Subgroups — #15870771

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124624	C₂	1	1	yes	maximal, characteristic
2	#13123776	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115780	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115611	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115435	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115435	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115111	C₂	1	1	yes	maximal, characteristic
8	#13115111	C₂	1	1	yes	maximal, characteristic
9	#13114856	C₂	1	1	yes	maximal, characteristic
10	#13114721	C₂	1	1	yes	maximal, characteristic, complemented
11	#13114716	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114708	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114678	C₂	1	1	yes	maximal, characteristic
14	#13114671	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
19	#11719175	C₂²	1	1	yes	characteristic
20	C₁₃×#405	—	2	1	no	—
21	C₁₃×#405	—	2	1	no	—
22	C₁₃×#405	C₂²	1	1	yes	characteristic
23	C₁₃×#405	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×M₁₆	—	2	1	no	—
25	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	—	2	1	no	—
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₂×#88077	C₂²	1	1	yes	characteristic
29	C₂×#88077	C₂²	1	1	yes	characteristic
30	#11718894	C₂²	1	1	yes	characteristic
31	#11718894	C₂²	1	1	yes	characteristic
32	C₂×#88062	C₂²	1	1	yes	characteristic
33	C₂×#88062	C₂²	1	1	yes	characteristic
34	#11718763	C₂²	1	1	yes	characteristic
35	#11718763	C₂²	1	1	yes	characteristic
36	#11718762	C₂²	1	1	yes	characteristic
37	#11718762	C₂²	1	1	yes	characteristic
38	C₂×#88055	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
40	#11718683	C₄	1	1	yes	characteristic, complemented
41	#11718683	C₄	1	1	yes	characteristic, complemented
42	#11718682	C₄	1	1	yes	characteristic, complemented
43	#11718681	C₄	1	1	yes	characteristic, complemented
44	#11718670	C₄	1	1	yes	characteristic, complemented
45	#11718670	C₄	1	1	yes	characteristic, complemented
46	#11718669	C₄	1	1	yes	characteristic, complemented
47	#11718668	C₄	1	1	yes	characteristic, complemented
48	#11718659	C₂²	1	1	yes	characteristic
49	#11718659	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
51	#11718585	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
53	#11718362	—	2	1	no	—
54	#11718362	—	2	1	no	—
55	#11718362	—	2	1	no	—
56	#11718362	—	2	1	no	—
57	#11718150	C₂²	1	1	yes	characteristic
58	#11718150	C₂²	1	1	yes	characteristic
59	#11718147	C₂²	1	1	yes	characteristic
60	#11718147	C₂²	1	1	yes	characteristic
61	#11718147	C₂²	1	1	yes	characteristic
62	#11718147	C₂²	1	1	yes	characteristic
63	#11718142	C₂²	1	1	yes	characteristic
64	#11718142	C₂²	1	1	yes	characteristic
65	#11718124	C₂²	1	1	yes	characteristic
66	#11718124	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₁₃×#131	—	2	2	no	—
69	C₁₃×#131	—	2	2	no	—
70	C₁₃×#131	—	2	2	no	—
71	C₁₃×#131	Q₈	1	4	yes	complemented
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×D₄×C₁₃	—	2	1	no	—
83	C₄×D₄×C₁₃	—	2	1	no	—
84	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#117	—	2	1	no	—
87	C₁₃×#117	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	#88180	C₂³	1	1	yes	characteristic
91	#88180	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊Dic₁₃	—	2	1	no	—
93	#88178	—	2	1	no	—
94	#88178	—	2	1	no	—
95	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₂×#6099	C₂³	1	1	yes	characteristic
98	C₂×#6099	C₂³	1	1	yes	characteristic
99	C₂²×#1055	C₂³	1	1	yes	characteristic
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	#88124	C₂×C₄	1	1	yes	characteristic
102	#88124	C₂×C₄	1	1	yes	characteristic
103	#88123	C₂×C₄	1	1	yes	characteristic
104	#88123	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₂₆	—	2	1	no	—
106	C₄×Dic₂₆	—	2	1	no	—
107	C₁₃×#97	—	2	1	no	—
108	C₁₃×#97	—	2	1	no	—
109	C₁₃×#97	—	2	1	no	—
110	C₁₃×#97	D₄	1	1	yes	characteristic
111	C₁₃×#97	D₄	1	1	yes	characteristic
112	C₁₃×#97	D₄	1	1	yes	characteristic
113	C₁₃×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	—	2	1	no	—
116	C₄×C₈×C₁₃	—	2	1	no	—
117	#88077	—	2	2	no	—
118	#88077	—	2	2	no	—
119	#88075	C₂×C₄	1	1	yes	characteristic
120	#88075	C₂×C₄	1	1	yes	characteristic
121	#88075	C₂×C₄	1	1	yes	characteristic
122	#88075	C₂×C₄	1	1	yes	characteristic
123	#88072	C₂×C₄	1	1	yes	characteristic
124	#88072	C₂×C₄	1	1	yes	characteristic
125	#88072	C₂×C₄	1	1	yes	characteristic
126	#88072	C₂×C₄	1	1	yes	characteristic
127	#88071	—	2	1	no	—
128	#88062	—	2	2	no	—
129	#88062	—	2	2	no	—
130	#88055	—	2	1	no	—
131	#88055	—	2	1	no	—
132	#88055	—	2	2	no	—
133	#88054	—	2	1	no	—
134	#88054	—	2	1	no	—
135	#88054	—	2	1	no	—
136	#88054	—	2	1	no	—
137	C₈×Dic₁₃	—	2	1	no	—
138	C₈×Dic₁₃	—	2	1	no	—
139	C₈×Dic₁₃	—	2	2	no	—
140	#88048	C₂×C₄	1	1	yes	characteristic
141	#88048	C₂×C₄	1	1	yes	characteristic
142	#88048	C₂×C₄	1	1	yes	characteristic
143	#88048	C₂×C₄	1	1	yes	characteristic
144	#88047	C₂×C₄	1	1	yes	characteristic
145	#88047	C₂×C₄	1	1	yes	characteristic
146	#88047	C₂×C₄	1	1	yes	characteristic
147	#88047	C₂×C₄	1	1	yes	characteristic
148	C₄⋊#1055	—	2	1	no	—
149	C₄⋊#1055	—	2	1	no	—
150	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
151	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
152	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
153	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
154	#21629	—	13	1	no	maximal, Sylow
155	C₁₃×#41	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	C₂×Q₈	1	2	yes	—
158	C₁₃×#41	#41	1	2	yes	—
159	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²×Dic₁₃	—	2	1	no	—
169	C₂²×Dic₁₃	—	2	1	no	—
170	C₂×Dic₂₆	—	2	1	no	—
171	C₂×Dic₂₆	—	2	1	no	—
172	C₁₃×M₁₆	—	2	4	no	—
173	C₁₃×M₁₆	—	2	1	no	—
174	C₁₃×M₁₆	—	2	1	no	—
175	C₁₃×M₁₆	—	2	4	no	—
176	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
177	C₁₃×M₁₆	#41	1	2	yes	—
178	C₂×C₈×C₁₃	—	2	4	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	4	no	—
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
189	C₂×C₈×C₁₃	#41	1	2	yes	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²⋊Dic₁₃	—	2	1	no	—
205	C₂²⋊Dic₁₃	—	2	1	no	—
206	C₄⋊Dic₁₃	—	2	1	no	—
207	C₄⋊Dic₁₃	—	2	1	no	—
208	C₄⋊Dic₁₃	—	4	2	no	—
209	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
213	#6101	—	2	1	no	—
214	#6101	—	2	1	no	—
215	#6101	—	2	1	no	—
216	#6101	—	2	1	no	—
217	C₄×Dic₁₃	—	2	1	no	—
218	C₄×Dic₁₃	—	2	1	no	—
219	C₄×Dic₁₃	—	2	1	no	—
220	C₄×Dic₁₃	—	2	1	no	—
221	C₄×Dic₁₃	—	2	1	no	—
222	C₄×Dic₁₃	—	2	1	no	—
223	#6099	—	2	1	no	—
224	#6099	—	2	1	no	—
225	#6099	—	2	1	no	—
226	#6099	—	2	1	no	—
227	C₂×#1055	—	2	1	no	—
228	C₂×#1055	—	2	1	no	—
229	C₂×#1055	—	2	1	no	—
230	C₂×#1055	—	2	1	no	—
231	C₂×#1055	—	2	1	no	—
232	C₂×#1055	—	2	1	no	—
233	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
234	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
235	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
236	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
237	#3076	—	13	1	no	—
238	#2961	—	13	1	no	—
239	#2875	D₁₃	1	1	yes	characteristic
240	#1986	—	13	1	no	—
241	#1950	—	13	1	no	—
242	#1922	—	13	1	no	—
243	#1922	—	13	1	no	—
244	#1866	—	13	1	no	—
245	#1866	—	13	1	no	—
246	#1806	—	13	1	no	—
247	#1773	—	13	1	no	—
248	#1772	—	13	1	no	—
249	#1771	—	13	1	no	—
250	#1765	—	13	1	no	—
251	#1764	—	13	1	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
254	Q₈×C₁₃	—	2	1	no	—
255	Q₈×C₁₃	C₄×Q₈	1	2	yes	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	1	no	—
259	D₄×C₁₃	C₄×Q₈	1	2	yes	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	8	1	no	—
268	C₂×C₄×C₁₃	—	8	1	no	—
269	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
279	C₂×Dic₁₃	—	2	2	no	—
280	C₂×Dic₁₃	—	2	1	no	—
281	C₂×Dic₁₃	—	2	1	no	—
282	C₂×Dic₁₃	—	2	1	no	—
283	C₂×Dic₁₃	—	2	1	no	—
284	C₂×Dic₁₃	—	4	1	no	—
285	C₂×Dic₁₃	—	4	1	no	—
286	C₂×Dic₁₃	—	4	1	no	—
287	C₂×Dic₁₃	—	4	1	no	—
288	C₂×Dic₁₃	—	4	1	no	—
289	Dic₂₆	—	8	1	no	—
290	Dic₂₆	—	8	1	no	—
291	C₈×C₁₃	—	2	2	no	—
292	C₈×C₁₃	—	2	1	no	—
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	2	1	no	—
295	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
296	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
297	#1055	—	2	1	no	—
298	#1055	—	2	1	no	—
299	#1055	—	2	1	no	—
300	#1055	—	2	1	no	—
301	#1055	—	4	1	no	—
302	#1055	—	4	1	no	—
303	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
304	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
305	#533	—	13	1	no	—
306	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
307	#479	—	13	1	no	—
308	#479	—	13	1	no	—
309	#478	—	13	1	no	—
310	#478	—	13	1	no	—
311	#477	—	13	1	no	—
312	#476	—	13	1	no	—
313	#475	—	13	1	no	—
314	#474	—	13	1	no	—
315	#446	—	26	1	no	—
316	#446	—	26	1	no	—
317	#446	—	26	1	no	—
318	#446	—	26	1	no	—
319	C₂×#108	—	13	1	no	—
320	C₂×#108	—	13	1	no	—
321	#427	—	13	1	no	—
322	#427	—	13	1	no	—
323	#424	—	13	1	no	—
324	#424	—	13	1	no	—
325	#423	—	13	1	no	—
326	C₂×C₄⋊C₈	—	13	1	no	—
327	C₂×#104	—	13	1	no	—
328	C₂×#104	—	13	1	no	—
329	#416	—	13	1	no	—
330	#416	—	13	1	no	—
331	#405	—	2	1	no	—
332	#405	—	2	1	no	—
333	#405	—	13	1	no	—
334	#405	—	13	1	no	—
335	#405	C₂×D₁₃	1	1	yes	characteristic
336	#405	C₂×D₁₃	1	1	yes	characteristic
337	C₄×M₁₆	—	2	1	no	—
338	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
339	C₂×#97	—	2	1	no	—
340	C₂×#97	—	13	1	no	—
341	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
342	C₂×C₄×C₈	—	13	1	no	—
343	C₄×C₄⋊C₄	—	13	1	no	—
344	#341	—	13	1	no	—
345	#341	—	13	1	no	—
346	#339	—	13	1	no	—
347	#339	—	13	1	no	—
348	#339	—	13	1	no	—
349	#339	—	13	1	no	—
350	#339	—	13	1	no	—
351	#339	—	13	1	no	—
352	#336	—	13	1	no	—
353	#336	—	13	1	no	—
354	C₂²×C₁₃	—	2	1	no	—
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
360	C₂²×C₁₃	#529	1	1	yes	characteristic
361	C₂²×C₁₃	#533	1	1	yes	characteristic
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
370	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
371	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
372	C₄×C₁₃	#525	1	1	yes	characteristic
373	Dic₁₃	—	4	2	no	—
374	Dic₁₃	—	4	1	no	—
375	Dic₁₃	—	4	1	no	—
376	Dic₁₃	—	4	1	no	—
377	Dic₁₃	—	4	1	no	—
378	Dic₁₃	—	8	1	no	—
379	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
380	#131	—	2	2	no	—
381	#131	—	2	2	no	—
382	#131	—	2	2	no	—
383	#131	Dic₂₆	1	4	yes	complemented
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	13	1	no	—
387	C₂×M₁₆	—	13	1	no	—
388	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
389	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	13	1	no	—
393	C₂²×C₈	—	13	1	no	—
394	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
396	C₄⋊Q₈	—	13	1	no	—
397	C₄⋊Q₈	—	13	1	no	—
398	#125	—	13	1	no	—
399	#125	—	13	1	no	—
400	C₂²⋊Q₈	—	26	1	no	—
401	C₂²⋊Q₈	—	26	1	no	—
402	C₄×Q₈	—	26	1	no	—
403	C₄×Q₈	—	26	1	no	—
404	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
405	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
409	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
410	#117	—	2	1	no	—
411	#117	—	13	1	no	—
412	#117	—	13	1	no	—
413	#117	C₂²×D₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	—	26	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	13	1	no	—
417	C₂×C₄²	—	13	1	no	—
418	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
419	#108	—	26	2	no	—
420	#108	—	26	2	no	—
421	#107	—	13	1	no	—
422	#107	—	13	1	no	—
423	#107	—	13	1	no	—
424	#107	—	13	1	no	—
425	#106	—	13	1	no	—
426	#106	—	13	1	no	—
427	#106	—	13	1	no	—
428	#106	—	13	1	no	—
429	C₄⋊C₈	—	13	1	no	—
430	C₄⋊C₈	—	13	1	no	—
431	C₄⋊C₈	—	13	1	no	—
432	C₄⋊C₈	—	13	1	no	—
433	C₄⋊C₈	—	26	1	no	—
434	C₄⋊C₈	—	26	1	no	—
435	C₄⋊C₈	—	26	1	no	—
436	C₄⋊C₈	—	26	1	no	—
437	C₄⋊C₈	—	26	1	no	—
438	C₄⋊C₈	—	26	1	no	—
439	#104	—	26	2	no	—
440	#104	—	26	2	no	—
441	#103	—	13	1	no	—
442	#103	—	13	1	no	—
443	#103	—	13	1	no	—
444	#103	—	13	1	no	—
445	#102	—	13	1	no	—
446	#102	—	13	1	no	—
447	#102	—	13	1	no	—
448	#102	—	13	1	no	—
449	#97	—	2	1	no	—
450	#97	—	2	1	no	—
451	#97	—	2	1	no	—
452	#97	—	26	2	no	—
453	#97	—	26	1	no	—
454	#97	—	26	1	no	—
455	#97	C₂²⋊D₁₃	1	1	yes	characteristic
456	#97	C₂²⋊D₁₃	1	1	yes	characteristic
457	#97	C₂²⋊D₁₃	1	1	yes	characteristic
458	#97	C₂²⋊D₁₃	1	1	yes	characteristic
459	C₄×C₈	—	2	1	no	—
460	C₄×C₈	—	2	1	no	—
461	C₄×C₈	—	2	1	no	—
462	C₄×C₈	—	26	2	no	—
463	C₄×C₈	—	26	1	no	—
464	C₄×C₈	—	26	1	no	—
465	#95	—	26	1	no	—
466	C₂×C₁₃	—	2	1	no	—
467	C₂×C₁₃	—	2	1	no	—
468	C₂×C₁₃	—	4	2	no	—
469	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
470	C₂×C₁₃	#2956	1	1	yes	characteristic
471	C₂×C₁₃	#2957	1	1	yes	characteristic
472	#41	—	2	1	no	—
473	#41	—	2	1	no	—
474	#41	C₂×Dic₂₆	1	2	yes	—
475	#41	#6127	1	2	yes	—
476	C₂×Q₈	—	26	1	no	—
477	C₂×Q₈	—	26	1	no	—
478	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	26	1	no	—
485	C₂²×C₄	—	26	1	no	—
486	C₂²×C₄	#6127	1	1	yes	characteristic
487	C₂²×C₄	#6127	1	1	yes	characteristic
488	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
489	M₁₆	—	2	4	no	—
490	M₁₆	—	2	1	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	4	no	—
493	M₁₆	—	26	1	no	—
494	M₁₆	—	26	1	no	—
495	M₁₆	—	26	1	no	—
496	M₁₆	—	26	1	no	—
497	M₁₆	C₂×Dic₂₆	1	2	yes	—
498	M₁₆	#6127	1	2	yes	—
499	C₂×C₈	—	2	4	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	4	no	—
505	C₂×C₈	—	13	1	no	—
506	C₂×C₈	—	13	1	no	—
507	C₂×C₈	—	13	1	no	—
508	C₂×C₈	—	13	1	no	—
509	C₂×C₈	—	26	1	no	—
510	C₂×C₈	—	26	1	no	—
511	C₂×C₈	—	26	1	no	—
512	C₂×C₈	—	26	1	no	—
513	C₂×C₈	—	26	1	no	—
514	C₂×C₈	—	26	1	no	—
515	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
516	C₂×C₈	#6127	1	2	yes	—
517	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
518	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
519	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
520	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	13	1	no	—
524	C₄⋊C₄	—	13	1	no	—
525	C₄⋊C₄	—	13	1	no	—
526	C₄⋊C₄	—	13	1	no	—
527	C₄⋊C₄	—	26	1	no	—
528	C₄⋊C₄	—	26	1	no	—
529	C₄⋊C₄	—	26	1	no	—
530	C₄⋊C₄	—	26	1	no	—
531	C₄⋊C₄	—	26	1	no	—
532	C₄⋊C₄	—	26	1	no	—
533	C₄⋊C₄	—	52	2	no	—
534	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	26	1	no	—
540	C₂²⋊C₄	—	26	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	26	1	no	—
545	C₄²	—	26	1	no	—
546	C₄²	—	26	1	no	—
547	C₄²	—	26	1	no	—
548	C₄²	—	26	1	no	—
549	C₄²	—	26	1	no	—
550	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
551	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
552	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
553	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
554	C₁₃	#21629	1	1	yes	characteristic, complemented, Sylow
555	C₂³	—	2	1	no	—
556	C₂³	C₂×#6127	1	1	yes	characteristic
557	Q₈	—	2	1	no	—
558	Q₈	—	104	1	no	—
559	Q₈	—	104	1	no	—
560	Q₈	C₄×Dic₂₆	1	2	yes	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	1	no	—
564	D₄	C₄×Dic₂₆	1	2	yes	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	—	8	1	no	—
574	C₂×C₄	—	26	2	no	—
575	C₂×C₄	—	26	1	no	—
576	C₂×C₄	—	26	1	no	—
577	C₂×C₄	—	26	1	no	—
578	C₂×C₄	—	26	1	no	—
579	C₂×C₄	—	52	1	no	—
580	C₂×C₄	—	52	1	no	—
581	C₂×C₄	—	52	1	no	—
582	C₂×C₄	—	52	1	no	—
583	C₂×C₄	—	52	1	no	—
584	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
585	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
586	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
587	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
589	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂×#6127	1	1	yes	characteristic
591	C₂×C₄	C₂×#6127	1	1	yes	characteristic
592	C₂×C₄	C₂×#6127	1	1	yes	characteristic
593	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	1	no	—
598	C₈	—	26	1	no	—
599	C₈	—	26	1	no	—
600	C₈	—	26	1	no	—
601	C₈	—	26	1	no	—
602	C₈	—	52	1	no	—
603	C₈	—	52	1	no	—
604	C₈	#88178	1	2	yes	—
605	C₈	#88178	1	2	yes	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	#11719175	1	1	yes	characteristic
612	C₂²	#11719184	1	1	yes	characteristic
613	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	52	2	no	—
622	C₄	—	52	1	no	—
623	C₄	—	52	1	no	—
624	C₄	—	52	1	no	—
625	C₄	—	52	1	no	—
626	C₄	—	104	1	no	—
627	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
628	C₄	C₄×#6127	1	1	yes	characteristic
629	C₄	C₂×#88178	1	1	yes	characteristic
630	C₄	#11719496	1	1	yes	characteristic
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	4	2	no	—
634	C₂	C₄×#88178	1	1	yes	characteristic
635	C₂	#13123743	1	1	yes	characteristic
636	C₂	#13123751	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	C₁₃×#2875	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#41	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2875	D₁₃
hypocenter	C₁₃	#21629
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #2875

Complements

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

N	H ≅ G/N	type
2. #13123776	C₂	semidirect
3. #13115780	C₂	semidirect
4. #13115611	C₂	semidirect
5. #13115435	C₂	semidirect
6. #13115435	C₂	semidirect
10. #13114721	C₂	semidirect
11. #13114716	C₂	semidirect
12. #13114708	C₂	semidirect
40. #11718683	C₄	semidirect
41. #11718683	C₄	semidirect
42. #11718682	C₄	semidirect
43. #11718681	C₄	semidirect
44. #11718670	C₄	semidirect
45. #11718670	C₄	semidirect
46. #11718669	C₄	semidirect
47. #11718668	C₄	semidirect
71. C₁₃×#131	Q₈	semidirect
383. #131	Dic₂₆	semidirect
554. C₁₃	#21629	semidirect

Maximal subgroups

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

subgroup	index
#13124624	2
#13123776	2
#13115780	2
#13115611	2
#13115435	2
#13115111	2
#13114856	2
#13114721	2
#13114716	2
#13114708	2
#13114678	2
#13114671	2
C₁₃×#2875	2
#21629	13