Subgroups — #16727552

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128398	C₂	1	1	yes	maximal, characteristic
2	#13123850	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123844	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123839	C₂	1	1	yes	maximal, characteristic, complemented
5	#13123834	C₂	1	1	yes	maximal, characteristic, complemented
6	#13123825	C₂	1	2	yes	maximal, complemented
7	#13123824	C₂	1	2	yes	maximal, complemented
8	#13123813	C₂	1	1	yes	maximal, characteristic, complemented
9	#13123811	C₂	1	2	yes	maximal, complemented
10	#13123811	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123804	C₂	1	2	yes	maximal, complemented
12	C₈×#6129	C₂	1	1	yes	maximal, characteristic, complemented
13	#13123778	C₂	1	1	yes	maximal, characteristic, complemented
14	#13123765	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#6094	C₂	1	1	yes	maximal, characteristic, complemented
16	#13123556	C₂	1	2	yes	maximal, complemented
17	#13123525	C₂	1	2	yes	maximal, complemented
18	C₈×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#13123497	C₂	1	1	yes	maximal, characteristic, complemented
20	#13123489	C₂	1	2	yes	maximal, complemented
21	C₄×#88155	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#11718350	C₂	1	2	yes	maximal, complemented
23	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	#11719534	C₄	1	1	yes	characteristic
26	#11719529	C₄	1	1	yes	characteristic
27	C₂×#88155	C₂²	1	1	yes	characteristic
28	C₂×#88155	C₂²	1	1	yes	characteristic
29	C₂²×#6094	C₂²	1	2	yes	—
30	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
31	#11719286	C₄	1	1	yes	characteristic
32	#11719285	C₂²	1	1	yes	characteristic
33	#11719283	C₂²	1	1	yes	characteristic
34	#11719273	C₄	1	1	yes	characteristic
35	#11719261	C₄	1	2	yes	—
36	#11719259	C₄	1	1	yes	characteristic
37	#11719252	C₂²	1	2	yes	—
38	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
39	#11719245	C₄	1	2	yes	—
40	#11719244	C₄	1	1	yes	characteristic
41	#11719243	C₂²	1	2	yes	—
42	C₄×#6129	C₂²	1	1	yes	characteristic
43	#11719237	C₄	1	1	yes	characteristic
44	#11719236	C₄	1	2	yes	—
45	#11719234	C₄	1	1	yes	characteristic
46	#11719232	C₄	1	2	yes	—
47	#11719184	C₂²	1	2	yes	—
48	#11719184	C₂²	1	1	yes	characteristic
49	C₄×#6127	C₂²	1	1	yes	characteristic
50	C₂×#88126	C₂²	1	2	yes	—
51	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
56	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
57	C₁₃×#431	C₂²	1	2	yes	complemented
58	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
60	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
61	#11718772	C₂²	1	2	yes	—
62	#11718772	C₂²	1	2	yes	complemented
63	#11718772	C₂²	1	2	yes	complemented
64	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
65	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
66	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
67	#11718762	C₂²	1	1	yes	characteristic, complemented
68	#11718762	C₂²	1	1	yes	characteristic, complemented
69	C₂×#88055	C₂²	1	2	yes	complemented
70	C₂×C₈×Dic₁₃	C₂²	1	2	yes	complemented
71	#11718685	C₂²	1	1	yes	characteristic, complemented
72	#11718685	C₂²	1	1	yes	characteristic, complemented
73	#11718672	C₂²	1	2	yes	complemented
74	#11718672	C₂²	1	2	yes	complemented
75	D₄×#1055	C₂²	1	1	yes	characteristic
76	D₄×#1055	C₂²	1	1	yes	characteristic
77	#11718587	C₂²	1	2	yes	complemented
78	#11718587	C₂²	1	1	yes	characteristic, complemented
79	C₄×#6099	C₂²	1	1	yes	characteristic, complemented
80	C₂×#88043	C₂²	1	2	yes	complemented
81	#11718501	C₂²	1	2	yes	complemented
82	#11718501	C₂²	1	2	yes	complemented
83	#11718500	C₂²	1	2	yes	—
84	#11718500	C₂²	1	2	yes	—
85	#11718499	C₂²	1	1	yes	characteristic
86	#11718498	C₂²	1	1	yes	characteristic
87	#11718497	C₂²	1	2	yes	complemented
88	#11718497	C₂²	1	2	yes	complemented
89	#11718496	C₂²	1	1	yes	characteristic, complemented
90	#11718495	C₂²	1	1	yes	characteristic
91	#11718494	C₂²	1	1	yes	characteristic, complemented
92	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	#11718492	C₂²	1	1	yes	characteristic, complemented
94	#11718491	C₂²	1	1	yes	characteristic, complemented
95	#11718489	C₂²	1	2	yes	complemented
96	#11718489	C₂²	1	2	yes	complemented
97	#11718391	C₂²	1	2	yes	—
98	#11718391	C₂²	1	2	yes	complemented
99	#11718390	C₂²	1	2	yes	complemented
100	#11718389	C₂²	1	2	yes	complemented
101	#11718388	C₂²	1	2	yes	—
102	#11718387	C₂²	1	2	yes	—
103	#11718386	C₂²	1	2	yes	—
104	#11718386	C₂²	1	2	yes	complemented
105	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
106	#11718381	C₂²	1	2	yes	complemented
107	#11718380	C₂²	1	2	yes	complemented
108	#11718379	C₂²	1	2	yes	complemented
109	#11718351	C₂²	1	2	yes	complemented
110	#11718351	C₂²	1	2	yes	complemented
111	#11718351	C₂²	1	2	yes	complemented
112	#11718350	C₂²	1	1	yes	characteristic
113	#11718350	C₂²	1	2	yes	—
114	#11718350	C₂²	1	1	yes	characteristic
115	#11718350	C₂²	1	2	yes	—
116	#11718350	C₂²	1	2	yes	—
117	#11718350	C₂²	1	2	yes	complemented
118	#11718350	C₂²	1	2	yes	complemented
119	#11718350	C₂²	1	2	yes	complemented
120	#11718350	C₂²	1	2	yes	complemented
121	#11718350	C₂²	1	1	yes	characteristic, complemented
122	#11718350	C₂²	1	1	yes	characteristic, complemented
123	#11718349	C₂²	1	1	yes	characteristic
124	#11718349	C₂²	1	2	yes	complemented
125	C₄×#6094	C₂²	1	1	yes	characteristic
126	C₄×#6094	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₅₂	C₂²	1	1	yes	characteristic
128	C₈×D₅₂	C₂²	1	2	yes	complemented
129	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
130	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
131	#11718340	C₂²	1	1	yes	characteristic, complemented
132	#11718340	C₂²	1	2	yes	complemented
133	C₈×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
134	C₈×Dic₂₆	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
136	C₂×#6129	C₂×C₄	1	1	yes	characteristic
137	C₂×D₄×D₁₃	C₂×C₄	1	1	yes	characteristic
138	C₂×#6127	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
141	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
142	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
145	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
147	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
148	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
149	C₄×D₄×C₁₃	C₂³	1	2	yes	—
150	C₁₃×#117	C₂×C₄	1	2	yes	—
151	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	#88201	C₂×C₄	1	1	yes	characteristic
155	#88200	C₂×C₄	1	1	yes	characteristic
156	#88200	C₂×C₄	1	1	yes	characteristic
157	#88198	C₂×C₄	1	1	yes	characteristic
158	#88193	C₂×C₄	1	2	yes	—
159	#88193	C₂×C₄	1	2	yes	—
160	#88191	C₂×C₄	1	2	yes	—
161	#88189	C₂×C₄	1	2	yes	—
162	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
163	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
164	#88184	C₂×C₄	1	1	yes	characteristic
165	#88184	C₂×C₄	1	2	yes	—
166	#88183	C₂×C₄	1	2	yes	—
167	#88183	C₂×C₄	1	2	yes	—
168	#88183	C₂×C₄	1	2	yes	—
169	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
170	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
171	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
172	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
173	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
174	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
175	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
176	C₂×#6103	C₂×C₄	1	2	yes	—
177	C₂×#6103	C₂×C₄	1	2	yes	—
178	#88180	C₂³	1	1	yes	characteristic
179	#88178	C₂×C₄	1	1	yes	characteristic
180	#88178	C₂×C₄	1	2	yes	—
181	C₂×#6101	C₂×C₄	1	2	yes	—
182	C₂×#6101	C₂×C₄	1	2	yes	—
183	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
184	C₂×#6099	C₂³	1	1	yes	characteristic
185	C₂×#6099	C₂³	1	1	yes	characteristic
186	C₂²×#1055	C₂³	1	2	yes	—
187	C₂²×#1055	C₂³	1	2	yes	—
188	#88155	—	2	4	no	—
189	#88155	—	2	4	no	—
190	C₂×#6094	—	2	8	no	—
191	C₂×#6094	C₂³	1	2	yes	—
192	C₂×#6094	C₂³	1	2	yes	—
193	C₂×#6094	C₂³	1	2	yes	—
194	C₂×#6094	C₂³	1	1	yes	characteristic
195	C₂×#6094	C₂³	1	1	yes	characteristic
196	C₂×#6094	C₂³	1	1	yes	characteristic
197	C₂×#6094	C₂³	1	1	yes	characteristic
198	C₂×C₈×D₁₃	—	2	8	no	—
199	C₂×C₈×D₁₃	C₂³	1	2	yes	—
200	C₂×C₈×D₁₃	C₂³	1	2	yes	—
201	C₂×C₈×D₁₃	C₂³	1	2	yes	—
202	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
206	#88152	C₂×C₄	1	2	yes	—
207	#88152	C₂×C₄	1	2	yes	—
208	#88151	C₂×C₄	1	1	yes	characteristic
209	#88150	C₂×C₄	1	2	yes	—
210	#88150	C₂×C₄	1	2	yes	—
211	#88149	C₂×C₄	1	1	yes	characteristic
212	#88148	C₂×C₄	1	2	yes	—
213	#88148	C₂×C₄	1	2	yes	—
214	#88147	C₂×C₄	1	1	yes	characteristic
215	#88146	C₂×C₄	1	1	yes	characteristic
216	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
217	#88144	C₂×C₄	1	1	yes	characteristic
218	#88143	C₂×C₄	1	2	yes	—
219	#88143	C₂×C₄	1	2	yes	—
220	#88142	C₂×C₄	1	1	yes	characteristic
221	#88141	C₂×C₄	1	1	yes	characteristic
222	#88140	C₂×C₄	1	2	yes	—
223	#88139	C₂×C₄	1	2	yes	—
224	#88138	C₂×C₄	1	2	yes	—
225	#88137	C₂×C₄	1	2	yes	—
226	#88136	C₂×C₄	1	2	yes	—
227	#88135	C₂×C₄	1	2	yes	—
228	#88135	C₂×C₄	1	2	yes	—
229	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
230	#88133	C₂×C₄	1	2	yes	—
231	#88132	C₂×C₄	1	2	yes	—
232	#88132	C₂×C₄	1	2	yes	—
233	#88131	C₂×C₄	1	2	yes	—
234	#88130	C₂×C₄	1	2	yes	—
235	#88130	C₂×C₄	1	2	yes	—
236	#88130	C₂×C₄	1	2	yes	—
237	#88129	C₂×C₄	1	2	yes	—
238	#88129	C₂×C₄	1	1	yes	characteristic
239	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
240	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
241	C₄×D₅₂	C₂³	1	1	yes	characteristic
242	C₄×D₅₂	C₂³	1	2	yes	—
243	#88126	C₂×C₄	1	2	yes	—
244	#88126	C₂×C₄	1	2	yes	—
245	#88126	C₂×C₄	1	2	yes	—
246	#88126	C₂×C₄	1	2	yes	—
247	#88126	C₂³	1	1	yes	characteristic
248	#88126	C₂³	1	2	yes	—
249	#88126	C₂³	1	2	yes	—
250	#88126	C₂³	1	2	yes	—
251	#88126	C₂³	1	1	yes	characteristic
252	C₄²×D₁₃	C₂³	1	1	yes	characteristic
253	C₄²×D₁₃	C₂³	1	1	yes	characteristic
254	#88124	C₂×C₄	1	2	yes	—
255	#88124	C₂×C₄	1	1	yes	characteristic
256	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
257	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
258	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
259	C₄×Dic₂₆	C₂³	1	2	yes	—
260	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
263	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
264	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₁₃	C₂³	1	2	yes	—
269	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₁₃	C₂³	1	2	yes	—
273	C₄×C₈×C₁₃	C₂³	1	2	yes	—
274	C₂²⋊#1055	C₂³	1	2	yes	—
275	C₂²⋊#1055	C₂³	1	2	yes	—
276	C₂²⋊#1055	C₂³	1	2	yes	—
277	#88060	C₂³	1	2	yes	—
278	#88060	C₂³	1	2	yes	—
279	#88060	C₂³	1	2	yes	—
280	#88060	C₂³	1	2	yes	—
281	#88060	C₂³	1	2	yes	—
282	#88060	C₂³	1	2	yes	—
283	#88055	C₂³	1	1	yes	characteristic
284	#88055	C₂³	1	2	yes	—
285	#88055	C₂³	1	2	yes	—
286	#88055	C₂³	1	1	yes	characteristic
287	#88055	C₂³	1	1	yes	characteristic
288	#88055	C₂³	1	2	yes	—
289	#88055	C₂³	1	1	yes	characteristic
290	#88054	C₂³	1	2	yes	—
291	#88054	C₂³	1	2	yes	—
292	#88054	C₂³	1	2	yes	—
293	#88054	C₂³	1	2	yes	—
294	#88054	C₂³	1	2	yes	—
295	#88054	C₂³	1	2	yes	—
296	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
297	C₈×Dic₁₃	C₂³	1	2	yes	—
298	C₈×Dic₁₃	C₂³	1	2	yes	—
299	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
300	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
301	C₈×Dic₁₃	C₂³	1	2	yes	—
302	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
303	C₄⋊#1055	C₂³	1	1	yes	characteristic
304	C₄⋊#1055	C₂³	1	1	yes	characteristic
305	C₄⋊#1055	C₂³	1	2	yes	—
306	C₄⋊#1055	C₂³	1	2	yes	—
307	#88043	C₂³	1	2	yes	—
308	#88043	C₂³	1	2	yes	—
309	#88043	C₂³	1	1	yes	characteristic
310	#88043	C₂³	1	2	yes	—
311	#88043	C₂³	1	1	yes	characteristic
312	C₄×#1055	C₂³	1	1	yes	characteristic
313	C₄×#1055	C₂³	1	1	yes	characteristic
314	#60215	—	13	1	no	maximal, Sylow
315	C₂³×D₁₃	C₂²×C₄	1	2	yes	—
316	C₁₃×#41	—	2	4	no	—
317	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
319	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
321	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
323	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
327	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
328	C₂×C₂²⋊D₁₃	C₂²×C₄	1	1	yes	characteristic
329	C₂×C₂²⋊D₁₃	C₂²×C₄	1	1	yes	characteristic
330	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
331	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
332	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
333	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
334	#6129	—	2	4	no	—
335	D₄×D₁₃	—	2	4	no	—
336	#6127	—	2	2	no	—
337	#6127	—	2	2	no	—
338	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
340	C₂×D₅₂	C₂²×C₄	1	2	yes	—
341	C₂×C₄×D₁₃	—	2	4	no	—
342	C₂×C₄×D₁₃	—	2	4	no	—
343	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
351	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
353	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
354	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
355	C₂×C₈×C₁₃	—	2	4	no	—
356	C₂×C₈×C₁₃	—	2	4	no	—
357	C₂×C₈×C₁₃	—	2	2	no	—
358	C₂×C₈×C₁₃	—	2	2	no	—
359	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
361	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
369	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
370	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
371	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
372	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
374	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
375	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
376	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
378	C₄²×C₁₃	C₂⁴	1	2	yes	—
379	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
381	C₂²⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
382	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
384	#6103	C₂²×C₄	1	1	yes	characteristic
385	#6103	C₂²×C₄	1	1	yes	characteristic
386	#6103	C₂²×C₄	1	2	yes	—
387	#6103	C₂²×C₄	1	2	yes	—
388	#6103	C₂²×C₄	1	2	yes	—
389	#6103	C₂²×C₄	1	2	yes	—
390	#6103	C₂²×C₄	1	2	yes	—
391	#6103	C₂²×C₄	1	2	yes	—
392	#6103	C₂²×C₄	1	1	yes	characteristic
393	#6103	C₂²×C₄	1	1	yes	characteristic
394	#6103	C₂²×C₄	1	2	yes	—
395	#6103	C₂²×C₄	1	2	yes	—
396	#6103	C₂²×C₄	1	2	yes	—
397	#6103	C₂²×C₄	1	2	yes	—
398	#6103	C₂²×C₄	1	2	yes	—
399	#6103	C₂²×C₄	1	2	yes	—
400	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
403	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
404	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
406	#6101	C₂²×C₄	1	1	yes	characteristic
407	#6101	C₂²×C₄	1	1	yes	characteristic
408	#6101	C₂²×C₄	1	1	yes	characteristic
409	#6101	C₂²×C₄	1	1	yes	characteristic
410	#6101	C₂²×C₄	1	2	yes	—
411	#6101	C₂²×C₄	1	2	yes	—
412	#6101	C₂²×C₄	1	2	yes	—
413	#6101	C₂²×C₄	1	2	yes	—
414	#6101	C₂²×C₄	1	2	yes	—
415	#6101	C₂²×C₄	1	2	yes	—
416	#6101	C₂²×C₄	1	2	yes	—
417	#6101	C₂²×C₄	1	2	yes	—
418	#6101	C₂²×C₄	1	2	yes	—
419	#6101	C₂²×C₄	1	2	yes	—
420	#6101	C₂²×C₄	1	2	yes	—
421	#6101	C₂²×C₄	1	2	yes	—
422	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
424	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
425	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
426	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
427	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
428	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
429	C₄×Dic₁₃	C₂⁴	1	2	yes	—
430	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
431	#6099	—	2	2	no	—
432	#6099	—	2	2	no	—
433	C₂×#1055	—	2	4	no	—
434	C₂×#1055	—	2	4	no	—
435	C₂×#1055	C₂⁴	1	2	yes	—
436	C₂×#1055	C₂⁴	1	1	yes	characteristic
437	C₂×#1055	C₂⁴	1	1	yes	characteristic
438	C₂×#1055	C₂⁴	1	2	yes	—
439	C₂×#1055	C₂⁴	1	1	yes	characteristic
440	C₂×#1055	C₂⁴	1	1	yes	characteristic
441	#6094	—	2	4	no	—
442	#6094	—	2	2	no	—
443	#6094	—	2	4	no	—
444	#6094	—	2	2	no	—
445	#6094	—	2	4	no	—
446	#6094	—	2	2	no	—
447	#6094	#41	1	4	yes	complemented
448	C₈×D₁₃	—	2	4	no	—
449	C₈×D₁₃	—	2	2	no	—
450	C₈×D₁₃	—	2	4	no	—
451	C₈×D₁₃	—	2	2	no	—
452	C₈×D₁₃	—	2	4	no	—
453	C₈×D₁₃	—	2	2	no	—
454	C₈×D₁₃	#41	1	4	yes	complemented
455	#3475	—	13	1	no	—
456	#2970	—	13	1	no	—
457	#2970	—	13	1	no	—
458	#2969	—	13	1	no	—
459	#2969	—	13	1	no	—
460	#2968	—	13	2	no	—
461	#2968	—	13	2	no	—
462	#2966	—	13	1	no	—
463	#2966	—	13	2	no	—
464	#2966	—	13	2	no	—
465	#2966	—	13	1	no	—
466	C₈×#41	—	13	1	no	—
467	C₈×#41	D₁₃	1	1	yes	characteristic, complemented
468	#2962	—	13	1	no	—
469	#2960	—	13	1	no	—
470	D₄×M₁₆	—	13	1	no	—
471	#2933	—	13	2	no	—
472	#2929	—	13	2	no	—
473	C₂×C₈×D₄	—	13	1	no	—
474	#2925	—	13	1	no	—
475	#2924	—	13	2	no	—
476	C₄×#131	—	13	1	no	—
477	C₂×#405	—	13	2	no	—
478	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
479	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
480	C₂²×D₁₃	—	2	4	no	—
481	C₂²×D₁₃	—	2	4	no	—
482	C₂²×D₁₃	—	4	2	no	—
483	C₂²×D₁₃	C₂³×C₄	1	2	yes	—
484	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
485	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
486	Q₈×C₁₃	—	2	2	no	—
487	D₄×C₁₃	—	2	4	no	—
488	D₄×C₁₃	#131	1	4	yes	complemented
489	C₂×C₄×C₁₃	—	2	4	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	2	no	—
492	C₂×C₄×C₁₃	—	2	2	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	1	no	—
495	C₂×C₄×C₁₃	—	4	2	no	—
496	C₂×C₄×C₁₃	—	4	1	no	—
497	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
498	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
499	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
500	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
501	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
503	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
504	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
505	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
506	C₂²⋊D₁₃	—	2	4	no	—
507	C₂²⋊D₁₃	—	2	4	no	—
508	C₂²⋊D₁₃	—	2	2	no	—
509	C₂²⋊D₁₃	—	2	2	no	—
510	C₂²⋊D₁₃	—	4	2	no	—
511	C₂×Dic₁₃	—	2	4	no	—
512	C₂×Dic₁₃	—	2	4	no	—
513	C₂×Dic₁₃	—	4	2	no	—
514	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
515	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
516	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
517	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
518	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
519	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
520	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
521	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
522	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
523	D₅₂	—	2	2	no	—
524	D₅₂	—	2	2	no	—
525	D₅₂	—	4	2	no	—
526	C₄×D₁₃	—	2	4	no	—
527	C₄×D₁₃	—	2	2	no	—
528	C₄×D₁₃	—	2	2	no	—
529	C₄×D₁₃	—	2	2	no	—
530	C₄×D₁₃	—	2	1	no	—
531	C₄×D₁₃	—	2	1	no	—
532	C₄×D₁₃	—	2	2	no	—
533	C₄×D₁₃	—	2	4	no	—
534	C₄×D₁₃	—	4	1	no	—
535	C₄×D₁₃	—	4	1	no	—
536	C₄×D₁₃	C₂×#41	1	2	yes	—
537	C₄×D₁₃	C₂×#41	1	2	yes	—
538	Dic₂₆	—	2	2	no	—
539	Dic₂₆	—	2	2	no	—
540	Dic₂₆	—	4	2	no	—
541	C₈×C₁₃	—	2	2	no	—
542	C₈×C₁₃	—	2	1	no	—
543	C₈×C₁₃	—	2	2	no	—
544	C₈×C₁₃	—	2	1	no	—
545	C₈×C₁₃	C₂×#41	1	2	yes	—
546	C₈×C₁₃	C₂×#41	1	2	yes	—
547	#1055	—	2	2	no	—
548	#1055	—	2	1	no	—
549	#1055	—	2	1	no	—
550	#1055	—	2	2	no	—
551	#1055	C₂×#41	1	2	yes	—
552	#1055	C₂×#41	1	2	yes	—
553	C₂×#131	—	13	1	no	—
554	C₂×#131	—	13	1	no	—
555	C₂²×M₁₆	—	13	2	no	—
556	C₂³×C₈	—	13	2	no	—
557	#556	—	13	1	no	—
558	#555	—	13	1	no	—
559	#554	—	13	1	no	—
560	#553	—	13	2	no	—
561	#552	—	13	1	no	—
562	#552	—	13	1	no	—
563	#552	—	13	2	no	—
564	#551	—	13	2	no	—
565	#551	—	13	2	no	—
566	#547	—	13	1	no	—
567	#546	—	13	1	no	—
568	#546	—	13	1	no	—
569	#533	—	13	1	no	—
570	#529	—	13	1	no	—
571	#529	—	13	2	no	—
572	#529	—	13	2	no	—
573	#529	—	13	1	no	—
574	#525	—	13	2	no	—
575	C₄×#41	—	13	1	no	—
576	C₄×#41	—	13	1	no	—
577	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
578	C₂×C₄×D₄	—	13	1	no	—
579	C₂×#117	—	13	2	no	—
580	#446	—	13	1	no	—
581	#446	—	13	1	no	—
582	#446	—	13	2	no	—
583	#446	—	13	2	no	—
584	#446	—	13	1	no	—
585	#446	—	13	2	no	—
586	#446	—	13	1	no	—
587	C₈×Q₈	—	13	1	no	—
588	C₈×Q₈	—	13	1	no	—
589	C₈×Q₈	—	13	2	no	—
590	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
591	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
592	#436	—	13	1	no	—
593	#436	—	13	2	no	—
594	#436	—	13	2	no	—
595	#436	—	13	1	no	—
596	#435	—	13	2	no	—
597	#435	—	13	2	no	—
598	#435	—	13	2	no	—
599	#435	—	13	2	no	—
600	#435	—	13	2	no	—
601	#435	—	13	2	no	—
602	#435	—	13	2	no	—
603	#435	—	13	2	no	—
604	#435	—	13	2	no	—
605	#435	—	13	2	no	—
606	C₈×D₄	—	13	2	no	—
607	C₈×D₄	—	13	2	no	—
608	C₈×D₄	—	13	2	no	—
609	C₈×D₄	—	13	1	no	—
610	C₈×D₄	—	13	1	no	—
611	C₈×D₄	—	13	1	no	—
612	C₈×D₄	—	13	2	no	—
613	C₈×D₄	—	13	2	no	—
614	C₈×D₄	—	13	1	no	—
615	C₈×D₄	—	13	2	no	—
616	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
617	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
618	C₈×D₄	C₂×D₁₃	1	2	yes	complemented
619	C₈×D₄	C₂×D₁₃	1	2	yes	complemented
620	#433	—	13	2	no	—
621	#433	—	13	2	no	—
622	#433	—	13	2	no	—
623	#433	—	13	2	no	—
624	#433	—	13	2	no	—
625	#433	—	13	2	no	—
626	#432	—	13	2	no	—
627	#432	—	13	1	no	—
628	#432	—	13	1	no	—
629	#432	—	13	2	no	—
630	#431	—	13	1	no	—
631	#431	—	13	2	no	—
632	#431	C₂×D₁₃	1	2	yes	complemented
633	#431	C₂×D₁₃	1	1	yes	characteristic, complemented
634	#424	—	13	2	no	—
635	#424	—	13	2	no	—
636	#423	—	13	1	no	—
637	C₂×C₄⋊C₈	—	13	1	no	—
638	#408	—	13	2	no	—
639	#407	—	13	2	no	—
640	C₂×C₂²⋊C₈	—	13	2	no	—
641	#405	—	13	1	no	—
642	#405	—	13	1	no	—
643	#405	—	13	1	no	—
644	#405	—	13	2	no	—
645	#405	—	13	2	no	—
646	#405	—	13	2	no	—
647	#405	—	13	2	no	—
648	#405	—	13	2	no	—
649	#405	—	13	2	no	—
650	#405	—	13	2	no	—
651	#405	—	13	1	no	—
652	#405	—	13	1	no	—
653	#405	—	13	1	no	—
654	C₄×M₁₆	—	13	1	no	—
655	C₄×M₁₆	—	13	1	no	—
656	C₄×M₁₆	—	13	1	no	—
657	C₂×#97	—	13	2	no	—
658	C₂×#97	—	13	2	no	—
659	C₂×C₄×C₈	—	13	2	no	—
660	C₂×C₄×C₈	—	13	1	no	—
661	C₂×C₄×C₈	—	13	1	no	—
662	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	complemented
663	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
664	C₂²×C₁₃	—	2	2	no	—
665	C₂²×C₁₃	—	2	2	no	—
666	C₂²×C₁₃	—	2	1	no	—
667	C₂²×C₁₃	—	2	1	no	—
668	C₂²×C₁₃	—	2	1	no	—
669	C₂²×C₁₃	C₂×#131	1	4	yes	—
670	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
671	C₂×D₁₃	—	2	1	no	—
672	C₂×D₁₃	—	2	1	no	—
673	C₂×D₁₃	—	2	2	no	—
674	C₂×D₁₃	—	2	1	no	—
675	C₂×D₁₃	—	2	1	no	—
676	C₂×D₁₃	—	2	2	no	—
677	C₂×D₁₃	—	2	1	no	—
678	C₂×D₁₃	—	2	2	no	—
679	C₂×D₁₃	—	4	8	no	—
680	C₂×D₁₃	C₄×#41	1	2	yes	—
681	C₄×C₁₃	—	2	1	no	—
682	C₄×C₁₃	—	2	2	no	—
683	C₄×C₁₃	—	2	1	no	—
684	C₄×C₁₃	—	2	2	no	—
685	C₄×C₁₃	—	2	2	no	—
686	C₄×C₁₃	—	2	1	no	—
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	C₂×#131	1	2	yes	—
689	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
690	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
691	Dic₁₃	—	2	1	no	—
692	Dic₁₃	—	2	2	no	—
693	Dic₁₃	—	2	2	no	—
694	Dic₁₃	—	2	1	no	—
695	Dic₁₃	—	2	1	no	—
696	Dic₁₃	—	2	1	no	—
697	Dic₁₃	—	2	2	no	—
698	Dic₁₃	—	2	1	no	—
699	Dic₁₃	C₄×#41	1	2	yes	—
700	C₂×#41	—	13	1	no	—
701	C₂×#41	—	13	1	no	—
702	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
703	C₂²×D₄	—	13	1	no	—
704	C₂³×C₄	—	13	2	no	—
705	#131	—	26	4	no	—
706	#131	—	26	4	no	—
707	C₂×M₁₆	—	13	1	no	—
708	C₂×M₁₆	—	13	1	no	—
709	C₂×M₁₆	—	13	1	no	—
710	C₂×M₁₆	—	13	2	no	—
711	C₂×M₁₆	—	13	2	no	—
712	C₂×M₁₆	—	13	2	no	—
713	C₂×M₁₆	—	13	1	no	—
714	C₂×M₁₆	—	13	1	no	—
715	C₂×M₁₆	—	13	1	no	—
716	C₂×M₁₆	—	26	8	no	—
717	C₂²×C₈	—	13	1	no	—
718	C₂²×C₈	—	13	2	no	—
719	C₂²×C₈	—	13	2	no	—
720	C₂²×C₈	—	13	2	no	—
721	C₂²×C₈	—	13	2	no	—
722	C₂²×C₈	—	13	1	no	—
723	C₂²×C₈	—	13	1	no	—
724	C₂²×C₈	—	13	2	no	—
725	C₂²×C₈	—	13	1	no	—
726	C₂²×C₈	—	26	8	no	—
727	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
728	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
729	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
730	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
731	C₄⋊Q₈	—	13	1	no	—
732	C₄⋊Q₈	—	13	1	no	—
733	#126	—	13	2	no	—
734	#126	—	13	2	no	—
735	#126	—	13	2	no	—
736	#126	—	13	2	no	—
737	#126	—	13	2	no	—
738	#126	—	13	2	no	—
739	#125	—	13	2	no	—
740	#125	—	13	1	no	—
741	#125	—	13	2	no	—
742	#125	—	13	2	no	—
743	#125	—	13	1	no	—
744	#124	—	13	1	no	—
745	#124	—	13	2	no	—
746	#124	—	13	1	no	—
747	#124	—	13	2	no	—
748	#123	—	13	2	no	—
749	#123	—	13	2	no	—
750	#123	—	13	2	no	—
751	#123	—	13	2	no	—
752	#123	—	13	2	no	—
753	#123	—	13	2	no	—
754	#123	—	13	2	no	—
755	#123	—	13	2	no	—
756	C₂²⋊Q₈	—	13	1	no	—
757	C₂²⋊Q₈	—	13	1	no	—
758	C₂²⋊Q₈	—	13	1	no	—
759	C₂²⋊Q₈	—	13	2	no	—
760	C₂²⋊Q₈	—	13	2	no	—
761	C₂²⋊Q₈	—	13	1	no	—
762	C₂²⋊Q₈	—	13	2	no	—
763	C₂²⋊Q₈	—	13	2	no	—
764	C₂²⋊Q₈	—	13	2	no	—
765	#121	—	13	2	no	—
766	#121	—	13	2	no	—
767	#121	—	13	2	no	—
768	#121	—	13	1	no	—
769	#121	—	13	1	no	—
770	#121	—	13	2	no	—
771	#120	—	13	2	no	—
772	#120	—	13	2	no	—
773	C₄×Q₈	—	13	1	no	—
774	C₄×Q₈	—	13	1	no	—
775	C₄×Q₈	—	13	1	no	—
776	C₄×Q₈	—	13	1	no	—
777	C₄×Q₈	—	13	2	no	—
778	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
780	C₄×D₄	—	13	1	no	—
781	C₄×D₄	—	13	1	no	—
782	C₄×D₄	—	13	1	no	—
783	C₄×D₄	—	13	1	no	—
784	C₄×D₄	—	13	1	no	—
785	C₄×D₄	—	13	1	no	—
786	C₄×D₄	—	13	2	no	—
787	C₄×D₄	—	13	2	no	—
788	C₄×D₄	—	13	2	no	—
789	C₄×D₄	—	13	1	no	—
790	C₄×D₄	—	13	2	no	—
791	C₄×D₄	—	13	2	no	—
792	C₄×D₄	—	13	1	no	—
793	C₄×D₄	—	13	1	no	—
794	C₄×D₄	—	13	1	no	—
795	C₄×D₄	—	13	2	no	—
796	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
797	C₄×D₄	C₄×D₁₃	1	2	yes	—
798	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
799	C₄×D₄	C₂²×D₁₃	1	2	yes	—
800	#117	—	13	1	no	—
801	#117	—	13	1	no	—
802	#117	—	13	2	no	—
803	#117	—	13	2	no	—
804	#117	—	13	2	no	—
805	#117	—	13	2	no	—
806	#117	—	13	2	no	—
807	#117	—	13	1	no	—
808	#117	—	13	2	no	—
809	#117	—	13	2	no	—
810	#117	—	13	2	no	—
811	#117	—	13	1	no	—
812	#117	C₄×D₁₃	1	2	yes	—
813	#117	C₄×D₁₃	1	1	yes	characteristic
814	C₂×C₄⋊C₄	—	13	2	no	—
815	C₂×C₄⋊C₄	—	13	2	no	—
816	C₂×C₄⋊C₄	—	13	1	no	—
817	C₂×C₂²⋊C₄	—	13	2	no	—
818	C₂×C₂²⋊C₄	—	13	2	no	—
819	C₂×C₂²⋊C₄	—	13	2	no	—
820	C₂×C₄²	—	13	2	no	—
821	C₂×C₄²	—	13	1	no	—
822	C₂×C₄²	—	13	1	no	—
823	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
824	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
825	C₄⋊C₈	—	13	2	no	—
826	C₄⋊C₈	—	13	2	no	—
827	C₄⋊C₈	—	13	2	no	—
828	C₄⋊C₈	—	13	2	no	—
829	C₄⋊C₈	—	13	2	no	—
830	C₄⋊C₈	—	13	2	no	—
831	C₄⋊C₈	—	13	1	no	—
832	C₄⋊C₈	—	13	1	no	—
833	C₄⋊C₈	—	13	2	no	—
834	C₄⋊C₈	—	13	2	no	—
835	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
838	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
839	C₂²⋊C₈	—	13	2	no	—
840	C₂²⋊C₈	—	13	2	no	—
841	C₂²⋊C₈	—	13	2	no	—
842	C₂²⋊C₈	—	13	2	no	—
843	C₂²⋊C₈	—	13	2	no	—
844	C₂²⋊C₈	—	13	2	no	—
845	C₂²⋊C₈	—	13	2	no	—
846	C₂²⋊C₈	—	13	2	no	—
847	C₂²⋊C₈	—	13	2	no	—
848	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
849	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
850	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
851	#97	—	13	1	no	—
852	#97	—	13	2	no	—
853	#97	—	13	2	no	—
854	#97	—	13	2	no	—
855	#97	—	13	1	no	—
856	#97	—	13	1	no	—
857	#97	—	13	1	no	—
858	#97	—	13	1	no	—
859	#97	—	13	2	no	—
860	#97	—	13	2	no	—
861	#97	—	13	2	no	—
862	#97	—	13	1	no	—
863	C₄×C₈	—	13	2	no	—
864	C₄×C₈	—	13	1	no	—
865	C₄×C₈	—	13	1	no	—
866	C₄×C₈	—	13	2	no	—
867	C₄×C₈	—	13	1	no	—
868	C₄×C₈	—	13	2	no	—
869	C₄×C₈	—	13	1	no	—
870	C₄×C₈	—	13	1	no	—
871	C₄×C₈	—	13	1	no	—
872	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
873	C₄×C₈	C₂²×D₁₃	1	2	yes	—
874	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
875	C₄×C₈	C₂²×D₁₃	1	2	yes	—
876	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
877	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
878	C₄×C₈	C₂²×D₁₃	1	2	yes	—
879	C₂×C₁₃	—	2	4	no	—
880	C₂×C₁₃	—	4	1	no	—
881	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
882	C₂×C₁₃	C₂²×#131	1	1	yes	characteristic
883	C₂×C₁₃	#3573	1	1	yes	characteristic
884	D₁₃	—	2	2	no	—
885	D₁₃	—	4	1	no	—
886	D₁₃	—	4	2	no	—
887	C₂⁴	—	13	2	no	—
888	#41	—	2	4	no	—
889	#41	—	26	2	no	—
890	#41	—	26	2	no	—
891	#41	—	26	4	no	—
892	C₂×Q₈	—	13	1	no	—
893	C₂×Q₈	—	13	1	no	—
894	C₂×Q₈	—	13	2	no	—
895	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
896	C₂×D₄	—	13	1	no	—
897	C₂×D₄	—	13	2	no	—
898	C₂×D₄	—	13	1	no	—
899	C₂×D₄	—	13	2	no	—
900	C₂×D₄	—	13	2	no	—
901	C₂×D₄	—	13	1	no	—
902	C₂×D₄	—	13	1	no	—
903	C₂×D₄	—	13	2	no	—
904	C₂×D₄	—	26	4	no	—
905	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
906	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
907	C₂²×C₄	—	13	1	no	—
908	C₂²×C₄	—	13	2	no	—
909	C₂²×C₄	—	13	2	no	—
910	C₂²×C₄	—	13	2	no	—
911	C₂²×C₄	—	13	1	no	—
912	C₂²×C₄	—	13	1	no	—
913	C₂²×C₄	—	13	2	no	—
914	C₂²×C₄	—	13	2	no	—
915	C₂²×C₄	—	13	1	no	—
916	C₂²×C₄	—	13	2	no	—
917	C₂²×C₄	—	13	1	no	—
918	C₂²×C₄	—	13	1	no	—
919	C₂²×C₄	—	26	4	no	—
920	C₂²×C₄	—	26	4	no	—
921	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
922	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
923	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
924	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
925	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
926	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
927	M₁₆	—	13	4	no	—
928	M₁₆	—	26	4	no	—
929	M₁₆	—	26	2	no	—
930	M₁₆	—	26	4	no	—
931	M₁₆	—	26	2	no	—
932	M₁₆	—	26	2	no	—
933	M₁₆	—	26	2	no	—
934	M₁₆	—	26	4	no	—
935	M₁₆	—	26	2	no	—
936	C₂×C₈	—	2	4	no	—
937	C₂×C₈	—	2	4	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	13	1	no	—
941	C₂×C₈	—	13	1	no	—
942	C₂×C₈	—	13	4	no	—
943	C₂×C₈	—	13	2	no	—
944	C₂×C₈	—	13	1	no	—
945	C₂×C₈	—	13	1	no	—
946	C₂×C₈	—	13	2	no	—
947	C₂×C₈	—	26	4	no	—
948	C₂×C₈	—	26	2	no	—
949	C₂×C₈	—	26	4	no	—
950	C₂×C₈	—	26	2	no	—
951	C₂×C₈	—	26	4	no	—
952	C₂×C₈	—	26	4	no	—
953	C₂×C₈	—	26	4	no	—
954	C₂×C₈	—	26	2	no	—
955	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
956	C₂×C₈	C₂³×D₁₃	1	2	yes	—
957	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
958	C₂×C₈	C₂³×D₁₃	1	2	yes	—
959	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
961	C₄⋊C₄	—	13	1	no	—
962	C₄⋊C₄	—	13	1	no	—
963	C₄⋊C₄	—	13	2	no	—
964	C₄⋊C₄	—	13	2	no	—
965	C₄⋊C₄	—	13	2	no	—
966	C₄⋊C₄	—	13	2	no	—
967	C₄⋊C₄	—	13	2	no	—
968	C₄⋊C₄	—	13	2	no	—
969	C₄⋊C₄	—	13	1	no	—
970	C₄⋊C₄	—	13	2	no	—
971	C₄⋊C₄	—	13	1	no	—
972	C₄⋊C₄	—	13	1	no	—
973	C₄⋊C₄	—	13	1	no	—
974	C₄⋊C₄	—	13	2	no	—
975	C₄⋊C₄	—	13	2	no	—
976	C₄⋊C₄	—	13	1	no	—
977	C₄⋊C₄	—	13	1	no	—
978	C₄⋊C₄	—	13	2	no	—
979	C₄⋊C₄	—	13	2	no	—
980	C₄⋊C₄	—	13	2	no	—
981	C₄⋊C₄	—	13	2	no	—
982	C₄⋊C₄	—	13	2	no	—
983	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
986	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
987	C₂²⋊C₄	—	13	2	no	—
988	C₂²⋊C₄	—	13	2	no	—
989	C₂²⋊C₄	—	13	1	no	—
990	C₂²⋊C₄	—	13	1	no	—
991	C₂²⋊C₄	—	13	2	no	—
992	C₂²⋊C₄	—	13	1	no	—
993	C₂²⋊C₄	—	13	1	no	—
994	C₂²⋊C₄	—	13	2	no	—
995	C₂²⋊C₄	—	13	2	no	—
996	C₂²⋊C₄	—	13	2	no	—
997	C₂²⋊C₄	—	13	2	no	—
998	C₂²⋊C₄	—	13	2	no	—
999	C₂²⋊C₄	—	13	2	no	—
1000	C₂²⋊C₄	—	13	2	no	—
1001	C₂²⋊C₄	—	13	2	no	—
1002	C₂²⋊C₄	—	13	1	no	—
1003	C₂²⋊C₄	—	13	2	no	—
1004	C₂²⋊C₄	—	13	1	no	—
1005	C₂²⋊C₄	—	13	2	no	—
1006	C₂²⋊C₄	—	13	2	no	—
1007	C₂²⋊C₄	—	13	2	no	—
1008	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1011	C₄²	—	13	2	no	—
1012	C₄²	—	13	2	no	—
1013	C₄²	—	13	1	no	—
1014	C₄²	—	13	1	no	—
1015	C₄²	—	13	1	no	—
1016	C₄²	—	13	1	no	—
1017	C₄²	—	13	1	no	—
1018	C₄²	—	13	1	no	—
1019	C₄²	—	13	2	no	—
1020	C₄²	C₂×C₄×D₁₃	1	2	yes	—
1021	C₄²	C₂×C₄×D₁₃	1	2	yes	—
1022	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1023	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1024	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1025	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1026	C₄²	C₂³×D₁₃	1	2	yes	—
1027	C₁₃	#60215	1	1	yes	characteristic, complemented, Sylow
1028	C₂³	—	13	1	no	—
1029	C₂³	—	13	2	no	—
1030	C₂³	—	13	1	no	—
1031	C₂³	—	26	4	no	—
1032	C₂³	—	26	4	no	—
1033	C₂³	—	52	2	no	—
1034	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
1035	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	26	2	no	—
1038	Q₈	—	26	2	no	—
1039	Q₈	—	52	2	no	—
1040	D₄	—	2	4	no	—
1041	D₄	—	26	2	no	—
1042	D₄	—	26	2	no	—
1043	D₄	—	26	2	no	—
1044	D₄	—	26	4	no	—
1045	D₄	—	26	4	no	—
1046	D₄	—	26	2	no	—
1047	D₄	—	52	2	no	—
1048	D₄	—	52	2	no	—
1049	D₄	#88155	1	4	yes	complemented
1050	C₂×C₄	—	2	4	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	13	1	no	—
1059	C₂×C₄	—	13	2	no	—
1060	C₂×C₄	—	13	2	no	—
1061	C₂×C₄	—	13	1	no	—
1062	C₂×C₄	—	13	1	no	—
1063	C₂×C₄	—	13	1	no	—
1064	C₂×C₄	—	13	2	no	—
1065	C₂×C₄	—	13	2	no	—
1066	C₂×C₄	—	13	1	no	—
1067	C₂×C₄	—	13	1	no	—
1068	C₂×C₄	—	13	2	no	—
1069	C₂×C₄	—	26	4	no	—
1070	C₂×C₄	—	26	4	no	—
1071	C₂×C₄	—	26	4	no	—
1072	C₂×C₄	—	26	4	no	—
1073	C₂×C₄	—	26	2	no	—
1074	C₂×C₄	—	26	2	no	—
1075	C₂×C₄	—	26	2	no	—
1076	C₂×C₄	—	26	1	no	—
1077	C₂×C₄	—	26	1	no	—
1078	C₂×C₄	—	26	2	no	—
1079	C₂×C₄	—	52	1	no	—
1080	C₂×C₄	—	52	1	no	—
1081	C₂×C₄	—	52	2	no	—
1082	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1083	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1088	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1089	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1090	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	2	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	13	2	no	—
1096	C₈	—	13	2	no	—
1097	C₈	—	26	2	no	—
1098	C₈	—	26	1	no	—
1099	C₈	—	26	1	no	—
1100	C₈	—	26	2	no	—
1101	C₈	#41×D₁₃	1	2	yes	—
1102	C₈	#41×D₁₃	1	2	yes	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	13	2	no	—
1109	C₂²	—	26	1	no	—
1110	C₂²	—	26	1	no	—
1111	C₂²	—	26	1	no	—
1112	C₂²	—	26	2	no	—
1113	C₂²	—	26	1	no	—
1114	C₂²	—	26	2	no	—
1115	C₂²	—	26	2	no	—
1116	C₂²	—	26	1	no	—
1117	C₂²	—	52	8	no	—
1118	C₂²	C₂×#88155	1	4	yes	—
1119	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	13	2	no	—
1128	C₄	—	26	1	no	—
1129	C₄	—	26	1	no	—
1130	C₄	—	26	2	no	—
1131	C₄	—	26	1	no	—
1132	C₄	—	26	2	no	—
1133	C₄	—	26	1	no	—
1134	C₄	—	26	2	no	—
1135	C₄	—	26	1	no	—
1136	C₄	C₂×#88155	1	2	yes	—
1137	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
1138	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
1139	C₂	—	2	4	no	—
1140	C₂	—	4	1	no	—
1141	C₂	—	26	2	no	—
1142	C₂	—	52	2	no	—
1143	C₂	—	52	1	no	—
1144	C₂	C₄×#41×D₁₃	1	1	yes	characteristic
1145	C₂	C₂²×#88155	1	1	yes	characteristic
1146	C₂	#13129547	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₈×C₁₃×#41	C₂
prime radical	#13128398	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₈×#41	D₁₃
hypocenter	C₁₃	#60215
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. #13123850	C₂	semidirect
3. #13123844	C₂	semidirect
4. #13123839	C₂	semidirect
5. #13123834	C₂	semidirect
6. #13123825	C₂	semidirect
7. #13123824	C₂	semidirect
8. #13123813	C₂	semidirect
9. #13123811	C₂	semidirect
10. #13123811	C₂	semidirect
11. #13123804	C₂	semidirect
12. C₈×#6129	C₂	semidirect
13. #13123778	C₂	semidirect
14. #13123765	C₂	semidirect
15. D₄×#6094	C₂	semidirect
16. #13123556	C₂	semidirect
17. #13123525	C₂	semidirect
18. C₈×D₄×D₁₃	C₂	semidirect
19. #13123497	C₂	semidirect
20. #13123489	C₂	semidirect
21. C₄×#88155	C₂	semidirect
22. C₂×#11718350	C₂	semidirect
23. C₈×C₁₃×#41	C₂	semidirect
51. C₈×Q₈×C₁₃	C₂²	semidirect
52. C₈×Q₈×C₁₃	C₂²	semidirect
55. C₈×D₄×C₁₃	C₂²	semidirect
56. C₈×D₄×C₁₃	C₂²	semidirect
57. C₁₃×#431	C₂²	semidirect
58. C₁₃×#431	C₂²	semidirect
59. C₂×C₄×C₈×C₁₃	C₂²	semidirect
60. C₂×C₄×C₈×C₁₃	C₂²	semidirect
62. #11718772	C₂²	semidirect
63. #11718772	C₂²	semidirect
65. C₈×C₂²⋊D₁₃	C₂²	semidirect
66. C₈×C₂²⋊D₁₃	C₂²	semidirect
67. #11718762	C₂²	semidirect
68. #11718762	C₂²	semidirect
69. C₂×#88055	C₂²	semidirect
70. C₂×C₈×Dic₁₃	C₂²	semidirect
71. #11718685	C₂²	semidirect
72. #11718685	C₂²	semidirect
73. #11718672	C₂²	semidirect
74. #11718672	C₂²	semidirect
77. #11718587	C₂²	semidirect
78. #11718587	C₂²	semidirect
79. C₄×#6099	C₂²	semidirect
80. C₂×#88043	C₂²	semidirect
81. #11718501	C₂²	semidirect
82. #11718501	C₂²	semidirect
87. #11718497	C₂²	semidirect
88. #11718497	C₂²	semidirect
89. #11718496	C₂²	semidirect
91. #11718494	C₂²	semidirect
93. #11718492	C₂²	semidirect
94. #11718491	C₂²	semidirect
95. #11718489	C₂²	semidirect
96. #11718489	C₂²	semidirect
98. #11718391	C₂²	semidirect
99. #11718390	C₂²	semidirect
100. #11718389	C₂²	semidirect
104. #11718386	C₂²	semidirect
106. #11718381	C₂²	semidirect
107. #11718380	C₂²	semidirect
108. #11718379	C₂²	semidirect
109. #11718351	C₂²	semidirect
110. #11718351	C₂²	semidirect
111. #11718351	C₂²	semidirect
117. #11718350	C₂²	semidirect
118. #11718350	C₂²	semidirect
119. #11718350	C₂²	semidirect
120. #11718350	C₂²	semidirect
121. #11718350	C₂²	semidirect
122. #11718350	C₂²	semidirect
124. #11718349	C₂²	semidirect
126. C₄×#6094	C₂²	semidirect
128. C₈×D₅₂	C₂²	semidirect
130. C₄×C₈×D₁₃	C₂²	semidirect
131. #11718340	C₂²	semidirect
132. #11718340	C₂²	semidirect
133. C₈×Dic₂₆	C₂²	semidirect
134. C₈×Dic₂₆	C₂²	semidirect
447. #6094	#41	semidirect
454. C₈×D₁₃	#41	semidirect
467. C₈×#41	D₁₃	semidirect
488. D₄×C₁₃	#131	semidirect
590. C₈×Q₈	C₂×D₁₃	semidirect
591. C₈×Q₈	C₂×D₁₃	semidirect
618. C₈×D₄	C₂×D₁₃	semidirect
619. C₈×D₄	C₂×D₁₃	semidirect
632. #431	C₂×D₁₃	semidirect
633. #431	C₂×D₁₃	semidirect
662. C₂×C₄×C₈	C₂×D₁₃	semidirect
663. C₂×C₄×C₈	C₂×D₁₃	semidirect
1027. C₁₃	#60215	semidirect
1049. D₄	#88155	semidirect

Maximal subgroups

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

subgroup	index
#13128398	2
#13123850	2
#13123844	2
#13123839	2
#13123834	2
#13123825	2
#13123824	2
#13123813	2
#13123811	2
#13123804	2
C₈×#6129	2
#13123778	2
#13123765	2
D₄×#6094	2
#13123556	2
#13123525	2
C₈×D₄×D₁₃	2
#13123497	2
#13123489	2
C₄×#88155	2
C₂×#11718350	2
C₈×C₁₃×#41	2
#60215	13