Subgroups — C₈×#6817 #14418892

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6817	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#1220	C₂	1	4	yes	maximal, complemented
4	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₆₀	C₂	1	2	yes	maximal, complemented
6	#11750786	C₂	1	2	yes	maximal, complemented
7	C₄×C₈×D₁₅	C₂	1	2	yes	maximal, complemented
8	C₈×Dic₃₀	C₂	1	2	yes	maximal, complemented
9	C₈×#709	—	3	1	no	maximal, Hall
10	C₂×#6817	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₄×#1220	C₄	1	2	yes	—
14	C₄×#1220	C₂²	1	2	yes	—
15	#91815	C₄	1	1	yes	characteristic
16	C₂×C₈×D₁₅	C₂²	1	4	yes	—
17	C₄×D₆₀	C₄	1	1	yes	characteristic
18	C₄×D₆₀	C₂²	1	1	yes	characteristic
19	#91761	C₄	1	2	yes	—
20	C₄²×D₁₅	C₂²	1	2	yes	—
21	C₄×Dic₃₀	C₄	1	1	yes	characteristic
22	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	#91114	C₂²	1	2	yes	—
27	#91104	C₂²	1	4	yes	—
28	#91098	C₂²	1	4	yes	—
29	C₈×Dic₁₅	C₂²	1	4	yes	—
30	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
31	C₄×C₃⋊#168	C₂²	1	2	yes	—
32	C₈×#235	—	5	1	no	maximal, Hall
33	C₄×#709	—	3	1	no	—
34	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
35	C₈×C₂²⋊D₅	—	3	4	no	—
36	#65214	—	3	1	no	—
37	C₈×D₂₀	—	3	2	no	—
38	#64974	—	3	2	no	—
39	C₄×C₈×D₅	—	3	2	no	—
40	C₈×Dic₁₀	—	3	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×#1220	C₂×C₄	1	2	yes	—
45	#6817	C₈	1	8	yes	direct product factor
46	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
48	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
49	C₂×C₄×D₁₅	C₂³	1	2	yes	—
50	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	#6719	C₂×C₄	1	2	yes	—
59	#6714	C₂×C₄	1	2	yes	—
60	#6714	C₂×C₄	1	2	yes	—
61	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
62	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
63	#6712	C₂×C₄	1	2	yes	—
64	#6712	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
66	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
67	C₄×Dic₁₅	C₂³	1	2	yes	—
68	C₂×C₃⋊#168	C₂³	1	4	yes	—
69	C₈×D₁₅	—	2	8	no	—
70	C₄×#235	—	5	1	no	—
71	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic, complemented
72	C₈×#67	—	5	4	no	—
73	#4925	—	5	1	no	—
74	C₈×D₁₂	—	5	2	no	—
75	#4685	—	5	2	no	—
76	C₄×D₃×C₈	—	5	2	no	—
77	C₈×Dic₆	—	5	2	no	—
78	C₂×#709	—	3	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	—	3	2	no	—
82	C₄×C₂²⋊D₅	—	3	2	no	—
83	#4072	—	3	1	no	—
84	C₂×C₈×D₅	—	3	4	no	—
85	C₄×D₂₀	—	3	1	no	—
86	C₄×D₂₀	—	3	1	no	—
87	#4018	—	3	2	no	—
88	C₄²×D₅	—	3	2	no	—
89	C₄×Dic₁₀	—	3	1	no	—
90	C₄×Dic₁₀	—	3	1	no	—
91	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
92	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
94	C₂²⋊#168	—	3	2	no	—
95	#3952	—	3	4	no	—
96	#3946	—	3	4	no	—
97	C₈×Dic₅	—	3	4	no	—
98	C₄⋊#168	—	3	2	no	—
99	C₄×#168	—	3	2	no	—
100	C₈×#41	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	#1220	C₂×C₈	1	8	yes	complemented
113	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
114	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
115	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
116	D₆₀	C₂×C₈	1	4	yes	complemented
117	C₄×D₁₅	—	2	4	no	—
118	C₄×D₁₅	—	2	4	no	—
119	C₄×D₁₅	C₂×C₈	1	8	yes	complemented
120	Dic₃₀	C₂×C₈	1	4	yes	complemented
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	#41	1	4	yes	complemented
123	C₃⋊#168	—	2	4	no	—
124	C₂×#235	—	5	1	no	—
125	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
126	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
127	C₄×#67	—	5	2	no	—
128	C₄×#67	—	5	2	no	—
129	#926	—	5	1	no	—
130	C₂×D₃×C₈	—	5	4	no	—
131	C₄×D₁₂	—	5	1	no	—
132	C₄×D₁₂	—	5	1	no	—
133	#872	—	5	2	no	—
134	C₄²×D₃	—	5	2	no	—
135	C₄×Dic₆	—	5	1	no	—
136	C₄×Dic₆	—	5	1	no	—
137	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
138	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
139	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
140	#830	—	5	2	no	—
141	(C₂×D₃)⋊C₈	—	5	4	no	—
142	Dic₃⋊C₈	—	5	4	no	—
143	C₈×Dic₃	—	5	4	no	—
144	C₄⋊(C₃⋊C₈)	—	5	2	no	—
145	C₄×C₃⋊C₈	—	5	2	no	—
146	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	—	3	2	no	—
150	#709	—	3	8	no	—
151	C₂×D₂₀	—	3	1	no	—
152	C₂×C₄×D₅	—	3	2	no	—
153	C₂×C₄×D₅	—	3	2	no	—
154	C₂×C₄×D₅	—	3	2	no	—
155	C₂×Dic₁₀	—	3	1	no	—
156	C₂×C₅×C₈	—	2	4	no	—
157	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
158	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
159	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
160	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
161	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂²⋊Dic₅	—	3	2	no	—
164	#685	—	3	2	no	—
165	#685	—	3	2	no	—
166	C₄⋊Dic₅	—	3	1	no	—
167	C₄⋊Dic₅	—	3	1	no	—
168	#683	—	3	2	no	—
169	#683	—	3	2	no	—
170	C₄×Dic₅	—	3	2	no	—
171	C₄×Dic₅	—	3	2	no	—
172	C₄×Dic₅	—	3	2	no	—
173	C₂×#168	—	3	4	no	—
174	C₈×D₅	—	6	8	no	—
175	C₄×#41	—	15	1	no	—
176	C₈×Q₈	—	15	2	no	—
177	C₈×D₄	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	#431	—	15	1	no	—
180	#431	—	15	2	no	—
181	C₂×C₄×C₈	—	15	2	no	—
182	C₂×C₄×C₈	D₁₅	1	1	yes	characteristic, complemented
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×D₁₅	—	2	2	no	—
188	C₂×D₁₅	—	2	2	no	—
189	C₂×D₁₅	C₂²×C₈	1	4	yes	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	2	yes	—
196	Dic₁₅	—	2	2	no	—
197	Dic₁₅	—	2	2	no	—
198	Dic₁₅	C₂²×C₈	1	4	yes	—
199	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₂×#67	—	5	2	no	—
203	#235	—	5	8	no	—
204	C₂×D₁₂	—	5	1	no	—
205	C₂×C₄×D₃	—	5	2	no	—
206	C₂×C₄×D₃	—	5	2	no	—
207	C₂×C₄×D₃	—	5	2	no	—
208	C₂×Dic₆	—	5	1	no	—
209	C₂×C₃×C₈	—	2	4	no	—
210	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
211	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
212	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
216	#217	—	5	2	no	—
217	(C₂×D₃)⋊C₄	—	5	2	no	—
218	(C₂×D₃)⋊C₄	—	5	2	no	—
219	C₄⋊Dic₃	—	5	1	no	—
220	C₄⋊Dic₃	—	5	1	no	—
221	Dic₃⋊C₄	—	5	2	no	—
222	Dic₃⋊C₄	—	5	2	no	—
223	C₄×Dic₃	—	5	2	no	—
224	C₄×Dic₃	—	5	2	no	—
225	C₄×Dic₃	—	5	2	no	—
226	C₂×C₃⋊C₈	—	5	4	no	—
227	D₃×C₈	—	10	8	no	—
228	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂²×D₅	—	3	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	D₃×C₈	1	4	yes	complemented
233	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
239	C₂²⋊D₅	—	3	8	no	—
240	C₂×Dic₅	—	3	2	no	—
241	C₂×Dic₅	—	3	2	no	—
242	C₂×Dic₅	—	3	2	no	—
243	D₂₀	—	3	4	no	—
244	C₄×D₅	—	3	8	no	—
245	C₄×D₅	—	6	4	no	—
246	C₄×D₅	—	6	4	no	—
247	Dic₁₀	—	3	4	no	—
248	C₅×C₈	—	2	2	no	—
249	C₅×C₈	#235	1	4	yes	complemented
250	#168	—	6	4	no	—
251	C₂×#41	—	15	1	no	—
252	C₂²×C₈	—	15	4	no	—
253	C₂²×C₈	C₂×D₁₅	1	2	yes	—
254	C₄×Q₈	—	15	1	no	—
255	C₄×Q₈	—	15	1	no	—
256	C₄×D₄	—	15	2	no	—
257	C₄×D₄	—	15	2	no	—
258	C₄×D₄	—	15	1	no	—
259	C₄×D₄	—	15	1	no	—
260	#117	—	15	1	no	—
261	#117	—	15	2	no	—
262	C₂×C₄²	—	15	2	no	—
263	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
264	C₄⋊C₈	—	15	4	no	—
265	C₄⋊C₈	—	15	2	no	—
266	C₂²⋊C₈	—	15	2	no	—
267	C₂²⋊C₈	—	15	4	no	—
268	C₄×C₈	—	15	4	no	—
269	C₄×C₈	—	15	2	no	—
270	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
271	C₄×C₈	C₂×D₁₅	1	2	yes	—
272	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	D₁₅	—	2	4	no	—
278	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
279	C₂²×D₃	—	5	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	C₈×D₅	1	4	yes	complemented
283	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
289	#67	—	5	8	no	—
290	C₂×Dic₃	—	5	2	no	—
291	C₂×Dic₃	—	5	2	no	—
292	C₂×Dic₃	—	5	2	no	—
293	D₁₂	—	5	4	no	—
294	C₄×D₃	—	5	8	no	—
295	C₄×D₃	—	10	4	no	—
296	C₄×D₃	—	10	4	no	—
297	Dic₆	—	5	4	no	—
298	C₃×C₈	—	2	2	no	—
299	C₃×C₈	#709	1	4	yes	complemented
300	C₃⋊C₈	—	10	4	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
304	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
305	C₂×D₅	—	3	4	no	—
306	C₂×D₅	—	6	2	no	—
307	C₂×D₅	—	6	2	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
311	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
312	C₄×C₅	#901	1	2	yes	—
313	C₄×C₅	C₂×#235	1	2	yes	—
314	Dic₅	—	3	4	no	—
315	Dic₅	—	6	2	no	—
316	Dic₅	—	6	2	no	—
317	#41	—	15	8	no	—
318	C₂×Q₈	—	15	1	no	—
319	C₂×D₄	—	15	2	no	—
320	C₂×D₄	—	15	1	no	—
321	C₂²×C₄	—	15	2	no	—
322	C₂²×C₄	—	15	2	no	—
323	C₂²×C₄	—	15	2	no	—
324	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
325	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	15	4	no	—
329	C₂×C₈	—	30	8	no	—
330	C₂×C₈	C₂²×D₁₅	1	2	yes	—
331	C₂×C₈	C₂²×D₁₅	1	2	yes	—
332	C₄⋊C₄	—	15	2	no	—
333	C₄⋊C₄	—	15	2	no	—
334	C₄⋊C₄	—	15	1	no	—
335	C₄⋊C₄	—	15	1	no	—
336	C₂²⋊C₄	—	15	2	no	—
337	C₂²⋊C₄	—	15	2	no	—
338	C₂²⋊C₄	—	15	2	no	—
339	C₄²	—	15	2	no	—
340	C₄²	—	15	2	no	—
341	C₄²	—	15	2	no	—
342	C₄²	C₄×D₁₅	1	1	yes	characteristic
343	C₄²	C₄×D₁₅	1	1	yes	characteristic
344	C₄²	C₂²×D₁₅	1	1	yes	characteristic
345	C₄²	C₂²×D₁₅	1	1	yes	characteristic
346	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
350	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
351	C₂×D₃	—	5	4	no	—
352	C₂×D₃	—	10	2	no	—
353	C₂×D₃	—	10	2	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
357	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
358	C₃×C₄	#4047	1	2	yes	—
359	C₃×C₄	C₂×#709	1	2	yes	—
360	Dic₃	—	5	4	no	—
361	Dic₃	—	10	2	no	—
362	Dic₃	—	10	2	no	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	C₄×#235	1	1	yes	characteristic
365	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
366	C₂×C₅	C₂×#901	1	1	yes	characteristic
367	D₅	—	6	4	no	—
368	C₂³	—	15	2	no	—
369	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
370	Q₈	—	15	4	no	—
371	D₄	—	15	8	no	—
372	D₄	—	15	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	15	2	no	—
376	C₂×C₄	—	15	8	no	—
377	C₂×C₄	—	15	2	no	—
378	C₂×C₄	—	15	2	no	—
379	C₂×C₄	—	30	4	no	—
380	C₂×C₄	—	30	4	no	—
381	C₂×C₄	C₈×D₁₅	1	4	yes	complemented
382	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
383	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
384	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
385	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
386	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	30	4	no	—
390	C₈	#6817	1	4	yes	direct product factor
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	C₄×#709	1	1	yes	characteristic
393	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
394	C₂×C₃	C₂×#4047	1	1	yes	characteristic
395	D₃	—	10	4	no	—
396	C₅	C₈×#235	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	15	4	no	—
400	C₂²	—	30	2	no	—
401	C₂²	—	30	2	no	—
402	C₂²	C₂×C₈×D₁₅	1	2	yes	—
403	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	15	4	no	—
407	C₄	—	30	2	no	—
408	C₄	—	30	2	no	—
409	C₄	C₂×C₈×D₁₅	1	2	yes	—
410	C₄	C₂×C₈×D₁₅	1	2	yes	—
411	C₄	#91790	1	2	yes	—
412	C₄	C₂×#6817	1	2	yes	—
413	C₃	C₈×#709	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	30	4	no	—
416	C₂	C₄×#6817	1	1	yes	characteristic
417	C₂	C₂²×C₈×D₁₅	1	1	yes	characteristic
418	C₂	C₂×#91790	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂×D₁₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×#6817	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄×C₈	D₁₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
3. C₈×#1220	C₂	semidirect
4. #11751026	C₂	semidirect
5. C₈×D₆₀	C₂	semidirect
6. #11750786	C₂	semidirect
7. C₄×C₈×D₁₅	C₂	semidirect
8. C₈×Dic₃₀	C₂	semidirect
34. C₂×C₄×C₅×C₈	D₃	semidirect
45. #6817	C₈	direct (N × H)
71. C₂×C₃×C₄×C₈	D₅	semidirect
105. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
112. #1220	C₂×C₈	semidirect
116. D₆₀	C₂×C₈	semidirect
119. C₄×D₁₅	C₂×C₈	semidirect
120. Dic₃₀	C₂×C₈	semidirect
122. C₃×C₅×C₈	#41	semidirect
182. C₂×C₄×C₈	D₁₅	semidirect
232. C₂×C₄×C₅	D₃×C₈	semidirect
249. C₅×C₈	#235	semidirect
282. C₂×C₃×C₄	C₈×D₅	semidirect
299. C₃×C₈	#709	semidirect
346. C₃×C₅	C₈×#41	semidirect
381. C₂×C₄	C₈×D₁₅	semidirect
390. C₈	#6817	direct (N × H)
396. C₅	C₈×#235	semidirect
413. C₃	C₈×#709	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6817	2
C₂×C₃×C₄×C₅×C₈	2
C₈×#1220	2
#11751026	2
C₈×D₆₀	2
#11750786	2
C₄×C₈×D₁₅	2
C₈×Dic₃₀	2
C₈×#709	3
C₈×#235	5

Subgroups — C8×#6817 #14418892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#6817 #14418892