Subgroups — C₈×#88170 #15832294

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 596 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, complemented
2	C₈×#6129	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88170	C₂	1	1	yes	maximal, characteristic
4	C₈×#6107	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113640	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#6095	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113635	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#6104	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113628	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113581	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113217	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113215	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88170	C₄	1	1	yes	characteristic
17	C₄×#6131	C₂²	1	1	yes	characteristic
18	C₄×#6129	C₂²	1	1	yes	characteristic
19	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	SD₁₆×Dic₁₃	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₃	—	2	1	no	—
24	C₂×C₈×Dic₁₃	—	2	1	no	—
25	C₄×#6107	C₂²	1	1	yes	characteristic
26	Q₈×#1055	C₂²	1	1	yes	characteristic
27	C₄×#6104	C₂²	1	1	yes	characteristic
28	D₄×#1055	C₂²	1	1	yes	characteristic
29	#11718521	C₄	1	1	yes	characteristic
30	#11718513	C₄	1	1	yes	characteristic
31	#11718495	—	2	1	no	—
32	#11718495	C₂²	1	1	yes	characteristic
33	#11718494	—	2	1	no	—
34	#11718494	C₂²	1	1	yes	characteristic
35	#11718494	C₂²	1	1	yes	characteristic
36	#11718491	C₂²	1	1	yes	characteristic
37	#11718465	C₄	1	1	yes	characteristic
38	#11718451	C₄	1	1	yes	characteristic
39	#11718433	C₄	1	1	yes	characteristic
40	#11718417	C₄	1	1	yes	characteristic
41	#11718386	—	2	1	no	—
42	#11718379	—	2	1	no	—
43	C₄×#6095	C₂²	1	1	yes	characteristic
44	C₈×D₅₂	—	2	1	no	—
45	C₈×D₅₂	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₃	—	2	1	no	—
47	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
50	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
51	C₁₃×#334	C₂²	1	1	yes	characteristic
52	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₈²×C₁₃	C₂²	1	1	yes	characteristic
55	Q₈⋊#1055	C₂²	1	1	yes	characteristic
56	D₄⋊#1055	C₂²	1	1	yes	characteristic
57	#11718076	C₂²	1	1	yes	characteristic
58	#11718075	C₂²	1	1	yes	characteristic
59	#11718071	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	C₈×#1055	C₂²	1	1	yes	characteristic
65	C₈×#1055	C₂²	1	1	yes	characteristic
66	C₈×#1055	C₂²	1	1	yes	characteristic
67	C₂×#6131	C₂×C₄	1	1	yes	characteristic
68	C₂×#6129	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	—	2	1	no	—
71	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×#6107	C₂×C₄	1	1	yes	characteristic
75	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×#6104	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₃	—	2	1	no	—
78	C₂×C₄×Dic₁₃	—	2	1	no	—
79	C₂²×#1055	—	2	1	no	—
80	#88170	C₈	1	8	yes	direct product factor
81	C₂×#6095	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₁₃	—	2	1	no	—
83	C₂×C₈×D₁₃	—	2	1	no	—
84	C₂×C₈×D₁₃	—	2	1	no	—
85	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
88	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
89	#88147	—	2	1	no	—
90	#88147	C₂×C₄	1	1	yes	characteristic
91	#88146	—	2	1	no	—
92	#88146	C₂×C₄	1	1	yes	characteristic
93	#88146	C₂×C₄	1	1	yes	characteristic
94	#88141	C₂×C₄	1	1	yes	characteristic
95	#88135	—	2	1	no	—
96	#88131	—	2	1	no	—
97	C₄×D₅₂	—	2	1	no	—
98	C₄×D₅₂	C₂³	1	1	yes	characteristic
99	C₄²×D₁₃	—	2	1	no	—
100	C₄²×D₁₃	C₂³	1	1	yes	characteristic
101	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
102	C₁₃×#106	C₂×C₄	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₁₃×#103	C₂×C₄	1	1	yes	characteristic
107	C₁₃×#102	C₂×C₄	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₈	—	2	1	no	—
109	C₄×C₈×C₁₃	—	2	1	no	—
110	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	#88075	C₂×C₄	1	1	yes	characteristic
114	#88072	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊#1055	—	2	1	no	—
116	#88061	C₂×C₄	1	1	yes	characteristic
117	#88060	—	2	1	no	—
118	#88060	—	2	1	no	—
119	#88060	—	2	1	no	—
120	#88060	—	2	1	no	—
121	#88057	C₂×C₄	1	1	yes	characteristic
122	#88056	C₂×C₄	1	1	yes	characteristic
123	#88054	—	2	1	no	—
124	#88054	—	2	1	no	—
125	C₈×Dic₁₃	—	2	1	no	—
126	C₈×Dic₁₃	—	2	1	no	—
127	C₈×Dic₁₃	—	2	1	no	—
128	C₈×Dic₁₃	—	2	1	no	—
129	C₈×Dic₁₃	—	2	1	no	—
130	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
131	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₁₃	D₄	1	1	yes	characteristic
133	C₈×Dic₁₃	D₄	1	1	yes	characteristic
134	#88050	C₂×C₄	1	1	yes	characteristic
135	#88049	C₂×C₄	1	1	yes	characteristic
136	#88047	C₂×C₄	1	1	yes	characteristic
137	#88047	C₂×C₄	1	1	yes	characteristic
138	C₄⋊#1055	—	2	1	no	—
139	C₄⋊#1055	C₂³	1	1	yes	characteristic
140	C₄⋊#1055	C₂³	1	1	yes	characteristic
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×#135	—	13	1	no	maximal, Sylow
146	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂×C₂²⋊D₁₃	—	2	1	no	—
150	C₂²×Dic₁₃	—	2	1	no	—
151	C₂²×Dic₁₃	—	2	1	no	—
152	#6131	—	2	2	no	—
153	#6131	C₂×C₈	1	4	yes	complemented
154	#6129	—	2	2	no	—
155	#6129	C₂×C₈	1	4	yes	complemented
156	C₂×D₅₂	—	2	1	no	—
157	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₁₃	—	2	1	no	—
159	C₂×C₄×D₁₃	—	2	1	no	—
160	C₂×C₄×D₁₃	—	2	1	no	—
161	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
165	C₁₃×SD₁₆	C₂×C₈	1	4	yes	complemented
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	4	2	no	—
170	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
177	C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	—	2	1	no	—
181	#6107	C₂×C₈	1	4	yes	complemented
182	#6104	C₂×C₈	1	4	yes	complemented
183	#6103	—	2	1	no	—
184	#6103	—	2	1	no	—
185	#6103	—	2	1	no	—
186	#6103	—	2	1	no	—
187	C₄⋊Dic₁₃	—	2	1	no	—
188	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
190	#6101	—	2	1	no	—
191	#6101	—	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	—	2	1	no	—
197	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
199	C₄×Dic₁₃	#41	1	1	yes	characteristic
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	4	2	no	—
204	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
205	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
206	C₂×#1055	C₂×D₄	1	1	yes	characteristic
207	C₂×#1055	C₂×D₄	1	1	yes	characteristic
208	#6095	C₂×C₈	1	4	yes	complemented
209	C₈×D₁₃	—	2	4	no	—
210	C₈×D₁₃	—	2	2	no	—
211	C₈×D₁₃	—	2	2	no	—
212	C₈×D₁₃	—	2	2	no	—
213	C₈×D₁₃	—	4	2	no	—
214	C₈×D₁₃	—	4	2	no	—
215	C₈×D₁₃	C₂×C₈	1	4	yes	complemented
216	C₈×#41	—	13	1	no	—
217	C₈×#41	—	13	1	no	—
218	C₄×#135	—	13	1	no	—
219	C₈×Q₁₆	—	13	1	no	—
220	C₈×Q₁₆	—	13	1	no	—
221	C₈×SD₁₆	—	13	1	no	—
222	C₈×SD₁₆	—	13	1	no	—
223	C₈×SD₁₆	—	13	1	no	—
224	C₈×SD₁₆	D₁₃	1	1	yes	characteristic, complemented
225	C₈×D₈	—	13	1	no	—
226	C₈×D₈	—	13	1	no	—
227	#1564	—	13	1	no	—
228	#1476	—	13	1	no	—
229	#1476	—	13	1	no	—
230	C₂×C₈²	—	13	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂²×D₁₃	—	2	1	no	—
233	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	C₂²×C₈	1	2	yes	—
236	D₄×C₁₃	—	2	1	no	—
237	D₄×C₁₃	C₂²×C₈	1	2	yes	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
246	C₂²⋊D₁₃	—	2	4	no	—
247	C₂×Dic₁₃	—	2	1	no	—
248	C₂×Dic₁₃	—	2	4	no	—
249	C₂×Dic₁₃	—	2	1	no	—
250	C₂×Dic₁₃	—	2	1	no	—
251	C₂×Dic₁₃	—	4	2	no	—
252	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
253	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
255	D₅₂	—	2	4	no	—
256	D₅₂	—	2	1	no	—
257	D₅₂	C₂²×C₈	1	2	yes	—
258	C₄×D₁₃	—	2	1	no	—
259	C₄×D₁₃	—	2	1	no	—
260	C₄×D₁₃	—	2	4	no	—
261	C₄×D₁₃	—	2	2	no	—
262	C₄×D₁₃	—	4	1	no	—
263	C₄×D₁₃	—	4	1	no	—
264	C₄×D₁₃	—	4	2	no	—
265	C₄×D₁₃	C₂²×C₈	1	2	yes	—
266	C₄×D₁₃	#131	1	2	yes	—
267	Dic₂₆	—	2	1	no	—
268	Dic₂₆	C₂²×C₈	1	2	yes	—
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	4	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	C₂²×C₈	1	2	yes	—
275	C₈×C₁₃	#135	1	2	yes	complemented
276	#1055	—	2	2	no	—
277	#1055	—	2	1	no	—
278	#1055	—	2	1	no	—
279	#1055	—	4	1	no	—
280	#1055	—	4	1	no	—
281	#1055	C₂²×C₈	1	2	yes	—
282	#1055	#135	1	2	yes	complemented
283	C₂×#135	—	13	1	no	—
284	C₄×#41	—	13	1	no	—
285	C₄×#41	—	13	1	no	—
286	C₈×Q₈	—	13	1	no	—
287	C₈×Q₈	—	13	1	no	—
288	C₈×Q₈	—	13	1	no	—
289	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic
290	C₄×Q₁₆	—	13	1	no	—
291	C₄×Q₁₆	—	13	1	no	—
292	C₄×SD₁₆	—	13	1	no	—
293	C₄×SD₁₆	—	13	1	no	—
294	C₄×SD₁₆	—	13	1	no	—
295	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
296	C₄×D₈	—	13	1	no	—
297	C₄×D₈	—	13	1	no	—
298	C₈×D₄	—	13	1	no	—
299	C₈×D₄	—	13	1	no	—
300	C₈×D₄	—	13	1	no	—
301	C₈×D₄	—	26	1	no	—
302	C₈×D₄	—	26	1	no	—
303	C₈×D₄	—	26	1	no	—
304	C₈×D₄	—	26	1	no	—
305	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
306	#431	—	13	1	no	—
307	#431	—	13	1	no	—
308	#431	—	26	1	no	—
309	#431	—	26	1	no	—
310	#427	—	13	1	no	—
311	#416	—	13	1	no	—
312	#416	—	13	1	no	—
313	C₂×C₄×C₈	—	13	1	no	—
314	C₂×C₄×C₈	—	13	1	no	—
315	C₂×C₄×C₈	—	13	1	no	—
316	C₂×C₄×C₈	—	26	1	no	—
317	C₂×C₄×C₈	—	26	1	no	—
318	#335	—	13	1	no	—
319	#335	—	13	1	no	—
320	#334	—	13	1	no	—
321	#334	C₂×D₁₃	1	1	yes	characteristic
322	Q₈⋊C₈	—	13	1	no	—
323	Q₈⋊C₈	—	13	1	no	—
324	Q₈⋊C₈	—	13	1	no	—
325	Q₈⋊C₈	C₂×D₁₃	1	1	yes	characteristic
326	D₄⋊C₈	—	13	1	no	—
327	D₄⋊C₈	—	13	1	no	—
328	D₄⋊C₈	—	13	1	no	—
329	D₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
330	C₈²	—	13	1	no	—
331	C₈²	—	13	1	no	—
332	C₈²	—	13	1	no	—
333	C₈²	C₂×D₁₃	1	1	yes	characteristic
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	2	2	no	—
341	C₂×D₁₃	—	4	1	no	—
342	C₂×D₁₃	—	4	1	no	—
343	C₂×D₁₃	C₈×D₄	1	2	yes	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
349	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
350	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
351	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
352	Dic₁₃	—	2	2	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	—	4	1	no	—
355	Dic₁₃	—	4	1	no	—
356	Dic₁₃	C₈×D₄	1	2	yes	—
357	Dic₁₃	#443	1	2	yes	—
358	C₂×#41	—	13	1	no	—
359	C₂×#41	—	13	1	no	—
360	#135	—	13	8	no	—
361	C₂×Q₁₆	—	13	1	no	—
362	C₂×SD₁₆	—	13	1	no	—
363	C₂×SD₁₆	C₄×D₁₃	1	1	yes	characteristic
364	C₂×D₈	—	13	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	13	1	no	—
367	C₂²×C₈	—	13	1	no	—
368	C₂²×C₈	—	13	1	no	—
369	C₂²×C₈	—	13	1	no	—
370	C₂²×C₈	—	26	1	no	—
371	C₂²×C₈	—	26	1	no	—
372	C₂²×C₈	—	26	1	no	—
373	C₂²×C₈	—	26	1	no	—
374	C₄×Q₈	—	13	1	no	—
375	C₄×Q₈	—	13	1	no	—
376	C₄×Q₈	—	13	1	no	—
377	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
378	C₄×D₄	—	13	1	no	—
379	C₄×D₄	—	13	1	no	—
380	C₄×D₄	—	13	1	no	—
381	C₄×D₄	—	26	1	no	—
382	C₄×D₄	—	26	1	no	—
383	C₄×D₄	—	26	1	no	—
384	C₄×D₄	—	26	1	no	—
385	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
386	#117	—	13	1	no	—
387	#117	—	13	1	no	—
388	#117	—	26	1	no	—
389	#117	—	26	1	no	—
390	C₂×C₄²	—	13	1	no	—
391	C₂×C₄²	—	26	1	no	—
392	C₂×C₄²	—	26	1	no	—
393	#107	—	13	1	no	—
394	#107	—	13	1	no	—
395	#106	—	13	1	no	—
396	#106	C₄×D₁₃	1	1	yes	characteristic
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	13	1	no	—
399	C₄⋊C₈	—	13	1	no	—
400	C₄⋊C₈	—	26	1	no	—
401	C₄⋊C₈	—	26	1	no	—
402	C₄⋊C₈	—	26	1	no	—
403	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
405	#103	—	13	1	no	—
406	#103	—	13	1	no	—
407	#103	—	13	1	no	—
408	#103	C₄×D₁₃	1	1	yes	characteristic
409	#102	—	13	1	no	—
410	#102	—	13	1	no	—
411	#102	—	13	1	no	—
412	#102	C₄×D₁₃	1	1	yes	characteristic
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	26	1	no	—
415	C₂²⋊C₈	—	26	1	no	—
416	C₂²⋊C₈	—	26	1	no	—
417	C₂²⋊C₈	—	26	1	no	—
418	C₂²⋊C₈	—	26	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	—	13	1	no	—
421	C₄×C₈	—	13	1	no	—
422	C₄×C₈	—	13	1	no	—
423	C₄×C₈	—	13	1	no	—
424	C₄×C₈	—	13	1	no	—
425	C₄×C₈	—	13	1	no	—
426	C₄×C₈	—	13	1	no	—
427	C₄×C₈	—	26	1	no	—
428	C₄×C₈	—	26	1	no	—
429	C₄×C₈	—	26	1	no	—
430	C₄×C₈	—	26	1	no	—
431	C₄×C₈	—	26	1	no	—
432	C₄×C₈	—	26	1	no	—
433	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
438	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
439	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
440	D₁₃	—	2	2	no	—
441	D₁₃	—	4	2	no	—
442	#41	—	13	4	no	—
443	#41	—	13	4	no	—
444	#41	—	26	2	no	—
445	#41	—	26	2	no	—
446	C₂×Q₈	—	13	1	no	—
447	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
448	C₂×D₄	—	13	1	no	—
449	C₂×D₄	—	26	1	no	—
450	C₂×D₄	—	26	1	no	—
451	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	13	1	no	—
454	C₂²×C₄	—	13	1	no	—
455	C₂²×C₄	—	13	1	no	—
456	C₂²×C₄	—	26	1	no	—
457	C₂²×C₄	—	26	1	no	—
458	C₂²×C₄	—	26	1	no	—
459	C₂²×C₄	—	26	1	no	—
460	C₂²×C₄	—	26	1	no	—
461	Q₁₆	—	13	4	no	—
462	SD₁₆	—	13	4	no	—
463	SD₁₆	C₈×D₁₃	1	4	yes	complemented
464	D₈	—	13	4	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	4	2	no	—
469	C₂×C₈	—	13	1	no	—
470	C₂×C₈	—	13	1	no	—
471	C₂×C₈	—	13	4	no	—
472	C₂×C₈	—	13	1	no	—
473	C₂×C₈	—	13	1	no	—
474	C₂×C₈	—	26	2	no	—
475	C₂×C₈	—	26	2	no	—
476	C₂×C₈	—	26	4	no	—
477	C₂×C₈	—	26	1	no	—
478	C₂×C₈	—	26	2	no	—
479	C₂×C₈	—	26	1	no	—
480	C₂×C₈	—	26	1	no	—
481	C₂×C₈	—	52	2	no	—
482	C₂×C₈	—	52	2	no	—
483	C₂×C₈	—	52	2	no	—
484	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
486	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
487	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	26	1	no	—
492	C₄⋊C₄	—	26	1	no	—
493	C₄⋊C₄	—	26	1	no	—
494	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	26	1	no	—
498	C₂²⋊C₄	—	26	1	no	—
499	C₂²⋊C₄	—	26	1	no	—
500	C₂²⋊C₄	—	26	1	no	—
501	C₂²⋊C₄	—	26	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	13	1	no	—
504	C₄²	—	13	1	no	—
505	C₄²	—	13	1	no	—
506	C₄²	—	26	1	no	—
507	C₄²	—	26	1	no	—
508	C₄²	—	26	1	no	—
509	C₄²	—	26	1	no	—
510	C₄²	—	26	1	no	—
511	C₄²	C₂³×D₁₃	1	1	yes	characteristic
512	C₁₃	C₈×#135	1	1	yes	characteristic, complemented, Sylow
513	C₂³	—	2	1	no	—
514	C₂³	—	13	1	no	—
515	C₂³	—	26	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	13	2	no	—
518	Q₈	—	26	1	no	—
519	Q₈	C₂×C₈×D₁₃	1	2	yes	—
520	D₄	—	2	1	no	—
521	D₄	—	13	2	no	—
522	D₄	—	26	4	no	—
523	D₄	—	26	4	no	—
524	D₄	—	26	1	no	—
525	D₄	C₂×C₈×D₁₃	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	13	1	no	—
532	C₂×C₄	—	13	1	no	—
533	C₂×C₄	—	13	2	no	—
534	C₂×C₄	—	13	2	no	—
535	C₂×C₄	—	13	1	no	—
536	C₂×C₄	—	26	2	no	—
537	C₂×C₄	—	26	4	no	—
538	C₂×C₄	—	26	4	no	—
539	C₂×C₄	—	26	1	no	—
540	C₂×C₄	—	26	1	no	—
541	C₂×C₄	—	26	1	no	—
542	C₂×C₄	—	26	1	no	—
543	C₂×C₄	—	26	1	no	—
544	C₂×C₄	—	52	2	no	—
545	C₂×C₄	—	52	2	no	—
546	C₂×C₄	—	52	1	no	—
547	C₂×C₄	—	52	1	no	—
548	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
550	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	13	2	no	—
557	C₈	—	13	2	no	—
558	C₈	—	26	2	no	—
559	C₈	—	26	1	no	—
560	C₈	—	26	1	no	—
561	C₈	—	52	1	no	—
562	C₈	—	52	1	no	—
563	C₈	C₂×C₈×D₁₃	1	2	yes	—
564	C₈	#88170	1	2	yes	direct product factor
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	13	2	no	—
569	C₂²	—	26	1	no	—
570	C₂²	—	26	1	no	—
571	C₂²	—	26	2	no	—
572	C₂²	—	52	1	no	—
573	C₂²	—	52	1	no	—
574	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	13	2	no	—
580	C₄	—	13	2	no	—
581	C₄	—	26	1	no	—
582	C₄	—	26	2	no	—
583	C₄	—	52	1	no	—
584	C₄	—	52	1	no	—
585	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
586	C₄	D₁₃×#131	1	1	yes	characteristic
587	C₄	C₂×#88170	1	1	yes	characteristic
588	C₄	D₁₃×#135	1	1	yes	characteristic
589	C₂	—	4	2	no	—
590	C₂	—	26	2	no	—
591	C₂	—	52	2	no	—
592	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
593	C₂	C₄×#88170	1	1	yes	characteristic
594	C₂	D₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×SD₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88170	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×SD₁₆	D₁₃
hypocenter	C₁₃	C₈×#135
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₈×#6131	C₂	semidirect
2. C₈×#6129	C₂	semidirect
4. C₈×#6107	C₂	semidirect
5. #13113640	C₂	semidirect
6. C₈×#6095	C₂	semidirect
7. SD₁₆×#1055	C₂	semidirect
8. #13113635	C₂	semidirect
9. C₈×#6104	C₂	semidirect
10. #13113628	C₂	semidirect
11. #13113581	C₂	semidirect
12. #13113217	C₂	semidirect
13. #13113215	C₂	semidirect
14. C₈²×D₁₃	C₂	semidirect
15. C₈×C₁₃×SD₁₆	C₂	semidirect
80. #88170	C₈	direct (N × H)
153. #6131	C₂×C₈	semidirect
155. #6129	C₂×C₈	semidirect
165. C₁₃×SD₁₆	C₂×C₈	semidirect
181. #6107	C₂×C₈	semidirect
182. #6104	C₂×C₈	semidirect
208. #6095	C₂×C₈	semidirect
215. C₈×D₁₃	C₂×C₈	semidirect
224. C₈×SD₁₆	D₁₃	semidirect
275. C₈×C₁₃	#135	semidirect
282. #1055	#135	semidirect
463. SD₁₆	C₈×D₁₃	semidirect
512. C₁₃	C₈×#135	semidirect
564. C₈	#88170	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×#6129	2
C₄×#88170	2
C₈×#6107	2
#13113640	2
C₈×#6095	2
SD₁₆×#1055	2
#13113635	2
C₈×#6104	2
#13113628	2
#13113581	2
#13113217	2
#13113215	2
C₈²×D₁₃	2
C₈×C₁₃×SD₁₆	2
C₈×#135	13

Subgroups — C8×#88170 #15832294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88170 #15832294