Subgroups — C₈×#88172 #15832345

Order 3328.

714 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6131	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88172	C₂	1	1	yes	maximal, characteristic
4	#13113655	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113652	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113651	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113647	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#6107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#6095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#6106	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113587	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113229	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113222	C₂	1	1	yes	maximal, characteristic
14	C₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88172	C₄	1	1	yes	characteristic
17	C₄×#6131	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
19	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	#11718845	C₄	1	1	yes	characteristic
23	C₄×#6107	C₂²	1	1	yes	characteristic
24	C₄×#6106	C₂²	1	1	yes	characteristic
25	Q₈×#1055	C₂²	1	1	yes	characteristic
26	Q₈×#1055	C₂²	1	1	yes	characteristic
27	#11718550	C₄	1	1	yes	characteristic
28	#11718542	C₄	1	1	yes	characteristic
29	#11718495	—	2	1	no	—
30	#11718495	C₂²	1	1	yes	characteristic
31	#11718494	—	2	1	no	—
32	#11718494	C₂²	1	1	yes	characteristic
33	D₁₃×C₄⋊C₈	—	2	1	no	—
34	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	#11718491	—	2	1	no	—
36	#11718491	C₂²	1	1	yes	characteristic
37	#11718478	C₄	1	1	yes	characteristic
38	#11718464	C₄	1	1	yes	characteristic
39	#11718463	C₄	1	1	yes	characteristic
40	#11718450	C₄	1	1	yes	characteristic
41	C₄×#6095	C₂²	1	1	yes	characteristic
42	C₄×#6094	C₂²	1	1	yes	characteristic
43	C₈×D₅₂	—	2	1	no	—
44	C₈×D₅₂	C₂²	1	1	yes	characteristic
45	#11718346	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₃	—	2	1	no	—
47	C₄×C₈×D₁₃	—	2	1	no	—
48	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
49	C₈×Dic₂₆	—	2	1	no	—
50	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
51	C₁₃×#335	C₂²	1	1	yes	characteristic
52	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
54	C₈²×C₁₃	C₂²	1	1	yes	characteristic
55	Q₈⋊#1055	C₂²	1	1	yes	characteristic
56	Q₈⋊#1055	C₂²	1	1	yes	characteristic
57	#11718076	C₂²	1	1	yes	characteristic
58	#11718075	C₂²	1	1	yes	characteristic
59	#11718072	C₂²	1	1	yes	characteristic
60	#11718071	C₂²	1	1	yes	characteristic
61	#11718051	C₂²	1	1	yes	characteristic
62	#11718049	C₂²	1	1	yes	characteristic
63	#11718048	C₂²	1	1	yes	characteristic
64	#11718047	C₂²	1	1	yes	characteristic
65	#11718046	C₂²	1	1	yes	characteristic
66	C₈×#1055	C₂²	1	1	yes	characteristic
67	C₂×#6131	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
73	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×#6107	C₂×C₄	1	1	yes	characteristic
75	C₂×#6106	C₂×C₄	1	1	yes	characteristic
76	#88172	C₈	1	8	yes	direct product factor
77	C₂×#6095	C₂×C₄	1	1	yes	characteristic
78	C₂×#6094	C₂×C₄	1	1	yes	characteristic
79	C₂×#6094	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₃	—	2	1	no	—
81	C₂×C₈×D₁₃	—	2	1	no	—
82	C₂×C₈×D₁₃	—	2	1	no	—
83	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
84	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
85	#88147	—	2	1	no	—
86	#88147	C₂×C₄	1	1	yes	characteristic
87	#88146	—	2	1	no	—
88	#88146	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₁₃	—	2	1	no	—
90	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
91	#88141	—	2	1	no	—
92	#88141	C₂×C₄	1	1	yes	characteristic
93	C₄×D₅₂	—	2	1	no	—
94	C₄×D₅₂	C₂³	1	1	yes	characteristic
95	C₄²×D₁₃	—	2	1	no	—
96	C₄²×D₁₃	—	2	1	no	—
97	C₄²×D₁₃	C₂³	1	1	yes	characteristic
98	C₄×Dic₂₆	—	2	1	no	—
99	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
100	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
101	C₁₃×C₄⋊C₈	—	2	1	no	—
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₁₃	—	2	1	no	—
108	C₄×C₈×C₁₃	—	2	1	no	—
109	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	#88075	C₂×C₄	1	1	yes	characteristic
113	#88075	C₂×C₄	1	1	yes	characteristic
114	#88061	C₂×C₄	1	1	yes	characteristic
115	#88060	—	2	1	no	—
116	#88060	—	2	1	no	—
117	#88060	—	2	1	no	—
118	#88060	—	2	1	no	—
119	#88057	C₂×C₄	1	1	yes	characteristic
120	#88056	C₂×C₄	1	1	yes	characteristic
121	#88055	C₂×C₄	1	1	yes	characteristic
122	#88055	C₂×C₄	1	1	yes	characteristic
123	#88054	—	2	1	no	—
124	#88054	—	2	1	no	—
125	#88054	—	2	1	no	—
126	#88054	—	2	1	no	—
127	C₈×Dic₁₃	—	2	1	no	—
128	C₈×Dic₁₃	—	2	1	no	—
129	C₈×Dic₁₃	—	2	1	no	—
130	C₈×Dic₁₃	D₄	1	1	yes	characteristic
131	C₈×Dic₁₃	D₄	1	1	yes	characteristic
132	#88050	C₂×C₄	1	1	yes	characteristic
133	#88049	C₂×C₄	1	1	yes	characteristic
134	#88048	C₂×C₄	1	1	yes	characteristic
135	#88047	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#1055	—	2	1	no	—
137	C₄⋊#1055	—	2	1	no	—
138	C₄⋊#1055	C₂³	1	1	yes	characteristic
139	C₄⋊#1055	C₂³	1	1	yes	characteristic
140	C₄×#1055	—	2	1	no	—
141	C₄×#1055	—	2	1	no	—
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	C₈×#137	—	13	1	no	maximal, Sylow
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	#6131	—	2	2	no	—
149	#6131	C₂×C₈	1	4	yes	—
150	Q₈×D₁₃	—	2	2	no	—
151	Q₈×D₁₃	C₂×C₈	1	4	yes	complemented
152	C₂×D₅₂	—	2	1	no	—
153	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₁₃	—	2	1	no	—
155	C₂×C₄×D₁₃	—	2	1	no	—
156	C₂×C₄×D₁₃	—	2	1	no	—
157	C₂×C₄×D₁₃	—	2	1	no	—
158	C₂×C₄×D₁₃	—	2	1	no	—
159	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
162	C₂×Dic₂₆	—	2	1	no	—
163	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
164	C₁₃×Q₁₆	C₂×C₈	1	4	yes	complemented
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	#6107	C₂×C₈	1	4	yes	complemented
180	#6106	C₂×C₈	1	4	yes	complemented
181	#6103	—	2	1	no	—
182	#6103	—	2	1	no	—
183	#6103	—	2	1	no	—
184	C₄⋊Dic₁₃	—	2	1	no	—
185	C₄⋊Dic₁₃	—	2	1	no	—
186	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
188	#6101	—	2	1	no	—
189	#6101	—	2	1	no	—
190	#6101	—	2	1	no	—
191	C₄×Dic₁₃	—	2	1	no	—
192	C₄×Dic₁₃	—	2	1	no	—
193	C₄×Dic₁₃	—	2	1	no	—
194	C₄×Dic₁₃	—	2	1	no	—
195	C₄×Dic₁₃	—	2	1	no	—
196	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
198	C₄×Dic₁₃	#41	1	1	yes	characteristic
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
203	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
204	C₂×#1055	C₂×D₄	1	1	yes	characteristic
205	C₂×#1055	C₂×D₄	1	1	yes	characteristic
206	#6095	C₂×C₈	1	4	yes	complemented
207	#6094	—	2	2	no	—
208	#6094	C₂×C₈	1	4	yes	complemented
209	C₈×D₁₃	—	2	2	no	—
210	C₈×D₁₃	—	4	1	no	—
211	C₈×D₁₃	—	4	2	no	—
212	C₈×D₁₃	—	4	2	no	—
213	C₈×D₁₃	—	4	2	no	—
214	C₈×#41	—	13	1	no	—
215	C₂×C₈×Q₈	—	13	1	no	—
216	C₄×#137	—	13	1	no	—
217	#1579	—	13	1	no	—
218	#1579	—	13	1	no	—
219	SD₁₆⋊C₈	—	13	1	no	—
220	SD₁₆⋊C₈	—	13	1	no	—
221	C₈×Q₁₆	—	13	1	no	—
222	C₈×Q₁₆	D₁₃	1	1	yes	characteristic, complemented
223	C₈×SD₁₆	—	13	1	no	—
224	C₈×SD₁₆	—	13	1	no	—
225	#1565	—	13	1	no	—
226	#1479	—	13	1	no	—
227	#1477	—	13	1	no	—
228	C₈×M₁₆	—	13	1	no	—
229	C₂²×D₁₃	—	2	1	no	—
230	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	C₂²×C₈	1	2	yes	—
234	Q₈×C₁₃	C₂²×C₈	1	2	yes	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
242	C₂×Dic₁₃	—	2	1	no	—
243	C₂×Dic₁₃	—	2	1	no	—
244	C₂×Dic₁₃	—	2	1	no	—
245	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
246	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
247	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
248	D₅₂	—	2	4	no	—
249	D₅₂	—	2	1	no	—
250	D₅₂	C₂²×C₈	1	2	yes	—
251	C₄×D₁₃	—	2	4	no	—
252	C₄×D₁₃	—	2	1	no	—
253	C₄×D₁₃	—	2	1	no	—
254	C₄×D₁₃	—	2	4	no	—
255	C₄×D₁₃	—	4	1	no	—
256	C₄×D₁₃	—	4	2	no	—
257	C₄×D₁₃	—	4	2	no	—
258	C₄×D₁₃	—	4	1	no	—
259	C₄×D₁₃	—	4	1	no	—
260	C₄×D₁₃	C₂²×C₈	1	2	yes	—
261	C₄×D₁₃	#131	1	2	yes	—
262	Dic₂₆	—	2	1	no	—
263	Dic₂₆	—	2	4	no	—
264	Dic₂₆	C₂²×C₈	1	2	yes	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	C₂²×C₈	1	2	yes	—
271	C₈×C₁₃	#137	1	2	yes	complemented
272	#1055	—	2	1	no	—
273	#1055	—	2	1	no	—
274	#1055	—	2	1	no	—
275	#1055	—	4	1	no	—
276	#1055	—	4	1	no	—
277	#1055	—	4	1	no	—
278	#1055	C₂²×C₈	1	2	yes	—
279	C₂×#137	—	13	1	no	—
280	C₄×#41	—	13	1	no	—
281	C₂×C₄×Q₈	—	13	1	no	—
282	C₈×Q₈	—	13	1	no	—
283	C₈×Q₈	—	13	1	no	—
284	C₈×Q₈	—	13	1	no	—
285	C₈×Q₈	—	13	1	no	—
286	C₈×Q₈	—	26	1	no	—
287	C₈×Q₈	—	26	1	no	—
288	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
289	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
290	#441	—	13	1	no	—
291	#441	—	13	1	no	—
292	#440	—	13	1	no	—
293	#440	—	13	1	no	—
294	C₄×Q₁₆	—	13	1	no	—
295	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
296	C₄×SD₁₆	—	13	1	no	—
297	C₄×SD₁₆	—	13	1	no	—
298	C₈×D₄	—	13	1	no	—
299	C₈×D₄	—	13	1	no	—
300	C₈×D₄	—	26	1	no	—
301	C₈×D₄	—	26	1	no	—
302	#431	—	13	1	no	—
303	#431	—	13	1	no	—
304	#431	—	26	1	no	—
305	#428	—	13	1	no	—
306	C₂×C₄⋊C₈	—	13	1	no	—
307	C₂×C₄⋊C₈	—	26	1	no	—
308	#419	—	13	1	no	—
309	#417	—	13	1	no	—
310	C₄×M₁₆	—	13	1	no	—
311	C₂×C₄×C₈	—	13	1	no	—
312	C₂×C₄×C₈	—	26	1	no	—
313	C₂×C₄×C₈	—	26	1	no	—
314	#335	—	13	1	no	—
315	#335	C₂×D₁₃	1	1	yes	characteristic
316	#334	—	13	1	no	—
317	#334	—	13	1	no	—
318	Q₈⋊C₈	—	13	1	no	—
319	Q₈⋊C₈	—	13	1	no	—
320	Q₈⋊C₈	—	13	1	no	—
321	Q₈⋊C₈	—	13	1	no	—
322	Q₈⋊C₈	C₂×D₁₃	1	1	yes	characteristic
323	Q₈⋊C₈	C₂×D₁₃	1	1	yes	characteristic
324	D₄⋊C₈	—	13	1	no	—
325	D₄⋊C₈	—	13	1	no	—
326	#322	—	13	1	no	—
327	#322	—	13	1	no	—
328	C₈²	—	13	1	no	—
329	C₈²	C₂×D₁₃	1	1	yes	characteristic
330	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	2	no	—
334	C₂×D₁₃	—	4	1	no	—
335	C₂×D₁₃	—	4	1	no	—
336	C₂×D₁₃	C₈×D₄	1	2	yes	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
343	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
344	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
345	C₄×C₁₃	#575	1	1	yes	characteristic
346	Dic₁₃	—	2	2	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	4	1	no	—
350	Dic₁₃	—	4	1	no	—
351	Dic₁₃	C₈×D₄	1	2	yes	—
352	C₂×#41	—	13	1	no	—
353	C₂²×Q₈	—	13	1	no	—
354	#137	—	13	8	no	—
355	C₂×Q₁₆	—	13	1	no	—
356	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic
357	C₂×SD₁₆	—	13	1	no	—
358	C₂×SD₁₆	—	13	1	no	—
359	C₂×M₁₆	—	13	1	no	—
360	C₂×M₁₆	—	13	1	no	—
361	C₂²×C₈	—	13	1	no	—
362	C₂²×C₈	—	13	1	no	—
363	C₂²×C₈	—	26	1	no	—
364	C₂²×C₈	—	26	1	no	—
365	C₂²×C₈	—	26	1	no	—
366	C₄×Q₈	—	13	1	no	—
367	C₄×Q₈	—	13	1	no	—
368	C₄×Q₈	—	13	1	no	—
369	C₄×Q₈	—	13	1	no	—
370	C₄×Q₈	—	26	1	no	—
371	C₄×Q₈	—	26	1	no	—
372	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
373	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
374	C₄×D₄	—	13	1	no	—
375	C₄×D₄	—	13	1	no	—
376	C₄×D₄	—	26	1	no	—
377	C₄×D₄	—	26	1	no	—
378	#117	—	13	1	no	—
379	#117	—	26	1	no	—
380	C₂×C₄⋊C₄	—	13	1	no	—
381	C₂×C₄⋊C₄	—	26	1	no	—
382	C₂×C₄²	—	13	1	no	—
383	C₂×C₄²	—	26	1	no	—
384	C₂×C₄²	—	26	1	no	—
385	#107	—	13	1	no	—
386	#107	C₄×D₁₃	1	1	yes	characteristic
387	#106	—	13	1	no	—
388	#106	—	13	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	13	1	no	—
392	C₄⋊C₈	—	13	1	no	—
393	C₄⋊C₈	—	26	1	no	—
394	C₄⋊C₈	—	26	1	no	—
395	C₄⋊C₈	—	26	1	no	—
396	C₄⋊C₈	—	26	1	no	—
397	C₄⋊C₈	—	26	1	no	—
398	C₄⋊C₈	—	26	1	no	—
399	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
401	#103	—	13	1	no	—
402	#103	—	13	1	no	—
403	#103	—	13	1	no	—
404	#103	—	13	1	no	—
405	#103	C₄×D₁₃	1	1	yes	characteristic
406	#103	C₄×D₁₃	1	1	yes	characteristic
407	#102	—	13	1	no	—
408	#102	—	13	1	no	—
409	C₂²⋊C₈	—	26	1	no	—
410	C₂²⋊C₈	—	26	1	no	—
411	C₂²⋊C₈	—	26	1	no	—
412	C₂²⋊C₈	—	26	1	no	—
413	#97	—	13	1	no	—
414	#97	—	13	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	13	1	no	—
418	C₄×C₈	—	13	1	no	—
419	C₄×C₈	—	13	1	no	—
420	C₄×C₈	—	13	1	no	—
421	C₄×C₈	—	13	1	no	—
422	C₄×C₈	—	26	1	no	—
423	C₄×C₈	—	26	1	no	—
424	C₄×C₈	—	26	1	no	—
425	C₄×C₈	—	26	1	no	—
426	C₄×C₈	—	26	1	no	—
427	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
430	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
431	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
432	C₂×C₁₃	#2955	1	1	yes	characteristic
433	D₁₃	—	2	2	no	—
434	D₁₃	—	4	2	no	—
435	#41	—	13	4	no	—
436	#41	—	26	2	no	—
437	C₂×Q₈	—	13	4	no	—
438	C₂×Q₈	—	13	1	no	—
439	C₂×Q₈	—	26	1	no	—
440	C₂×Q₈	—	26	2	no	—
441	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
442	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
443	C₂×D₄	—	13	1	no	—
444	C₂×D₄	—	26	1	no	—
445	C₂²×C₄	—	13	1	no	—
446	C₂²×C₄	—	13	1	no	—
447	C₂²×C₄	—	13	1	no	—
448	C₂²×C₄	—	26	1	no	—
449	C₂²×C₄	—	26	1	no	—
450	C₂²×C₄	—	26	1	no	—
451	C₂²×C₄	—	26	1	no	—
452	C₂²×C₄	—	26	1	no	—
453	Q₁₆	—	13	4	no	—
454	Q₁₆	C₈×D₁₃	1	4	yes	complemented
455	SD₁₆	—	13	4	no	—
456	SD₁₆	—	13	4	no	—
457	M₁₆	—	13	4	no	—
458	M₁₆	—	26	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	13	1	no	—
463	C₂×C₈	—	13	1	no	—
464	C₂×C₈	—	13	1	no	—
465	C₂×C₈	—	13	1	no	—
466	C₂×C₈	—	26	2	no	—
467	C₂×C₈	—	26	1	no	—
468	C₂×C₈	—	26	1	no	—
469	C₂×C₈	—	26	1	no	—
470	C₂×C₈	—	52	1	no	—
471	C₂×C₈	—	52	2	no	—
472	C₂×C₈	—	52	2	no	—
473	C₂×C₈	—	52	2	no	—
474	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
476	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
477	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	13	1	no	—
481	C₄⋊C₄	—	13	1	no	—
482	C₄⋊C₄	—	26	1	no	—
483	C₄⋊C₄	—	26	1	no	—
484	C₄⋊C₄	—	26	1	no	—
485	C₄⋊C₄	—	26	1	no	—
486	C₄⋊C₄	—	26	1	no	—
487	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
489	C₂²⋊C₄	—	26	1	no	—
490	C₂²⋊C₄	—	26	1	no	—
491	C₂²⋊C₄	—	26	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	13	1	no	—
495	C₄²	—	13	1	no	—
496	C₄²	—	13	1	no	—
497	C₄²	—	26	1	no	—
498	C₄²	—	26	1	no	—
499	C₄²	—	26	1	no	—
500	C₄²	—	26	1	no	—
501	C₄²	—	26	1	no	—
502	C₄²	C₂³×D₁₃	1	1	yes	characteristic
503	C₁₃	C₈×#137	1	1	yes	characteristic, complemented, Sylow
504	C₂³	—	13	1	no	—
505	C₂³	—	26	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	13	2	no	—
509	Q₈	—	26	4	no	—
510	Q₈	—	26	1	no	—
511	Q₈	C₂×C₈×D₁₃	1	2	yes	—
512	Q₈	C₂×C₈×D₁₃	1	2	yes	—
513	D₄	—	13	2	no	—
514	D₄	—	26	4	no	—
515	D₄	—	26	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	13	1	no	—
521	C₂×C₄	—	13	2	no	—
522	C₂×C₄	—	13	2	no	—
523	C₂×C₄	—	13	1	no	—
524	C₂×C₄	—	13	1	no	—
525	C₂×C₄	—	26	4	no	—
526	C₂×C₄	—	26	4	no	—
527	C₂×C₄	—	26	1	no	—
528	C₂×C₄	—	26	1	no	—
529	C₂×C₄	—	26	1	no	—
530	C₂×C₄	—	26	1	no	—
531	C₂×C₄	—	26	1	no	—
532	C₂×C₄	—	52	1	no	—
533	C₂×C₄	—	52	2	no	—
534	C₂×C₄	—	52	2	no	—
535	C₂×C₄	—	52	1	no	—
536	C₂×C₄	—	52	1	no	—
537	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
539	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	13	2	no	—
546	C₈	—	26	1	no	—
547	C₈	—	26	1	no	—
548	C₈	—	26	1	no	—
549	C₈	—	52	1	no	—
550	C₈	—	52	1	no	—
551	C₈	—	52	1	no	—
552	C₈	C₂×C₈×D₁₃	1	2	yes	—
553	C₈	#88172	1	2	yes	direct product factor
554	C₂²	—	13	2	no	—
555	C₂²	—	26	1	no	—
556	C₂²	—	26	1	no	—
557	C₂²	—	26	2	no	—
558	C₂²	—	52	1	no	—
559	C₂²	—	52	1	no	—
560	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	13	2	no	—
567	C₄	—	26	1	no	—
568	C₄	—	26	1	no	—
569	C₄	—	26	2	no	—
570	C₄	—	52	1	no	—
571	C₄	—	52	1	no	—
572	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
573	C₄	D₁₃×#131	1	1	yes	characteristic
574	C₄	C₂×#88172	1	1	yes	characteristic
575	C₄	#11719473	1	1	yes	characteristic
576	C₂	—	26	2	no	—
577	C₂	—	52	2	no	—
578	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
579	C₂	C₄×#88172	1	1	yes	characteristic
580	C₂	#13123734	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×Q₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6131	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×Q₁₆	D₁₃
hypocenter	C₁₃	C₈×#137
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈×D₁₃	C₂	semidirect
4. #13113655	C₂	semidirect
5. #13113652	C₂	semidirect
6. #13113651	C₂	semidirect
7. #13113647	C₂	semidirect
8. C₈×#6107	C₂	semidirect
9. C₈×#6095	C₂	semidirect
10. C₈×#6106	C₂	semidirect
11. #13113587	C₂	semidirect
12. #13113229	C₂	semidirect
14. C₈×#6094	C₂	semidirect
15. C₈×C₁₃×Q₁₆	C₂	semidirect
76. #88172	C₈	direct (N × H)
151. Q₈×D₁₃	C₂×C₈	semidirect
164. C₁₃×Q₁₆	C₂×C₈	semidirect
179. #6107	C₂×C₈	semidirect
180. #6106	C₂×C₈	semidirect
206. #6095	C₂×C₈	semidirect
208. #6094	C₂×C₈	semidirect
222. C₈×Q₁₆	D₁₃	semidirect
271. C₈×C₁₃	#137	semidirect
454. Q₁₆	C₈×D₁₃	semidirect
503. C₁₃	C₈×#137	semidirect
553. C₈	#88172	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#6131	2
C₈×Q₈×D₁₃	2
C₄×#88172	2
#13113655	2
#13113652	2
#13113651	2
#13113647	2
C₈×#6107	2
C₈×#6095	2
C₈×#6106	2
#13113587	2
#13113229	2
#13113222	2
C₈×#6094	2
C₈×C₁₃×Q₁₆	2
C₈×#137	13

Subgroups — C8×#88172 #15832345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88172 #15832345