Subgroups — C₁₃×#62914 #15749253

Order 3328.

7738 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×#3548	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3546	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3542	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3536	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3536	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3534	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3520	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3511	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3496	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3492	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
14	D₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
19	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
21	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
22	C₁₃×#562	C₂²	1	16	yes	complemented
23	C₁₃×#562	C₂²	1	16	yes	complemented
24	C₁₃×#560	C₂²	1	16	yes	complemented
25	C₁₃×#556	C₂²	1	4	yes	complemented
26	C₁₃×#555	C₂²	1	4	yes	complemented
27	C₁₃×#554	C₂²	1	8	yes	complemented
28	C₁₃×#554	C₂²	1	4	yes	complemented
29	C₁₃×#554	C₂²	1	8	yes	complemented
30	C₁₃×#553	C₂²	1	8	yes	complemented
31	C₁₃×#553	C₂²	1	8	yes	complemented
32	C₁₃×#552	C₂²	1	8	yes	complemented
33	C₁₃×#551	C₂²	1	16	yes	complemented
34	C₁₃×#550	C₂²	1	8	yes	complemented
35	C₁₃×#550	C₂²	1	2	yes	complemented
36	C₁₃×#550	C₂²	1	8	yes	complemented
37	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
38	C₁₃×#548	C₂²	1	8	yes	complemented
39	C₁₃×#548	C₂²	1	4	yes	complemented
40	C₁₃×#548	C₂²	1	8	yes	complemented
41	C₁₃×#547	C₂²	1	4	yes	complemented
42	C₁₃×#547	C₂²	1	4	yes	complemented
43	C₁₃×#547	C₂²	1	4	yes	complemented
44	C₁₃×#547	C₂²	1	8	yes	complemented
45	C₁₃×#547	C₂²	1	8	yes	complemented
46	C₁₃×#547	C₂²	1	4	yes	complemented
47	C₁₃×#547	C₂²	1	2	yes	complemented
48	C₁₃×#547	C₂²	1	4	yes	complemented
49	C₁₃×#546	C₂²	1	8	yes	complemented
50	C₁₃×#546	C₂²	1	8	yes	complemented
51	C₁₃×#546	C₂²	1	16	yes	complemented
52	C₁₃×#546	C₂²	1	16	yes	complemented
53	C₁₃×#546	C₂²	1	16	yes	complemented
54	C₁₃×#546	C₂²	1	8	yes	complemented
55	C₁₃×#546	C₂²	1	8	yes	complemented
56	C₁₃×#546	C₂²	1	8	yes	complemented
57	C₁₃×#546	C₂²	1	4	yes	complemented
58	D₄²×C₁₃	C₂²	1	16	yes	complemented
59	D₄²×C₁₃	C₂²	1	8	yes	complemented
60	D₄²×C₁₃	C₂²	1	4	yes	complemented
61	D₄²×C₁₃	C₂²	1	4	yes	complemented
62	D₄²×C₁₃	C₂²	1	2	yes	complemented
63	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#543	C₂²	1	8	yes	complemented
65	C₁₃×#542	C₂²	1	8	yes	complemented
66	C₁₃×#542	C₂²	1	4	yes	complemented
67	C₁₃×#542	C₂²	1	8	yes	complemented
68	C₁₃×#540	C₂²	1	16	yes	complemented
69	C₁₃×#540	C₂²	1	4	yes	complemented
70	C₁₃×#539	C₂²	1	16	yes	complemented
71	C₁₃×#539	C₂²	1	8	yes	complemented
72	C₁₃×#538	C₂²	1	4	yes	complemented
73	C₁₃×#538	C₂²	1	16	yes	complemented
74	C₁₃×#538	C₂²	1	8	yes	complemented
75	C₁₃×#537	C₂²	1	8	yes	complemented
76	C₁₃×#537	C₂²	1	8	yes	complemented
77	C₁₃×#537	C₂²	1	8	yes	complemented
78	C₁₃×#537	C₂²	1	8	yes	complemented
79	C₁₃×#537	C₂²	1	8	yes	complemented
80	C₁₃×#537	C₂²	1	8	yes	complemented
81	C₁₃×#537	C₂²	1	4	yes	complemented
82	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#537	C₂²	1	4	yes	complemented
84	C₁₃×#537	C₂²	1	2	yes	complemented
85	C₁₃×#535	C₂²	1	8	yes	complemented
86	C₁₃×#535	C₂²	1	8	yes	complemented
87	C₁₃×#535	C₂²	1	4	yes	complemented
88	C₁₃×#535	C₂²	1	2	yes	complemented
89	C₁₃×#534	C₂²	1	4	yes	complemented
90	C₁₃×#534	C₂²	1	16	yes	complemented
91	C₁₃×#533	C₂²	1	4	yes	complemented
92	C₁₃×#532	C₂²	1	4	yes	complemented
93	C₁₃×#532	C₂²	1	4	yes	complemented
94	C₁₃×#532	C₂²	1	4	yes	complemented
95	C₁₃×#532	C₂²	1	2	yes	complemented
96	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#529	C₂²	1	4	yes	complemented
98	C₁₃×#525	C₂²	1	8	yes	complemented
99	C₁₃×#525	C₂²	1	8	yes	complemented
100	C₁₃×#525	C₂²	1	8	yes	complemented
101	C₁₃×#525	C₂²	1	4	yes	complemented
102	C₁₃×#525	C₂²	1	4	yes	complemented
103	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
104	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
105	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
106	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
107	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
108	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
109	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
110	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
111	C₁₃×#520	C₂²	1	4	yes	complemented
112	C₁₃×#520	C₂²	1	4	yes	complemented
113	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
114	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
115	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
117	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₁₃×H(5,𝔽₂)	—	4	16	no	—
119	C₁₃×H(5,𝔽₂)	—	4	8	no	—
120	C₂×C₁₃×#41	—	4	16	no	—
121	C₂×C₁₃×#41	—	4	8	no	—
122	C₂×C₁₃×#41	C₂³	1	2	yes	—
123	C₂×C₁₃×#41	C₂³	1	4	yes	—
124	C₂×C₁₃×#41	C₂³	1	4	yes	—
125	C₂×C₁₃×#41	C₂³	1	4	yes	—
126	C₂×C₁₃×#41	C₂³	1	8	yes	—
127	C₂×C₁₃×#41	C₂³	1	8	yes	—
128	C₂×C₁₃×#41	C₂³	1	8	yes	—
129	C₂×C₁₃×#41	C₂³	1	8	yes	—
130	C₂×C₁₃×#41	C₂³	1	8	yes	—
131	C₂×C₁₃×#41	C₂³	1	4	yes	—
132	C₂×C₁₃×#41	C₂³	1	8	yes	—
133	C₂×C₁₃×#41	C₂³	1	4	yes	—
134	C₂×C₁₃×#41	C₂³	1	4	yes	—
135	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
136	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
140	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
141	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
142	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
143	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
144	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
145	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
146	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
147	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
148	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
150	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
152	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
153	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
156	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
157	C₁₃×#127	C₂³	1	2	yes	—
158	C₁₃×#127	C₂³	1	4	yes	—
159	C₁₃×#127	C₂³	1	4	yes	—
160	C₁₃×#127	C₂³	1	16	yes	—
161	C₁₃×#126	C₂³	1	8	yes	—
162	C₁₃×#126	C₂³	1	16	yes	—
163	C₁₃×#126	C₂³	1	16	yes	—
164	C₁₃×#125	C₂³	1	4	yes	—
165	C₁₃×#125	C₂³	1	8	yes	—
166	C₁₃×#125	C₂³	1	16	yes	—
167	C₁₃×#124	C₂³	1	4	yes	—
168	C₁₃×#124	C₂³	1	8	yes	—
169	C₁₃×#124	C₂³	1	8	yes	—
170	C₁₃×#124	C₂³	1	8	yes	—
171	C₁₃×#124	C₂³	1	4	yes	—
172	C₁₃×#124	C₂³	1	16	yes	—
173	C₁₃×#124	C₂³	1	16	yes	—
174	C₁₃×#123	C₂³	1	16	yes	—
175	C₁₃×#123	C₂³	1	16	yes	—
176	C₁₃×#123	C₂³	1	16	yes	—
177	C₁₃×#123	C₂³	1	8	yes	—
178	C₁₃×#123	C₂³	1	8	yes	—
179	C₁₃×#123	C₂³	1	16	yes	—
180	C₁₃×#123	C₂³	1	8	yes	—
181	C₁₃×#123	C₂³	1	8	yes	—
182	C₁₃×#123	C₂³	1	8	yes	—
183	C₁₃×#123	C₂³	1	16	yes	—
184	C₁₃×#123	C₂³	1	16	yes	—
185	C₁₃×#123	C₂³	1	16	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	16	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	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
204	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
205	C₁₃×#121	C₂³	1	8	yes	—
206	C₁₃×#121	C₂³	1	4	yes	—
207	C₁₃×#121	C₂³	1	4	yes	—
208	C₁₃×#121	C₂³	1	8	yes	—
209	C₁₃×#121	C₂³	1	4	yes	—
210	C₁₃×#121	C₂³	1	8	yes	—
211	C₁₃×#121	C₂³	1	4	yes	—
212	C₁₃×#121	C₂³	1	4	yes	—
213	C₁₃×#121	C₂³	1	16	yes	—
214	C₁₃×#121	C₂³	1	16	yes	—
215	C₁₃×#121	C₂³	1	8	yes	—
216	C₁₃×#121	C₂³	1	8	yes	—
217	C₁₃×#121	C₂³	1	8	yes	—
218	C₁₃×#121	C₂³	1	8	yes	—
219	C₁₃×#121	C₂³	1	8	yes	—
220	C₁₃×#121	C₂³	1	16	yes	—
221	C₁₃×#121	C₂³	1	8	yes	—
222	C₁₃×#121	C₂³	1	16	yes	—
223	C₁₃×#121	C₂³	1	16	yes	—
224	C₁₃×#121	C₂³	1	16	yes	—
225	C₁₃×#121	C₂³	1	8	yes	—
226	C₁₃×#121	C₂³	1	4	yes	—
227	C₁₃×#121	C₂³	1	4	yes	—
228	C₁₃×#121	C₂³	1	4	yes	—
229	C₁₃×#121	C₂³	1	8	yes	—
230	C₁₃×#121	C₂³	1	8	yes	—
231	C₁₃×#121	C₂³	1	8	yes	—
232	C₁₃×#121	C₂³	1	8	yes	—
233	C₁₃×#121	C₂³	1	4	yes	—
234	C₁₃×#121	C₂³	1	8	yes	—
235	C₁₃×#121	C₂³	1	4	yes	—
236	C₁₃×#121	C₂³	1	4	yes	—
237	C₁₃×#121	C₂³	1	8	yes	—
238	C₁₃×#121	C₂³	1	16	yes	—
239	C₁₃×#121	C₂³	1	16	yes	—
240	C₁₃×#121	C₂³	1	16	yes	—
241	C₁₃×#120	C₂³	1	8	yes	—
242	C₁₃×#120	C₂³	1	8	yes	—
243	C₁₃×#120	C₂³	1	16	yes	—
244	C₁₃×#120	C₂³	1	8	yes	—
245	C₁₃×#120	C₂³	1	8	yes	—
246	C₁₃×#120	C₂³	1	16	yes	—
247	C₁₃×#120	C₂³	1	16	yes	—
248	C₁₃×#120	C₂³	1	16	yes	—
249	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
250	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
251	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
252	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	4	yes	—
255	C₄×D₄×C₁₃	C₂³	1	8	yes	—
256	C₄×D₄×C₁₃	C₂³	1	4	yes	—
257	C₄×D₄×C₁₃	C₂³	1	4	yes	—
258	C₄×D₄×C₁₃	C₂³	1	4	yes	—
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₄×D₄×C₁₃	C₂³	1	8	yes	—
261	C₄×D₄×C₁₃	C₂³	1	4	yes	—
262	C₄×D₄×C₁₃	C₂³	1	4	yes	—
263	C₄×D₄×C₁₃	C₂³	1	4	yes	—
264	C₄×D₄×C₁₃	C₂³	1	2	yes	—
265	C₄×D₄×C₁₃	C₂³	1	4	yes	—
266	C₄×D₄×C₁₃	C₂³	1	2	yes	—
267	C₄×D₄×C₁₃	C₂³	1	16	yes	—
268	C₄×D₄×C₁₃	C₂³	1	16	yes	—
269	C₄×D₄×C₁₃	C₂³	1	8	yes	—
270	C₄×D₄×C₁₃	C₂³	1	4	yes	—
271	C₄×D₄×C₁₃	C₂³	1	8	yes	—
272	C₄×D₄×C₁₃	C₂³	1	8	yes	—
273	C₄×D₄×C₁₃	C₂³	1	16	yes	—
274	C₄×D₄×C₁₃	C₂³	1	16	yes	—
275	C₄×D₄×C₁₃	C₂³	1	8	yes	—
276	C₁₃×#117	C₂³	1	2	yes	—
277	C₁₃×#117	C₂³	1	4	yes	—
278	C₁₃×#117	C₂³	1	4	yes	—
279	C₁₃×#117	C₂³	1	8	yes	—
280	C₁₃×#117	C₂³	1	8	yes	—
281	C₁₃×#117	C₂³	1	8	yes	—
282	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
284	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
285	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
286	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
287	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
289	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
290	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
291	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
292	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
293	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
294	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
295	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
296	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
297	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
298	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
299	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
300	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
302	#62914	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
303	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
304	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
305	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
306	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
307	C₁₃×#41	—	2	16	no	—
308	C₁₃×#41	—	2	8	no	—
309	C₁₃×#41	—	2	16	no	—
310	C₁₃×#41	—	4	16	no	—
311	C₁₃×#41	—	4	8	no	—
312	C₁₃×#41	—	4	16	no	—
313	C₁₃×#41	—	4	16	no	—
314	C₁₃×#41	—	4	16	no	—
315	C₁₃×#41	—	4	8	no	—
316	C₁₃×#41	—	4	8	no	—
317	C₁₃×#41	—	4	8	no	—
318	C₁₃×#41	—	4	16	no	—
319	C₁₃×#41	—	4	16	no	—
320	C₂×Q₈×C₁₃	—	4	8	no	—
321	C₂×Q₈×C₁₃	—	4	4	no	—
322	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
324	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
325	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
326	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
328	C₂×D₄×C₁₃	—	2	4	no	—
329	C₂×D₄×C₁₃	—	2	16	no	—
330	C₂×D₄×C₁₃	—	2	4	no	—
331	C₂×D₄×C₁₃	—	4	8	no	—
332	C₂×D₄×C₁₃	—	4	8	no	—
333	C₂×D₄×C₁₃	—	4	16	no	—
334	C₂×D₄×C₁₃	—	4	16	no	—
335	C₂×D₄×C₁₃	—	4	8	no	—
336	C₂×D₄×C₁₃	—	4	16	no	—
337	C₂×D₄×C₁₃	—	4	32	no	—
338	C₂×D₄×C₁₃	—	4	16	no	—
339	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
341	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
342	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
343	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
344	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
345	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
346	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
347	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
348	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
350	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
351	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
352	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
353	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
354	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
355	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
356	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
357	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
358	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
359	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
360	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
361	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₁₃	—	2	8	no	—
363	C₂²×C₄×C₁₃	—	4	16	no	—
364	C₂²×C₄×C₁₃	—	4	4	no	—
365	C₂²×C₄×C₁₃	—	4	8	no	—
366	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
368	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
369	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
371	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
372	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
373	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
374	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
375	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
377	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
378	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
379	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
380	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
383	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
384	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
388	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
390	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
391	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
392	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
393	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
394	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
395	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
396	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
399	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
400	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
402	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
403	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
404	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
405	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
407	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
408	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
409	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
410	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
411	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
412	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
413	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
415	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
416	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
417	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
418	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
419	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
420	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
421	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
422	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
423	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
424	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
425	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
426	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
427	C₄²×C₁₃	C₂⁴	1	2	yes	—
428	C₄²×C₁₃	C₂⁴	1	2	yes	—
429	C₄²×C₁₃	C₂⁴	1	4	yes	—
430	C₄²×C₁₃	C₂⁴	1	4	yes	—
431	C₄²×C₁₃	C₂⁴	1	4	yes	—
432	C₄²×C₁₃	C₂⁴	1	16	yes	—
433	#3548	C₂×C₁₃	1	4	yes	complemented
434	#3546	C₂×C₁₃	1	4	yes	complemented
435	#3542	C₂×C₁₃	1	8	yes	complemented
436	#3536	C₂×C₁₃	1	8	yes	complemented
437	#3536	C₂×C₁₃	1	4	yes	complemented
438	#3534	C₂×C₁₃	1	8	yes	complemented
439	#3520	C₂×C₁₃	1	4	yes	complemented
440	#3511	C₂×C₁₃	1	2	yes	complemented
441	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
442	#3496	C₂×C₁₃	1	4	yes	complemented
443	#3492	C₂×C₁₃	1	2	yes	complemented
444	#3488	C₂×C₁₃	1	4	yes	complemented
445	#3488	C₂×C₁₃	1	4	yes	complemented
446	D₄×#41	C₂×C₁₃	1	2	yes	complemented
447	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
449	C₂×#537	C₂×C₁₃	1	2	yes	complemented
450	C₂³×C₁₃	—	2	4	no	—
451	C₂³×C₁₃	—	2	4	no	—
452	C₂³×C₁₃	—	2	16	no	—
453	C₂³×C₁₃	—	2	4	no	—
454	C₂³×C₁₃	—	4	2	no	—
455	C₂³×C₁₃	—	4	8	no	—
456	C₂³×C₁₃	—	4	2	no	—
457	C₂³×C₁₃	—	4	2	no	—
458	C₂³×C₁₃	—	4	8	no	—
459	C₂³×C₁₃	—	4	8	no	—
460	C₂³×C₁₃	—	4	8	no	—
461	C₂³×C₁₃	—	4	8	no	—
462	C₂³×C₁₃	C₂⁵	1	8	yes	—
463	C₂³×C₁₃	C₂⁵	1	4	yes	—
464	C₂³×C₁₃	C₂⁵	1	4	yes	—
465	C₂³×C₁₃	C₂⁵	1	2	yes	—
466	C₂³×C₁₃	C₂⁵	1	2	yes	—
467	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
468	Q₈×C₁₃	—	2	4	no	—
469	Q₈×C₁₃	—	2	8	no	—
470	Q₈×C₁₃	—	2	8	no	—
471	Q₈×C₁₃	—	4	8	no	—
472	Q₈×C₁₃	—	4	4	no	—
473	Q₈×C₁₃	—	4	4	no	—
474	D₄×C₁₃	—	2	16	no	—
475	D₄×C₁₃	—	2	4	no	—
476	D₄×C₁₃	—	2	16	no	—
477	D₄×C₁₃	—	2	16	no	—
478	D₄×C₁₃	—	2	8	no	—
479	D₄×C₁₃	—	2	8	no	—
480	D₄×C₁₃	—	2	8	no	—
481	D₄×C₁₃	—	2	2	no	—
482	D₄×C₁₃	—	2	8	no	—
483	D₄×C₁₃	—	2	4	no	—
484	D₄×C₁₃	—	4	4	no	—
485	D₄×C₁₃	—	4	8	no	—
486	D₄×C₁₃	—	4	8	no	—
487	D₄×C₁₃	—	4	16	no	—
488	D₄×C₁₃	—	4	16	no	—
489	D₄×C₁₃	—	4	8	no	—
490	D₄×C₁₃	—	4	8	no	—
491	D₄×C₁₃	—	4	8	no	—
492	D₄×C₁₃	—	4	8	no	—
493	D₄×C₁₃	—	4	4	no	—
494	D₄×C₁₃	—	4	8	no	—
495	D₄×C₁₃	—	4	8	no	—
496	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
497	C₂×C₄×C₁₃	—	2	4	no	—
498	C₂×C₄×C₁₃	—	2	16	no	—
499	C₂×C₄×C₁₃	—	2	8	no	—
500	C₂×C₄×C₁₃	—	2	8	no	—
501	C₂×C₄×C₁₃	—	2	2	no	—
502	C₂×C₄×C₁₃	—	2	8	no	—
503	C₂×C₄×C₁₃	—	2	8	no	—
504	C₂×C₄×C₁₃	—	2	16	no	—
505	C₂×C₄×C₁₃	—	2	8	no	—
506	C₂×C₄×C₁₃	—	4	2	no	—
507	C₂×C₄×C₁₃	—	4	4	no	—
508	C₂×C₄×C₁₃	—	4	8	no	—
509	C₂×C₄×C₁₃	—	4	4	no	—
510	C₂×C₄×C₁₃	—	4	8	no	—
511	C₂×C₄×C₁₃	—	4	8	no	—
512	C₂×C₄×C₁₃	—	4	8	no	—
513	C₂×C₄×C₁₃	—	4	1	no	—
514	C₂×C₄×C₁₃	—	4	4	no	—
515	C₂×C₄×C₁₃	—	4	16	no	—
516	C₂×C₄×C₁₃	—	4	8	no	—
517	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
518	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
519	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
520	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
521	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
522	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
523	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
524	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
525	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
526	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
527	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
528	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
529	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
530	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
531	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
532	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
533	#562	C₂²×C₁₃	1	16	yes	complemented
534	#562	C₂²×C₁₃	1	16	yes	complemented
535	#560	C₂²×C₁₃	1	16	yes	complemented
536	#556	C₂²×C₁₃	1	4	yes	complemented
537	#555	C₂²×C₁₃	1	4	yes	complemented
538	#554	C₂²×C₁₃	1	8	yes	complemented
539	#554	C₂²×C₁₃	1	4	yes	complemented
540	#554	C₂²×C₁₃	1	8	yes	complemented
541	#553	C₂²×C₁₃	1	8	yes	complemented
542	#553	C₂²×C₁₃	1	8	yes	complemented
543	#552	C₂²×C₁₃	1	8	yes	complemented
544	#551	C₂²×C₁₃	1	16	yes	complemented
545	#550	C₂²×C₁₃	1	2	yes	complemented
546	#550	C₂²×C₁₃	1	8	yes	complemented
547	#550	C₂²×C₁₃	1	8	yes	complemented
548	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
549	#548	C₂²×C₁₃	1	4	yes	complemented
550	#548	C₂²×C₁₃	1	8	yes	complemented
551	#548	C₂²×C₁₃	1	8	yes	complemented
552	#547	C₂²×C₁₃	1	4	yes	complemented
553	#547	C₂²×C₁₃	1	8	yes	complemented
554	#547	C₂²×C₁₃	1	4	yes	complemented
555	#547	C₂²×C₁₃	1	4	yes	complemented
556	#547	C₂²×C₁₃	1	2	yes	complemented
557	#547	C₂²×C₁₃	1	8	yes	complemented
558	#547	C₂²×C₁₃	1	4	yes	complemented
559	#547	C₂²×C₁₃	1	4	yes	complemented
560	#546	C₂²×C₁₃	1	8	yes	complemented
561	#546	C₂²×C₁₃	1	4	yes	complemented
562	#546	C₂²×C₁₃	1	8	yes	complemented
563	#546	C₂²×C₁₃	1	16	yes	complemented
564	#546	C₂²×C₁₃	1	16	yes	complemented
565	#546	C₂²×C₁₃	1	8	yes	complemented
566	#546	C₂²×C₁₃	1	16	yes	complemented
567	#546	C₂²×C₁₃	1	8	yes	complemented
568	#546	C₂²×C₁₃	1	8	yes	complemented
569	D₄²	C₂²×C₁₃	1	4	yes	complemented
570	D₄²	C₂²×C₁₃	1	2	yes	complemented
571	D₄²	C₂²×C₁₃	1	16	yes	complemented
572	D₄²	C₂²×C₁₃	1	8	yes	complemented
573	D₄²	C₂²×C₁₃	1	4	yes	complemented
574	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
575	#543	C₂²×C₁₃	1	8	yes	complemented
576	#542	C₂²×C₁₃	1	4	yes	complemented
577	#542	C₂²×C₁₃	1	8	yes	complemented
578	#542	C₂²×C₁₃	1	8	yes	complemented
579	#540	C₂²×C₁₃	1	4	yes	complemented
580	#540	C₂²×C₁₃	1	16	yes	complemented
581	#539	C₂²×C₁₃	1	8	yes	complemented
582	#539	C₂²×C₁₃	1	16	yes	complemented
583	#538	C₂²×C₁₃	1	4	yes	complemented
584	#538	C₂²×C₁₃	1	16	yes	complemented
585	#538	C₂²×C₁₃	1	8	yes	complemented
586	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	#537	C₂²×C₁₃	1	4	yes	complemented
588	#537	C₂²×C₁₃	1	2	yes	complemented
589	#537	C₂²×C₁₃	1	8	yes	complemented
590	#537	C₂²×C₁₃	1	8	yes	complemented
591	#537	C₂²×C₁₃	1	8	yes	complemented
592	#537	C₂²×C₁₃	1	8	yes	complemented
593	#537	C₂²×C₁₃	1	8	yes	complemented
594	#537	C₂²×C₁₃	1	4	yes	complemented
595	#537	C₂²×C₁₃	1	8	yes	complemented
596	#535	C₂²×C₁₃	1	2	yes	complemented
597	#535	C₂²×C₁₃	1	8	yes	complemented
598	#535	C₂²×C₁₃	1	8	yes	complemented
599	#535	C₂²×C₁₃	1	4	yes	complemented
600	#534	C₂²×C₁₃	1	4	yes	complemented
601	#534	C₂²×C₁₃	1	16	yes	complemented
602	#533	C₂²×C₁₃	1	4	yes	complemented
603	#532	C₂²×C₁₃	1	4	yes	complemented
604	#532	C₂²×C₁₃	1	2	yes	complemented
605	#532	C₂²×C₁₃	1	4	yes	complemented
606	#532	C₂²×C₁₃	1	4	yes	complemented
607	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#529	C₂²×C₁₃	1	4	yes	complemented
609	#525	C₂²×C₁₃	1	4	yes	complemented
610	#525	C₂²×C₁₃	1	4	yes	complemented
611	#525	C₂²×C₁₃	1	8	yes	complemented
612	#525	C₂²×C₁₃	1	8	yes	complemented
613	#525	C₂²×C₁₃	1	8	yes	complemented
614	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
615	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
616	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
617	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
618	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
619	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
620	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
621	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
622	#520	C₂²×C₁₃	1	4	yes	complemented
623	#520	C₂²×C₁₃	1	4	yes	complemented
624	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
625	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
628	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
629	C₂²×C₁₃	—	2	2	no	—
630	C₂²×C₁₃	—	2	1	no	—
631	C₂²×C₁₃	—	2	1	no	—
632	C₂²×C₁₃	—	2	2	no	—
633	C₂²×C₁₃	—	2	2	no	—
634	C₂²×C₁₃	—	2	4	no	—
635	C₂²×C₁₃	—	2	4	no	—
636	C₂²×C₁₃	—	2	8	no	—
637	C₂²×C₁₃	—	2	4	no	—
638	C₂²×C₁₃	—	2	2	no	—
639	C₂²×C₁₃	—	2	8	no	—
640	C₂²×C₁₃	—	2	4	no	—
641	C₂²×C₁₃	—	2	4	no	—
642	C₂²×C₁₃	—	2	2	no	—
643	C₂²×C₁₃	—	2	8	no	—
644	C₂²×C₁₃	—	2	4	no	—
645	C₂²×C₁₃	—	4	8	no	—
646	C₂²×C₁₃	—	8	4	no	—
647	C₂²×C₁₃	—	8	16	no	—
648	C₂²×C₁₃	—	16	8	no	—
649	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
650	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
651	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
652	C₄×C₁₃	—	2	4	no	—
653	C₄×C₁₃	—	2	4	no	—
654	C₄×C₁₃	—	2	4	no	—
655	C₄×C₁₃	—	2	1	no	—
656	C₄×C₁₃	—	2	8	no	—
657	C₄×C₁₃	—	2	8	no	—
658	C₄×C₁₃	—	2	4	no	—
659	C₄×C₁₃	—	2	2	no	—
660	C₄×C₁₃	—	2	4	no	—
661	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
662	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
663	H(5,𝔽₂)	—	4	16	no	—
664	H(5,𝔽₂)	—	4	8	no	—
665	C₂×#41	—	4	16	no	—
666	C₂×#41	—	4	8	no	—
667	C₂×#41	C₂³×C₁₃	1	2	yes	—
668	C₂×#41	C₂³×C₁₃	1	4	yes	—
669	C₂×#41	C₂³×C₁₃	1	4	yes	—
670	C₂×#41	C₂³×C₁₃	1	4	yes	—
671	C₂×#41	C₂³×C₁₃	1	8	yes	—
672	C₂×#41	C₂³×C₁₃	1	8	yes	—
673	C₂×#41	C₂³×C₁₃	1	8	yes	—
674	C₂×#41	C₂³×C₁₃	1	8	yes	—
675	C₂×#41	C₂³×C₁₃	1	8	yes	—
676	C₂×#41	C₂³×C₁₃	1	4	yes	—
677	C₂×#41	C₂³×C₁₃	1	8	yes	—
678	C₂×#41	C₂³×C₁₃	1	4	yes	—
679	C₂×#41	C₂³×C₁₃	1	4	yes	—
680	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
681	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
682	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
684	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
685	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
686	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
687	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
688	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
689	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
690	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
691	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
692	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
693	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
694	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
695	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
696	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
697	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
698	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
699	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
701	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
702	#127	C₂³×C₁₃	1	2	yes	—
703	#127	C₂³×C₁₃	1	4	yes	—
704	#127	C₂³×C₁₃	1	4	yes	—
705	#127	C₂³×C₁₃	1	16	yes	—
706	#126	C₂³×C₁₃	1	8	yes	—
707	#126	C₂³×C₁₃	1	16	yes	—
708	#126	C₂³×C₁₃	1	16	yes	—
709	#125	C₂³×C₁₃	1	4	yes	—
710	#125	C₂³×C₁₃	1	8	yes	—
711	#125	C₂³×C₁₃	1	16	yes	—
712	#124	C₂³×C₁₃	1	4	yes	—
713	#124	C₂³×C₁₃	1	8	yes	—
714	#124	C₂³×C₁₃	1	8	yes	—
715	#124	C₂³×C₁₃	1	8	yes	—
716	#124	C₂³×C₁₃	1	4	yes	—
717	#124	C₂³×C₁₃	1	16	yes	—
718	#124	C₂³×C₁₃	1	16	yes	—
719	#123	C₂³×C₁₃	1	16	yes	—
720	#123	C₂³×C₁₃	1	16	yes	—
721	#123	C₂³×C₁₃	1	16	yes	—
722	#123	C₂³×C₁₃	1	8	yes	—
723	#123	C₂³×C₁₃	1	8	yes	—
724	#123	C₂³×C₁₃	1	16	yes	—
725	#123	C₂³×C₁₃	1	8	yes	—
726	#123	C₂³×C₁₃	1	8	yes	—
727	#123	C₂³×C₁₃	1	8	yes	—
728	#123	C₂³×C₁₃	1	16	yes	—
729	#123	C₂³×C₁₃	1	16	yes	—
730	#123	C₂³×C₁₃	1	16	yes	—
731	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
732	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
733	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
734	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
735	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
736	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
737	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
738	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
739	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
740	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
741	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
742	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
743	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
744	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
745	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
746	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
747	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
748	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
749	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
750	#121	C₂³×C₁₃	1	8	yes	—
751	#121	C₂³×C₁₃	1	4	yes	—
752	#121	C₂³×C₁₃	1	8	yes	—
753	#121	C₂³×C₁₃	1	4	yes	—
754	#121	C₂³×C₁₃	1	8	yes	—
755	#121	C₂³×C₁₃	1	4	yes	—
756	#121	C₂³×C₁₃	1	4	yes	—
757	#121	C₂³×C₁₃	1	4	yes	—
758	#121	C₂³×C₁₃	1	16	yes	—
759	#121	C₂³×C₁₃	1	16	yes	—
760	#121	C₂³×C₁₃	1	8	yes	—
761	#121	C₂³×C₁₃	1	8	yes	—
762	#121	C₂³×C₁₃	1	8	yes	—
763	#121	C₂³×C₁₃	1	8	yes	—
764	#121	C₂³×C₁₃	1	8	yes	—
765	#121	C₂³×C₁₃	1	16	yes	—
766	#121	C₂³×C₁₃	1	8	yes	—
767	#121	C₂³×C₁₃	1	16	yes	—
768	#121	C₂³×C₁₃	1	16	yes	—
769	#121	C₂³×C₁₃	1	16	yes	—
770	#121	C₂³×C₁₃	1	8	yes	—
771	#121	C₂³×C₁₃	1	4	yes	—
772	#121	C₂³×C₁₃	1	4	yes	—
773	#121	C₂³×C₁₃	1	4	yes	—
774	#121	C₂³×C₁₃	1	8	yes	—
775	#121	C₂³×C₁₃	1	8	yes	—
776	#121	C₂³×C₁₃	1	8	yes	—
777	#121	C₂³×C₁₃	1	8	yes	—
778	#121	C₂³×C₁₃	1	4	yes	—
779	#121	C₂³×C₁₃	1	8	yes	—
780	#121	C₂³×C₁₃	1	4	yes	—
781	#121	C₂³×C₁₃	1	4	yes	—
782	#121	C₂³×C₁₃	1	8	yes	—
783	#121	C₂³×C₁₃	1	16	yes	—
784	#121	C₂³×C₁₃	1	16	yes	—
785	#121	C₂³×C₁₃	1	16	yes	—
786	#120	C₂³×C₁₃	1	8	yes	—
787	#120	C₂³×C₁₃	1	8	yes	—
788	#120	C₂³×C₁₃	1	16	yes	—
789	#120	C₂³×C₁₃	1	8	yes	—
790	#120	C₂³×C₁₃	1	8	yes	—
791	#120	C₂³×C₁₃	1	16	yes	—
792	#120	C₂³×C₁₃	1	16	yes	—
793	#120	C₂³×C₁₃	1	16	yes	—
794	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
795	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
796	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
797	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
798	C₄×D₄	C₂³×C₁₃	1	2	yes	—
799	C₄×D₄	C₂³×C₁₃	1	4	yes	—
800	C₄×D₄	C₂³×C₁₃	1	8	yes	—
801	C₄×D₄	C₂³×C₁₃	1	4	yes	—
802	C₄×D₄	C₂³×C₁₃	1	4	yes	—
803	C₄×D₄	C₂³×C₁₃	1	4	yes	—
804	C₄×D₄	C₂³×C₁₃	1	2	yes	—
805	C₄×D₄	C₂³×C₁₃	1	8	yes	—
806	C₄×D₄	C₂³×C₁₃	1	4	yes	—
807	C₄×D₄	C₂³×C₁₃	1	4	yes	—
808	C₄×D₄	C₂³×C₁₃	1	4	yes	—
809	C₄×D₄	C₂³×C₁₃	1	2	yes	—
810	C₄×D₄	C₂³×C₁₃	1	4	yes	—
811	C₄×D₄	C₂³×C₁₃	1	2	yes	—
812	C₄×D₄	C₂³×C₁₃	1	16	yes	—
813	C₄×D₄	C₂³×C₁₃	1	16	yes	—
814	C₄×D₄	C₂³×C₁₃	1	8	yes	—
815	C₄×D₄	C₂³×C₁₃	1	4	yes	—
816	C₄×D₄	C₂³×C₁₃	1	8	yes	—
817	C₄×D₄	C₂³×C₁₃	1	8	yes	—
818	C₄×D₄	C₂³×C₁₃	1	16	yes	—
819	C₄×D₄	C₂³×C₁₃	1	16	yes	—
820	C₄×D₄	C₂³×C₁₃	1	8	yes	—
821	#117	C₂³×C₁₃	1	2	yes	—
822	#117	C₂³×C₁₃	1	4	yes	—
823	#117	C₂³×C₁₃	1	4	yes	—
824	#117	C₂³×C₁₃	1	8	yes	—
825	#117	C₂³×C₁₃	1	8	yes	—
826	#117	C₂³×C₁₃	1	8	yes	—
827	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
829	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
830	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
831	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
832	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
834	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
835	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
836	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
837	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
838	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
842	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
843	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
844	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
845	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
847	C₂×C₁₃	—	2	2	no	—
848	C₂×C₁₃	—	2	4	no	—
849	C₂×C₁₃	—	4	2	no	—
850	C₂×C₁₃	—	4	4	no	—
851	C₂×C₁₃	—	4	4	no	—
852	C₂×C₁₃	—	4	8	no	—
853	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
855	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
856	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
857	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
858	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
859	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
860	#41	—	2	16	no	—
861	#41	—	2	8	no	—
862	#41	—	2	16	no	—
863	#41	—	4	16	no	—
864	#41	—	4	8	no	—
865	#41	—	4	16	no	—
866	#41	—	4	16	no	—
867	#41	—	4	16	no	—
868	#41	—	4	8	no	—
869	#41	—	4	8	no	—
870	#41	—	4	8	no	—
871	#41	—	4	16	no	—
872	#41	—	4	16	no	—
873	C₂×Q₈	—	4	8	no	—
874	C₂×Q₈	—	4	4	no	—
875	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
876	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
877	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
878	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
879	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
880	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	16	no	—
883	C₂×D₄	—	2	4	no	—
884	C₂×D₄	—	4	8	no	—
885	C₂×D₄	—	4	8	no	—
886	C₂×D₄	—	4	16	no	—
887	C₂×D₄	—	4	16	no	—
888	C₂×D₄	—	4	8	no	—
889	C₂×D₄	—	4	16	no	—
890	C₂×D₄	—	4	32	no	—
891	C₂×D₄	—	4	16	no	—
892	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
893	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
894	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
895	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
896	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
897	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
898	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
899	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
900	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
901	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
903	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
904	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
905	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
906	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
907	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
908	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
909	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
910	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
911	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
912	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
913	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
914	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₂²×C₄	—	2	8	no	—
916	C₂²×C₄	—	4	16	no	—
917	C₂²×C₄	—	4	4	no	—
918	C₂²×C₄	—	4	8	no	—
919	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
921	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
922	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
924	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
925	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
926	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
927	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
928	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
930	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
931	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
932	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
933	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
934	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
936	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
937	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
938	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
939	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
941	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
942	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
945	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
946	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
947	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
948	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
949	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
950	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
952	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
953	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
955	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
956	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
957	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
958	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
959	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
961	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
962	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
963	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
964	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
965	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
966	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
967	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
968	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
969	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
970	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
971	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
972	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
973	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
974	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
975	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
976	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
977	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
978	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
979	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
980	C₄²	C₂⁴×C₁₃	1	2	yes	—
981	C₄²	C₂⁴×C₁₃	1	2	yes	—
982	C₄²	C₂⁴×C₁₃	1	4	yes	—
983	C₄²	C₂⁴×C₁₃	1	4	yes	—
984	C₄²	C₂⁴×C₁₃	1	4	yes	—
985	C₄²	C₂⁴×C₁₃	1	16	yes	—
986	C₁₃	#62914	1	1	yes	characteristic, direct product factor, Sylow
987	C₂³	—	2	4	no	—
988	C₂³	—	2	4	no	—
989	C₂³	—	2	16	no	—
990	C₂³	—	2	4	no	—
991	C₂³	—	4	2	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	2	no	—
994	C₂³	—	4	2	no	—
995	C₂³	—	4	8	no	—
996	C₂³	—	4	8	no	—
997	C₂³	—	4	8	no	—
998	C₂³	—	4	8	no	—
999	C₂³	C₂⁵×C₁₃	1	8	yes	—
1000	C₂³	C₂⁵×C₁₃	1	4	yes	—
1001	C₂³	C₂⁵×C₁₃	1	4	yes	—
1002	C₂³	C₂⁵×C₁₃	1	2	yes	—
1003	C₂³	C₂⁵×C₁₃	1	2	yes	—
1004	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1005	Q₈	—	2	4	no	—
1006	Q₈	—	2	8	no	—
1007	Q₈	—	2	8	no	—
1008	Q₈	—	4	8	no	—
1009	Q₈	—	4	4	no	—
1010	Q₈	—	4	4	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	4	no	—
1013	D₄	—	2	16	no	—
1014	D₄	—	2	16	no	—
1015	D₄	—	2	8	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	8	no	—
1020	D₄	—	2	4	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	4	8	no	—
1023	D₄	—	4	8	no	—
1024	D₄	—	4	16	no	—
1025	D₄	—	4	16	no	—
1026	D₄	—	4	8	no	—
1027	D₄	—	4	8	no	—
1028	D₄	—	4	8	no	—
1029	D₄	—	4	8	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	8	no	—
1032	D₄	—	4	8	no	—
1033	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
1034	C₂×C₄	—	2	4	no	—
1035	C₂×C₄	—	2	16	no	—
1036	C₂×C₄	—	2	8	no	—
1037	C₂×C₄	—	2	8	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	8	no	—
1040	C₂×C₄	—	2	8	no	—
1041	C₂×C₄	—	2	16	no	—
1042	C₂×C₄	—	2	8	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	8	no	—
1046	C₂×C₄	—	4	4	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	16	no	—
1051	C₂×C₄	—	4	8	no	—
1052	C₂×C₄	—	4	1	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
1055	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1056	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1057	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1058	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1059	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1060	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1061	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1062	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1063	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1064	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1065	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	2	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	4	no	—
1072	C₂²	—	2	4	no	—
1073	C₂²	—	2	8	no	—
1074	C₂²	—	2	4	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	8	no	—
1077	C₂²	—	2	4	no	—
1078	C₂²	—	2	4	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	8	no	—
1081	C₂²	—	2	4	no	—
1082	C₂²	—	4	8	no	—
1083	C₂²	—	8	4	no	—
1084	C₂²	—	8	16	no	—
1085	C₂²	—	16	8	no	—
1086	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1087	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1088	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1089	C₄	—	2	4	no	—
1090	C₄	—	2	4	no	—
1091	C₄	—	2	4	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	8	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	4	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	4	no	—
1098	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1099	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	4	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	4	4	no	—
1104	C₂	—	4	4	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	C₁₃×2₋¹⁺⁶	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×#3548	C₂	semidirect
2. C₁₃×#3546	C₂	semidirect
3. C₁₃×#3542	C₂	semidirect
4. C₁₃×#3536	C₂	semidirect
5. C₁₃×#3536	C₂	semidirect
6. C₁₃×#3534	C₂	semidirect
7. C₁₃×#3520	C₂	semidirect
8. C₁₃×#3511	C₂	semidirect
9. C₁₃×#3496	C₂	semidirect
10. C₁₃×#3496	C₂	semidirect
11. C₁₃×#3492	C₂	semidirect
12. C₁₃×#3488	C₂	semidirect
13. C₁₃×#3488	C₂	semidirect
14. D₄×C₁₃×#41	C₂	semidirect
15. C₂×C₁₃×#547	C₂	semidirect
16. C₁₃×#3460	C₂	semidirect
17. C₂×C₁₃×#537	C₂	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₁₃×#562	C₂²	semidirect
23. C₁₃×#562	C₂²	semidirect
24. C₁₃×#560	C₂²	semidirect
25. C₁₃×#556	C₂²	semidirect
26. C₁₃×#555	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
30. C₁₃×#553	C₂²	semidirect
31. C₁₃×#553	C₂²	semidirect
32. C₁₃×#552	C₂²	semidirect
33. C₁₃×#551	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. C₁₃×#550	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
38. C₁₃×#548	C₂²	semidirect
39. C₁₃×#548	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
41. C₁₃×#547	C₂²	semidirect
42. C₁₃×#547	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#547	C₂²	semidirect
46. C₁₃×#547	C₂²	semidirect
47. C₁₃×#547	C₂²	semidirect
48. C₁₃×#547	C₂²	semidirect
49. C₁₃×#546	C₂²	semidirect
50. C₁₃×#546	C₂²	semidirect
51. C₁₃×#546	C₂²	semidirect
52. C₁₃×#546	C₂²	semidirect
53. C₁₃×#546	C₂²	semidirect
54. C₁₃×#546	C₂²	semidirect
55. C₁₃×#546	C₂²	semidirect
56. C₁₃×#546	C₂²	semidirect
57. C₁₃×#546	C₂²	semidirect
58. D₄²×C₁₃	C₂²	semidirect
59. D₄²×C₁₃	C₂²	semidirect
60. D₄²×C₁₃	C₂²	semidirect
61. D₄²×C₁₃	C₂²	semidirect
62. D₄²×C₁₃	C₂²	semidirect
63. C₁₃×#544	C₂²	semidirect
64. C₁₃×#543	C₂²	semidirect
65. C₁₃×#542	C₂²	semidirect
66. C₁₃×#542	C₂²	semidirect
67. C₁₃×#542	C₂²	semidirect
68. C₁₃×#540	C₂²	semidirect
69. C₁₃×#540	C₂²	semidirect
70. C₁₃×#539	C₂²	semidirect
71. C₁₃×#539	C₂²	semidirect
72. C₁₃×#538	C₂²	semidirect
73. C₁₃×#538	C₂²	semidirect
74. C₁₃×#538	C₂²	semidirect
75. C₁₃×#537	C₂²	semidirect
76. C₁₃×#537	C₂²	semidirect
77. C₁₃×#537	C₂²	semidirect
78. C₁₃×#537	C₂²	semidirect
79. C₁₃×#537	C₂²	semidirect
80. C₁₃×#537	C₂²	semidirect
81. C₁₃×#537	C₂²	semidirect
82. C₁₃×#537	C₂²	semidirect
83. C₁₃×#537	C₂²	semidirect
84. C₁₃×#537	C₂²	semidirect
85. C₁₃×#535	C₂²	semidirect
86. C₁₃×#535	C₂²	semidirect
87. C₁₃×#535	C₂²	semidirect
88. C₁₃×#535	C₂²	semidirect
89. C₁₃×#534	C₂²	semidirect
90. C₁₃×#534	C₂²	semidirect
91. C₁₃×#533	C₂²	semidirect
92. C₁₃×#532	C₂²	semidirect
93. C₁₃×#532	C₂²	semidirect
94. C₁₃×#532	C₂²	semidirect
95. C₁₃×#532	C₂²	semidirect
96. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
97. C₁₃×#529	C₂²	semidirect
98. C₁₃×#525	C₂²	semidirect
99. C₁₃×#525	C₂²	semidirect
100. C₁₃×#525	C₂²	semidirect
101. C₁₃×#525	C₂²	semidirect
102. C₁₃×#525	C₂²	semidirect
103. C₂×C₁₃×#123	C₂²	semidirect
104. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
105. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
106. C₂×C₁₃×#121	C₂²	semidirect
107. C₂×C₁₃×#121	C₂²	semidirect
108. C₂×C₁₃×#121	C₂²	semidirect
109. C₂×C₁₃×#121	C₂²	semidirect
110. C₂×C₁₃×#121	C₂²	semidirect
111. C₁₃×#520	C₂²	semidirect
112. C₁₃×#520	C₂²	semidirect
113. C₄×C₁₃×#41	C₂²	semidirect
114. C₂×C₄×D₄×C₁₃	C₂²	semidirect
115. C₂×C₄×D₄×C₁₃	C₂²	semidirect
116. C₂×C₄×D₄×C₁₃	C₂²	semidirect
117. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
302. #62914	C₁₃	direct (N × H)
433. #3548	C₂×C₁₃	semidirect
434. #3546	C₂×C₁₃	semidirect
435. #3542	C₂×C₁₃	semidirect
436. #3536	C₂×C₁₃	semidirect
437. #3536	C₂×C₁₃	semidirect
438. #3534	C₂×C₁₃	semidirect
439. #3520	C₂×C₁₃	semidirect
440. #3511	C₂×C₁₃	semidirect
441. #3496	C₂×C₁₃	semidirect
442. #3496	C₂×C₁₃	semidirect
443. #3492	C₂×C₁₃	semidirect
444. #3488	C₂×C₁₃	semidirect
445. #3488	C₂×C₁₃	semidirect
446. D₄×#41	C₂×C₁₃	semidirect
447. C₂×#547	C₂×C₁₃	semidirect
448. #3460	C₂×C₁₃	semidirect
449. C₂×#537	C₂×C₁₃	semidirect
496. D₄×C₁₃	H(5,𝔽₂)	semidirect
517. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
529. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
530. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
531. C₂²×#41	C₂²×C₁₃	semidirect
532. C₂²×#41	C₂²×C₁₃	semidirect
533. #562	C₂²×C₁₃	semidirect
534. #562	C₂²×C₁₃	semidirect
535. #560	C₂²×C₁₃	semidirect
536. #556	C₂²×C₁₃	semidirect
537. #555	C₂²×C₁₃	semidirect
538. #554	C₂²×C₁₃	semidirect
539. #554	C₂²×C₁₃	semidirect
540. #554	C₂²×C₁₃	semidirect
541. #553	C₂²×C₁₃	semidirect
542. #553	C₂²×C₁₃	semidirect
543. #552	C₂²×C₁₃	semidirect
544. #551	C₂²×C₁₃	semidirect
545. #550	C₂²×C₁₃	semidirect
546. #550	C₂²×C₁₃	semidirect
547. #550	C₂²×C₁₃	semidirect
548. D₄×Q₈	C₂²×C₁₃	semidirect
549. #548	C₂²×C₁₃	semidirect
550. #548	C₂²×C₁₃	semidirect
551. #548	C₂²×C₁₃	semidirect
552. #547	C₂²×C₁₃	semidirect
553. #547	C₂²×C₁₃	semidirect
554. #547	C₂²×C₁₃	semidirect
555. #547	C₂²×C₁₃	semidirect
556. #547	C₂²×C₁₃	semidirect
557. #547	C₂²×C₁₃	semidirect
558. #547	C₂²×C₁₃	semidirect
559. #547	C₂²×C₁₃	semidirect
560. #546	C₂²×C₁₃	semidirect
561. #546	C₂²×C₁₃	semidirect
562. #546	C₂²×C₁₃	semidirect
563. #546	C₂²×C₁₃	semidirect
564. #546	C₂²×C₁₃	semidirect
565. #546	C₂²×C₁₃	semidirect
566. #546	C₂²×C₁₃	semidirect
567. #546	C₂²×C₁₃	semidirect
568. #546	C₂²×C₁₃	semidirect
569. D₄²	C₂²×C₁₃	semidirect
570. D₄²	C₂²×C₁₃	semidirect
571. D₄²	C₂²×C₁₃	semidirect
572. D₄²	C₂²×C₁₃	semidirect
573. D₄²	C₂²×C₁₃	semidirect
574. #544	C₂²×C₁₃	semidirect
575. #543	C₂²×C₁₃	semidirect
576. #542	C₂²×C₁₃	semidirect
577. #542	C₂²×C₁₃	semidirect
578. #542	C₂²×C₁₃	semidirect
579. #540	C₂²×C₁₃	semidirect
580. #540	C₂²×C₁₃	semidirect
581. #539	C₂²×C₁₃	semidirect
582. #539	C₂²×C₁₃	semidirect
583. #538	C₂²×C₁₃	semidirect
584. #538	C₂²×C₁₃	semidirect
585. #538	C₂²×C₁₃	semidirect
586. #537	C₂²×C₁₃	semidirect
587. #537	C₂²×C₁₃	semidirect
588. #537	C₂²×C₁₃	semidirect
589. #537	C₂²×C₁₃	semidirect
590. #537	C₂²×C₁₃	semidirect
591. #537	C₂²×C₁₃	semidirect
592. #537	C₂²×C₁₃	semidirect
593. #537	C₂²×C₁₃	semidirect
594. #537	C₂²×C₁₃	semidirect
595. #537	C₂²×C₁₃	semidirect
596. #535	C₂²×C₁₃	semidirect
597. #535	C₂²×C₁₃	semidirect
598. #535	C₂²×C₁₃	semidirect
599. #535	C₂²×C₁₃	semidirect
600. #534	C₂²×C₁₃	semidirect
601. #534	C₂²×C₁₃	semidirect
602. #533	C₂²×C₁₃	semidirect
603. #532	C₂²×C₁₃	semidirect
604. #532	C₂²×C₁₃	semidirect
605. #532	C₂²×C₁₃	semidirect
606. #532	C₂²×C₁₃	semidirect
607. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
608. #529	C₂²×C₁₃	semidirect
609. #525	C₂²×C₁₃	semidirect
610. #525	C₂²×C₁₃	semidirect
611. #525	C₂²×C₁₃	semidirect
612. #525	C₂²×C₁₃	semidirect
613. #525	C₂²×C₁₃	semidirect
614. C₂×#123	C₂²×C₁₃	semidirect
615. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
616. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
617. C₂×#121	C₂²×C₁₃	semidirect
618. C₂×#121	C₂²×C₁₃	semidirect
619. C₂×#121	C₂²×C₁₃	semidirect
620. C₂×#121	C₂²×C₁₃	semidirect
621. C₂×#121	C₂²×C₁₃	semidirect
622. #520	C₂²×C₁₃	semidirect
623. #520	C₂²×C₁₃	semidirect
624. C₄×#41	C₂²×C₁₃	semidirect
625. C₂×C₄×D₄	C₂²×C₁₃	semidirect
626. C₂×C₄×D₄	C₂²×C₁₃	semidirect
627. C₂×C₄×D₄	C₂²×C₁₃	semidirect
628. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
986. C₁₃	#62914	direct (N × H)
1033. D₄	C₁₃×H(5,𝔽₂)	semidirect
1054. 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×#3548	2
C₁₃×#3546	2
C₁₃×#3542	2
C₁₃×#3536	2
C₁₃×#3534	2
C₁₃×#3520	2
C₁₃×#3511	2
C₁₃×#3496	2
C₁₃×#3492	2
C₁₃×#3488	2
D₄×C₁₃×#41	2
C₂×C₁₃×#547	2
C₁₃×#3460	2
C₂×C₁₃×#537	2
#62914	13

Subgroups — C13×#62914 #15749253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62914 #15749253