Subgroups — C₂×#11751216 #14427686

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#91819	C₂	1	2	yes	maximal, complemented
3	C₂²×D₁₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751216	C₂	1	8	yes	maximal, direct product factor
5	C₂×#91105	C₂	1	2	yes	maximal, complemented
6	C₂×#91102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65404	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×#1220	—	2	2	no	—
10	C₂²×D₆₀	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	—	2	4	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	complemented
15	#91819	—	2	4	no	—
16	#91819	C₂²	1	8	yes	complemented
17	C₂×#6714	—	2	2	no	—
18	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
19	C₂×D₁₂₀	—	2	4	no	—
20	C₂×D₁₂₀	C₂²	1	4	yes	complemented
21	#91105	C₂²	1	8	yes	complemented
22	#91102	C₂²	1	4	yes	complemented
23	C₂×#5115	—	5	1	no	maximal, Hall
24	C₂³×C₅×C₈	D₃	1	1	yes	characteristic, complemented
25	C₂×#4076	—	3	2	no	—
26	C₂²×D₄₀	—	3	1	no	—
27	#65404	—	3	8	no	—
28	C₂×#3953	—	3	2	no	—
29	C₂×#3950	—	3	1	no	—
30	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
31	C₂³×D₁₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×#1220	—	2	8	no	—
39	C₂×#1220	—	4	8	no	—
40	C₂²×Dic₁₅	—	2	2	no	—
41	C₂×D₆₀	—	2	4	no	—
42	C₂×D₆₀	—	2	4	no	—
43	C₂×D₆₀	—	2	2	no	—
44	C₂×D₆₀	C₂³	1	4	yes	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	—	2	8	no	—
47	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	#6714	—	2	8	no	—
51	C₄⋊Dic₁₅	—	2	2	no	—
52	C₄⋊Dic₁₅	C₂³	1	4	yes	—
53	D₁₂₀	—	2	8	no	—
54	C₂³×C₃×C₈	D₅	1	1	yes	characteristic, complemented
55	C₂×#930	—	5	2	no	—
56	C₂²×D₂₄	—	5	1	no	—
57	#5115	—	5	8	no	—
58	C₂×#821	—	5	2	no	—
59	C₂×#818	—	5	1	no	—
60	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₂²⋊D₅	—	6	2	no	—
62	C₂²×D₂₀	—	3	2	no	—
63	C₂²×C₅×C₈	—	2	4	no	—
64	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂×D₃	1	4	yes	complemented
67	#4076	—	3	8	no	—
68	#4076	—	6	4	no	—
69	C₂×#685	—	6	2	no	—
70	C₂×C₄⋊Dic₅	—	3	2	no	—
71	C₂×D₄₀	—	3	4	no	—
72	C₂×D₄₀	—	6	4	no	—
73	#3953	—	3	8	no	—
74	#3950	—	3	4	no	—
75	C₂×#466	—	15	1	no	Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	D₈	1	4	yes	complemented
79	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×D₁₅	—	2	4	no	—
82	C₂²×D₁₅	—	4	4	no	—
83	C₂²×D₁₅	—	4	4	no	—
84	C₂²×D₁₅	—	4	4	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	#1220	—	4	16	no	—
95	C₂×Dic₁₅	—	2	4	no	—
96	C₂×Dic₁₅	—	4	4	no	—
97	D₆₀	—	2	4	no	—
98	D₆₀	—	2	4	no	—
99	D₆₀	—	4	4	no	—
100	C₃×C₅×C₈	—	2	2	no	—
101	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
102	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
103	C₂²×#67	—	10	2	no	—
104	C₂²×D₁₂	—	5	2	no	—
105	C₂²×C₃×C₈	—	2	4	no	—
106	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂×D₅	1	4	yes	complemented
109	#930	—	5	8	no	—
110	#930	—	10	4	no	—
111	C₂×(C₂×D₃)⋊C₄	—	10	2	no	—
112	C₂×C₄⋊Dic₃	—	5	2	no	—
113	C₂×D₂₄	—	5	4	no	—
114	C₂×D₂₄	—	10	4	no	—
115	#821	—	5	8	no	—
116	#818	—	5	4	no	—
117	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
118	C₂³×D₅	—	6	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
122	C₂²×C₄×C₅	D₁₂	1	2	yes	—
123	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
124	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₂×C₂²⋊D₅	—	6	8	no	—
126	C₂×C₂²⋊D₅	—	12	8	no	—
127	C₂²×Dic₅	—	6	2	no	—
128	C₂×D₂₀	—	3	4	no	—
129	C₂×D₂₀	—	6	4	no	—
130	C₂×D₂₀	—	6	4	no	—
131	C₂×D₂₀	—	6	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	8	no	—
134	C₂×C₅×C₈	#67	1	4	yes	complemented
135	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
136	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
137	#685	—	6	8	no	—
138	C₄⋊Dic₅	—	3	4	no	—
139	C₄⋊Dic₅	—	6	2	no	—
140	D₄₀	—	6	8	no	—
141	C₂²×D₈	—	15	1	no	—
142	C₂³×C₈	D₁₅	1	1	yes	characteristic, complemented
143	C₂×#121	—	15	2	no	—
144	#466	—	15	8	no	—
145	C₂×#107	—	15	1	no	—
146	C₂×#102	—	15	2	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	8	no	—
150	C₂²×C₃×C₅	#121	1	2	yes	—
151	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
152	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
153	C₂²×C₃×C₅	#135	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₂×D₁₅	—	4	4	no	—
156	C₂×D₁₅	—	4	4	no	—
157	C₂×D₁₅	—	4	4	no	—
158	C₂×D₁₅	—	8	8	no	—
159	C₃×C₄×C₅	—	2	2	no	—
160	C₃×C₄×C₅	#121	1	2	yes	—
161	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
163	Dic₁₅	—	4	4	no	—
164	C₂⁴×C₃	D₂₀	1	1	yes	characteristic
165	C₂³×D₃	—	10	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
169	C₂²×C₃×C₄	D₂₀	1	2	yes	—
170	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
171	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
172	C₂×#67	—	10	8	no	—
173	C₂×#67	—	20	8	no	—
174	C₂²×Dic₃	—	10	2	no	—
175	C₂×D₁₂	—	5	4	no	—
176	C₂×D₁₂	—	10	4	no	—
177	C₂×D₁₂	—	10	4	no	—
178	C₂×D₁₂	—	10	2	no	—
179	C₂×C₃×C₈	—	2	2	no	—
180	C₂×C₃×C₈	—	2	8	no	—
181	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
182	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
183	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
184	(C₂×D₃)⋊C₄	—	10	8	no	—
185	C₄⋊Dic₃	—	5	4	no	—
186	C₄⋊Dic₃	—	10	2	no	—
187	D₂₄	—	10	8	no	—
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	—	2	2	no	—
190	C₂³×C₅	D₂₄	1	4	yes	complemented
191	C₂³×C₅	C₂×D₁₂	1	2	yes	—
192	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
193	C₂²×D₅	—	6	4	no	—
194	C₂²×D₅	—	12	4	no	—
195	C₂²×D₅	—	12	4	no	—
196	C₂²×D₅	—	12	4	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
202	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
203	C₂×C₄×C₅	#235	1	2	yes	—
204	C₂×C₄×C₅	C₂×#67	1	2	yes	—
205	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
206	C₂²⋊D₅	—	12	16	no	—
207	C₂×Dic₅	—	6	4	no	—
208	C₂×Dic₅	—	12	4	no	—
209	D₂₀	—	6	4	no	—
210	D₂₀	—	6	4	no	—
211	D₂₀	—	12	4	no	—
212	C₅×C₈	—	2	2	no	—
213	C₅×C₈	C₂×#67	1	4	yes	complemented
214	C₂²×D₄	—	15	2	no	—
215	C₂²×D₄	—	30	2	no	—
216	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
217	C₂×D₈	—	15	4	no	—
218	C₂×D₈	—	30	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
221	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
222	C₂²×C₈	C₂×D₁₅	1	4	yes	complemented
223	#121	—	15	8	no	—
224	#121	—	30	4	no	—
225	C₂×C₄⋊C₄	—	15	2	no	—
226	C₂×C₂²⋊C₄	—	30	2	no	—
227	#107	—	15	4	no	—
228	#102	—	15	8	no	—
229	C₂×C₃×C₅	—	2	4	no	—
230	C₂×C₃×C₅	#466	1	4	yes	complemented
231	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
234	D₁₅	—	8	4	no	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	D₄₀	1	4	yes	complemented
238	C₂³×C₃	C₂×D₂₀	1	2	yes	—
239	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
240	C₂²×D₃	—	10	4	no	—
241	C₂²×D₃	—	20	4	no	—
242	C₂²×D₃	—	20	4	no	—
243	C₂²×D₃	—	20	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
249	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
250	C₂×C₃×C₄	#709	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
252	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
253	#67	—	20	16	no	—
254	C₂×Dic₃	—	10	4	no	—
255	C₂×Dic₃	—	20	4	no	—
256	D₁₂	—	10	4	no	—
257	D₁₂	—	10	4	no	—
258	D₁₂	—	20	4	no	—
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	8	no	—
264	C₂²×C₅	C₂×D₂₄	1	2	yes	—
265	C₂²×C₅	C₂×D₂₄	1	4	yes	complemented
266	C₂²×C₅	#904	1	2	yes	—
267	C₂²×C₅	#930	1	2	yes	—
268	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
269	C₂×D₅	—	12	4	no	—
270	C₂×D₅	—	12	4	no	—
271	C₂×D₅	—	12	4	no	—
272	C₂×D₅	—	24	8	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	#930	1	2	yes	—
275	C₄×C₅	C₂×#235	1	1	yes	characteristic
276	C₄×C₅	C₂²×#67	1	1	yes	characteristic
277	Dic₅	—	12	4	no	—
278	C₂⁴	—	30	2	no	—
279	C₂⁴	D₆₀	1	1	yes	characteristic
280	C₂×D₄	—	15	4	no	—
281	C₂×D₄	—	30	8	no	—
282	C₂×D₄	—	30	2	no	—
283	C₂×D₄	—	30	4	no	—
284	C₂×D₄	—	30	4	no	—
285	C₂×D₄	—	60	8	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	30	2	no	—
289	C₂²×C₄	D₆₀	1	2	yes	—
290	C₂²×C₄	D₆₀	1	1	yes	characteristic
291	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
292	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
293	D₈	—	30	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	#1220	1	4	yes	complemented
297	C₂×C₈	C₂²×D₁₅	1	2	yes	—
298	C₂×C₈	C₂²×D₁₅	1	2	yes	—
299	C₄⋊C₄	—	15	4	no	—
300	C₄⋊C₄	—	30	2	no	—
301	C₂²⋊C₄	—	30	8	no	—
302	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	8	no	—
306	C₂²×C₃	C₂×D₄₀	1	2	yes	—
307	C₂²×C₃	C₂×D₄₀	1	4	yes	complemented
308	C₂²×C₃	#4050	1	2	yes	—
309	C₂²×C₃	#4076	1	2	yes	—
310	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
311	C₂×D₃	—	20	4	no	—
312	C₂×D₃	—	20	4	no	—
313	C₂×D₃	—	20	4	no	—
314	C₂×D₃	—	40	8	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	#4076	1	2	yes	—
317	C₃×C₄	C₂×#709	1	1	yes	characteristic
318	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
319	Dic₃	—	20	4	no	—
320	C₂×C₅	—	2	4	no	—
321	C₂×C₅	#5115	1	4	yes	complemented
322	C₂×C₅	C₂²×D₂₄	1	1	yes	characteristic
323	C₂×C₅	C₂×#904	1	1	yes	characteristic
324	C₂×C₅	C₂×#930	1	1	yes	characteristic
325	D₅	—	24	4	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	30	4	no	—
329	C₂³	—	60	4	no	—
330	C₂³	—	60	4	no	—
331	C₂³	—	60	4	no	—
332	C₂³	D₁₂₀	1	4	yes	complemented
333	C₂³	C₂×D₆₀	1	2	yes	—
334	C₂³	C₂×D₆₀	1	1	yes	characteristic
335	D₄	—	30	4	no	—
336	D₄	—	30	4	no	—
337	D₄	—	60	16	no	—
338	D₄	—	60	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	30	4	no	—
344	C₂×C₄	—	60	4	no	—
345	C₂×C₄	C₂×D₆₀	1	2	yes	—
346	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
347	C₂×C₄	#6817	1	2	yes	—
348	C₂×C₄	C₂×#1220	1	2	yes	—
349	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	C₂×#1220	1	4	yes	complemented
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	#65404	1	4	yes	complemented
354	C₂×C₃	C₂²×D₄₀	1	1	yes	characteristic
355	C₂×C₃	C₂×#4050	1	1	yes	characteristic
356	C₂×C₃	C₂×#4076	1	1	yes	characteristic
357	D₃	—	40	4	no	—
358	C₅	C₂×#5115	1	1	yes	characteristic, complemented, Sylow
359	C₂²	—	2	2	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	60	4	no	—
363	C₂²	—	60	4	no	—
364	C₂²	—	60	4	no	—
365	C₂²	—	120	8	no	—
366	C₂²	C₂×D₁₂₀	1	2	yes	—
367	C₂²	C₂×D₁₂₀	1	4	yes	complemented
368	C₂²	#91793	1	2	yes	—
369	C₂²	#91819	1	2	yes	—
370	C₂²	C₂²×D₆₀	1	1	yes	characteristic
371	C₄	—	2	2	no	—
372	C₄	—	60	4	no	—
373	C₄	#91819	1	2	yes	—
374	C₄	C₂×#6817	1	1	yes	characteristic
375	C₄	C₂²×#1220	1	1	yes	characteristic
376	C₃	C₂×#65404	1	1	yes	characteristic, complemented, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	120	4	no	—
379	C₂	#11751216	1	4	yes	direct product factor
380	C₂	C₂²×D₁₂₀	1	1	yes	characteristic
381	C₂	C₂×#91793	1	1	yes	characteristic
382	C₂	C₂×#91819	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₆₀
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂³×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂³×C₈	D₁₅
hypocenter	C₃×C₅	C₂×#466
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×C₈	C₂	semidirect
2. C₂×#91819	C₂	semidirect
3. C₂²×D₁₂₀	C₂	semidirect
4. #11751216	C₂	direct (N × H)
5. C₂×#91105	C₂	semidirect
6. C₂×#91102	C₂	semidirect
14. C₂²×C₃×C₅×C₈	C₂²	semidirect
16. #91819	C₂²	semidirect
20. C₂×D₁₂₀	C₂²	semidirect
21. #91105	C₂²	semidirect
22. #91102	C₂²	semidirect
24. C₂³×C₅×C₈	D₃	semidirect
47. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂³×C₃×C₈	D₅	semidirect
66. C₂²×C₅×C₈	C₂×D₃	semidirect
78. C₂³×C₃×C₅	D₈	semidirect
101. C₃×C₅×C₈	C₂×D₄	semidirect
108. C₂²×C₃×C₈	C₂×D₅	semidirect
134. C₂×C₅×C₈	#67	semidirect
142. C₂³×C₈	D₁₅	semidirect
152. C₂²×C₃×C₅	C₂×D₈	semidirect
181. C₂×C₃×C₈	C₂²⋊D₅	semidirect
190. C₂³×C₅	D₂₄	semidirect
213. C₅×C₈	C₂×#67	semidirect
222. C₂²×C₈	C₂×D₁₅	semidirect
230. C₂×C₃×C₅	#466	semidirect
237. C₂³×C₃	D₄₀	semidirect
260. C₃×C₈	C₂×C₂²⋊D₅	semidirect
265. C₂²×C₅	C₂×D₂₄	semidirect
296. C₂×C₈	#1220	semidirect
302. C₃×C₅	C₂×#466	semidirect
307. C₂²×C₃	C₂×D₄₀	semidirect
321. C₂×C₅	#5115	semidirect
332. C₂³	D₁₂₀	semidirect
351. C₈	C₂×#1220	semidirect
353. C₂×C₃	#65404	semidirect
358. C₅	C₂×#5115	semidirect
367. C₂²	C₂×D₁₂₀	semidirect
376. C₃	C₂×#65404	semidirect
379. C₂	#11751216	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×C₈	2
C₂×#91819	2
C₂²×D₁₂₀	2
#11751216	2
C₂×#91105	2
C₂×#91102	2
C₂×#65404	3
C₂×#5115	5

Subgroups — C2×#11751216 #14427686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751216 #14427686