Subgroups — #16742934

Order 3328.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128712	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128655	C₂	1	1	yes	maximal, characteristic, complemented
3	#13127648	C₂	1	2	yes	maximal, complemented
4	#13127626	C₂	1	2	yes	maximal, complemented
5	#13127563	C₂	1	2	yes	maximal, complemented
6	#13127541	C₂	1	2	yes	maximal, complemented
7	#13127530	C₂	1	2	yes	maximal, complemented
8	#13127505	C₂	1	2	yes	maximal, complemented
9	#13127494	C₂	1	2	yes	maximal, complemented
10	#13127469	C₂	1	2	yes	maximal, complemented
11	#13125194	C₂	1	2	yes	maximal, complemented
12	C₂×#11718355	C₂	1	1	yes	maximal, characteristic, complemented
13	#13124670	C₂	1	2	yes	maximal, complemented
14	#13124651	C₂	1	1	yes	maximal, characteristic, complemented
15	#13124373	C₂	1	2	yes	maximal, complemented
16	#13124316	C₂	1	1	yes	maximal, characteristic, complemented
17	#13123770	C₂	1	1	yes	maximal, characteristic, complemented
18	#13123671	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	#11719535	C₂²	1	2	yes	—
24	#11719532	C₂²	1	2	yes	—
25	C₂×#88203	C₂²	1	2	yes	—
26	#11719290	C₂²	1	2	yes	—
27	#11719290	C₂²	1	2	yes	—
28	#11719275	C₂²	1	2	yes	complemented
29	Q₈×Dic₂₆	C₂²	1	2	yes	complemented
30	#11719258	C₂²	1	2	yes	—
31	#11719258	C₂²	1	2	yes	—
32	#11719255	—	2	2	no	—
33	#11719255	—	2	2	no	—
34	#11719248	—	2	2	no	—
35	#11719248	C₂²	1	2	yes	complemented
36	D₄×Dic₂₆	—	2	2	no	—
37	D₄×Dic₂₆	C₂²	1	2	yes	complemented
38	#11719240	—	2	2	no	—
39	#11719226	C₂²	1	2	yes	—
40	#11719224	—	2	2	no	—
41	#11719224	C₂²	1	2	yes	—
42	#11719182	—	2	1	no	—
43	#11719182	—	2	1	no	—
44	C₂×#88128	C₂²	1	1	yes	characteristic
45	#11719175	—	2	1	no	—
46	#11719175	C₂²	1	1	yes	characteristic
47	C₂×#88123	—	2	1	no	—
48	C₂×#88123	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
53	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
54	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#427	C₂²	1	1	yes	characteristic
58	C₁₃×#416	C₂²	1	1	yes	characteristic
59	C₁₃×#416	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
61	#11718893	C₂²	1	2	yes	—
62	#11718846	C₂²	1	4	yes	complemented
63	#11718826	C₂²	1	4	yes	complemented
64	#11718824	C₂²	1	4	yes	complemented
65	#11718811	C₂²	1	4	yes	complemented
66	C₂×#88061	C₂²	1	2	yes	—
67	C₂×#88061	C₂²	1	2	yes	—
68	#11718763	C₂²	1	2	yes	—
69	#11718762	C₂²	1	2	yes	—
70	#11718688	C₂²	1	2	yes	—
71	#11718688	C₂²	1	2	yes	—
72	#11718682	C₂²	1	2	yes	complemented
73	#11718681	C₂²	1	2	yes	complemented
74	#11718676	C₂²	1	2	yes	—
75	#11718676	C₂²	1	2	yes	—
76	#11718669	C₂²	1	2	yes	complemented
77	#11718668	C₂²	1	2	yes	complemented
78	#11718662	C₂²	1	2	yes	—
79	#11718656	C₂²	1	2	yes	—
80	#11718585	C₂²	1	1	yes	characteristic
81	#11718552	C₂²	1	4	yes	complemented
82	#11718551	C₂²	1	4	yes	complemented
83	#11718532	C₂²	1	4	yes	complemented
84	#11718531	C₂²	1	4	yes	complemented
85	#11718478	C₂²	1	4	yes	complemented
86	#11718461	C₂²	1	4	yes	complemented
87	#11718456	C₂²	1	4	yes	complemented
88	#11718449	C₂²	1	4	yes	complemented
89	#11718446	C₂²	1	4	yes	complemented
90	#11718425	C₂²	1	4	yes	complemented
91	#11718421	C₂²	1	4	yes	complemented
92	#11718417	C₂²	1	4	yes	complemented
93	#11718355	C₂²	1	2	yes	—
94	#11718355	C₂²	1	2	yes	—
95	#11718355	C₂²	1	2	yes	—
96	#11718355	C₂²	1	2	yes	—
97	#11718340	C₂²	1	2	yes	complemented
98	#11718340	C₂²	1	2	yes	complemented
99	C₈×Dic₂₆	C₂²	1	2	yes	complemented
100	C₈×Dic₂₆	C₂²	1	2	yes	complemented
101	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂×#6127	—	2	2	no	—
104	C₂×#6127	—	2	2	no	—
105	C₂²×D₅₂	—	2	1	no	—
106	C₂²×D₅₂	—	2	1	no	—
107	C₂²×D₅₂	C₂³	1	2	yes	—
108	C₂²×Dic₂₆	—	2	1	no	—
109	C₂²×Dic₂₆	—	2	2	no	—
110	C₁₃×#135	—	2	4	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
119	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₁₃	—	2	1	no	—
122	C₄×D₄×C₁₃	—	2	1	no	—
123	C₄×D₄×C₁₃	—	2	1	no	—
124	C₄×D₄×C₁₃	—	2	1	no	—
125	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#117	—	2	1	no	—
130	C₁₃×#117	—	2	1	no	—
131	C₁₃×#117	C₂³	1	1	yes	characteristic
132	C₁₃×#117	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	—	2	1	no	—
134	C₂×C₄²×C₁₃	—	2	1	no	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	#88203	—	2	8	no	—
137	#88201	C₂³	1	4	yes	—
138	Q₈×Dic₁₃	C₂³	1	4	yes	—
139	C₂×#6106	C₂³	1	4	yes	—
140	#88194	C₂³	1	4	yes	—
141	#88191	—	2	4	no	—
142	D₄×Dic₁₃	—	2	4	no	—
143	D₄×Dic₁₃	C₂³	1	4	yes	—
144	C₂×#6104	C₂³	1	4	yes	—
145	#88184	—	2	2	no	—
146	#88184	—	2	2	no	—
147	#88184	—	2	2	no	—
148	#88184	—	2	2	no	—
149	#88180	—	2	2	no	—
150	#88180	C₂³	1	2	yes	—
151	C₂×C₄⋊Dic₁₃	—	2	1	no	—
152	C₂×C₄⋊Dic₁₃	—	2	2	no	—
153	C₂×C₄⋊Dic₁₃	—	2	2	no	—
154	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
155	#88178	—	2	2	no	—
156	#88178	—	2	2	no	—
157	#88178	D₄	1	2	yes	—
158	#88178	D₄	1	2	yes	—
159	C₂×#6099	C₂³	1	2	yes	—
160	#88148	—	2	4	no	—
161	#88148	—	2	4	no	—
162	#88147	C₂³	1	4	yes	—
163	#88147	C₂³	1	4	yes	—
164	#88144	—	2	4	no	—
165	#88144	C₂³	1	4	yes	—
166	#88142	—	2	4	no	—
167	#88142	C₂³	1	4	yes	—
168	#88138	—	2	4	no	—
169	#88138	—	2	4	no	—
170	C₂²⋊C₄×D₁₃	—	2	4	no	—
171	#88132	—	2	4	no	—
172	#88132	—	2	4	no	—
173	#88132	—	2	4	no	—
174	#88129	—	2	2	no	—
175	#88129	—	2	2	no	—
176	#88128	—	2	1	no	—
177	#88128	—	2	1	no	—
178	#88128	C₂³	1	2	yes	—
179	#88128	C₂³	1	2	yes	—
180	C₄×D₅₂	—	2	2	no	—
181	C₄×D₅₂	—	2	2	no	—
182	C₄×D₅₂	—	2	2	no	—
183	C₄×D₅₂	—	2	2	no	—
184	#88124	—	2	2	no	—
185	#88124	D₄	1	2	yes	—
186	#88123	—	2	2	no	—
187	#88123	—	2	1	no	—
188	#88123	—	2	1	no	—
189	#88123	—	2	2	no	—
190	#88123	—	2	2	no	—
191	#88123	D₄	1	1	yes	characteristic
192	#88123	D₄	1	1	yes	characteristic
193	#88123	C₂³	1	2	yes	—
194	#88123	C₂³	1	2	yes	—
195	C₄×Dic₂₆	—	2	2	no	—
196	C₄×Dic₂₆	—	2	2	no	—
197	C₄×Dic₂₆	C₂³	1	2	yes	—
198	C₄×Dic₂₆	C₂³	1	2	yes	—
199	C₁₃×#107	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	1	yes	characteristic
201	C₁₃×#106	C₂³	1	1	yes	characteristic
202	C₁₃×#106	C₂³	1	1	yes	characteristic
203	C₁₃×#103	C₂³	1	1	yes	characteristic
204	C₁₃×#103	C₂³	1	1	yes	characteristic
205	C₁₃×#103	C₂³	1	1	yes	characteristic
206	C₁₃×#103	C₂³	1	1	yes	characteristic
207	C₁₃×#102	C₂³	1	1	yes	characteristic
208	C₁₃×#102	C₂³	1	1	yes	characteristic
209	C₁₃×#102	C₂³	1	1	yes	characteristic
210	C₁₃×#102	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
214	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
215	#88075	C₂³	1	4	yes	—
216	#88072	C₂³	1	4	yes	—
217	#88061	C₂³	1	4	yes	—
218	#88061	C₂³	1	4	yes	—
219	#88061	C₂³	1	4	yes	—
220	#88061	C₂³	1	4	yes	—
221	#88055	C₂³	1	4	yes	—
222	#88054	C₂³	1	4	yes	—
223	#88054	C₂³	1	4	yes	—
224	C₈×Dic₁₃	C₂³	1	4	yes	—
225	#88049	C₂³	1	4	yes	—
226	#88049	C₂³	1	4	yes	—
227	#88048	C₂³	1	4	yes	—
228	#88047	C₂³	1	4	yes	—
229	C₄⋊#1055	C₂³	1	2	yes	—
230	C₄⋊#1055	C₂³	1	2	yes	—
231	#61329	—	13	1	no	maximal, Sylow
232	C₂³×D₁₃	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	#41	1	4	yes	complemented
237	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₁₃	—	2	1	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₂²⋊D₁₃	—	2	4	no	—
253	C₂×C₂²⋊D₁₃	—	2	4	no	—
254	C₂²×Dic₁₃	—	2	2	no	—
255	C₂²×Dic₁₃	—	2	4	no	—
256	#6127	—	8	4	no	—
257	#6127	—	8	4	no	—
258	C₂×D₅₂	—	2	4	no	—
259	C₂×D₅₂	—	2	4	no	—
260	C₂×D₅₂	—	2	2	no	—
261	C₂×D₅₂	—	2	2	no	—
262	C₂×D₅₂	—	2	2	no	—
263	C₂×D₅₂	—	2	2	no	—
264	C₂×D₅₂	—	2	2	no	—
265	C₂×D₅₂	—	8	2	no	—
266	C₂×D₅₂	—	8	2	no	—
267	C₂×D₅₂	C₂⁴	1	4	yes	—
268	C₂×C₄×D₁₃	—	2	4	no	—
269	C₂×C₄×D₁₃	—	2	4	no	—
270	C₂×Dic₂₆	—	2	2	no	—
271	C₂×Dic₂₆	—	2	2	no	—
272	C₂×Dic₂₆	—	2	4	no	—
273	C₂×Dic₂₆	—	8	4	no	—
274	C₂×Dic₂₆	—	8	2	no	—
275	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
276	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
277	C₁₃×Q₁₆	—	2	2	no	—
278	C₁₃×SD₁₆	—	2	2	no	—
279	C₁₃×SD₁₆	—	2	2	no	—
280	C₁₃×D₈	—	2	2	no	—
281	C₂×C₈×C₁₃	—	2	2	no	—
282	C₂×C₈×C₁₃	—	2	2	no	—
283	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
292	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
293	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
294	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₁₃×C₂²⋊C₄	—	2	1	no	—
298	C₁₃×C₂²⋊C₄	—	2	1	no	—
299	C₁₃×C₂²⋊C₄	—	2	1	no	—
300	C₁₃×C₂²⋊C₄	—	2	1	no	—
301	C₄²×C₁₃	—	2	1	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	1	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	—	2	1	no	—
306	C₄²×C₁₃	—	2	1	no	—
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²⋊Dic₁₃	—	2	4	no	—
312	C₂²⋊Dic₁₃	C₂×D₄	1	4	yes	—
313	#6106	—	2	8	no	—
314	#6104	—	2	8	no	—
315	#6103	—	2	4	no	—
316	#6103	—	2	4	no	—
317	#6103	—	2	4	no	—
318	#6103	—	2	4	no	—
319	C₄⋊Dic₁₃	—	2	2	no	—
320	C₄⋊Dic₁₃	—	2	2	no	—
321	C₄⋊Dic₁₃	—	2	2	no	—
322	C₄⋊Dic₁₃	—	2	4	no	—
323	C₄⋊Dic₁₃	—	2	4	no	—
324	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
325	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
326	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
327	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
328	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
329	#6101	—	2	4	no	—
330	#6101	—	2	4	no	—
331	#6101	C₂×D₄	1	4	yes	—
332	#6101	C₂×D₄	1	4	yes	—
333	C₄×Dic₁₃	—	2	4	no	—
334	C₄×Dic₁₃	C₂⁴	1	4	yes	—
335	#6099	—	2	4	no	—
336	C₂×#1055	C₂⁴	1	4	yes	—
337	#3508	—	13	1	no	—
338	#3503	—	13	1	no	—
339	#3375	—	13	2	no	—
340	#3373	—	13	2	no	—
341	#3368	—	13	2	no	—
342	#3366	—	13	2	no	—
343	#3365	—	13	2	no	—
344	#3362	—	13	2	no	—
345	#3361	—	13	2	no	—
346	#3358	—	13	2	no	—
347	#3136	—	13	2	no	—
348	C₂×#486	—	13	1	no	—
349	#3081	—	13	2	no	—
350	#3079	—	13	1	no	—
351	#3045	—	13	2	no	—
352	#3038	—	13	1	no	—
353	#2960	—	13	1	no	—
354	#2946	—	13	2	no	—
355	C₄×#135	D₁₃	1	1	yes	characteristic, complemented
356	C₂³×C₁₃	—	2	1	no	—
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂²×D₁₃	—	2	4	no	—
360	C₂²×D₁₃	—	4	4	no	—
361	C₂²×D₁₃	—	8	2	no	—
362	C₂²×D₁₃	—	8	2	no	—
363	Q₈×C₁₃	—	2	1	no	—
364	Q₈×C₁₃	—	2	1	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	C₂×#41	1	2	yes	—
367	D₄×C₁₃	—	2	4	no	—
368	D₄×C₁₃	—	2	1	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	—	2	1	no	—
371	D₄×C₁₃	—	4	2	no	—
372	D₄×C₁₃	C₂×#41	1	2	yes	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	4	2	no	—
383	C₂×C₄×C₁₃	—	4	2	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	2	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
393	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
394	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
395	C₂²⋊D₁₃	—	8	4	no	—
396	C₂²⋊D₁₃	—	8	4	no	—
397	C₂×Dic₁₃	—	2	4	no	—
398	C₂×Dic₁₃	—	8	4	no	—
399	C₂×Dic₁₃	—	8	2	no	—
400	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
401	C₂×Dic₁₃	C₂²×D₄	1	4	yes	—
402	D₅₂	—	2	4	no	—
403	D₅₂	—	2	4	no	—
404	D₅₂	—	4	4	no	—
405	D₅₂	—	4	4	no	—
406	D₅₂	—	4	4	no	—
407	D₅₂	—	8	2	no	—
408	D₅₂	—	8	2	no	—
409	C₄×D₁₃	—	8	4	no	—
410	C₄×D₁₃	—	8	4	no	—
411	Dic₂₆	—	2	4	no	—
412	Dic₂₆	—	2	4	no	—
413	Dic₂₆	—	4	4	no	—
414	Dic₂₆	—	8	4	no	—
415	Dic₂₆	—	8	2	no	—
416	C₈×C₁₃	—	2	1	no	—
417	C₈×C₁₃	—	2	1	no	—
418	C₈×C₁₃	—	2	1	no	—
419	C₈×C₁₃	—	2	1	no	—
420	#1055	—	2	4	no	—
421	C₂×AGL(1,ℤ/8)	—	13	2	no	—
422	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
423	#559	—	13	2	no	—
424	#559	—	13	2	no	—
425	Q₈²	—	13	2	no	—
426	#557	—	13	2	no	—
427	#554	—	13	2	no	—
428	#554	—	26	2	no	—
429	#550	—	13	2	no	—
430	#550	—	13	2	no	—
431	D₄×Q₈	—	13	2	no	—
432	D₄×Q₈	—	26	2	no	—
433	#546	—	26	2	no	—
434	#546	—	26	2	no	—
435	#544	—	13	2	no	—
436	#544	—	26	2	no	—
437	#540	—	26	2	no	—
438	#535	—	13	2	no	—
439	#533	—	13	1	no	—
440	#533	—	26	1	no	—
441	#532	—	26	1	no	—
442	#532	—	26	1	no	—
443	C₂×C₄⋊Q₈	—	13	1	no	—
444	C₂×C₄⋊Q₈	—	26	1	no	—
445	C₂×#127	—	13	1	no	—
446	#520	—	13	2	no	—
447	#518	—	13	2	no	—
448	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
449	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
450	#490	—	13	4	no	—
451	#489	—	13	4	no	—
452	#488	—	13	4	no	—
453	#486	—	13	4	no	—
454	#486	—	13	2	no	—
455	#486	—	13	2	no	—
456	#486	—	13	2	no	—
457	#486	—	13	2	no	—
458	#478	—	13	4	no	—
459	#478	—	13	4	no	—
460	#477	—	13	2	no	—
461	#476	—	13	2	no	—
462	#476	—	13	4	no	—
463	#475	—	13	2	no	—
464	#474	—	13	2	no	—
465	#474	—	13	4	no	—
466	#464	—	13	4	no	—
467	#463	—	13	4	no	—
468	#460	—	13	4	no	—
469	#460	—	13	2	no	—
470	#460	—	13	2	no	—
471	#459	—	13	4	no	—
472	#459	—	13	2	no	—
473	#459	—	13	2	no	—
474	#446	—	13	2	no	—
475	#446	—	13	2	no	—
476	C₈×Q₈	—	13	2	no	—
477	C₈×Q₈	—	13	2	no	—
478	#442	—	13	4	no	—
479	#440	—	13	4	no	—
480	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
481	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
482	C₄×SD₁₆	—	13	4	no	—
483	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
484	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
485	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
486	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
487	C₄×D₈	—	13	4	no	—
488	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic, complemented
489	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic, complemented
490	#428	—	13	2	no	—
491	#427	C₂×D₁₃	1	1	yes	characteristic
492	#424	—	13	2	no	—
493	#423	—	13	1	no	—
494	#418	—	13	2	no	—
495	#417	—	13	2	no	—
496	#416	C₂×D₁₃	1	1	yes	characteristic
497	#416	C₂×D₁₃	1	1	yes	characteristic
498	C₂×#102	—	13	2	no	—
499	C₂×#102	—	13	2	no	—
500	#405	—	13	2	no	—
501	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	#548	1	2	yes	—
511	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
512	C₂×D₁₃	—	4	4	no	—
513	C₂×D₁₃	—	4	4	no	—
514	C₂×D₁₃	—	4	4	no	—
515	C₂×D₁₃	—	16	4	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	1	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	1	no	—
524	C₄×C₁₃	#548	1	2	yes	—
525	C₄×C₁₃	#576	1	2	yes	—
526	C₄×C₁₃	#577	1	2	yes	—
527	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
528	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
529	Dic₁₃	—	2	4	no	—
530	Dic₁₃	—	2	4	no	—
531	Dic₁₃	—	4	4	no	—
532	C₂×#41	—	26	2	no	—
533	C₂×#41	—	26	2	no	—
534	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
535	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
536	C₂²×Q₈	—	26	2	no	—
537	C₂²×Q₈	—	26	1	no	—
538	C₂²×D₄	—	13	2	no	—
539	C₂²×D₄	—	26	1	no	—
540	C₂²×D₄	—	26	1	no	—
541	AGL(1,ℤ/8)	—	26	8	no	—
542	#135	—	2	4	no	—
543	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
544	C₂×SD₁₆	—	13	4	no	—
545	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
546	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
547	C₂×D₈	—	13	4	no	—
548	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
549	C₂×M₁₆	—	13	2	no	—
550	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
551	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
552	C₄⋊Q₈	—	13	4	no	—
553	C₄⋊Q₈	—	13	1	no	—
554	C₄⋊Q₈	—	13	1	no	—
555	C₄⋊Q₈	—	13	2	no	—
556	C₄⋊Q₈	—	13	2	no	—
557	C₄⋊Q₈	—	26	2	no	—
558	C₄⋊Q₈	—	26	2	no	—
559	C₄⋊Q₈	—	26	2	no	—
560	C₄⋊Q₈	—	26	4	no	—
561	C₄⋊Q₈	—	26	1	no	—
562	C₄⋊Q₈	—	26	1	no	—
563	#127	—	13	4	no	—
564	#127	—	13	2	no	—
565	#127	—	13	2	no	—
566	#127	—	26	1	no	—
567	#127	—	26	1	no	—
568	#125	—	13	4	no	—
569	#125	—	13	2	no	—
570	#125	—	26	2	no	—
571	#125	—	26	4	no	—
572	#124	—	13	4	no	—
573	#124	—	26	2	no	—
574	#124	—	26	2	no	—
575	#123	—	26	4	no	—
576	#123	—	26	4	no	—
577	C₂²⋊Q₈	—	13	2	no	—
578	C₂²⋊Q₈	—	13	2	no	—
579	C₂²⋊Q₈	—	26	4	no	—
580	C₂²⋊Q₈	—	26	4	no	—
581	C₂²⋊Q₈	—	26	4	no	—
582	C₂²⋊Q₈	—	26	2	no	—
583	C₂²⋊Q₈	—	26	2	no	—
584	#121	—	26	4	no	—
585	#121	—	26	4	no	—
586	#121	—	26	2	no	—
587	#121	—	26	2	no	—
588	#121	—	26	2	no	—
589	#121	—	26	2	no	—
590	#120	—	26	4	no	—
591	C₄×Q₈	—	13	2	no	—
592	C₄×Q₈	—	13	2	no	—
593	C₄×Q₈	—	13	4	no	—
594	C₄×Q₈	—	26	2	no	—
595	C₄×Q₈	—	26	2	no	—
596	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
597	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
598	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
599	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	13	4	no	—
605	C₄×D₄	—	13	4	no	—
606	C₄×D₄	—	13	4	no	—
607	C₄×D₄	—	26	2	no	—
608	C₄×D₄	—	26	2	no	—
609	C₄×D₄	—	26	2	no	—
610	C₄×D₄	—	26	2	no	—
611	C₄×D₄	—	26	4	no	—
612	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
613	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
616	#117	—	2	1	no	—
617	#117	—	2	1	no	—
618	#117	—	13	2	no	—
619	#117	—	26	2	no	—
620	#117	C₂²×D₁₃	1	1	yes	characteristic
621	#117	C₂²×D₁₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	—	13	2	no	—
623	C₂×C₄⋊C₄	—	26	2	no	—
624	C₂×C₄⋊C₄	—	26	2	no	—
625	C₂×C₄⋊C₄	—	26	1	no	—
626	C₂×C₂²⋊C₄	—	26	4	no	—
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
630	#107	—	13	4	no	—
631	#107	C₂²×D₁₃	1	1	yes	characteristic
632	#107	C₂²×D₁₃	1	1	yes	characteristic
633	#106	—	13	4	no	—
634	#106	C₂²×D₁₃	1	1	yes	characteristic
635	#106	C₂²×D₁₃	1	1	yes	characteristic
636	C₄⋊C₈	—	13	4	no	—
637	C₄⋊C₈	—	13	4	no	—
638	C₄⋊C₈	—	13	2	no	—
639	C₄⋊C₈	—	13	2	no	—
640	#103	—	13	4	no	—
641	#103	C₂²×D₁₃	1	1	yes	characteristic
642	#103	C₂²×D₁₃	1	1	yes	characteristic
643	#103	C₂²×D₁₃	1	1	yes	characteristic
644	#103	C₂²×D₁₃	1	1	yes	characteristic
645	#102	—	13	4	no	—
646	#102	—	13	4	no	—
647	#102	—	13	4	no	—
648	#102	—	13	4	no	—
649	#102	—	13	4	no	—
650	#102	—	13	4	no	—
651	#102	—	13	4	no	—
652	#102	C₂²×D₁₃	1	1	yes	characteristic
653	#102	C₂²×D₁₃	1	1	yes	characteristic
654	#102	C₂²×D₁₃	1	1	yes	characteristic
655	#102	C₂²×D₁₃	1	1	yes	characteristic
656	#97	—	13	4	no	—
657	C₄×C₈	—	13	4	no	—
658	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
659	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
660	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
661	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
662	C₂×C₁₃	—	2	2	no	—
663	C₂×C₁₃	—	4	2	no	—
664	C₂×C₁₃	—	8	1	no	—
665	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
666	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
667	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
668	D₁₃	—	8	4	no	—
669	C₂⁴	—	26	2	no	—
670	#41	—	2	2	no	—
671	#41	—	2	2	no	—
672	#41	—	2	2	no	—
673	#41	—	104	4	no	—
674	#41	—	104	4	no	—
675	#41	#6127	1	4	yes	complemented
676	C₂×Q₈	—	13	2	no	—
677	C₂×Q₈	—	13	2	no	—
678	C₂×Q₈	—	26	4	no	—
679	C₂×Q₈	—	26	2	no	—
680	C₂×Q₈	—	26	2	no	—
681	C₂×Q₈	—	104	2	no	—
682	C₂×Q₈	—	104	4	no	—
683	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
684	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	13	4	no	—
688	C₂×D₄	—	26	4	no	—
689	C₂×D₄	—	26	4	no	—
690	C₂×D₄	—	26	4	no	—
691	C₂×D₄	—	26	2	no	—
692	C₂×D₄	—	26	2	no	—
693	C₂×D₄	—	26	2	no	—
694	C₂×D₄	—	26	2	no	—
695	C₂×D₄	—	26	2	no	—
696	C₂×D₄	—	26	4	no	—
697	C₂×D₄	—	104	2	no	—
698	C₂×D₄	—	104	2	no	—
699	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
700	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	26	4	no	—
708	C₂²×C₄	—	26	4	no	—
709	C₂²×C₄	—	26	4	no	—
710	C₂²×C₄	—	26	2	no	—
711	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
712	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
714	Q₁₆	—	2	2	no	—
715	SD₁₆	—	2	2	no	—
716	SD₁₆	—	2	2	no	—
717	SD₁₆	—	26	8	no	—
718	D₈	—	2	2	no	—
719	D₈	—	26	8	no	—
720	M₁₆	—	26	4	no	—
721	C₂×C₈	—	2	2	no	—
722	C₂×C₈	—	2	2	no	—
723	C₂×C₈	—	13	4	no	—
724	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
725	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
726	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
727	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	13	2	no	—
733	C₄⋊C₄	—	13	2	no	—
734	C₄⋊C₄	—	13	2	no	—
735	C₄⋊C₄	—	13	2	no	—
736	C₄⋊C₄	—	13	4	no	—
737	C₄⋊C₄	—	13	4	no	—
738	C₄⋊C₄	—	13	4	no	—
739	C₄⋊C₄	—	26	4	no	—
740	C₄⋊C₄	—	26	4	no	—
741	C₄⋊C₄	—	26	4	no	—
742	C₄⋊C₄	—	26	4	no	—
743	C₄⋊C₄	—	26	2	no	—
744	C₄⋊C₄	—	26	2	no	—
745	C₄⋊C₄	—	26	2	no	—
746	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	13	4	no	—
757	C₂²⋊C₄	—	26	4	no	—
758	C₂²⋊C₄	—	26	4	no	—
759	C₂²⋊C₄	—	26	4	no	—
760	C₂²⋊C₄	—	26	4	no	—
761	C₂²⋊C₄	—	26	4	no	—
762	C₄²	—	2	1	no	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	1	no	—
767	C₄²	—	2	1	no	—
768	C₄²	—	13	4	no	—
769	C₄²	—	26	4	no	—
770	C₄²	D₄×D₁₃	1	1	yes	characteristic
771	C₄²	D₄×D₁₃	1	1	yes	characteristic
772	C₄²	C₂³×D₁₃	1	1	yes	characteristic
773	C₄²	C₂³×D₁₃	1	1	yes	characteristic
774	C₁₃	#61329	1	1	yes	characteristic, complemented, Sylow
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	26	4	no	—
778	C₂³	—	52	4	no	—
779	C₂³	—	104	2	no	—
780	C₂³	—	104	2	no	—
781	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
782	Q₈	—	2	1	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	26	4	no	—
786	Q₈	—	26	4	no	—
787	Q₈	—	52	4	no	—
788	Q₈	—	104	2	no	—
789	Q₈	—	104	4	no	—
790	Q₈	C₂×#6127	1	2	yes	—
791	D₄	—	2	4	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	4	2	no	—
796	D₄	—	26	4	no	—
797	D₄	—	26	4	no	—
798	D₄	—	52	4	no	—
799	D₄	—	52	4	no	—
800	D₄	—	52	4	no	—
801	D₄	—	104	2	no	—
802	D₄	—	104	2	no	—
803	D₄	—	104	4	no	—
804	D₄	—	104	4	no	—
805	D₄	C₂×#6127	1	2	yes	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	13	4	no	—
821	C₂×C₄	—	13	4	no	—
822	C₂×C₄	—	26	4	no	—
823	C₂×C₄	—	104	4	no	—
824	C₂×C₄	—	104	4	no	—
825	C₂×C₄	—	104	4	no	—
826	C₂×C₄	—	104	2	no	—
827	C₂×C₄	C₂×#6127	1	2	yes	—
828	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
829	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
833	C₂×C₄	#88257	1	2	yes	—
834	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	26	4	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	52	4	no	—
849	C₂²	—	52	4	no	—
850	C₂²	—	52	4	no	—
851	C₂²	—	208	4	no	—
852	C₂²	#11719257	1	2	yes	—
853	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	26	4	no	—
863	C₄	—	26	4	no	—
864	C₄	—	52	4	no	—
865	C₄	#11719257	1	2	yes	—
866	C₄	#11719474	1	2	yes	—
867	C₄	#11719475	1	2	yes	—
868	C₄	C₂²×#6127	1	1	yes	characteristic
869	C₄	C₂×#88257	1	1	yes	characteristic
870	C₂	—	2	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	1	no	—
873	C₂	—	104	4	no	—
874	C₂	C₂×#11719257	1	1	yes	characteristic
875	C₂	C₂×#11719474	1	1	yes	characteristic
876	C₂	C₂×#11719475	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂³×D₄
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#61329
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13128712	C₂	semidirect
2. #13128655	C₂	semidirect
3. #13127648	C₂	semidirect
4. #13127626	C₂	semidirect
5. #13127563	C₂	semidirect
6. #13127541	C₂	semidirect
7. #13127530	C₂	semidirect
8. #13127505	C₂	semidirect
9. #13127494	C₂	semidirect
10. #13127469	C₂	semidirect
11. #13125194	C₂	semidirect
12. C₂×#11718355	C₂	semidirect
13. #13124670	C₂	semidirect
14. #13124651	C₂	semidirect
15. #13124373	C₂	semidirect
16. #13124316	C₂	semidirect
17. #13123770	C₂	semidirect
18. #13123671	C₂	semidirect
19. C₄×C₁₃×#135	C₂	semidirect
28. #11719275	C₂²	semidirect
29. Q₈×Dic₂₆	C₂²	semidirect
35. #11719248	C₂²	semidirect
37. D₄×Dic₂₆	C₂²	semidirect
49. C₄×C₁₃×Q₁₆	C₂²	semidirect
50. C₄×C₁₃×Q₁₆	C₂²	semidirect
51. C₄×C₁₃×SD₁₆	C₂²	semidirect
52. C₄×C₁₃×SD₁₆	C₂²	semidirect
53. C₄×C₁₃×SD₁₆	C₂²	semidirect
54. C₄×C₁₃×SD₁₆	C₂²	semidirect
55. C₄×C₁₃×D₈	C₂²	semidirect
56. C₄×C₁₃×D₈	C₂²	semidirect
62. #11718846	C₂²	semidirect
63. #11718826	C₂²	semidirect
64. #11718824	C₂²	semidirect
65. #11718811	C₂²	semidirect
72. #11718682	C₂²	semidirect
73. #11718681	C₂²	semidirect
76. #11718669	C₂²	semidirect
77. #11718668	C₂²	semidirect
81. #11718552	C₂²	semidirect
82. #11718551	C₂²	semidirect
83. #11718532	C₂²	semidirect
84. #11718531	C₂²	semidirect
85. #11718478	C₂²	semidirect
86. #11718461	C₂²	semidirect
87. #11718456	C₂²	semidirect
88. #11718449	C₂²	semidirect
89. #11718446	C₂²	semidirect
90. #11718425	C₂²	semidirect
91. #11718421	C₂²	semidirect
92. #11718417	C₂²	semidirect
97. #11718340	C₂²	semidirect
98. #11718340	C₂²	semidirect
99. C₈×Dic₂₆	C₂²	semidirect
100. C₈×Dic₂₆	C₂²	semidirect
236. C₁₃×#41	#41	semidirect
355. C₄×#135	D₁₃	semidirect
480. C₄×Q₁₆	C₂×D₁₃	semidirect
481. C₄×Q₁₆	C₂×D₁₃	semidirect
483. C₄×SD₁₆	C₂×D₁₃	semidirect
484. C₄×SD₁₆	C₂×D₁₃	semidirect
485. C₄×SD₁₆	C₂×D₁₃	semidirect
486. C₄×SD₁₆	C₂×D₁₃	semidirect
488. C₄×D₈	C₂×D₁₃	semidirect
489. C₄×D₈	C₂×D₁₃	semidirect
675. #41	#6127	semidirect
774. C₁₃	#61329	semidirect

Maximal subgroups

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

subgroup	index
#13128712	2
#13128655	2
#13127648	2
#13127626	2
#13127563	2
#13127541	2
#13127530	2
#13127505	2
#13127494	2
#13127469	2
#13125194	2
C₂×#11718355	2
#13124670	2
#13124651	2
#13124373	2
#13124316	2
#13123770	2
#13123671	2
C₄×C₁₃×#135	2
#61329	13