Subgroups — #15834773

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125425	C₂	1	1	yes	maximal, characteristic
2	#13123840	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113748	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113724	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113712	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113700	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113672	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113663	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113648	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#6104	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113586	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113253	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113247	C₂	1	1	yes	maximal, characteristic, complemented
14	#13113139	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#131	—	2	1	no	—
17	C₁₃×#532	C₂²	1	1	yes	characteristic
18	#11719184	C₂²	1	1	yes	characteristic
19	C₁₃×#436	C₂²	1	1	yes	characteristic
20	C₁₃×#436	C₂²	1	1	yes	characteristic
21	C₁₃×#435	—	2	1	no	—
22	C₁₃×#435	—	2	1	no	—
23	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₁₃×#408	—	2	1	no	—
27	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	#11718789	—	2	1	no	—
29	#11718788	—	2	1	no	—
30	#11718750	C₄	1	1	yes	characteristic
31	#11718741	C₄	1	1	yes	characteristic
32	#11718735	C₄	1	1	yes	characteristic
33	#11718732	C₄	1	1	yes	characteristic
34	#11718703	C₄	1	1	yes	characteristic
35	#11718703	C₄	1	1	yes	characteristic
36	#11718700	C₄	1	1	yes	characteristic
37	#11718700	C₄	1	1	yes	characteristic
38	C₄×#6105	C₂²	1	1	yes	characteristic
39	C₄×#6105	C₂²	1	1	yes	characteristic
40	C₄×#6104	C₂²	1	1	yes	characteristic
41	C₄×#6104	C₂²	1	1	yes	characteristic
42	#11718586	C₂²	1	1	yes	characteristic
43	C₄×#6099	C₂²	1	1	yes	characteristic
44	C₄×#6099	C₂²	1	1	yes	characteristic
45	#11718370	—	2	1	no	—
46	#11718369	—	2	1	no	—
47	#11718349	C₂²	1	1	yes	characteristic
48	C₈×D₅₂	C₂²	1	1	yes	characteristic
49	#11718340	C₂²	1	1	yes	characteristic
50	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
51	D₄⋊#1055	C₂²	1	1	yes	characteristic
52	D₄⋊#1055	C₂²	1	1	yes	characteristic
53	D₄⋊#1055	C₂²	1	1	yes	characteristic
54	D₄⋊#1055	C₂²	1	1	yes	characteristic
55	#11718076	C₂²	1	1	yes	characteristic
56	#11718076	C₂²	1	1	yes	characteristic
57	#11718075	C₂²	1	1	yes	characteristic
58	#11718075	C₂²	1	1	yes	characteristic
59	#11718072	C₂²	1	1	yes	characteristic
60	#11718072	C₂²	1	1	yes	characteristic
61	#11718071	C₂²	1	1	yes	characteristic
62	#11718071	C₂²	1	1	yes	characteristic
63	#11718047	C₂²	1	1	yes	characteristic
64	#11718046	C₂²	1	1	yes	characteristic
65	#11718046	C₂²	1	1	yes	characteristic
66	C₈×#1055	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₁₃×#131	—	4	4	no	—
69	C₂×C₁₃×M₁₆	—	2	1	no	—
70	C₂×C₁₃×M₁₆	—	2	1	no	—
71	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	—	2	1	no	—
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
78	C₁₃×#124	—	2	1	no	—
79	C₁₃×#121	—	2	1	no	—
80	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
82	C₄×D₄×C₁₃	—	2	1	no	—
83	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×#6105	C₂×C₄	1	1	yes	characteristic
87	C₂×#6105	C₂×C₄	1	1	yes	characteristic
88	C₂×#6104	C₂×C₄	1	1	yes	characteristic
89	C₂×#6104	C₂×C₄	1	1	yes	characteristic
90	#88184	C₂×C₄	1	1	yes	characteristic
91	#88183	—	2	1	no	—
92	C₄×C₂²⋊D₁₃	—	2	1	no	—
93	#88178	C₂×C₄	1	1	yes	characteristic
94	C₂×#6099	—	2	1	no	—
95	C₂×#6099	C₂×C₄	1	1	yes	characteristic
96	C₂×#6099	C₂×C₄	1	1	yes	characteristic
97	C₂×#6094	—	2	1	no	—
98	C₂×C₈×D₁₃	—	2	1	no	—
99	#88130	—	2	1	no	—
100	#88129	C₂×C₄	1	1	yes	characteristic
101	C₄×D₅₂	C₂³	1	1	yes	characteristic
102	#88126	—	2	1	no	—
103	#88124	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊C₈	—	2	1	no	—
106	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₈	—	2	1	no	—
109	C₁₃×C₂²⋊C₈	—	2	1	no	—
110	C₁₃×C₂²⋊C₈	—	2	1	no	—
111	C₁₃×C₂²⋊C₈	—	2	1	no	—
112	C₁₃×#97	D₄	1	1	yes	characteristic
113	C₁₃×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	#88072	C₂×C₄	1	1	yes	characteristic
117	#88072	C₂×C₄	1	1	yes	characteristic
118	#88072	C₂×C₄	1	1	yes	characteristic
119	#88072	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊#1055	—	2	1	no	—
121	#88060	—	2	1	no	—
122	#88060	—	2	1	no	—
123	#88055	—	2	1	no	—
124	#88054	—	2	1	no	—
125	#88054	—	2	1	no	—
126	C₈×Dic₁₃	—	2	1	no	—
127	#88050	C₂×C₄	1	1	yes	characteristic
128	#88050	C₂×C₄	1	1	yes	characteristic
129	#88049	C₂×C₄	1	1	yes	characteristic
130	#88049	C₂×C₄	1	1	yes	characteristic
131	#88048	C₂×C₄	1	1	yes	characteristic
132	#88048	C₂×C₄	1	1	yes	characteristic
133	#88047	C₂×C₄	1	1	yes	characteristic
134	#88047	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#1055	C₂³	1	1	yes	characteristic
136	C₄⋊#1055	C₂³	1	1	yes	characteristic
137	#88043	—	2	1	no	—
138	#88043	C₂×C₄	1	1	yes	characteristic
139	#88043	C₂×C₄	1	1	yes	characteristic
140	C₄×#1055	—	2	1	no	—
141	C₄×#1055	C₂³	1	1	yes	characteristic
142	C₄×#1055	C₂³	1	1	yes	characteristic
143	C₄×#1055	C₂³	1	1	yes	characteristic
144	C₄×#1055	C₂³	1	1	yes	characteristic
145	#18076	—	13	1	no	maximal, Sylow
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	4	2	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
160	C₂×C₂²⋊D₁₃	—	2	1	no	—
161	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₁₃	—	2	1	no	—
163	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	4	1	no	—
166	C₁₃×M₁₆	—	4	2	no	—
167	C₁₃×M₁₆	—	4	2	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	4	2	no	—
171	C₂×C₈×C₁₃	—	4	2	no	—
172	C₂×C₈×C₁₃	—	4	2	no	—
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
180	C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₃	#41	1	1	yes	characteristic
187	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	—	2	1	no	—
189	#6105	—	2	2	no	—
190	#6105	—	4	1	no	—
191	#6104	—	2	2	no	—
192	#6104	—	4	1	no	—
193	#6103	—	2	1	no	—
194	#6103	—	2	1	no	—
195	#6103	—	2	1	no	—
196	#6103	—	2	1	no	—
197	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
199	#6101	—	2	1	no	—
200	#6101	—	2	1	no	—
201	#6101	—	2	1	no	—
202	#6101	—	2	1	no	—
203	C₄×Dic₁₃	—	2	1	no	—
204	#6099	—	2	2	no	—
205	#6099	—	4	1	no	—
206	#6099	—	4	2	no	—
207	C₂×#1055	—	2	1	no	—
208	C₂×#1055	—	2	1	no	—
209	C₂×#1055	—	2	1	no	—
210	C₂×#1055	—	2	1	no	—
211	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
212	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
213	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
214	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
215	#6094	—	4	2	no	—
216	C₈×D₁₃	—	4	2	no	—
217	#3171	—	13	1	no	—
218	#2969	—	13	1	no	—
219	#2935	D₁₃	1	1	yes	characteristic, complemented
220	#1594	—	13	1	no	—
221	#1590	—	13	1	no	—
222	#1588	—	13	1	no	—
223	#1586	—	13	1	no	—
224	#1582	—	13	1	no	—
225	#1581	—	13	1	no	—
226	SD₁₆⋊C₈	—	13	1	no	—
227	C₈×D₈	—	13	1	no	—
228	#1565	—	13	1	no	—
229	#1484	—	13	1	no	—
230	#1483	—	13	1	no	—
231	#1455	—	13	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
235	C₂²×D₁₃	—	2	1	no	—
236	Q₈×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	8	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
262	C₂²⋊D₁₃	—	8	1	no	—
263	C₂×Dic₁₃	—	2	1	no	—
264	C₂×Dic₁₃	—	2	1	no	—
265	C₂×Dic₁₃	—	2	1	no	—
266	D₅₂	—	2	1	no	—
267	D₅₂	—	2	1	no	—
268	C₄×D₁₃	—	4	1	no	—
269	C₄×D₁₃	—	4	1	no	—
270	Dic₂₆	—	2	1	no	—
271	Dic₂₆	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
278	#1055	—	2	2	no	—
279	#1055	—	2	1	no	—
280	#1055	—	2	1	no	—
281	#1055	—	2	1	no	—
282	#1055	—	4	1	no	—
283	#1055	—	4	1	no	—
284	#1055	—	4	1	no	—
285	#1055	#131	1	2	yes	complemented
286	C₂×#131	—	2	1	no	—
287	#532	C₂×D₁₃	1	1	yes	characteristic
288	#529	—	13	1	no	—
289	#501	—	13	1	no	—
290	#496	—	13	1	no	—
291	#490	—	13	1	no	—
292	#489	—	13	1	no	—
293	#469	—	13	1	no	—
294	#469	—	13	1	no	—
295	#468	—	13	1	no	—
296	#468	—	13	1	no	—
297	#446	—	13	1	no	—
298	C₈×Q₈	—	13	1	no	—
299	C₄×SD₁₆	—	13	1	no	—
300	C₄×SD₁₆	—	13	1	no	—
301	C₄×D₈	—	13	1	no	—
302	C₄×D₈	—	13	1	no	—
303	#436	—	13	1	no	—
304	#436	—	26	1	no	—
305	#436	C₂×D₁₃	1	1	yes	characteristic
306	#436	C₂×D₁₃	1	1	yes	characteristic
307	#435	—	2	1	no	—
308	#435	—	2	1	no	—
309	#435	—	26	1	no	—
310	C₈×D₄	—	13	1	no	—
311	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
312	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
313	#433	—	26	1	no	—
314	#431	—	13	1	no	—
315	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
316	#408	—	2	1	no	—
317	#405	—	26	1	no	—
318	C₄×M₁₆	—	13	1	no	—
319	C₄×M₁₆	—	13	1	no	—
320	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
321	#335	—	13	1	no	—
322	#335	—	13	1	no	—
323	#334	—	13	1	no	—
324	#334	—	13	1	no	—
325	Q₈⋊C₈	—	13	1	no	—
326	Q₈⋊C₈	—	13	1	no	—
327	D₄⋊C₈	—	13	1	no	—
328	D₄⋊C₈	—	13	1	no	—
329	D₄⋊C₈	—	13	1	no	—
330	D₄⋊C₈	—	13	1	no	—
331	D₄⋊C₈	—	13	1	no	—
332	D₄⋊C₈	—	13	1	no	—
333	#322	—	13	1	no	—
334	#322	—	13	1	no	—
335	#322	—	13	1	no	—
336	C₈²	—	13	1	no	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂×D₁₃	—	4	1	no	—
348	C₂×D₁₃	—	4	1	no	—
349	C₂×D₁₃	—	4	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	—	2	1	no	—
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
357	C₄×C₁₃	#568	1	1	yes	characteristic
358	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
359	C₄×C₁₃	#575	1	1	yes	characteristic
360	Dic₁₃	—	4	1	no	—
361	Dic₁₃	—	4	1	no	—
362	Dic₁₃	—	4	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×SD₁₆	—	13	1	no	—
365	C₂×SD₁₆	—	13	1	no	—
366	C₂×D₈	—	13	1	no	—
367	C₂×D₈	—	13	1	no	—
368	#131	—	4	4	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	13	1	no	—
372	C₂×M₁₆	—	13	1	no	—
373	C₂×M₁₆	—	26	1	no	—
374	C₂×M₁₆	—	26	1	no	—
375	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
376	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	26	1	no	—
381	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
382	#127	C₄×D₁₃	1	1	yes	characteristic
383	#126	—	26	1	no	—
384	#125	—	13	1	no	—
385	#124	—	2	1	no	—
386	#124	—	13	1	no	—
387	#123	—	26	1	no	—
388	C₂²⋊Q₈	—	13	1	no	—
389	#121	—	2	1	no	—
390	#121	—	13	1	no	—
391	#121	C₄×D₁₃	1	1	yes	characteristic
392	#121	C₄×D₁₃	1	1	yes	characteristic
393	C₄×Q₈	—	13	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	13	1	no	—
396	C₄×D₄	—	26	1	no	—
397	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
398	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
399	#117	—	26	1	no	—
400	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
401	#107	—	13	1	no	—
402	#107	—	13	1	no	—
403	#106	—	13	1	no	—
404	#106	—	13	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	13	1	no	—
407	C₄⋊C₈	—	13	1	no	—
408	C₄⋊C₈	—	26	1	no	—
409	C₄⋊C₈	—	26	1	no	—
410	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
412	#103	—	13	1	no	—
413	#103	—	13	1	no	—
414	#102	—	13	1	no	—
415	#102	—	13	1	no	—
416	#102	—	13	1	no	—
417	#102	—	13	1	no	—
418	#102	—	13	1	no	—
419	#102	—	13	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	—	2	1	no	—
424	C₂²⋊C₈	—	26	1	no	—
425	C₂²⋊C₈	—	26	1	no	—
426	C₂²⋊C₈	—	26	1	no	—
427	#97	—	13	1	no	—
428	#97	—	13	1	no	—
429	#97	—	26	1	no	—
430	#97	—	26	1	no	—
431	#97	C₂²⋊D₁₃	1	1	yes	characteristic
432	#97	C₂²⋊D₁₃	1	1	yes	characteristic
433	C₄×C₈	—	13	1	no	—
434	C₄×C₈	—	13	1	no	—
435	C₄×C₈	—	13	1	no	—
436	C₄×C₈	—	13	1	no	—
437	C₄×C₈	—	26	1	no	—
438	C₄×C₈	—	26	1	no	—
439	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
440	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
441	C₂×C₁₃	—	4	1	no	—
442	C₂×C₁₃	—	8	1	no	—
443	C₂×C₁₃	—	8	1	no	—
444	C₂×C₁₃	#2935	1	1	yes	characteristic
445	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
446	C₂×C₁₃	#2956	1	1	yes	characteristic
447	D₁₃	—	8	1	no	—
448	#41	—	4	2	no	—
449	#41	—	4	2	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	13	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	13	1	no	—
457	C₂×D₄	—	26	1	no	—
458	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
459	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	26	1	no	—
463	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
464	C₂²×C₄	#6127	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
466	SD₁₆	—	26	2	no	—
467	SD₁₆	—	52	1	no	—
468	D₈	—	26	2	no	—
469	D₈	—	52	1	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	2	no	—
473	M₁₆	—	4	2	no	—
474	M₁₆	—	26	2	no	—
475	M₁₆	—	52	2	no	—
476	M₁₆	—	52	1	no	—
477	M₁₆	—	52	2	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	—	4	2	no	—
483	C₂×C₈	—	13	1	no	—
484	C₂×C₈	—	13	1	no	—
485	C₂×C₈	—	13	1	no	—
486	C₂×C₈	—	13	1	no	—
487	C₂×C₈	—	26	1	no	—
488	C₂×C₈	—	26	1	no	—
489	C₂×C₈	—	26	1	no	—
490	C₂×C₈	—	26	1	no	—
491	C₂×C₈	—	52	2	no	—
492	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
493	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
494	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
495	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	13	1	no	—
498	C₄⋊C₄	—	13	1	no	—
499	C₄⋊C₄	—	26	1	no	—
500	C₄⋊C₄	—	26	1	no	—
501	C₄⋊C₄	—	26	1	no	—
502	C₄⋊C₄	—	26	1	no	—
503	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	26	1	no	—
510	C₂²⋊C₄	—	26	1	no	—
511	C₂²⋊C₄	—	26	1	no	—
512	C₂²⋊C₄	—	26	1	no	—
513	C₂²⋊C₄	—	26	1	no	—
514	C₄²	—	26	1	no	—
515	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
516	C₄²	#6127	1	1	yes	characteristic
517	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
518	C₄²	C₂³×D₁₃	1	1	yes	characteristic
519	C₁₃	#18076	1	1	yes	characteristic, complemented, Sylow
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	26	1	no	—
523	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
524	Q₈	—	4	2	no	—
525	Q₈	—	26	1	no	—
526	Q₈	—	26	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	8	1	no	—
535	D₄	—	26	1	no	—
536	D₄	—	26	1	no	—
537	D₄	—	104	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	26	1	no	—
550	C₂×C₄	—	26	1	no	—
551	C₂×C₄	—	26	1	no	—
552	C₂×C₄	—	52	1	no	—
553	C₂×C₄	—	52	1	no	—
554	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
555	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
556	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂×#6127	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	13	2	no	—
566	C₈	—	26	2	no	—
567	C₈	—	26	1	no	—
568	C₈	—	26	1	no	—
569	C₈	—	26	1	no	—
570	C₈	—	52	1	no	—
571	C₈	—	52	1	no	—
572	C₈	—	52	1	no	—
573	C₈	#88186	1	2	yes	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	52	1	no	—
584	C₂²	—	52	1	no	—
585	C₂²	—	52	1	no	—
586	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	52	1	no	—
594	C₄	—	52	1	no	—
595	C₄	—	52	1	no	—
596	C₄	D₁₃×#131	1	1	yes	characteristic
597	C₄	#11719455	1	1	yes	characteristic
598	C₄	C₂×#88186	1	1	yes	characteristic
599	C₄	#11719527	1	1	yes	characteristic
600	C₂	—	4	1	no	—
601	C₂	—	8	1	no	—
602	C₂	—	8	1	no	—
603	C₂	—	104	1	no	—
604	C₂	#13123578	1	1	yes	characteristic
605	C₂	C₄×#88186	1	1	yes	characteristic
606	C₂	#13123743	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2935	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13125425	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2935	D₁₃
hypocenter	C₁₃	#18076
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #13123840	C₂	semidirect
3. #13113748	C₂	semidirect
4. #13113724	C₂	semidirect
5. #13113712	C₂	semidirect
6. #13113700	C₂	semidirect
7. #13113672	C₂	semidirect
8. #13113663	C₂	semidirect
9. #13113648	C₂	semidirect
10. C₈×#6104	C₂	semidirect
11. #13113586	C₂	semidirect
12. #13113253	C₂	semidirect
13. #13113247	C₂	semidirect
14. #13113139	C₂	semidirect
15. C₁₃×#2935	C₂	semidirect
219. #2935	D₁₃	semidirect
285. #1055	#131	semidirect
519. C₁₃	#18076	semidirect

Maximal subgroups

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

subgroup	index
#13125425	2
#13123840	2
#13113748	2
#13113724	2
#13113712	2
#13113700	2
#13113672	2
#13113663	2
#13113648	2
C₈×#6104	2
#13113586	2
#13113253	2
#13113247	2
#13113139	2
C₁₃×#2935	2
#18076	13