Subgroups — C₂×#11751184 #14425865

Order 1920.

1088 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6717	C₂	1	2	yes	maximal
3	C₂×C₄×D₆₀	C₂	1	1	yes	maximal, characteristic
4	C₂×#91119	C₂	1	2	yes	maximal, complemented
5	#11751184	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65372	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×D₆₀	C₂²	1	1	yes	characteristic
10	C₂²×C₄×D₁₅	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×#6717	—	2	8	no	—
17	C₂×#6717	C₂²	1	8	yes	—
18	C₂×#6714	—	2	1	no	—
19	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃⋊#168	C₂²	1	2	yes	—
21	C₄×D₆₀	—	2	2	no	—
22	C₄×D₆₀	C₂²	1	4	yes	—
23	#91119	C₂²	1	8	yes	complemented
24	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
25	C₂×#5083	—	5	1	no	maximal, Hall
26	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
27	C₂²×#688	—	3	2	no	—
28	C₂×C₄×D₂₀	—	3	1	no	—
29	C₂×#3967	—	3	2	no	—
30	#65372	—	3	8	no	—
31	C₂×C₄⋊#168	—	3	1	no	—
32	C₂³×D₁₅	—	2	1	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×Dic₁₅	—	2	1	no	—
42	C₂×D₆₀	—	2	1	no	—
43	C₂×D₆₀	—	2	2	no	—
44	C₂×D₆₀	D₄	1	4	yes	—
45	C₂×D₆₀	C₂³	1	2	yes	—
46	C₂×C₄×D₁₅	—	2	4	no	—
47	C₂×C₄×D₁₅	—	4	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	4	no	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄²×C₅	C₂³	1	2	yes	—
52	#6717	—	2	16	no	—
53	#6714	—	2	4	no	—
54	C₄⋊Dic₁₅	—	2	1	no	—
55	C₄⋊Dic₁₅	C₂³	1	2	yes	—
56	C₂×C₃⋊#168	—	2	4	no	—
57	C₂×C₃⋊#168	C₂³	1	4	yes	—
58	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
59	C₂²×#215	—	5	2	no	—
60	C₂×C₄×D₁₂	—	5	1	no	—
61	C₂×#835	—	5	2	no	—
62	#5083	—	5	8	no	—
63	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
64	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
65	C₂²×D₂₀	—	3	1	no	—
66	C₂²×C₄×D₅	—	6	1	no	—
67	C₅×C₄⋊Q₈	—	2	2	no	—
68	C₅×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂×#688	—	3	8	no	—
73	C₂×#688	—	6	8	no	—
74	C₂×#685	—	6	1	no	—
75	C₂×C₄⋊Dic₅	—	3	1	no	—
76	C₂²×#168	—	3	2	no	—
77	C₄×D₂₀	—	3	4	no	—
78	C₄×D₂₀	—	6	2	no	—
79	#3967	—	3	8	no	—
80	C₄⋊#168	—	3	4	no	—
81	C₂×#461	—	15	1	no	Sylow
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×D₁₅	—	2	4	no	—
84	C₂²×D₁₅	—	2	2	no	—
85	C₂²×D₁₅	—	4	2	no	—
86	C₂²×D₁₅	—	4	2	no	—
87	C₃×C₅×Q₈	—	2	4	no	—
88	C₃×C₅×Q₈	—	2	4	no	—
89	C₃×C₅×Q₈	—	4	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	4	4	no	—
93	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	complemented
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	#41	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×Dic₁₅	—	2	2	no	—
101	C₂×Dic₁₅	—	4	2	no	—
102	D₆₀	—	2	4	no	—
103	D₆₀	—	2	2	no	—
104	D₆₀	C₂×D₄	1	4	yes	—
105	C₄×D₁₅	—	4	8	no	—
106	C₃⋊#168	—	2	4	no	—
107	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
108	C₂²×D₁₂	—	5	1	no	—
109	C₂²×C₄×D₃	—	10	1	no	—
110	C₃×C₄⋊Q₈	—	2	2	no	—
111	C₃×C₄⋊Q₈	C₂×D₅	1	4	yes	complemented
112	C₂×C₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
115	C₂×#215	—	5	8	no	—
116	C₂×#215	—	10	8	no	—
117	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
118	C₂×C₄⋊Dic₃	—	5	1	no	—
119	C₂²×C₃⋊C₈	—	5	2	no	—
120	C₄×D₁₂	—	5	4	no	—
121	C₄×D₁₂	—	10	2	no	—
122	#835	—	5	8	no	—
123	C₄⋊(C₃⋊C₈)	—	5	4	no	—
124	C₂³×D₅	—	6	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	4	no	—
127	C₂×C₅×Q₈	—	2	4	no	—
128	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	#67	1	1	yes	characteristic
131	C₂²×C₄×C₅	#67	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₂²×Dic₅	—	6	1	no	—
134	C₂×D₂₀	—	3	4	no	—
135	C₂×D₂₀	—	3	2	no	—
136	C₂×D₂₀	—	6	2	no	—
137	C₂×D₂₀	—	6	1	no	—
138	C₂×C₄×D₅	—	6	4	no	—
139	C₂×C₄×D₅	—	12	4	no	—
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₄²×C₅	#67	1	2	yes	—
143	C₄²×C₅	C₂²×D₃	1	2	yes	—
144	#688	—	6	16	no	—
145	#685	—	6	4	no	—
146	C₄⋊Dic₅	—	3	2	no	—
147	C₄⋊Dic₅	—	6	1	no	—
148	C₂×#168	—	3	4	no	—
149	C₂×#168	—	6	4	no	—
150	C₂²×SD₁₆	—	15	2	no	—
151	C₂×C₄⋊Q₈	D₁₅	1	1	yes	characteristic, complemented
152	C₂×C₄×D₄	—	15	1	no	—
153	#461	—	15	8	no	—
154	C₂×C₄⋊C₈	—	15	1	no	—
155	C₂×#103	—	15	2	no	—
156	C₂²×C₃×C₅	#121	1	2	yes	—
157	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
158	C₂²×C₃×C₅	#137	1	2	yes	—
159	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
160	C₂×D₁₅	—	2	4	no	—
161	C₂×D₁₅	—	4	2	no	—
162	C₂×D₁₅	—	4	2	no	—
163	C₂×D₁₅	—	4	8	no	—
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	#121	1	2	yes	—
167	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	complemented
168	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
170	Dic₁₅	—	4	2	no	—
171	C₂³×D₃	—	10	1	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	4	no	—
174	C₂×C₃×Q₈	—	2	4	no	—
175	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
180	C₂²×Dic₃	—	10	1	no	—
181	C₂×D₁₂	—	5	4	no	—
182	C₂×D₁₂	—	5	2	no	—
183	C₂×D₁₂	—	10	2	no	—
184	C₂×D₁₂	—	10	1	no	—
185	C₂×C₄×D₃	—	10	4	no	—
186	C₂×C₄×D₃	—	20	4	no	—
187	C₃×C₄⋊C₄	—	2	4	no	—
188	C₃×C₄⋊C₄	—	2	4	no	—
189	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
190	C₃×C₄²	C₂²×D₅	1	2	yes	—
191	#215	—	10	16	no	—
192	(C₂×D₃)⋊C₄	—	10	4	no	—
193	C₄⋊Dic₃	—	5	2	no	—
194	C₄⋊Dic₃	—	10	1	no	—
195	C₂×C₃⋊C₈	—	5	4	no	—
196	C₂×C₃⋊C₈	—	10	4	no	—
197	C₂³×C₅	C₂×#67	1	1	yes	characteristic
198	C₂²×D₅	—	6	4	no	—
199	C₂²×D₅	—	6	2	no	—
200	C₂²×D₅	—	12	2	no	—
201	C₂²×D₅	—	12	2	no	—
202	C₅×Q₈	—	2	4	no	—
203	C₅×Q₈	—	2	4	no	—
204	C₅×Q₈	—	4	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	4	4	no	—
208	C₂×C₄×C₅	#215	1	4	yes	complemented
209	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	#237	1	2	yes	—
211	C₂×C₄×C₅	C₂×#67	1	2	yes	—
212	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×#67	1	2	yes	—
214	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
215	C₂×Dic₅	—	6	2	no	—
216	C₂×Dic₅	—	12	2	no	—
217	D₂₀	—	3	4	no	—
218	D₂₀	—	6	4	no	—
219	D₂₀	—	6	2	no	—
220	C₄×D₅	—	12	8	no	—
221	#168	—	6	4	no	—
222	C₂²×Q₈	C₂×D₁₅	1	2	yes	—
223	C₂²×D₄	—	15	1	no	—
224	C₂³×C₄	—	30	1	no	—
225	C₂×SD₁₆	—	15	8	no	—
226	C₂×SD₁₆	—	30	8	no	—
227	C₂²×C₈	—	15	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×D₁₅	1	4	yes	complemented
230	C₄×D₄	—	15	4	no	—
231	C₄×D₄	—	30	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	15	1	no	—
235	C₂×C₂²⋊C₄	—	30	1	no	—
236	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
237	C₄⋊C₈	—	15	4	no	—
238	#103	—	15	8	no	—
239	C₂×C₃×C₅	#461	1	4	yes	complemented
240	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
242	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
243	D₁₅	—	4	4	no	—
244	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
245	C₂²×D₃	—	10	2	no	—
246	C₂²×D₃	—	10	4	no	—
247	C₂²×D₃	—	20	2	no	—
248	C₂²×D₃	—	20	2	no	—
249	C₃×Q₈	—	2	4	no	—
250	C₃×Q₈	—	2	4	no	—
251	C₃×Q₈	—	4	4	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	#688	1	4	yes	complemented
256	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
257	C₂×C₃×C₄	#711	1	2	yes	—
258	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₂×Dic₃	—	10	2	no	—
263	C₂×Dic₃	—	20	2	no	—
264	D₁₂	—	5	4	no	—
265	D₁₂	—	10	2	no	—
266	D₁₂	—	10	4	no	—
267	C₄×D₃	—	20	8	no	—
268	C₃⋊C₈	—	10	4	no	—
269	C₂²×C₅	#938	1	2	yes	—
270	C₂²×C₅	C₂×#215	1	2	yes	—
271	C₂²×C₅	#942	1	2	yes	—
272	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
273	C₂×D₅	—	6	4	no	—
274	C₂×D₅	—	12	2	no	—
275	C₂×D₅	—	12	2	no	—
276	C₂×D₅	—	12	8	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	4	no	—
279	C₄×C₅	#938	1	2	yes	—
280	C₄×C₅	C₂×#215	1	4	yes	complemented
281	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
282	C₄×C₅	C₂×#237	1	1	yes	characteristic
283	Dic₅	—	12	2	no	—
284	C₂⁴	—	30	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₂²×D₁₅	1	4	yes	—
289	C₂×D₄	—	15	4	no	—
290	C₂×D₄	—	15	2	no	—
291	C₂×D₄	—	30	2	no	—
292	C₂×D₄	—	30	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	30	1	no	—
295	C₂²×C₄	—	30	4	no	—
296	C₂²×C₄	—	60	4	no	—
297	C₂²×C₄	#1220	1	1	yes	characteristic
298	C₂²×C₄	#1220	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
300	SD₁₆	—	30	16	no	—
301	C₂×C₈	—	15	4	no	—
302	C₂×C₈	—	30	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	15	2	no	—
306	C₄⋊C₄	—	30	1	no	—
307	C₂²⋊C₄	—	30	4	no	—
308	C₄²	#1220	1	2	yes	—
309	C₄²	C₂²×D₁₅	1	2	yes	—
310	C₃×C₅	C₂×#461	1	1	yes	characteristic, complemented, Hall
311	C₂²×C₃	#4084	1	2	yes	—
312	C₂²×C₃	C₂×#688	1	2	yes	—
313	C₂²×C₃	#4088	1	2	yes	—
314	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
315	C₂×D₃	—	10	4	no	—
316	C₂×D₃	—	20	8	no	—
317	C₂×D₃	—	20	2	no	—
318	C₂×D₃	—	20	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	4	4	no	—
321	C₃×C₄	#4084	1	2	yes	—
322	C₃×C₄	C₂×#688	1	4	yes	complemented
323	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
324	C₃×C₄	C₂×#711	1	1	yes	characteristic
325	Dic₃	—	20	2	no	—
326	C₂×C₅	#5083	1	4	yes	complemented
327	C₂×C₅	C₂×#938	1	1	yes	characteristic
328	C₂×C₅	C₂²×#215	1	1	yes	characteristic
329	C₂×C₅	C₂×#942	1	1	yes	characteristic
330	D₅	—	12	4	no	—
331	C₂³	—	30	4	no	—
332	C₂³	—	30	2	no	—
333	C₂³	—	60	2	no	—
334	C₂³	—	60	2	no	—
335	C₂³	C₂×#1220	1	1	yes	characteristic
336	Q₈	—	2	4	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	4	no	—
339	D₄	—	15	4	no	—
340	D₄	—	30	4	no	—
341	D₄	—	30	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	30	2	no	—
346	C₂×C₄	—	60	2	no	—
347	C₂×C₄	—	60	8	no	—
348	C₂×C₄	#6717	1	4	yes	complemented
349	C₂×C₄	D₄×D₁₅	1	2	yes	—
350	C₂×C₄	#6819	1	2	yes	—
351	C₂×C₄	C₂×#1220	1	2	yes	—
352	C₂×C₄	C₂×#1220	1	1	yes	characteristic
353	C₂×C₄	C₂×#1220	1	2	yes	—
354	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
355	C₈	—	30	4	no	—
356	C₂×C₃	#65372	1	4	yes	complemented
357	C₂×C₃	C₂×#4084	1	1	yes	characteristic
358	C₂×C₃	C₂²×#688	1	1	yes	characteristic
359	C₂×C₃	C₂×#4088	1	1	yes	characteristic
360	D₃	—	20	4	no	—
361	C₅	C₂×#5083	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	30	4	no	—
363	C₂²	—	60	8	no	—
364	C₂²	—	60	2	no	—
365	C₂²	—	60	2	no	—
366	C₂²	#91827	1	2	yes	—
367	C₂²	C₂×#6717	1	2	yes	—
368	C₂²	#91831	1	2	yes	—
369	C₂²	C₂²×#1220	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	60	2	no	—
373	C₄	#91827	1	2	yes	—
374	C₄	C₂×#6717	1	4	yes	complemented
375	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
376	C₄	C₂×#6819	1	1	yes	characteristic
377	C₃	C₂×#65372	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	60	4	no	—
379	C₂	#11751184	1	4	yes	direct product factor
380	C₂	C₂×#91827	1	1	yes	characteristic
381	C₂	C₂²×#6717	1	1	yes	characteristic
382	C₂	C₂×#91831	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1220
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
hypercenter	C₂×C₄⋊Q₈	D₁₅
hypocenter	C₃×C₅	C₂×#461
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₂×#91119	C₂	semidirect
5. #11751184	C₂	direct (N × H)
6. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. #91119	C₂²	semidirect
24. C₄⋊(C₃⋊#168)	C₂²	semidirect
26. C₂×C₅×C₄⋊Q₈	D₃	semidirect
58. C₂×C₃×C₄⋊Q₈	D₅	semidirect
68. C₅×C₄⋊Q₈	C₂×D₃	semidirect
93. C₂×C₃×C₄×C₅	SD₁₆	semidirect
111. C₃×C₄⋊Q₈	C₂×D₅	semidirect
151. C₂×C₄⋊Q₈	D₁₅	semidirect
167. C₃×C₄×C₅	C₂×SD₁₆	semidirect
208. C₂×C₄×C₅	#215	semidirect
229. C₄⋊Q₈	C₂×D₁₅	semidirect
239. C₂×C₃×C₅	#461	semidirect
255. C₂×C₃×C₄	#688	semidirect
280. C₄×C₅	C₂×#215	semidirect
310. C₃×C₅	C₂×#461	semidirect
322. C₃×C₄	C₂×#688	semidirect
326. C₂×C₅	#5083	semidirect
348. C₂×C₄	#6717	semidirect
356. C₂×C₃	#65372	semidirect
361. C₅	C₂×#5083	semidirect
374. C₄	C₂×#6717	semidirect
377. C₃	C₂×#65372	semidirect
379. C₂	#11751184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₂²×#6717	2
C₂×C₄×D₆₀	2
C₂×#91119	2
#11751184	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×#65372	3
C₂×#5083	5

Subgroups — C2×#11751184 #14425865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751184 #14425865