Subgroups — #15879412

Order 3328.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
2	#13117281	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115818	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115781	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115285	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115280	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115139	C₂	1	1	yes	maximal, characteristic, complemented
8	#13115139	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114935	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114935	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114856	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114646	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11718124	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#556	C₄	1	1	yes	characteristic, complemented
17	C₁₃×#555	C₄	1	1	yes	characteristic, complemented
18	C₁₃×#554	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#553	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#553	C₄	1	1	yes	characteristic, complemented
21	C₁₃×#552	—	2	1	no	—
22	C₁₃×#552	C₄	1	1	yes	characteristic, complemented
23	C₁₃×#552	C₄	1	1	yes	characteristic, complemented
24	C₁₃×#551	—	2	1	no	—
25	C₁₃×#551	—	2	1	no	—
26	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
27	C₁₃×#546	—	2	1	no	—
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#525	C₂²	1	1	yes	characteristic
33	C₁₃×#525	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×#41	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₂×#88180	C₂²	1	1	yes	characteristic
40	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
41	C₂²×#6099	C₂²	1	1	yes	characteristic
42	C₂²×#6099	C₂²	1	1	yes	characteristic
43	C₂×#88077	C₂²	1	1	yes	characteristic
44	C₂×#88077	C₂²	1	1	yes	characteristic
45	C₂×#88077	C₂²	1	1	yes	characteristic
46	C₂×#88077	C₂²	1	1	yes	characteristic
47	#11718881	—	2	1	no	—
48	C₄×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
50	#11718868	C₂²	1	1	yes	characteristic
51	#11718868	C₂²	1	1	yes	characteristic
52	#11718673	—	2	1	no	—
53	#11718672	—	2	1	no	—
54	#11718672	—	2	1	no	—
55	D₄×#1055	—	2	1	no	—
56	#11718642	—	2	1	no	—
57	#11718612	—	2	1	no	—
58	#11718611	—	2	1	no	—
59	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
60	#11718593	C₂²	1	1	yes	characteristic
61	#11718585	C₂²	1	1	yes	characteristic
62	C₄×#6099	C₂²	1	1	yes	characteristic
63	#11718124	C₂²	1	1	yes	characteristic
64	#11718124	C₂²	1	1	yes	characteristic
65	#11718124	C₂²	1	1	yes	characteristic
66	#11718124	C₂²	1	1	yes	characteristic
67	#11718124	C₂²	1	1	yes	characteristic
68	#11718124	C₂²	1	1	yes	characteristic
69	#11718124	C₂²	1	1	yes	characteristic
70	#11718124	C₂²	1	1	yes	characteristic
71	#11718124	C₂²	1	1	yes	characteristic
72	#11718124	C₂²	1	1	yes	characteristic
73	#11718124	C₂²	1	1	yes	characteristic
74	#11718124	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×Dic₁₃	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
82	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
83	C₁₃×#126	—	2	1	no	—
84	C₁₃×#126	—	2	1	no	—
85	C₁₃×#126	—	2	1	no	—
86	C₁₃×#126	—	2	1	no	—
87	C₁₃×#126	—	2	1	no	—
88	C₁₃×#126	—	2	1	no	—
89	C₁₃×#125	—	2	1	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	C₂×C₄	1	1	yes	characteristic, complemented
93	C₁₃×#125	C₂×C₄	1	1	yes	characteristic, complemented
94	C₁₃×#124	—	2	1	no	—
95	C₁₃×#124	—	2	1	no	—
96	C₁₃×#124	—	2	1	no	—
97	C₁₃×#123	—	2	1	no	—
98	C₁₃×#123	—	2	1	no	—
99	C₁₃×#123	—	2	1	no	—
100	C₁₃×#123	—	2	1	no	—
101	C₁₃×#123	—	2	1	no	—
102	C₁₃×#123	—	2	1	no	—
103	C₁₃×#123	—	2	1	no	—
104	C₁₃×#123	—	2	1	no	—
105	C₁₃×C₂²⋊Q₈	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	1	no	—
107	C₁₃×C₂²⋊Q₈	—	2	1	no	—
108	C₁₃×C₂²⋊Q₈	—	2	1	no	—
109	C₁₃×C₂²⋊Q₈	—	2	1	no	—
110	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
111	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
112	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
113	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
114	C₁₃×#121	—	2	1	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#121	C₂×C₄	1	1	yes	characteristic, complemented
120	C₁₃×#121	C₂×C₄	1	1	yes	characteristic, complemented
121	C₁₃×#120	—	2	1	no	—
122	C₁₃×#120	—	2	1	no	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
125	C₄×Q₈×C₁₃	—	2	1	no	—
126	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
127	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
128	C₄×D₄×C₁₃	—	2	1	no	—
129	C₄×D₄×C₁₃	—	2	1	no	—
130	C₄×D₄×C₁₃	—	2	1	no	—
131	C₄×D₄×C₁₃	—	2	1	no	—
132	C₄×D₄×C₁₃	—	2	1	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
138	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
139	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
140	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
141	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
142	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
143	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
144	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
145	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
146	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	—	2	1	no	—
149	C₁₃×#117	—	2	1	no	—
150	C₁₃×#117	—	2	1	no	—
151	C₁₃×#117	—	2	1	no	—
152	C₁₃×#117	—	2	1	no	—
153	C₁₃×#117	—	2	1	no	—
154	C₁₃×#117	—	2	1	no	—
155	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
156	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
157	C₁₃×#117	C₂×C₄	1	1	yes	characteristic, complemented
158	C₁₃×#117	C₂×C₄	1	1	yes	characteristic, complemented
159	C₁₃×#117	C₂³	1	1	yes	characteristic
160	C₁₃×#117	C₂³	1	1	yes	characteristic
161	C₁₃×#117	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
163	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
165	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
166	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	—	2	1	no	—
173	C₂×C₄²×C₁₃	—	2	1	no	—
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
176	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
177	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
178	#88180	—	2	2	no	—
179	#88180	—	4	1	no	—
180	C₂×C₄⋊Dic₁₃	—	2	1	no	—
181	C₂×C₄⋊Dic₁₃	—	2	1	no	—
182	C₂×C₄×Dic₁₃	—	2	2	no	—
183	C₂×C₄×Dic₁₃	—	2	1	no	—
184	C₂×C₄×Dic₁₃	—	4	1	no	—
185	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
189	C₂×#6099	—	2	1	no	—
190	C₂×#6099	—	2	1	no	—
191	C₂×#6099	—	2	2	no	—
192	C₂×#6099	—	2	2	no	—
193	C₂×#6099	—	4	1	no	—
194	C₂×#6099	—	4	1	no	—
195	C₂×#6099	C₂³	1	1	yes	characteristic
196	C₂×#6099	C₂³	1	1	yes	characteristic
197	C₂×#6099	C₂³	1	1	yes	characteristic
198	C₂×#6099	C₂³	1	1	yes	characteristic
199	C₂²×#1055	—	2	1	no	—
200	C₂²×#1055	—	2	1	no	—
201	#88077	—	2	2	no	—
202	#88077	—	2	2	no	—
203	#88077	—	4	1	no	—
204	#88077	—	4	1	no	—
205	#88071	—	2	1	no	—
206	#88071	—	2	1	no	—
207	#88071	—	2	1	no	—
208	#88071	—	2	1	no	—
209	#88071	—	2	1	no	—
210	C₂²⋊#1055	—	2	1	no	—
211	C₂²⋊#1055	—	2	1	no	—
212	C₂²⋊#1055	—	2	1	no	—
213	C₂²⋊#1055	—	2	1	no	—
214	C₄⋊#1055	—	2	1	no	—
215	C₄⋊#1055	—	2	1	no	—
216	#88043	—	2	1	no	—
217	C₄×#1055	—	2	1	no	—
218	#22506	—	13	1	no	maximal, Sylow
219	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₁₃×#41	—	2	1	no	—
222	C₁₃×#41	—	2	1	no	—
223	C₁₃×#41	—	2	1	no	—
224	C₁₃×#41	—	2	1	no	—
225	C₁₃×#41	—	4	4	no	—
226	C₂×Q₈×C₁₃	—	2	1	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	4	2	no	—
235	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
236	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
237	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
238	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
239	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	1	no	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×Dic₁₃	—	2	1	no	—
269	C₂²×Dic₁₃	—	2	1	no	—
270	C₂²×Dic₁₃	—	2	1	no	—
271	C₂²×Dic₁₃	—	2	1	no	—
272	C₂²×Dic₁₃	—	4	2	no	—
273	C₂²×Dic₁₃	—	4	2	no	—
274	C₂²×Dic₁₃	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
293	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
294	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
295	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
297	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
301	C₁₃×C₂²⋊C₄	—	2	1	no	—
302	C₁₃×C₂²⋊C₄	—	2	1	no	—
303	C₁₃×C₂²⋊C₄	—	2	1	no	—
304	C₁₃×C₂²⋊C₄	—	2	1	no	—
305	C₁₃×C₂²⋊C₄	—	2	1	no	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	1	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
319	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
320	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
322	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
323	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
324	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
325	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	1	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
336	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₂²⋊Dic₁₃	—	4	2	no	—
340	C₂²⋊Dic₁₃	—	4	2	no	—
341	C₂²⋊Dic₁₃	—	4	2	no	—
342	C₄⋊Dic₁₃	—	4	2	no	—
343	C₄⋊Dic₁₃	—	4	2	no	—
344	C₄×Dic₁₃	—	2	1	no	—
345	C₄×Dic₁₃	—	2	1	no	—
346	C₄×Dic₁₃	—	2	1	no	—
347	C₄×Dic₁₃	—	2	1	no	—
348	C₄×Dic₁₃	—	2	1	no	—
349	C₄×Dic₁₃	—	2	1	no	—
350	C₄×Dic₁₃	—	2	1	no	—
351	C₄×Dic₁₃	—	4	2	no	—
352	C₄×Dic₁₃	#41	1	2	yes	complemented
353	#6099	—	2	1	no	—
354	#6099	—	2	1	no	—
355	#6099	—	2	1	no	—
356	#6099	—	2	1	no	—
357	#6099	—	2	1	no	—
358	#6099	—	2	1	no	—
359	#6099	—	2	1	no	—
360	#6099	—	4	2	no	—
361	#6099	—	4	2	no	—
362	#6099	#41	1	2	yes	complemented
363	C₂×#1055	—	2	1	no	—
364	C₂×#1055	—	2	1	no	—
365	C₂×#1055	—	2	1	no	—
366	C₂×#1055	—	2	1	no	—
367	C₂×#1055	—	4	2	no	—
368	C₂×#1055	—	4	2	no	—
369	#3475	D₁₃	1	1	yes	characteristic
370	D₄×M₁₆	—	13	1	no	—
371	#2290	—	13	1	no	—
372	#1995	—	13	1	no	—
373	#1986	—	13	1	no	—
374	#1897	—	13	1	no	—
375	#1896	—	13	1	no	—
376	#1871	—	13	1	no	—
377	#1871	—	13	1	no	—
378	#1826	—	13	1	no	—
379	#1826	—	13	1	no	—
380	#1806	—	13	1	no	—
381	#1759	—	13	1	no	—
382	#1733	—	13	1	no	—
383	C₂×#339	—	13	1	no	—
384	C₂³×C₁₃	—	2	1	no	—
385	C₂³×C₁₃	—	2	1	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	1	no	—
388	C₂³×C₁₃	—	2	1	no	—
389	C₂³×C₁₃	—	2	1	no	—
390	C₂³×C₁₃	—	4	1	no	—
391	C₂³×C₁₃	—	4	1	no	—
392	C₂³×C₁₃	—	4	1	no	—
393	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	Q₈×C₁₃	—	2	1	no	—
399	Q₈×C₁₃	—	2	1	no	—
400	Q₈×C₁₃	—	4	2	no	—
401	Q₈×C₁₃	—	8	1	no	—
402	D₄×C₁₃	—	2	2	no	—
403	D₄×C₁₃	—	2	2	no	—
404	D₄×C₁₃	—	2	1	no	—
405	D₄×C₁₃	—	2	1	no	—
406	D₄×C₁₃	—	4	1	no	—
407	D₄×C₁₃	—	4	1	no	—
408	D₄×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	4	1	no	—
410	D₄×C₁₃	—	4	1	no	—
411	D₄×C₁₃	—	4	2	no	—
412	D₄×C₁₃	—	8	1	no	—
413	D₄×C₁₃	—	8	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	4	1	no	—
442	C₂×C₄×C₁₃	—	4	1	no	—
443	C₂×C₄×C₁₃	—	4	2	no	—
444	C₂×C₄×C₁₃	—	4	2	no	—
445	C₂×C₄×C₁₃	—	4	2	no	—
446	C₂×C₄×C₁₃	—	4	1	no	—
447	C₂×C₄×C₁₃	—	4	1	no	—
448	C₂×C₄×C₁₃	—	8	1	no	—
449	C₂×C₄×C₁₃	—	8	1	no	—
450	C₂×C₄×C₁₃	—	8	1	no	—
451	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
463	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
464	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
465	C₂×Dic₁₃	—	2	2	no	—
466	C₂×Dic₁₃	—	2	2	no	—
467	C₂×Dic₁₃	—	4	1	no	—
468	C₂×Dic₁₃	—	4	1	no	—
469	C₂×Dic₁₃	—	4	1	no	—
470	C₂×Dic₁₃	—	4	8	no	—
471	C₂×Dic₁₃	—	4	1	no	—
472	C₂×Dic₁₃	—	4	1	no	—
473	C₂×Dic₁₃	—	4	1	no	—
474	C₂×Dic₁₃	—	4	1	no	—
475	C₂×Dic₁₃	—	4	1	no	—
476	C₂×Dic₁₃	—	4	1	no	—
477	C₂×Dic₁₃	—	4	1	no	—
478	#1055	—	2	2	no	—
479	#1055	—	4	1	no	—
480	#1055	—	4	1	no	—
481	#1055	—	4	1	no	—
482	C₂²×M₁₆	—	13	1	no	—
483	C₂²×M₁₆	—	13	1	no	—
484	#556	Dic₁₃	1	1	yes	characteristic, complemented
485	#555	Dic₁₃	1	1	yes	characteristic, complemented
486	#554	Dic₁₃	1	1	yes	characteristic, complemented
487	#553	Dic₁₃	1	1	yes	characteristic, complemented
488	#553	Dic₁₃	1	1	yes	characteristic, complemented
489	#552	—	2	1	no	—
490	#552	Dic₁₃	1	1	yes	characteristic, complemented
491	#552	Dic₁₃	1	1	yes	characteristic, complemented
492	#551	—	2	1	no	—
493	#551	—	2	1	no	—
494	#547	Dic₁₃	1	1	yes	characteristic, complemented
495	#546	—	2	1	no	—
496	#533	C₂×D₁₃	1	1	yes	characteristic
497	#529	—	2	1	no	—
498	#529	—	2	1	no	—
499	#529	—	2	1	no	—
500	#525	C₂×D₁₃	1	1	yes	characteristic
501	#525	C₂×D₁₃	1	1	yes	characteristic
502	C₄×#41	—	2	1	no	—
503	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
505	C₂×#117	—	13	1	no	—
506	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
507	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
508	C₂²×C₄²	—	13	1	no	—
509	#436	—	26	1	no	—
510	#435	—	26	1	no	—
511	#435	—	26	1	no	—
512	C₈×D₄	—	26	1	no	—
513	#423	—	13	1	no	—
514	C₂×#104	—	13	1	no	—
515	C₂×#104	—	13	1	no	—
516	C₂×#104	—	13	1	no	—
517	C₂×#104	—	13	1	no	—
518	#407	—	13	1	no	—
519	#407	—	13	1	no	—
520	C₄×M₁₆	—	13	1	no	—
521	#388	—	26	1	no	—
522	#387	—	26	1	no	—
523	#386	—	26	1	no	—
524	#385	—	26	1	no	—
525	C₄×C₄⋊C₄	—	13	1	no	—
526	C₄×C₂²⋊C₄	—	13	1	no	—
527	C₄×C₂²⋊C₄	—	13	1	no	—
528	#376	—	13	1	no	—
529	#339	—	13	1	no	—
530	#339	—	13	1	no	—
531	#339	—	13	1	no	—
532	#339	—	13	1	no	—
533	#339	—	13	1	no	—
534	#339	—	13	1	no	—
535	#339	—	13	1	no	—
536	#339	—	13	1	no	—
537	#339	—	13	1	no	—
538	#339	—	13	1	no	—
539	#339	—	13	1	no	—
540	#339	—	13	1	no	—
541	C₂²×C₁₃	—	2	1	no	—
542	C₂²×C₁₃	—	2	1	no	—
543	C₂²×C₁₃	—	2	1	no	—
544	C₂²×C₁₃	—	2	1	no	—
545	C₂²×C₁₃	—	2	1	no	—
546	C₂²×C₁₃	—	2	1	no	—
547	C₂²×C₁₃	—	2	1	no	—
548	C₂²×C₁₃	—	2	1	no	—
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	1	no	—
551	C₂²×C₁₃	—	2	1	no	—
552	C₂²×C₁₃	—	2	1	no	—
553	C₂²×C₁₃	—	2	1	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	4	1	no	—
557	C₂²×C₁₃	—	4	1	no	—
558	C₂²×C₁₃	—	4	1	no	—
559	C₂²×C₁₃	—	8	1	no	—
560	C₂²×C₁₃	—	8	1	no	—
561	C₂²×C₁₃	#421	1	2	yes	—
562	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
563	C₂²×C₁₃	#546	1	1	yes	characteristic
564	C₂²×C₁₃	#547	1	1	yes	characteristic
565	C₄×C₁₃	—	2	1	no	—
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	1	no	—
568	C₄×C₁₃	—	2	1	no	—
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	1	no	—
571	C₄×C₁₃	—	2	1	no	—
572	C₄×C₁₃	—	2	1	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	—	4	1	no	—
575	C₄×C₁₃	—	4	1	no	—
576	C₄×C₁₃	—	4	1	no	—
577	C₄×C₁₃	—	4	1	no	—
578	C₄×C₁₃	—	4	1	no	—
579	C₄×C₁₃	—	4	1	no	—
580	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
581	C₄×C₁₃	#520	1	1	yes	characteristic
582	C₄×C₁₃	#546	1	1	yes	characteristic
583	C₄×C₁₃	#547	1	1	yes	characteristic
584	Dic₁₃	—	4	2	no	—
585	Dic₁₃	—	4	2	no	—
586	Dic₁₃	—	8	1	no	—
587	Dic₁₃	—	8	1	no	—
588	C₂×#41	—	2	1	no	—
589	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
590	C₂²×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
591	C₂³×C₄	—	26	1	no	—
592	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
593	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
594	C₂×M₁₆	—	13	1	no	—
595	C₂×M₁₆	—	13	1	no	—
596	C₂×M₁₆	—	13	1	no	—
597	C₂×M₁₆	—	13	1	no	—
598	C₂×M₁₆	—	26	1	no	—
599	C₂×M₁₆	—	26	1	no	—
600	C₂×M₁₆	—	26	2	no	—
601	C₂×M₁₆	—	26	2	no	—
602	C₂×M₁₆	—	52	1	no	—
603	C₂×M₁₆	—	52	1	no	—
604	C₂²×C₈	—	26	1	no	—
605	C₂²×C₈	—	26	1	no	—
606	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
607	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
608	#126	—	2	1	no	—
609	#126	—	2	1	no	—
610	#126	—	2	1	no	—
611	#126	—	2	1	no	—
612	#126	—	2	1	no	—
613	#126	—	2	1	no	—
614	#125	—	2	1	no	—
615	#125	—	2	1	no	—
616	#125	—	2	1	no	—
617	#125	C₂×Dic₁₃	1	1	yes	characteristic, complemented
618	#125	C₂×Dic₁₃	1	1	yes	characteristic, complemented
619	#124	—	2	1	no	—
620	#124	—	2	1	no	—
621	#124	—	2	1	no	—
622	#123	—	2	1	no	—
623	#123	—	2	1	no	—
624	#123	—	2	1	no	—
625	#123	—	2	1	no	—
626	#123	—	2	1	no	—
627	#123	—	2	1	no	—
628	#123	—	2	1	no	—
629	#123	—	2	1	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂²⋊Q₈	—	2	1	no	—
634	C₂²⋊Q₈	—	2	1	no	—
635	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
636	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
637	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
638	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
639	#121	—	2	1	no	—
640	#121	—	2	1	no	—
641	#121	—	2	1	no	—
642	#121	C₂×Dic₁₃	1	1	yes	characteristic
643	#121	C₂×Dic₁₃	1	1	yes	characteristic
644	#121	C₂×Dic₁₃	1	1	yes	characteristic, complemented
645	#121	C₂×Dic₁₃	1	1	yes	characteristic, complemented
646	#120	—	2	1	no	—
647	#120	—	2	1	no	—
648	C₄×Q₈	—	2	1	no	—
649	C₄×Q₈	—	2	1	no	—
650	C₄×Q₈	—	2	1	no	—
651	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
652	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic, complemented
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
663	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
664	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
665	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
666	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic, complemented
667	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic, complemented
668	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
669	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
670	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
671	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
672	#117	—	2	1	no	—
673	#117	—	2	1	no	—
674	#117	—	2	1	no	—
675	#117	—	2	1	no	—
676	#117	—	2	1	no	—
677	#117	—	2	1	no	—
678	#117	—	2	1	no	—
679	#117	—	2	1	no	—
680	#117	—	26	2	no	—
681	#117	—	52	1	no	—
682	#117	C₂×Dic₁₃	1	1	yes	characteristic
683	#117	C₂×Dic₁₃	1	1	yes	characteristic
684	#117	C₂×Dic₁₃	1	1	yes	characteristic, complemented
685	#117	C₂×Dic₁₃	1	1	yes	characteristic, complemented
686	#117	C₂²×D₁₃	1	1	yes	characteristic
687	#117	C₂²×D₁₃	1	1	yes	characteristic
688	#117	C₂²×D₁₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	—	26	1	no	—
690	C₂×C₄⋊C₄	—	26	1	no	—
691	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic, complemented
694	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic, complemented
695	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	—	2	1	no	—
697	C₂×C₂²⋊C₄	—	2	1	no	—
698	C₂×C₂²⋊C₄	—	26	1	no	—
699	C₂×C₂²⋊C₄	—	26	1	no	—
700	C₂×C₂²⋊C₄	—	26	1	no	—
701	C₂×C₂²⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
703	C₂×C₄²	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	—	13	1	no	—
707	C₂×C₄²	—	13	1	no	—
708	C₂×C₄²	—	13	1	no	—
709	C₂×C₄²	—	13	1	no	—
710	C₂×C₄²	—	26	2	no	—
711	C₂×C₄²	—	26	1	no	—
712	C₂×C₄²	—	52	1	no	—
713	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
714	C₄⋊C₈	—	26	1	no	—
715	C₄⋊C₈	—	26	1	no	—
716	#104	—	26	2	no	—
717	#104	—	26	2	no	—
718	#104	—	52	1	no	—
719	#104	—	52	1	no	—
720	C₂²⋊C₈	—	26	1	no	—
721	C₂²⋊C₈	—	26	1	no	—
722	C₂²⋊C₈	—	26	1	no	—
723	C₂²⋊C₈	—	26	1	no	—
724	#97	—	26	1	no	—
725	C₄×C₈	—	26	1	no	—
726	#95	—	26	1	no	—
727	#95	—	26	1	no	—
728	#95	—	26	1	no	—
729	#95	—	26	1	no	—
730	#95	—	26	1	no	—
731	C₂×C₁₃	—	2	1	no	—
732	C₂×C₁₃	—	2	1	no	—
733	C₂×C₁₃	—	2	2	no	—
734	C₂×C₁₃	—	4	1	no	—
735	C₂×C₁₃	—	4	1	no	—
736	C₂×C₁₃	—	4	1	no	—
737	C₂×C₁₃	—	8	1	no	—
738	C₂×C₁₃	#2339	1	1	yes	characteristic
739	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
740	C₂×C₁₃	#2901	1	1	yes	characteristic
741	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
742	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
743	#41	—	2	1	no	—
744	#41	—	2	1	no	—
745	#41	—	2	1	no	—
746	#41	—	2	1	no	—
747	#41	—	4	4	no	—
748	C₂×Q₈	—	2	1	no	—
749	C₂×Q₈	—	2	1	no	—
750	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
758	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
759	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
760	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
761	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	26	1	no	—
778	C₂²×C₄	—	26	1	no	—
779	C₂²×C₄	—	26	1	no	—
780	C₂²×C₄	—	26	1	no	—
781	C₂²×C₄	—	52	2	no	—
782	C₂²×C₄	—	52	2	no	—
783	C₂²×C₄	—	52	2	no	—
784	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
791	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
792	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
797	M₁₆	—	13	2	no	—
798	M₁₆	—	26	1	no	—
799	M₁₆	—	26	1	no	—
800	M₁₆	—	26	1	no	—
801	M₁₆	—	26	1	no	—
802	M₁₆	—	26	1	no	—
803	M₁₆	—	26	1	no	—
804	M₁₆	—	26	1	no	—
805	M₁₆	—	52	2	no	—
806	M₁₆	—	52	2	no	—
807	C₂×C₈	—	26	1	no	—
808	C₂×C₈	—	26	1	no	—
809	C₂×C₈	—	26	1	no	—
810	C₂×C₈	—	26	1	no	—
811	C₂×C₈	—	52	2	no	—
812	C₂×C₈	—	52	2	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	52	2	no	—
830	C₄⋊C₄	—	52	2	no	—
831	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
833	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
834	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
838	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
839	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
840	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
841	C₂²⋊C₄	—	2	1	no	—
842	C₂²⋊C₄	—	2	1	no	—
843	C₂²⋊C₄	—	2	1	no	—
844	C₂²⋊C₄	—	2	1	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	1	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	1	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	1	no	—
855	C₂²⋊C₄	—	2	1	no	—
856	C₂²⋊C₄	—	2	1	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	52	2	no	—
859	C₂²⋊C₄	—	52	2	no	—
860	C₂²⋊C₄	—	52	2	no	—
861	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
869	C₄²	—	2	1	no	—
870	C₄²	—	2	1	no	—
871	C₄²	—	2	1	no	—
872	C₄²	—	2	1	no	—
873	C₄²	—	2	1	no	—
874	C₄²	—	2	1	no	—
875	C₄²	—	2	1	no	—
876	C₄²	—	2	1	no	—
877	C₄²	—	2	1	no	—
878	C₄²	—	13	2	no	—
879	C₄²	—	26	1	no	—
880	C₄²	—	26	1	no	—
881	C₄²	—	26	1	no	—
882	C₄²	—	26	1	no	—
883	C₄²	—	26	1	no	—
884	C₄²	—	26	1	no	—
885	C₄²	—	26	1	no	—
886	C₄²	—	52	2	no	—
887	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
888	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
889	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
890	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
891	C₁₃	#22506	1	1	yes	characteristic, complemented, Sylow
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	1	no	—
901	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
902	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
903	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
904	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
905	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
906	Q₈	—	2	1	no	—
907	Q₈	—	2	1	no	—
908	Q₈	—	4	2	no	—
909	Q₈	—	8	1	no	—
910	D₄	—	2	2	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	1	no	—
913	D₄	—	2	1	no	—
914	D₄	—	4	1	no	—
915	D₄	—	4	1	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	1	no	—
918	D₄	—	4	1	no	—
919	D₄	—	4	2	no	—
920	D₄	—	8	1	no	—
921	D₄	—	8	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	4	1	no	—
950	C₂×C₄	—	4	1	no	—
951	C₂×C₄	—	4	2	no	—
952	C₂×C₄	—	4	2	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	4	1	no	—
955	C₂×C₄	—	4	1	no	—
956	C₂×C₄	—	8	1	no	—
957	C₂×C₄	—	8	1	no	—
958	C₂×C₄	—	8	1	no	—
959	C₂×C₄	—	26	2	no	—
960	C₂×C₄	—	26	2	no	—
961	C₂×C₄	—	52	1	no	—
962	C₂×C₄	—	52	1	no	—
963	C₂×C₄	—	52	1	no	—
964	C₂×C₄	—	52	8	no	—
965	C₂×C₄	—	52	1	no	—
966	C₂×C₄	—	52	1	no	—
967	C₂×C₄	—	52	1	no	—
968	C₂×C₄	—	52	1	no	—
969	C₂×C₄	—	52	1	no	—
970	C₂×C₄	—	52	1	no	—
971	C₂×C₄	—	52	1	no	—
972	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
973	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
974	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
975	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
976	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
977	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
978	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
979	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
980	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
981	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
982	C₂×C₄	#88256	1	1	yes	characteristic
983	C₂×C₄	#88257	1	1	yes	characteristic
984	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
985	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
986	C₈	—	26	2	no	—
987	C₈	—	52	1	no	—
988	C₈	—	52	1	no	—
989	C₈	—	52	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	8	1	no	—
1009	C₂²	—	8	1	no	—
1010	C₂²	#11718897	1	2	yes	—
1011	C₂²	#11719529	1	1	yes	characteristic
1012	C₂²	#11719534	1	1	yes	characteristic
1013	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	1	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	52	2	no	—
1030	C₄	—	52	2	no	—
1031	C₄	—	104	1	no	—
1032	C₄	—	104	1	no	—
1033	C₄	#11719529	1	1	yes	characteristic
1034	C₄	#41×Dic₁₃	1	1	yes	characteristic
1035	C₄	#11719532	1	1	yes	characteristic
1036	C₄	#11719534	1	1	yes	characteristic
1037	C₂	—	2	1	no	—
1038	C₂	—	2	1	no	—
1039	C₂	—	2	2	no	—
1040	C₂	—	4	1	no	—
1041	C₂	—	4	1	no	—
1042	C₂	—	4	1	no	—
1043	C₂	—	8	1	no	—
1044	C₂	#13117666	1	1	yes	characteristic
1045	C₂	C₂×#11718897	1	1	yes	characteristic
1046	C₂	#13123383	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3475	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#3475	D₁₃
hypocenter	C₁₃	#22506
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. D₄×#6099	C₂	semidirect
2. #13117281	C₂	semidirect
3. #13115818	C₂	semidirect
4. #13115781	C₂	semidirect
5. #13115285	C₂	semidirect
6. #13115280	C₂	semidirect
7. #13115139	C₂	semidirect
8. #13115139	C₂	semidirect
9. #13114935	C₂	semidirect
10. #13114935	C₂	semidirect
11. #13114856	C₂	semidirect
12. #13114646	C₂	semidirect
13. #13114545	C₂	semidirect
14. C₂×#11718124	C₂	semidirect
16. C₁₃×#556	C₄	semidirect
17. C₁₃×#555	C₄	semidirect
18. C₁₃×#554	C₄	semidirect
19. C₁₃×#553	C₄	semidirect
20. C₁₃×#553	C₄	semidirect
22. C₁₃×#552	C₄	semidirect
23. C₁₃×#552	C₄	semidirect
26. C₁₃×#547	C₄	semidirect
81. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
82. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
92. C₁₃×#125	C₂×C₄	semidirect
93. C₁₃×#125	C₂×C₄	semidirect
112. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
113. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
119. C₁₃×#121	C₂×C₄	semidirect
120. C₁₃×#121	C₂×C₄	semidirect
126. C₄×Q₈×C₁₃	C₂×C₄	semidirect
127. C₄×Q₈×C₁₃	C₂×C₄	semidirect
141. C₄×D₄×C₁₃	C₂×C₄	semidirect
142. C₄×D₄×C₁₃	C₂×C₄	semidirect
157. C₁₃×#117	C₂×C₄	semidirect
158. C₁₃×#117	C₂×C₄	semidirect
164. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
165. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
352. C₄×Dic₁₃	#41	semidirect
362. #6099	#41	semidirect
484. #556	Dic₁₃	semidirect
485. #555	Dic₁₃	semidirect
486. #554	Dic₁₃	semidirect
487. #553	Dic₁₃	semidirect
488. #553	Dic₁₃	semidirect
490. #552	Dic₁₃	semidirect
491. #552	Dic₁₃	semidirect
494. #547	Dic₁₃	semidirect
606. C₄⋊Q₈	C₂×Dic₁₃	semidirect
607. C₄⋊Q₈	C₂×Dic₁₃	semidirect
617. #125	C₂×Dic₁₃	semidirect
618. #125	C₂×Dic₁₃	semidirect
637. C₂²⋊Q₈	C₂×Dic₁₃	semidirect
638. C₂²⋊Q₈	C₂×Dic₁₃	semidirect
644. #121	C₂×Dic₁₃	semidirect
645. #121	C₂×Dic₁₃	semidirect
651. C₄×Q₈	C₂×Dic₁₃	semidirect
652. C₄×Q₈	C₂×Dic₁₃	semidirect
666. C₄×D₄	C₂×Dic₁₃	semidirect
667. C₄×D₄	C₂×Dic₁₃	semidirect
684. #117	C₂×Dic₁₃	semidirect
685. #117	C₂×Dic₁₃	semidirect
693. C₂×C₄⋊C₄	C₂×Dic₁₃	semidirect
694. C₂×C₄⋊C₄	C₂×Dic₁₃	semidirect
891. C₁₃	#22506	semidirect

Maximal subgroups

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

subgroup	index
D₄×#6099	2
#13117281	2
#13115818	2
#13115781	2
#13115285	2
#13115280	2
#13115139	2
#13114935	2
#13114856	2
#13114646	2
#13114545	2
C₂×#11718124	2
C₁₃×#3475	2
#22506	13