³×C₁₃	semidirect
660. #125	C₂³×C₁₃	semidirect
661. #125	C₂³×C₁₃	semidirect
662. #125	C₂³×C₁₃	semidirect
663. #125	C₂³×C₁₃	semidirect
664. #125	C₂³×C₁₃	semidirect
667. #124	C₂³×C₁₃	semidirect
668. #124	C₂³×C₁₃	semidirect
678. #123	C₂³×C₁₃	semidirect
679. #123	C₂³×C₁₃	semidirect
680. #123	C₂³×C₁₃	semidirect
703. C₂²⋊Q₈	C₂³×C₁₃	semidirect
704. C₂²⋊Q₈	C₂³×C₁₃	semidirect
705. C₂²⋊Q₈	C₂³×C₁₃	semidirect
706. C₂²⋊Q₈	C₂³×C₁₃	semidirect
707. C₂²⋊Q₈	C₂³×C₁₃	semidirect
708. C₂²⋊Q₈	C₂³×C₁₃	semidirect
709. C₂²⋊Q₈	C₂³×C₁₃	semidirect
710. C₂²⋊Q₈	C₂³×C₁₃	semidirect
711. C₂²⋊Q₈	C₂³×C₁₃	semidirect
726. #121	C₂³×C₁₃	semidirect
727. #121	C₂³×C₁₃	semidirect
733. C₄×Q₈	C₂³×C₁₃	semidirect
734. C₄×Q₈	C₂³×C₁₃	semidirect
735. C₄×Q₈	C₂³×C₁₃	semidirect
736. C₄×Q₈	C₂³×C₁₃	semidirect
751. C₄×D₄	C₂³×C₁₃	semidirect
752. C₄×D₄	C₂³×C₁₃	semidirect
760. #117	C₂³×C₁₃	semidirect
761. #117	C₂³×C₁₃	semidirect
774. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
775. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
918. C₁₃	#62819	direct (N × H)
937. C₂³	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3541	2
C₁₃×#3538	2
C₁₃×#3536	2
C₁₃×#3535	2
C₁₃×#3520	2
C₁₃×#3505	2
C₁₃×#3501	2
C₁₃×#3495	2
C₁₃×#3492	2
C₁₃×#3490	2
C₁₃×#3489	2
C₁₃×#3486	2
C₂×C₁₃×#525	2
C₂²×C₁₃×C₂²⋊Q₈	2
#62819	13

Subgroups — C13×#62819 #15749158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62819 #15749158