Subgroups — #16727322

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128239	C₂	1	1	yes	maximal, characteristic
2	#13123785	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123784	C₂	1	2	yes	maximal, complemented
4	#13123783	C₂	1	1	yes	maximal, characteristic, complemented
5	#13123782	C₂	1	1	yes	maximal, characteristic, complemented
6	#13123782	C₂	1	1	yes	maximal, characteristic, complemented
7	#13123781	C₂	1	2	yes	maximal, complemented
8	#13123781	C₂	1	2	yes	maximal, complemented
9	#13123780	C₂	1	1	yes	maximal, characteristic, complemented
10	#13123780	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123779	C₂	1	1	yes	maximal, characteristic, complemented
12	#13123778	C₂	1	2	yes	maximal, complemented
13	#13123772	C₂	1	2	yes	maximal, complemented
14	#13123772	C₂	1	2	yes	maximal, complemented
15	#13123767	C₂	1	2	yes	maximal, complemented
16	#13123765	C₂	1	2	yes	maximal, complemented
17	#13123397	C₂	1	1	yes	maximal, characteristic
18	C₂×#11718500	C₂	1	1	yes	maximal, characteristic
19	D₁₃×#424	C₂	1	1	yes	maximal, characteristic
20	#13123253	C₂	1	1	yes	maximal, characteristic
21	#13123252	C₂	1	1	yes	maximal, characteristic
22	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
23	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
26	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
27	C₂²×#6094	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	#11719434	C₄	1	1	yes	characteristic
30	#11719434	C₄	1	1	yes	characteristic
31	#11719434	C₄	1	1	yes	characteristic
32	#11719434	C₄	1	1	yes	characteristic
33	#11719394	C₄	1	1	yes	characteristic
34	#11719394	C₄	1	1	yes	characteristic
35	#11719394	C₄	1	1	yes	characteristic
36	#11719394	C₄	1	1	yes	characteristic
37	#11719339	C₄	1	2	yes	—
38	#11719339	C₄	1	2	yes	—
39	#11719328	C₄	1	2	yes	—
40	#11719328	C₄	1	2	yes	—
41	#11719283	C₂²	1	2	yes	—
42	#11719283	C₂²	1	2	yes	—
43	#11719283	C₂²	1	2	yes	—
44	#11719283	C₂²	1	2	yes	—
45	D₁₃×#117	C₂²	1	1	yes	characteristic
46	D₁₃×#117	C₂²	1	1	yes	characteristic
47	#11719222	C₂²	1	1	yes	characteristic
48	#11719222	C₂²	1	1	yes	characteristic
49	C₂×#88126	C₂²	1	1	yes	characteristic
50	#11719175	C₂²	1	1	yes	characteristic
51	C₁₃×#446	C₂²	1	2	yes	complemented
52	C₁₃×#446	C₂²	1	2	yes	complemented
53	C₁₃×#446	C₂²	1	2	yes	complemented
54	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
55	C₁₃×#424	C₂²	1	1	yes	characteristic
56	C₁₃×#424	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₁₃×#405	C₂²	1	1	yes	characteristic
60	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
61	#11718783	C₂²	1	1	yes	characteristic
62	#11718783	C₂²	1	1	yes	characteristic
63	#11718780	C₂²	1	1	yes	characteristic
64	#11718780	C₂²	1	1	yes	characteristic
65	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
66	M₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
67	#11718763	C₂²	1	1	yes	characteristic
68	#11718763	C₂²	1	1	yes	characteristic
69	#11718762	C₂²	1	1	yes	characteristic
70	#11718762	C₂²	1	1	yes	characteristic
71	C₂×#88054	C₂²	1	1	yes	characteristic
72	C₂×#88054	C₂²	1	1	yes	characteristic
73	#11718685	C₂²	1	2	yes	complemented
74	#11718685	C₂²	1	2	yes	complemented
75	#11718685	C₂²	1	2	yes	complemented
76	Q₈×#1055	C₂²	1	2	yes	complemented
77	#11718660	C₂²	1	1	yes	characteristic
78	#11718660	C₂²	1	1	yes	characteristic
79	#11718658	C₂²	1	1	yes	characteristic
80	#11718658	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
82	C₄×#6099	C₂²	1	1	yes	characteristic
83	#11718500	C₂²	1	2	yes	—
84	#11718500	C₂²	1	2	yes	—
85	#11718500	C₂²	1	1	yes	characteristic
86	#11718500	C₂²	1	1	yes	characteristic
87	#11718500	C₂²	1	1	yes	characteristic
88	#11718500	C₂²	1	1	yes	characteristic
89	#11718500	C₂²	1	1	yes	characteristic
90	#11718500	C₂²	1	1	yes	characteristic
91	#11718500	C₂²	1	1	yes	characteristic
92	#11718500	C₂²	1	1	yes	characteristic
93	#11718500	C₂²	1	2	yes	—
94	#11718500	C₂²	1	2	yes	—
95	#11718498	C₂²	1	2	yes	—
96	#11718498	C₂²	1	2	yes	—
97	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
98	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
99	#11718492	C₂²	1	2	yes	complemented
100	#11718492	C₂²	1	2	yes	complemented
101	#11718492	C₂²	1	2	yes	complemented
102	#11718491	C₂²	1	2	yes	complemented
103	#11718491	C₂²	1	2	yes	complemented
104	#11718491	C₂²	1	2	yes	complemented
105	#11718489	C₂²	1	2	yes	complemented
106	#11718489	C₂²	1	2	yes	complemented
107	#11718489	C₂²	1	2	yes	complemented
108	#11718489	C₂²	1	2	yes	complemented
109	#11718489	C₂²	1	2	yes	complemented
110	#11718489	C₂²	1	2	yes	complemented
111	#11718369	C₂²	1	2	yes	—
112	#11718369	C₂²	1	2	yes	—
113	#11718369	C₂²	1	2	yes	—
114	#11718369	C₂²	1	2	yes	—
115	#11718368	C₂²	1	2	yes	—
116	D₁₃×#97	C₂²	1	2	yes	—
117	#11718362	C₂²	1	2	yes	complemented
118	#11718362	C₂²	1	2	yes	complemented
119	#11718362	C₂²	1	2	yes	complemented
120	#11718362	C₂²	1	2	yes	complemented
121	#11718362	C₂²	1	2	yes	complemented
122	#11718362	C₂²	1	2	yes	complemented
123	#11718350	C₂²	1	2	yes	—
124	#11718350	C₂²	1	2	yes	—
125	#11718350	C₂²	1	2	yes	—
126	#11718350	C₂²	1	2	yes	—
127	C₄×#6094	C₂²	1	2	yes	—
128	C₄×C₈×D₁₃	C₂²	1	2	yes	—
129	#11718340	C₂²	1	2	yes	complemented
130	#11718340	C₂²	1	2	yes	complemented
131	#11718340	C₂²	1	2	yes	complemented
132	C₈×Dic₂₆	C₂²	1	2	yes	complemented
133	C₈×Dic₂₆	C₂²	1	2	yes	complemented
134	C₈×Dic₂₆	C₂²	1	2	yes	complemented
135	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
142	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
143	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
144	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
146	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
148	C₁₃×#117	C₂³	1	1	yes	characteristic
149	C₁₃×#117	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	#88200	C₂×C₄	1	2	yes	—
152	#88200	C₂×C₄	1	2	yes	—
153	#88200	C₂×C₄	1	2	yes	—
154	#88200	C₂×C₄	1	2	yes	—
155	#88198	C₂×C₄	1	2	yes	—
156	#88198	C₂×C₄	1	2	yes	—
157	#88198	C₂×C₄	1	2	yes	—
158	#88198	C₂×C₄	1	2	yes	—
159	C₂×#6103	C₂×C₄	1	1	yes	characteristic
160	C₂×#6103	C₂×C₄	1	1	yes	characteristic
161	#88180	C₂³	1	1	yes	characteristic
162	#88180	C₂³	1	1	yes	characteristic
163	#88178	C₂×C₄	1	2	yes	—
164	#88178	C₂×C₄	1	2	yes	—
165	C₂×#6101	C₂×C₄	1	1	yes	characteristic
166	C₂×#6101	C₂×C₄	1	1	yes	characteristic
167	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
168	C₂×#6099	C₂³	1	1	yes	characteristic
169	C₂×#6099	C₂³	1	1	yes	characteristic
170	C₂²×#1055	C₂³	1	1	yes	characteristic
171	C₂²×#1055	C₂³	1	1	yes	characteristic
172	M₁₆×D₁₃	—	2	4	no	—
173	M₁₆×D₁₃	Q₈	1	8	yes	complemented
174	C₂×#6094	—	2	4	no	—
175	C₂×#6094	C₂³	1	1	yes	characteristic
176	C₂×#6094	C₂³	1	1	yes	characteristic
177	C₂×#6094	C₂³	1	1	yes	characteristic
178	C₂×#6094	C₂³	1	1	yes	characteristic
179	C₂×#6094	C₂³	1	2	yes	—
180	C₂×#6094	C₂³	1	2	yes	—
181	C₂×C₈×D₁₃	—	2	4	no	—
182	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₈×D₁₃	C₂³	1	2	yes	—
187	C₂×C₈×D₁₃	C₂³	1	2	yes	—
188	#88151	C₂×C₄	1	2	yes	—
189	#88151	C₂×C₄	1	2	yes	—
190	#88151	C₂×C₄	1	2	yes	—
191	#88151	C₂×C₄	1	2	yes	—
192	#88150	C₂×C₄	1	2	yes	—
193	#88150	C₂×C₄	1	2	yes	—
194	#88150	C₂×C₄	1	2	yes	—
195	#88150	C₂×C₄	1	2	yes	—
196	#88150	C₂×C₄	1	2	yes	—
197	#88150	C₂×C₄	1	2	yes	—
198	#88150	C₂×C₄	1	2	yes	—
199	#88150	C₂×C₄	1	2	yes	—
200	#88146	C₂×C₄	1	1	yes	characteristic
201	#88146	C₂×C₄	1	1	yes	characteristic
202	#88146	C₂×C₄	1	1	yes	characteristic
203	#88146	C₂×C₄	1	1	yes	characteristic
204	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
205	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
206	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
207	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
208	#88144	C₂×C₄	1	1	yes	characteristic
209	#88144	C₂×C₄	1	1	yes	characteristic
210	#88144	C₂×C₄	1	1	yes	characteristic
211	#88144	C₂×C₄	1	1	yes	characteristic
212	#88143	C₂×C₄	1	2	yes	—
213	#88143	C₂×C₄	1	2	yes	—
214	#88143	C₂×C₄	1	2	yes	—
215	#88143	C₂×C₄	1	2	yes	—
216	#88143	C₂×C₄	1	2	yes	—
217	#88143	C₂×C₄	1	2	yes	—
218	#88143	C₂×C₄	1	2	yes	—
219	#88143	C₂×C₄	1	2	yes	—
220	#88142	C₂×C₄	1	1	yes	characteristic
221	#88142	C₂×C₄	1	1	yes	characteristic
222	#88142	C₂×C₄	1	1	yes	characteristic
223	#88142	C₂×C₄	1	1	yes	characteristic
224	#88142	C₂×C₄	1	2	yes	—
225	#88142	C₂×C₄	1	2	yes	—
226	#88142	C₂×C₄	1	2	yes	—
227	#88142	C₂×C₄	1	2	yes	—
228	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
229	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
230	#88132	C₂×C₄	1	2	yes	—
231	#88132	C₂×C₄	1	2	yes	—
232	#88132	C₂×C₄	1	2	yes	—
233	#88132	C₂×C₄	1	2	yes	—
234	#88131	C₂×C₄	1	2	yes	—
235	#88131	C₂×C₄	1	2	yes	—
236	#88126	C₂×C₄	1	1	yes	characteristic
237	#88126	C₂×C₄	1	1	yes	characteristic
238	#88126	C₂×C₄	1	1	yes	characteristic
239	#88126	C₂×C₄	1	1	yes	characteristic
240	#88126	C₂³	1	1	yes	characteristic
241	#88126	C₂³	1	1	yes	characteristic
242	#88126	C₂³	1	1	yes	characteristic
243	#88126	C₂³	1	1	yes	characteristic
244	#88126	C₂³	1	2	yes	—
245	#88126	C₂³	1	2	yes	—
246	C₄²×D₁₃	C₂³	1	2	yes	—
247	C₄²×D₁₃	C₂³	1	2	yes	—
248	#88124	C₂×C₄	1	1	yes	characteristic
249	#88124	C₂×C₄	1	1	yes	characteristic
250	#88123	C₂×C₄	1	1	yes	characteristic
251	#88123	C₂×C₄	1	1	yes	characteristic
252	C₄×Dic₂₆	C₂³	1	2	yes	—
253	C₄×Dic₂₆	C₂³	1	2	yes	—
254	C₄×Dic₂₆	C₂³	1	2	yes	—
255	C₄×Dic₂₆	C₂³	1	2	yes	—
256	C₄×Dic₂₆	C₂³	1	2	yes	—
257	C₄×Dic₂₆	C₂³	1	2	yes	—
258	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₁₃×#97	C₂³	1	2	yes	—
267	C₁₃×#97	C₂³	1	2	yes	—
268	C₁₃×#97	C₂³	1	2	yes	—
269	C₄×C₈×C₁₃	C₂³	1	2	yes	—
270	C₄×C₈×C₁₃	C₂³	1	2	yes	—
271	C₄×C₈×C₁₃	C₂³	1	2	yes	—
272	#88055	C₂³	1	2	yes	—
273	#88055	C₂³	1	2	yes	—
274	#88055	C₂³	1	2	yes	—
275	#88055	C₂³	1	2	yes	—
276	#88055	C₂³	1	2	yes	—
277	#88055	C₂³	1	2	yes	—
278	#88054	C₂³	1	2	yes	—
279	#88054	C₂³	1	2	yes	—
280	#88054	C₂³	1	1	yes	characteristic
281	#88054	C₂³	1	1	yes	characteristic
282	#88054	C₂³	1	1	yes	characteristic
283	#88054	C₂³	1	1	yes	characteristic
284	#88054	C₂³	1	2	yes	—
285	#88054	C₂³	1	2	yes	—
286	#88054	C₂³	1	2	yes	—
287	#88054	C₂³	1	2	yes	—
288	#88054	C₂³	1	1	yes	characteristic
289	#88054	C₂³	1	1	yes	characteristic
290	#88054	C₂³	1	2	yes	—
291	#88054	C₂³	1	2	yes	—
292	#88054	C₂³	1	1	yes	characteristic
293	#88054	C₂³	1	1	yes	characteristic
294	C₈×Dic₁₃	C₂³	1	2	yes	—
295	C₈×Dic₁₃	C₂³	1	2	yes	—
296	C₈×Dic₁₃	C₂³	1	2	yes	—
297	C₈×Dic₁₃	C₂³	1	2	yes	—
298	C₈×Dic₁₃	C₂³	1	2	yes	—
299	C₈×Dic₁₃	C₂³	1	2	yes	—
300	C₄⋊#1055	C₂³	1	2	yes	—
301	C₄⋊#1055	C₂³	1	2	yes	—
302	C₄⋊#1055	C₂³	1	2	yes	—
303	C₄⋊#1055	C₂³	1	2	yes	—
304	C₄⋊#1055	C₂³	1	1	yes	characteristic
305	C₄⋊#1055	C₂³	1	1	yes	characteristic
306	C₄⋊#1055	C₂³	1	1	yes	characteristic
307	C₄⋊#1055	C₂³	1	1	yes	characteristic
308	#88043	C₂³	1	2	yes	—
309	#88043	C₂³	1	2	yes	—
310	#88043	C₂³	1	2	yes	—
311	C₄×#1055	C₂³	1	2	yes	—
312	C₄×#1055	C₂³	1	2	yes	—
313	C₄×#1055	C₂³	1	2	yes	—
314	#60193	—	13	1	no	maximal, Sylow
315	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
317	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
322	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
323	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
325	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
326	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
327	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
328	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
329	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
330	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
331	C₂×C₄×D₁₃	#41	1	4	yes	—
332	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
335	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
336	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
337	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
338	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
339	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
340	C₁₃×M₁₆	—	2	2	no	—
341	C₁₃×M₁₆	C₂×Q₈	1	4	yes	—
342	C₂×C₈×C₁₃	—	2	2	no	—
343	C₂×C₈×C₁₃	—	2	2	no	—
344	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
347	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
350	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
351	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
352	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
353	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
354	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
355	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
356	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
357	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
358	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
360	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
361	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
362	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
363	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
364	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₄²×C₁₃	C₂⁴	1	2	yes	—
366	C₄²×C₁₃	C₂⁴	1	2	yes	—
367	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
369	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
370	#6103	C₂²×C₄	1	1	yes	characteristic
371	#6103	C₂²×C₄	1	1	yes	characteristic
372	#6103	C₂²×C₄	1	1	yes	characteristic
373	#6103	C₂²×C₄	1	1	yes	characteristic
374	#6103	C₂²×C₄	1	1	yes	characteristic
375	#6103	C₂²×C₄	1	1	yes	characteristic
376	#6103	C₂²×C₄	1	1	yes	characteristic
377	#6103	C₂²×C₄	1	1	yes	characteristic
378	#6103	C₂²×C₄	1	2	yes	—
379	#6103	C₂²×C₄	1	2	yes	—
380	#6103	C₂²×C₄	1	2	yes	—
381	#6103	C₂²×C₄	1	2	yes	—
382	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
383	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
384	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
385	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
386	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
387	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
388	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
390	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
392	#6101	C₂²×C₄	1	2	yes	—
393	#6101	C₂²×C₄	1	2	yes	—
394	#6101	C₂²×C₄	1	2	yes	—
395	#6101	C₂²×C₄	1	2	yes	—
396	#6101	C₂²×C₄	1	2	yes	—
397	#6101	C₂²×C₄	1	2	yes	—
398	#6101	C₂²×C₄	1	2	yes	—
399	#6101	C₂²×C₄	1	2	yes	—
400	#6101	C₂²×C₄	1	2	yes	—
401	#6101	C₂²×C₄	1	2	yes	—
402	#6101	C₂²×C₄	1	2	yes	—
403	#6101	C₂²×C₄	1	2	yes	—
404	#6101	C₂²×C₄	1	1	yes	characteristic
405	#6101	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	1	yes	characteristic
411	#6101	C₂²×C₄	1	1	yes	characteristic
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	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
417	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
418	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
419	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
420	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₁₃	C₂⁴	1	2	yes	—
423	C₄×Dic₁₃	C₂⁴	1	2	yes	—
424	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
425	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
426	#6099	—	2	2	no	—
427	#6099	C₂×Q₈	1	4	yes	—
428	C₂×#1055	—	2	2	no	—
429	C₂×#1055	—	2	2	no	—
430	C₂×#1055	C₂⁴	1	1	yes	characteristic
431	C₂×#1055	C₂⁴	1	1	yes	characteristic
432	C₂×#1055	C₂⁴	1	2	yes	—
433	C₂×#1055	C₂⁴	1	1	yes	characteristic
434	C₂×#1055	C₂⁴	1	1	yes	characteristic
435	C₂×#1055	C₂⁴	1	2	yes	—
436	#6094	—	2	2	no	—
437	#6094	—	2	2	no	—
438	#6094	—	2	2	no	—
439	#6094	—	2	2	no	—
440	#6094	—	2	4	no	—
441	#6094	C₂×Q₈	1	8	yes	—
442	C₈×D₁₃	—	2	2	no	—
443	C₈×D₁₃	—	2	2	no	—
444	C₈×D₁₃	—	2	2	no	—
445	C₈×D₁₃	—	2	2	no	—
446	C₈×D₁₃	—	2	4	no	—
447	C₈×D₁₃	C₂×Q₈	1	8	yes	—
448	#3458	—	13	1	no	—
449	#2962	—	13	2	no	—
450	#2962	—	13	2	no	—
451	#2962	—	13	2	no	—
452	#2962	—	13	2	no	—
453	#2962	—	13	1	no	—
454	#2962	—	13	1	no	—
455	#2962	—	13	1	no	—
456	#2962	—	13	1	no	—
457	#2962	—	13	1	no	—
458	#2962	—	13	1	no	—
459	#2962	—	13	1	no	—
460	#2962	D₁₃	1	1	yes	characteristic, complemented
461	#2961	—	13	2	no	—
462	#2961	—	13	2	no	—
463	#2960	—	13	2	no	—
464	#2960	—	13	2	no	—
465	#2905	—	13	1	no	—
466	C₂×#424	—	13	1	no	—
467	C₂×#424	—	13	1	no	—
468	#2873	—	13	1	no	—
469	#2873	—	13	1	no	—
470	C₂×#405	—	13	1	no	—
471	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
472	C₂²×D₁₃	—	4	1	no	—
473	C₂²×D₁₃	—	4	1	no	—
474	C₂²×D₁₃	C₄×Q₈	1	4	yes	—
475	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
476	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
477	Q₈×C₁₃	—	4	2	no	—
478	Q₈×C₁₃	—	4	2	no	—
479	C₂×C₄×C₁₃	—	4	1	no	—
480	C₂×C₄×C₁₃	—	4	1	no	—
481	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
484	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
485	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
486	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
487	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
491	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
492	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
493	C₂×Dic₁₃	—	4	1	no	—
494	C₂×Dic₁₃	—	4	1	no	—
495	C₂×Dic₁₃	C₄×Q₈	1	4	yes	—
496	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
498	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
499	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
500	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
501	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
502	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
503	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
504	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
505	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
506	C₄×D₁₃	—	4	2	no	—
507	C₄×D₁₃	—	4	2	no	—
508	C₄×D₁₃	—	4	2	no	—
509	C₄×D₁₃	—	4	2	no	—
510	C₄×D₁₃	C₄×Q₈	1	4	yes	—
511	C₄×D₁₃	C₄×Q₈	1	4	yes	—
512	C₄×D₁₃	C₂²×Q₈	1	2	yes	—
513	C₄×D₁₃	C₂²×Q₈	1	2	yes	—
514	C₄×D₁₃	C₂×#41	1	2	yes	—
515	C₄×D₁₃	C₂×#41	1	2	yes	—
516	Dic₂₆	—	4	2	no	—
517	Dic₂₆	—	4	2	no	—
518	Dic₂₆	—	4	2	no	—
519	Dic₂₆	—	4	2	no	—
520	Dic₂₆	—	4	2	no	—
521	Dic₂₆	—	4	2	no	—
522	C₈×C₁₃	—	2	1	no	—
523	C₈×C₁₃	—	2	1	no	—
524	C₈×C₁₃	—	2	2	no	—
525	C₈×C₁₃	—	2	1	no	—
526	C₈×C₁₃	—	2	1	no	—
527	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
528	#1055	—	2	1	no	—
529	#1055	—	2	1	no	—
530	#1055	—	2	2	no	—
531	#1055	—	2	1	no	—
532	#1055	—	2	1	no	—
533	#1055	C₂²×Q₈	1	4	yes	—
534	C₂²×M₁₆	—	13	1	no	—
535	C₂²×M₁₆	—	13	1	no	—
536	C₂²×M₁₆	—	13	1	no	—
537	C₂³×C₈	—	13	1	no	—
538	#544	—	13	1	no	—
539	#544	—	13	1	no	—
540	#544	—	13	1	no	—
541	#544	—	13	1	no	—
542	#544	—	13	1	no	—
543	#544	—	13	1	no	—
544	#544	—	13	1	no	—
545	#544	—	13	1	no	—
546	#544	—	13	2	no	—
547	#544	—	13	2	no	—
548	#543	—	13	2	no	—
549	#543	—	13	2	no	—
550	#533	—	13	2	no	—
551	#533	—	13	2	no	—
552	#533	—	13	2	no	—
553	#533	—	13	2	no	—
554	#533	—	13	1	no	—
555	#533	—	13	1	no	—
556	#533	—	13	1	no	—
557	#533	C₂×D₁₃	1	1	yes	characteristic
558	C₂×#117	—	13	1	no	—
559	C₂×#117	—	13	1	no	—
560	C₂×#117	—	13	1	no	—
561	#446	—	13	2	no	—
562	#446	—	13	2	no	—
563	#446	—	13	2	no	—
564	#446	—	13	2	no	—
565	#446	—	13	2	no	—
566	#446	—	13	2	no	—
567	#446	—	13	2	no	—
568	#446	—	13	2	no	—
569	#446	—	13	2	no	—
570	#446	—	13	2	no	—
571	#446	—	13	2	no	—
572	#446	—	13	2	no	—
573	#446	—	13	2	no	—
574	#446	—	13	2	no	—
575	#446	—	13	2	no	—
576	#446	—	13	2	no	—
577	#446	—	13	2	no	—
578	#446	—	13	2	no	—
579	#446	—	13	2	no	—
580	#446	—	13	2	no	—
581	#446	—	13	2	no	—
582	#446	C₂×D₁₃	1	2	yes	complemented
583	#446	C₂×D₁₃	1	2	yes	complemented
584	#446	C₂×D₁₃	1	2	yes	complemented
585	C₈×Q₈	—	13	2	no	—
586	C₈×Q₈	—	13	2	no	—
587	C₈×Q₈	—	13	2	no	—
588	C₈×Q₈	—	13	2	no	—
589	C₈×Q₈	—	13	2	no	—
590	C₈×Q₈	—	13	2	no	—
591	C₈×Q₈	—	13	2	no	—
592	C₈×Q₈	C₂×D₁₃	1	2	yes	complemented
593	#424	—	13	1	no	—
594	#424	—	13	1	no	—
595	#424	—	13	1	no	—
596	#424	—	13	1	no	—
597	#424	—	13	1	no	—
598	#424	—	13	1	no	—
599	#424	—	13	2	no	—
600	#424	—	13	1	no	—
601	#424	—	13	1	no	—
602	#424	—	13	2	no	—
603	#424	—	13	1	no	—
604	#424	—	13	1	no	—
605	#424	—	13	1	no	—
606	#424	—	13	1	no	—
607	#424	—	13	1	no	—
608	#424	—	13	1	no	—
609	#424	—	13	2	no	—
610	#424	—	13	2	no	—
611	#424	C₂×D₁₃	1	1	yes	characteristic
612	#424	C₂×D₁₃	1	1	yes	characteristic
613	#423	—	13	2	no	—
614	#423	—	13	2	no	—
615	C₂×C₄⋊C₈	—	13	1	no	—
616	C₂×C₄⋊C₈	—	13	1	no	—
617	C₂×C₄⋊C₈	—	13	1	no	—
618	C₂×C₄⋊C₈	—	13	2	no	—
619	C₂×C₄⋊C₈	—	13	2	no	—
620	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
621	#405	—	13	1	no	—
622	#405	—	13	1	no	—
623	#405	—	13	1	no	—
624	#405	—	13	1	no	—
625	#405	—	13	1	no	—
626	#405	—	13	1	no	—
627	#405	—	13	2	no	—
628	#405	—	13	2	no	—
629	#405	—	13	2	no	—
630	#405	—	13	2	no	—
631	#405	—	13	2	no	—
632	#405	—	13	2	no	—
633	#405	—	13	2	no	—
634	#405	—	13	2	no	—
635	#405	C₂×D₁₃	1	1	yes	characteristic
636	#405	C₂×D₁₃	1	1	yes	characteristic
637	C₄×M₁₆	—	13	1	no	—
638	C₄×M₁₆	—	13	1	no	—
639	C₄×M₁₆	—	13	1	no	—
640	C₄×M₁₆	—	13	2	no	—
641	C₄×M₁₆	—	13	2	no	—
642	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
643	C₂×#97	—	13	2	no	—
644	C₂×C₄×C₈	—	13	2	no	—
645	C₂²×C₁₃	—	2	1	no	—
646	C₂²×C₁₃	—	2	1	no	—
647	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
648	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
649	C₂×D₁₃	—	2	1	no	—
650	C₂×D₁₃	—	2	1	no	—
651	C₂×D₁₃	—	2	1	no	—
652	C₂×D₁₃	—	2	1	no	—
653	C₂×D₁₃	—	4	4	no	—
654	C₂×D₁₃	C₂×C₄×Q₈	1	2	yes	—
655	C₂×D₁₃	C₂×C₄×Q₈	1	2	yes	—
656	C₄×C₁₃	—	2	1	no	—
657	C₄×C₁₃	—	2	1	no	—
658	C₄×C₁₃	—	2	2	no	—
659	C₄×C₁₃	—	2	2	no	—
660	C₄×C₁₃	—	2	2	no	—
661	C₄×C₁₃	—	2	2	no	—
662	C₄×C₁₃	—	2	1	no	—
663	C₄×C₁₃	—	2	1	no	—
664	C₄×C₁₃	C₂×C₄×Q₈	1	2	yes	—
665	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
666	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
667	Dic₁₃	—	2	2	no	—
668	Dic₁₃	—	2	2	no	—
669	Dic₁₃	—	2	2	no	—
670	Dic₁₃	—	2	2	no	—
671	Dic₁₃	—	2	1	no	—
672	Dic₁₃	—	2	1	no	—
673	Dic₁₃	—	2	1	no	—
674	Dic₁₃	—	2	1	no	—
675	Dic₁₃	C₂×C₄×Q₈	1	2	yes	—
676	Dic₁₃	C₂×C₄×Q₈	1	2	yes	—
677	C₂³×C₄	—	13	1	no	—
678	C₂×M₁₆	—	13	1	no	—
679	C₂×M₁₆	—	13	8	no	—
680	C₂×M₁₆	—	13	1	no	—
681	C₂×M₁₆	—	13	2	no	—
682	C₂×M₁₆	—	13	1	no	—
683	C₂×M₁₆	—	13	1	no	—
684	C₂×M₁₆	—	13	1	no	—
685	C₂×M₁₆	—	13	2	no	—
686	C₂×M₁₆	—	13	1	no	—
687	C₂×M₁₆	—	26	4	no	—
688	C₂×M₁₆	—	26	4	no	—
689	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
690	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
691	C₂²×C₈	—	13	2	no	—
692	C₂²×C₈	—	13	1	no	—
693	C₂²×C₈	—	13	1	no	—
694	C₂²×C₈	—	13	1	no	—
695	C₂²×C₈	—	13	1	no	—
696	C₂²×C₈	—	13	1	no	—
697	C₂²×C₈	—	13	1	no	—
698	C₂²×C₈	—	13	2	no	—
699	C₂²×C₈	—	26	4	no	—
700	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
701	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
702	C₄⋊Q₈	—	13	2	no	—
703	C₄⋊Q₈	—	13	2	no	—
704	C₄⋊Q₈	—	13	2	no	—
705	C₄⋊Q₈	—	13	2	no	—
706	C₄⋊Q₈	—	13	2	no	—
707	C₄⋊Q₈	—	13	2	no	—
708	C₄⋊Q₈	—	13	2	no	—
709	C₄⋊Q₈	—	13	2	no	—
710	C₄⋊Q₈	—	13	1	no	—
711	C₄⋊Q₈	—	13	1	no	—
712	C₄⋊Q₈	—	13	1	no	—
713	C₄⋊Q₈	—	13	1	no	—
714	C₄⋊Q₈	—	13	1	no	—
715	C₄⋊Q₈	—	13	1	no	—
716	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
717	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
718	#125	—	13	2	no	—
719	#125	—	13	2	no	—
720	#125	—	13	2	no	—
721	#125	—	13	2	no	—
722	#125	—	13	2	no	—
723	#125	—	13	2	no	—
724	#125	—	13	2	no	—
725	#125	—	13	2	no	—
726	#125	—	13	1	no	—
727	#125	—	13	1	no	—
728	#125	—	13	1	no	—
729	#125	—	13	1	no	—
730	#125	—	13	1	no	—
731	#125	—	13	1	no	—
732	#125	C₄×D₁₃	1	1	yes	characteristic
733	#125	C₄×D₁₃	1	1	yes	characteristic
734	C₂²⋊Q₈	—	13	2	no	—
735	C₂²⋊Q₈	—	13	2	no	—
736	C₂²⋊Q₈	—	13	2	no	—
737	C₂²⋊Q₈	—	13	2	no	—
738	C₂²⋊Q₈	—	13	2	no	—
739	C₂²⋊Q₈	—	13	2	no	—
740	C₂²⋊Q₈	—	13	2	no	—
741	C₂²⋊Q₈	—	13	2	no	—
742	C₂²⋊Q₈	—	13	2	no	—
743	C₂²⋊Q₈	—	13	2	no	—
744	C₂²⋊Q₈	—	13	2	no	—
745	C₂²⋊Q₈	—	13	2	no	—
746	C₂²⋊Q₈	—	13	2	no	—
747	C₂²⋊Q₈	—	13	2	no	—
748	C₂²⋊Q₈	—	13	2	no	—
749	C₂²⋊Q₈	—	13	2	no	—
750	C₂²⋊Q₈	—	13	2	no	—
751	C₂²⋊Q₈	—	13	2	no	—
752	C₂²⋊Q₈	—	13	2	no	—
753	C₂²⋊Q₈	—	13	2	no	—
754	C₂²⋊Q₈	—	13	2	no	—
755	C₂²⋊Q₈	—	13	2	no	—
756	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
757	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
758	C₄×Q₈	—	13	2	no	—
759	C₄×Q₈	—	13	2	no	—
760	C₄×Q₈	—	13	2	no	—
761	C₄×Q₈	—	13	2	no	—
762	C₄×Q₈	—	13	2	no	—
763	C₄×Q₈	—	13	2	no	—
764	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
765	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
766	#117	—	13	1	no	—
767	#117	—	13	1	no	—
768	#117	—	13	1	no	—
769	#117	—	13	1	no	—
770	#117	—	13	1	no	—
771	#117	—	13	1	no	—
772	#117	—	13	2	no	—
773	#117	—	13	2	no	—
774	#117	—	13	1	no	—
775	#117	—	13	1	no	—
776	#117	—	13	1	no	—
777	#117	—	13	1	no	—
778	#117	—	13	1	no	—
779	#117	—	13	1	no	—
780	#117	—	13	2	no	—
781	#117	—	13	2	no	—
782	#117	—	13	1	no	—
783	#117	—	13	1	no	—
784	#117	C₂²×D₁₃	1	1	yes	characteristic
785	#117	C₂²×D₁₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	—	13	1	no	—
787	C₂×C₄⋊C₄	—	13	1	no	—
788	C₂×C₄⋊C₄	—	13	1	no	—
789	C₂×C₄⋊C₄	—	13	1	no	—
790	C₂×C₄⋊C₄	—	13	1	no	—
791	C₂×C₄⋊C₄	—	13	1	no	—
792	C₂×C₂²⋊C₄	—	13	1	no	—
793	C₂×C₂²⋊C₄	—	13	1	no	—
794	C₂×C₂²⋊C₄	—	13	2	no	—
795	C₂×C₂²⋊C₄	—	13	2	no	—
796	C₂×C₄²	—	13	1	no	—
797	C₂×C₄²	—	13	2	no	—
798	C₂×C₄²	—	13	2	no	—
799	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
800	C₄⋊C₈	—	13	1	no	—
801	C₄⋊C₈	—	13	2	no	—
802	C₄⋊C₈	—	13	1	no	—
803	C₄⋊C₈	—	13	1	no	—
804	C₄⋊C₈	—	13	1	no	—
805	C₄⋊C₈	—	13	2	no	—
806	C₄⋊C₈	—	13	1	no	—
807	C₄⋊C₈	—	13	1	no	—
808	C₄⋊C₈	—	13	2	no	—
809	C₄⋊C₈	—	13	1	no	—
810	C₄⋊C₈	—	13	2	no	—
811	C₄⋊C₈	—	13	1	no	—
812	C₄⋊C₈	—	13	2	no	—
813	C₄⋊C₈	—	13	2	no	—
814	C₄⋊C₈	—	13	2	no	—
815	C₄⋊C₈	—	13	2	no	—
816	C₄⋊C₈	—	13	1	no	—
817	C₄⋊C₈	—	13	2	no	—
818	C₄⋊C₈	—	13	1	no	—
819	C₄⋊C₈	—	13	1	no	—
820	C₄⋊C₈	—	13	2	no	—
821	C₄⋊C₈	—	13	1	no	—
822	C₄⋊C₈	—	13	2	no	—
823	C₄⋊C₈	—	13	2	no	—
824	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
825	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
826	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
828	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
829	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
830	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
831	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
832	#97	—	13	2	no	—
833	#97	—	13	2	no	—
834	#97	—	13	2	no	—
835	#97	—	13	2	no	—
836	#97	—	13	2	no	—
837	#97	—	13	2	no	—
838	#97	—	13	2	no	—
839	#97	—	13	2	no	—
840	#97	—	13	2	no	—
841	#97	C₂²×D₁₃	1	2	yes	—
842	#97	C₂²×D₁₃	1	2	yes	—
843	#97	C₂²×D₁₃	1	2	yes	—
844	C₄×C₈	—	13	2	no	—
845	C₄×C₈	—	13	2	no	—
846	C₄×C₈	—	13	2	no	—
847	C₄×C₈	—	13	2	no	—
848	C₄×C₈	—	13	2	no	—
849	C₄×C₈	—	13	2	no	—
850	C₄×C₈	—	13	2	no	—
851	C₄×C₈	—	13	2	no	—
852	C₄×C₈	—	13	2	no	—
853	C₄×C₈	C₂²×D₁₃	1	2	yes	—
854	C₄×C₈	C₂²×D₁₃	1	2	yes	—
855	C₄×C₈	C₂²×D₁₃	1	2	yes	—
856	C₂×C₁₃	—	2	2	no	—
857	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
858	C₂×C₁₃	#3573	1	1	yes	characteristic
859	C₂×C₁₃	#3573	1	1	yes	characteristic
860	D₁₃	—	2	2	no	—
861	D₁₃	—	2	2	no	—
862	C₂⁴	—	13	1	no	—
863	C₂×Q₈	—	13	2	no	—
864	C₂×Q₈	—	13	2	no	—
865	C₂×Q₈	—	13	2	no	—
866	C₂×Q₈	—	13	2	no	—
867	C₂×Q₈	—	13	2	no	—
868	C₂×Q₈	—	13	2	no	—
869	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
870	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
871	C₂²×C₄	—	13	1	no	—
872	C₂²×C₄	—	13	1	no	—
873	C₂²×C₄	—	13	1	no	—
874	C₂²×C₄	—	13	4	no	—
875	C₂²×C₄	—	13	4	no	—
876	C₂²×C₄	—	13	1	no	—
877	C₂²×C₄	—	13	1	no	—
878	C₂²×C₄	—	13	1	no	—
879	C₂²×C₄	—	13	1	no	—
880	C₂²×C₄	—	13	2	no	—
881	C₂²×C₄	—	13	2	no	—
882	C₂²×C₄	—	13	2	no	—
883	C₂²×C₄	—	13	2	no	—
884	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
885	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
886	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
887	M₁₆	—	2	2	no	—
888	M₁₆	—	13	4	no	—
889	M₁₆	—	13	8	no	—
890	M₁₆	—	26	2	no	—
891	M₁₆	—	26	2	no	—
892	M₁₆	—	26	2	no	—
893	M₁₆	—	26	2	no	—
894	M₁₆	—	26	4	no	—
895	M₁₆	—	26	2	no	—
896	M₁₆	Q₈×D₁₃	1	4	yes	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	13	2	no	—
900	C₂×C₈	—	13	8	no	—
901	C₂×C₈	—	13	1	no	—
902	C₂×C₈	—	13	1	no	—
903	C₂×C₈	—	13	2	no	—
904	C₂×C₈	—	13	1	no	—
905	C₂×C₈	—	13	1	no	—
906	C₂×C₈	—	26	2	no	—
907	C₂×C₈	—	26	2	no	—
908	C₂×C₈	—	26	2	no	—
909	C₂×C₈	—	26	2	no	—
910	C₂×C₈	—	26	4	no	—
911	C₂×C₈	—	26	2	no	—
912	C₂×C₈	—	26	2	no	—
913	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₁₃	1	2	yes	—
916	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
917	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
918	C₂×C₈	C₂³×D₁₃	1	2	yes	—
919	C₄⋊C₄	—	13	2	no	—
920	C₄⋊C₄	—	13	2	no	—
921	C₄⋊C₄	—	13	2	no	—
922	C₄⋊C₄	—	13	2	no	—
923	C₄⋊C₄	—	13	1	no	—
924	C₄⋊C₄	—	13	1	no	—
925	C₄⋊C₄	—	13	1	no	—
926	C₄⋊C₄	—	13	1	no	—
927	C₄⋊C₄	—	13	1	no	—
928	C₄⋊C₄	—	13	1	no	—
929	C₄⋊C₄	—	13	1	no	—
930	C₄⋊C₄	—	13	1	no	—
931	C₄⋊C₄	—	13	1	no	—
932	C₄⋊C₄	—	13	1	no	—
933	C₄⋊C₄	—	13	1	no	—
934	C₄⋊C₄	—	13	1	no	—
935	C₄⋊C₄	—	13	2	no	—
936	C₄⋊C₄	—	13	2	no	—
937	C₄⋊C₄	—	13	2	no	—
938	C₄⋊C₄	—	13	2	no	—
939	C₄⋊C₄	—	13	2	no	—
940	C₄⋊C₄	—	13	2	no	—
941	C₄⋊C₄	—	13	2	no	—
942	C₄⋊C₄	—	13	2	no	—
943	C₄⋊C₄	—	13	2	no	—
944	C₄⋊C₄	—	13	2	no	—
945	C₄⋊C₄	—	13	2	no	—
946	C₄⋊C₄	—	13	2	no	—
947	C₄⋊C₄	—	13	2	no	—
948	C₄⋊C₄	—	13	2	no	—
949	C₄⋊C₄	—	13	2	no	—
950	C₄⋊C₄	—	13	2	no	—
951	C₄⋊C₄	—	13	2	no	—
952	C₄⋊C₄	—	13	2	no	—
953	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
958	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
959	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
960	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
961	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
962	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
963	C₂²⋊C₄	—	13	2	no	—
964	C₂²⋊C₄	—	13	2	no	—
965	C₂²⋊C₄	—	13	2	no	—
966	C₂²⋊C₄	—	13	2	no	—
967	C₂²⋊C₄	—	13	2	no	—
968	C₂²⋊C₄	—	13	2	no	—
969	C₂²⋊C₄	—	13	1	no	—
970	C₂²⋊C₄	—	13	1	no	—
971	C₂²⋊C₄	—	13	1	no	—
972	C₂²⋊C₄	—	13	1	no	—
973	C₂²⋊C₄	—	13	1	no	—
974	C₂²⋊C₄	—	13	1	no	—
975	C₂²⋊C₄	—	13	1	no	—
976	C₂²⋊C₄	—	13	1	no	—
977	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
978	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
979	C₄²	—	13	2	no	—
980	C₄²	—	13	2	no	—
981	C₄²	—	13	2	no	—
982	C₄²	—	13	2	no	—
983	C₄²	—	13	1	no	—
984	C₄²	—	13	1	no	—
985	C₄²	—	13	2	no	—
986	C₄²	—	13	1	no	—
987	C₄²	—	13	1	no	—
988	C₄²	—	13	2	no	—
989	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
990	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
991	C₄²	C₂³×D₁₃	1	1	yes	characteristic
992	C₄²	C₂³×D₁₃	1	2	yes	—
993	C₄²	C₂³×D₁₃	1	2	yes	—
994	C₄²	C₂³×D₁₃	1	1	yes	characteristic
995	C₁₃	#60193	1	1	yes	characteristic, complemented, Sylow
996	C₂³	—	13	1	no	—
997	C₂³	—	13	1	no	—
998	C₂³	—	13	4	no	—
999	C₂³	—	52	1	no	—
1000	C₂³	—	52	1	no	—
1001	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
1002	Q₈	—	4	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	52	2	no	—
1005	Q₈	—	52	2	no	—
1006	Q₈	—	52	2	no	—
1007	Q₈	—	52	2	no	—
1008	Q₈	—	52	2	no	—
1009	Q₈	—	52	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	13	4	no	—
1013	C₂×C₄	—	13	1	no	—
1014	C₂×C₄	—	13	1	no	—
1015	C₂×C₄	—	13	4	no	—
1016	C₂×C₄	—	13	4	no	—
1017	C₂×C₄	—	13	2	no	—
1018	C₂×C₄	—	13	2	no	—
1019	C₂×C₄	—	13	2	no	—
1020	C₂×C₄	—	13	2	no	—
1021	C₂×C₄	—	13	2	no	—
1022	C₂×C₄	—	13	2	no	—
1023	C₂×C₄	—	13	1	no	—
1024	C₂×C₄	—	13	1	no	—
1025	C₂×C₄	—	13	2	no	—
1026	C₂×C₄	—	13	2	no	—
1027	C₂×C₄	—	13	1	no	—
1028	C₂×C₄	—	13	1	no	—
1029	C₂×C₄	—	52	2	no	—
1030	C₂×C₄	—	52	2	no	—
1031	C₂×C₄	—	52	2	no	—
1032	C₂×C₄	—	52	2	no	—
1033	C₂×C₄	—	52	1	no	—
1034	C₂×C₄	—	52	1	no	—
1035	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1036	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1037	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1038	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1039	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1040	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1041	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1044	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
1045	C₂×C₄	#41×D₁₃	1	2	yes	—
1046	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	2	no	—
1052	C₈	—	13	4	no	—
1053	C₈	—	26	1	no	—
1054	C₈	—	26	1	no	—
1055	C₈	—	26	2	no	—
1056	C₈	—	26	1	no	—
1057	C₈	—	26	1	no	—
1058	C₈	C₂×Q₈×D₁₃	1	4	yes	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	13	2	no	—
1062	C₂²	—	13	2	no	—
1063	C₂²	—	26	1	no	—
1064	C₂²	—	26	1	no	—
1065	C₂²	—	26	1	no	—
1066	C₂²	—	26	1	no	—
1067	C₂²	—	52	4	no	—
1068	C₂²	C₄×Q₈×D₁₃	1	2	yes	—
1069	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	13	2	no	—
1079	C₄	—	13	2	no	—
1080	C₄	—	26	2	no	—
1081	C₄	—	26	2	no	—
1082	C₄	—	26	1	no	—
1083	C₄	—	26	1	no	—
1084	C₄	—	26	2	no	—
1085	C₄	—	26	2	no	—
1086	C₄	—	26	1	no	—
1087	C₄	—	26	1	no	—
1088	C₄	C₄×Q₈×D₁₃	1	2	yes	—
1089	C₄	C₂²×Q₈×D₁₃	1	1	yes	characteristic
1090	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
1091	C₂	—	2	2	no	—
1092	C₂	—	26	2	no	—
1093	C₂	—	26	2	no	—
1094	C₂	C₂×C₄×Q₈×D₁₃	1	1	yes	characteristic
1095	C₂	#13129547	1	1	yes	characteristic
1096	C₂	#13129549	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₁₃
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Fitting	C₁₃×#2962	C₂
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	#2962	D₁₃
hypocenter	C₁₃	#60193
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #13123785	C₂	semidirect
3. #13123784	C₂	semidirect
4. #13123783	C₂	semidirect
5. #13123782	C₂	semidirect
6. #13123782	C₂	semidirect
7. #13123781	C₂	semidirect
8. #13123781	C₂	semidirect
9. #13123780	C₂	semidirect
10. #13123780	C₂	semidirect
11. #13123779	C₂	semidirect
12. #13123778	C₂	semidirect
13. #13123772	C₂	semidirect
14. #13123772	C₂	semidirect
15. #13123767	C₂	semidirect
16. #13123765	C₂	semidirect
23. C₁₃×#2962	C₂	semidirect
51. C₁₃×#446	C₂²	semidirect
52. C₁₃×#446	C₂²	semidirect
53. C₁₃×#446	C₂²	semidirect
54. C₈×Q₈×C₁₃	C₂²	semidirect
73. #11718685	C₂²	semidirect
74. #11718685	C₂²	semidirect
75. #11718685	C₂²	semidirect
76. Q₈×#1055	C₂²	semidirect
99. #11718492	C₂²	semidirect
100. #11718492	C₂²	semidirect
101. #11718492	C₂²	semidirect
102. #11718491	C₂²	semidirect
103. #11718491	C₂²	semidirect
104. #11718491	C₂²	semidirect
105. #11718489	C₂²	semidirect
106. #11718489	C₂²	semidirect
107. #11718489	C₂²	semidirect
108. #11718489	C₂²	semidirect
109. #11718489	C₂²	semidirect
110. #11718489	C₂²	semidirect
117. #11718362	C₂²	semidirect
118. #11718362	C₂²	semidirect
119. #11718362	C₂²	semidirect
120. #11718362	C₂²	semidirect
121. #11718362	C₂²	semidirect
122. #11718362	C₂²	semidirect
129. #11718340	C₂²	semidirect
130. #11718340	C₂²	semidirect
131. #11718340	C₂²	semidirect
132. C₈×Dic₂₆	C₂²	semidirect
133. C₈×Dic₂₆	C₂²	semidirect
134. C₈×Dic₂₆	C₂²	semidirect
173. M₁₆×D₁₃	Q₈	semidirect
460. #2962	D₁₃	semidirect
582. #446	C₂×D₁₃	semidirect
583. #446	C₂×D₁₃	semidirect
584. #446	C₂×D₁₃	semidirect
592. C₈×Q₈	C₂×D₁₃	semidirect
995. C₁₃	#60193	semidirect

Maximal subgroups

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

subgroup	index
#13128239	2
#13123785	2
#13123784	2
#13123783	2
#13123782	2
#13123781	2
#13123780	2
#13123779	2
#13123778	2
#13123772	2
#13123767	2
#13123765	2
#13123397	2
C₂×#11718500	2
D₁₃×#424	2
#13123253	2
#13123252	2
D₁₃×#405	2
C₁₃×#2962	2
#60193	13