Subgroups — C₂×#11755200 #14478941

Order 1920.

3456 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	C₂²×#6821	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Q₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#11755200	C₂	1	16	yes	maximal, direct product factor
5	C₂×#91428	C₂	1	3	yes	maximal, complemented
6	C₂×#91418	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×#1200	C₂	1	3	yes	maximal, complemented
8	C₂×#91347	C₂	1	3	yes	maximal, complemented
9	C₂×C₄×#713	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×#6821	C₄	1	16	yes	complemented
12	C₂×#6821	C₂²	1	8	yes	—
13	C₂²×D₆₀	C₂²	1	3	yes	—
14	C₂²×C₄×D₁₅	C₂²	1	3	yes	—
15	C₂²×#1200	C₂²	1	3	yes	—
16	C₂²×#1200	C₂²	1	3	yes	—
17	C₅×Q₈×Dic₃	C₂²	1	8	yes	complemented
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	3	yes	—
20	C₃×Q₈×Dic₅	C₂²	1	8	yes	complemented
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	—
23	C₂×#6667	C₂²	1	6	yes	—
24	C₂×Dic₃×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×Dic₃×Dic₅	C₂²	1	3	yes	—
26	#91428	C₂²	1	24	yes	complemented
27	#91418	C₂²	1	24	yes	complemented
28	C₄×#1200	C₂²	1	24	yes	complemented
29	#91347	C₂²	1	24	yes	complemented
30	C₂×C₄×#239	—	5	1	no	maximal, Hall
31	C₂²×#713	—	3	1	no	—
32	C₂×C₄×C₅×Q₈	—	3	1	no	—
33	C₂×Q₈×Dic₅	D₃	1	1	yes	characteristic, complemented
34	C₄×#713	—	3	16	no	—
35	C₂×#4039	—	3	3	no	—
36	C₂×#4038	—	3	3	no	—
37	C₂×C₄×D₂₀	—	3	3	no	—
38	C₂×C₄²×D₅	—	3	3	no	—
39	C₂³×D₁₅	C₂³	1	3	yes	—
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	8	yes	complemented
41	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
43	C₂²×Dic₁₅	C₂³	1	1	yes	characteristic
44	#6821	C₂×C₄	1	64	yes	complemented
45	C₂×D₆₀	C₂×C₄	1	24	yes	complemented
46	C₂×D₆₀	C₂³	1	12	yes	—
47	C₂×C₄×D₁₅	C₂×C₄	1	24	yes	complemented
48	C₂×C₄×D₁₅	C₂³	1	12	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	3	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
51	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
52	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
53	C₂×#1200	—	2	12	no	—
54	C₂×#1200	—	2	12	no	—
55	C₂×#1200	C₂³	1	12	yes	—
56	C₂×#1200	C₂³	1	12	yes	—
57	C₅×C₄⋊Dic₃	C₂³	1	12	yes	—
58	C₄×C₅×Dic₃	C₂³	1	12	yes	—
59	C₃×C₄⋊Dic₅	C₂³	1	12	yes	—
60	C₃×C₄×Dic₅	C₂³	1	12	yes	—
61	#6667	C₂³	1	24	yes	—
62	Dic₃×Dic₅	C₂³	1	4	yes	—
63	Dic₃×Dic₅	C₂³	1	12	yes	—
64	C₂²×#239	—	5	1	no	—
65	C₂×C₃×C₄×Q₈	—	5	1	no	—
66	C₂×Q₈×Dic₃	D₅	1	1	yes	characteristic, complemented
67	C₄×#239	—	5	16	no	—
68	C₂×#893	—	5	3	no	—
69	C₂×#892	—	5	3	no	—
70	C₂×C₄×D₁₂	—	5	3	no	—
71	C₂×C₄²×D₃	—	5	3	no	—
72	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
73	C₂×#713	—	3	16	no	—
74	C₂×#713	—	3	8	no	—
75	C₂²×D₂₀	—	3	3	no	—
76	C₂²×C₄×D₅	—	3	3	no	—
77	C₂²×C₄×D₅	—	3	3	no	—
78	C₂²×C₄×D₅	—	3	3	no	—
79	C₄×C₅×Q₈	—	3	8	no	—
80	C₂×C₅×C₄⋊C₄	—	3	3	no	—
81	C₂×C₄²×C₅	—	3	3	no	—
82	Q₈×Dic₅	C₂×D₃	1	8	yes	complemented
83	C₂×#685	—	3	6	no	—
84	C₂×C₄⋊Dic₅	C₂×D₃	1	3	yes	—
85	C₂×C₄×Dic₅	—	3	1	no	—
86	C₂×C₄×Dic₅	—	3	3	no	—
87	C₂×C₄×Dic₅	C₂×D₃	1	3	yes	—
88	#4039	—	3	24	no	—
89	#4038	—	3	24	no	—
90	C₄×D₂₀	—	3	24	no	—
91	C₄²×D₅	—	3	24	no	—
92	C₂×C₄×#41	—	15	1	no	Sylow
93	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
94	C₂²×D₁₅	—	2	6	no	—
95	C₂²×D₁₅	—	2	6	no	—
96	C₂²×D₁₅	C₂²×C₄	1	12	yes	—
97	C₂²×D₁₅	C₂⁴	1	6	yes	—
98	C₃×C₅×Q₈	C₂²×C₄	1	16	yes	complemented
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	12	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
101	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
102	C₂×Dic₁₅	C₂⁴	1	2	yes	—
103	D₆₀	C₂²×C₄	1	48	yes	complemented
104	C₄×D₁₅	C₂²×C₄	1	48	yes	complemented
105	C₂×C₅×Dic₃	—	2	6	no	—
106	C₂×C₅×Dic₃	#41	1	4	yes	complemented
107	C₂×C₅×Dic₃	C₂⁴	1	6	yes	—
108	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
109	C₂×C₃×Dic₅	—	2	6	no	—
110	C₂×C₃×Dic₅	#41	1	4	yes	complemented
111	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
112	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
113	#1200	—	2	24	no	—
114	#1200	—	2	24	no	—
115	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
116	C₂×#239	—	5	16	no	—
117	C₂×#239	—	5	8	no	—
118	C₂²×D₁₂	—	5	3	no	—
119	C₂²×C₄×D₃	—	5	3	no	—
120	C₂²×C₄×D₃	—	5	3	no	—
121	C₂²×C₄×D₃	—	5	3	no	—
122	C₃×C₄×Q₈	—	5	8	no	—
123	C₂×C₃×C₄⋊C₄	—	5	3	no	—
124	C₂×C₃×C₄²	—	5	3	no	—
125	Q₈×Dic₃	C₂×D₅	1	8	yes	complemented
126	C₂×(C₂×D₃)⋊C₄	—	5	6	no	—
127	C₂×C₄⋊Dic₃	C₂×D₅	1	3	yes	—
128	C₂×C₄×Dic₃	—	5	1	no	—
129	C₂×C₄×Dic₃	—	5	3	no	—
130	C₂×C₄×Dic₃	C₂×D₅	1	3	yes	—
131	#893	—	5	24	no	—
132	#892	—	5	24	no	—
133	C₄×D₁₂	—	5	24	no	—
134	C₄²×D₃	—	5	24	no	—
135	C₂³×D₅	—	3	3	no	—
136	C₂×C₅×Q₈	C₄×D₃	1	8	yes	complemented
137	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
138	C₂²×C₄×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	3	3	no	—
140	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
141	C₂²×Dic₅	—	3	1	no	—
142	C₂²×Dic₅	C₂²×D₃	1	3	yes	—
143	C₂²×Dic₅	C₂²×D₃	1	1	yes	characteristic
144	#713	—	3	64	no	—
145	C₂×D₂₀	—	3	24	no	—
146	C₂×D₂₀	—	3	12	no	—
147	C₂×C₄×D₅	—	3	24	no	—
148	C₂×C₄×D₅	—	3	12	no	—
149	C₂×C₄×D₅	—	3	12	no	—
150	C₂×C₄×D₅	—	3	12	no	—
151	C₂×C₄×D₅	—	6	12	no	—
152	C₂×C₄×D₅	—	6	12	no	—
153	C₅×C₄⋊C₄	—	3	12	no	—
154	C₄²×C₅	—	3	12	no	—
155	#685	—	3	24	no	—
156	C₄⋊Dic₅	C₂²×D₃	1	12	yes	—
157	C₄×Dic₅	—	3	4	no	—
158	C₄×Dic₅	—	3	12	no	—
159	C₄×Dic₅	C₂²×D₃	1	12	yes	—
160	C₂²×#41	—	15	1	no	—
161	C₄×#41	—	15	16	no	—
162	C₂×C₄×Q₈	—	3	1	no	—
163	C₂×C₄×Q₈	—	5	1	no	—
164	C₂×C₄×D₄	—	15	3	no	—
165	C₂×C₄×D₄	—	15	3	no	—
166	C₂×#117	—	15	3	no	—
167	C₂²×C₄²	—	15	3	no	—
168	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
169	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
170	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
171	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
172	C₂×D₁₅	—	2	24	no	—
173	C₂×D₁₅	—	2	6	no	—
174	C₂×D₁₅	—	2	6	no	—
175	C₂×D₁₅	C₂³×C₄	1	12	yes	—
176	C₃×C₄×C₅	C₂³×C₄	1	12	yes	—
177	Dic₁₅	C₂³×C₄	1	4	yes	—
178	C₃×Dic₅	—	2	6	no	—
179	C₃×Dic₅	C₂×#41	1	4	yes	complemented
180	C₅×Dic₃	—	2	6	no	—
181	C₅×Dic₃	C₂×#41	1	4	yes	complemented
182	C₂³×D₃	—	5	3	no	—
183	C₂×C₃×Q₈	C₄×D₅	1	8	yes	complemented
184	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	3	no	—
187	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
188	C₂²×Dic₃	—	5	1	no	—
189	C₂²×Dic₃	C₂²×D₅	1	3	yes	—
190	C₂²×Dic₃	C₂²×D₅	1	1	yes	characteristic
191	#239	—	5	64	no	—
192	C₂×D₁₂	—	5	24	no	—
193	C₂×D₁₂	—	5	12	no	—
194	C₂×C₄×D₃	—	5	24	no	—
195	C₂×C₄×D₃	—	5	12	no	—
196	C₂×C₄×D₃	—	5	12	no	—
197	C₂×C₄×D₃	—	5	12	no	—
198	C₂×C₄×D₃	—	10	12	no	—
199	C₂×C₄×D₃	—	10	12	no	—
200	C₃×C₄⋊C₄	—	5	12	no	—
201	C₃×C₄²	—	5	12	no	—
202	(C₂×D₃)⋊C₄	—	5	24	no	—
203	C₄⋊Dic₃	C₂²×D₅	1	12	yes	—
204	C₄×Dic₃	—	5	4	no	—
205	C₄×Dic₃	—	5	12	no	—
206	C₄×Dic₃	C₂²×D₅	1	12	yes	—
207	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
208	C₂²×D₅	—	3	12	no	—
209	C₂²×D₅	—	3	6	no	—
210	C₂²×D₅	—	6	6	no	—
211	C₂²×D₅	—	6	6	no	—
212	C₅×Q₈	C₂×C₄×D₃	1	16	yes	complemented
213	C₂×C₄×C₅	—	3	4	no	—
214	C₂×C₄×C₅	—	3	2	no	—
215	C₂×C₄×C₅	—	3	6	no	—
216	C₂×C₄×C₅	—	6	6	no	—
217	C₂×C₄×C₅	C₂×C₄×D₃	1	12	yes	—
218	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
219	C₂×Dic₅	—	2	6	no	—
220	C₂×Dic₅	—	3	4	no	—
221	C₂×Dic₅	—	3	2	no	—
222	C₂×Dic₅	#239	1	4	yes	complemented
223	C₂×Dic₅	C₂³×D₃	1	6	yes	—
224	C₂×Dic₅	C₂³×D₃	1	2	yes	—
225	D₂₀	—	3	48	no	—
226	C₄×D₅	—	3	48	no	—
227	C₄×D₅	—	6	24	no	—
228	C₄×D₅	—	6	24	no	—
229	C₂×#41	—	15	16	no	—
230	C₂×#41	—	15	8	no	—
231	C₂²×Q₈	D₃×D₅	1	1	yes	characteristic
232	C₂²×D₄	—	15	3	no	—
233	C₂³×C₄	—	15	3	no	—
234	C₂³×C₄	—	15	3	no	—
235	C₂³×C₄	—	15	3	no	—
236	C₄×Q₈	—	3	8	no	—
237	C₄×Q₈	—	5	8	no	—
238	C₄×D₄	—	15	24	no	—
239	C₄×D₄	—	15	24	no	—
240	#117	—	15	24	no	—
241	C₂×C₄⋊C₄	—	3	3	no	—
242	C₂×C₄⋊C₄	—	5	3	no	—
243	C₂×C₂²⋊C₄	—	15	6	no	—
244	C₂×C₄²	—	3	3	no	—
245	C₂×C₄²	—	5	3	no	—
246	C₂×C₄²	—	15	24	no	—
247	C₂×C₄²	—	15	3	no	—
248	C₂×C₄²	—	15	1	no	—
249	C₂×C₃×C₅	C₄×#41	1	4	yes	complemented
250	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
252	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
253	D₁₅	—	2	12	no	—
254	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
255	C₂²×D₃	—	5	12	no	—
256	C₂²×D₃	—	5	6	no	—
257	C₂²×D₃	—	10	6	no	—
258	C₂²×D₃	—	10	6	no	—
259	C₃×Q₈	C₂×C₄×D₅	1	16	yes	complemented
260	C₂×C₃×C₄	—	5	4	no	—
261	C₂×C₃×C₄	—	5	2	no	—
262	C₂×C₃×C₄	—	5	6	no	—
263	C₂×C₃×C₄	—	10	6	no	—
264	C₂×C₃×C₄	C₂×C₄×D₅	1	12	yes	—
265	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
266	C₂×Dic₃	—	2	6	no	—
267	C₂×Dic₃	—	5	4	no	—
268	C₂×Dic₃	—	5	2	no	—
269	C₂×Dic₃	#713	1	4	yes	complemented
270	C₂×Dic₃	C₂³×D₅	1	6	yes	—
271	C₂×Dic₃	C₂³×D₅	1	2	yes	—
272	D₁₂	—	5	48	no	—
273	C₄×D₃	—	5	48	no	—
274	C₄×D₃	—	10	24	no	—
275	C₄×D₃	—	10	24	no	—
276	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
277	C₂²×C₅	C₂×#239	1	2	yes	—
278	C₂²×C₅	D₃×#41	1	2	yes	—
279	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
280	C₂×D₅	—	3	12	no	—
281	C₂×D₅	—	6	6	no	—
282	C₂×D₅	—	6	6	no	—
283	C₂×D₅	—	6	24	no	—
284	C₄×C₅	—	3	4	no	—
285	C₄×C₅	—	6	6	no	—
286	C₄×C₅	C₂²×C₄×D₃	1	12	yes	—
287	Dic₅	—	2	6	no	—
288	Dic₅	—	3	4	no	—
289	Dic₅	C₂×#239	1	4	yes	complemented
290	C₂⁴	—	15	3	no	—
291	#41	—	15	64	no	—
292	C₂×Q₈	#1200	1	8	yes	complemented
293	C₂×Q₈	C₂×D₃×D₅	1	4	yes	—
294	C₂×D₄	—	15	24	no	—
295	C₂×D₄	—	15	12	no	—
296	C₂²×C₄	—	3	1	no	—
297	C₂²×C₄	—	3	3	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	5	3	no	—
300	C₂²×C₄	—	15	12	no	—
301	C₂²×C₄	—	15	12	no	—
302	C₂²×C₄	—	15	1	no	—
303	C₂²×C₄	—	15	24	no	—
304	C₂²×C₄	—	15	12	no	—
305	C₂²×C₄	—	30	12	no	—
306	C₂²×C₄	—	30	12	no	—
307	C₂²×C₄	C₂×D₃×D₅	1	3	yes	—
308	C₄⋊C₄	—	3	12	no	—
309	C₄⋊C₄	—	5	12	no	—
310	C₂²⋊C₄	—	15	24	no	—
311	C₄²	—	3	12	no	—
312	C₄²	—	5	12	no	—
313	C₄²	—	15	4	no	—
314	C₄²	—	15	12	no	—
315	C₃×C₅	C₂×C₄×#41	1	1	yes	characteristic, complemented, Hall
316	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
317	C₂²×C₃	C₂×#713	1	2	yes	—
318	C₂²×C₃	D₅×#41	1	2	yes	—
319	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
320	C₂×D₃	—	5	12	no	—
321	C₂×D₃	—	10	24	no	—
322	C₂×D₃	—	10	6	no	—
323	C₂×D₃	—	10	6	no	—
324	C₃×C₄	—	5	4	no	—
325	C₃×C₄	—	10	6	no	—
326	C₃×C₄	C₂²×C₄×D₅	1	12	yes	—
327	Dic₃	—	2	6	no	—
328	Dic₃	—	5	4	no	—
329	Dic₃	C₂×#713	1	4	yes	complemented
330	C₂×C₅	C₄×#239	1	4	yes	complemented
331	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
332	C₂×C₅	C₂²×#239	1	1	yes	characteristic
333	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
334	D₅	—	6	12	no	—
335	C₂³	—	15	12	no	—
336	C₂³	—	15	6	no	—
337	C₂³	—	30	6	no	—
338	C₂³	—	30	6	no	—
339	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
340	Q₈	C₂×#1200	1	16	yes	complemented
341	D₄	—	15	48	no	—
342	C₂×C₄	—	3	4	no	—
343	C₂×C₄	—	3	2	no	—
344	C₂×C₄	—	3	6	no	—
345	C₂×C₄	—	5	4	no	—
346	C₂×C₄	—	5	2	no	—
347	C₂×C₄	—	5	6	no	—
348	C₂×C₄	—	6	6	no	—
349	C₂×C₄	—	10	6	no	—
350	C₂×C₄	—	15	4	no	—
351	C₂×C₄	—	15	2	no	—
352	C₂×C₄	—	15	48	no	—
353	C₂×C₄	—	30	24	no	—
354	C₂×C₄	—	30	24	no	—
355	C₂×C₄	C₂×#1200	1	12	yes	—
356	C₂×C₄	C₂²×D₃×D₅	1	6	yes	—
357	C₂×C₃	C₄×#713	1	4	yes	complemented
358	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
359	C₂×C₃	C₂²×#713	1	1	yes	characteristic
360	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
361	D₃	—	10	12	no	—
362	C₅	C₂×C₄×#239	1	1	yes	characteristic, complemented, Sylow
363	C₂²	—	15	12	no	—
364	C₂²	—	30	24	no	—
365	C₂²	—	30	6	no	—
366	C₂²	—	30	6	no	—
367	C₂²	D₅×#239	1	2	yes	—
368	C₂²	D₃×#713	1	2	yes	—
369	C₂²	C₂²×#1200	1	2	yes	—
370	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
371	C₄	—	3	4	no	—
372	C₄	—	5	4	no	—
373	C₄	—	6	6	no	—
374	C₄	—	10	6	no	—
375	C₄	—	15	4	no	—
376	C₄	C₂²×#1200	1	12	yes	—
377	C₃	C₂×C₄×#713	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	30	12	no	—
379	C₂	#11755200	1	4	yes	direct product factor
380	C₂	C₂×D₅×#239	1	1	yes	characteristic
381	C₂	C₂×D₃×#713	1	1	yes	characteristic
382	C₂	C₂³×#1200	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂²×C₃×C₅×Q₈	C₂²
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×#6821	C₂
cosocle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂²×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×C₄×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈×Dic₃	C₂	semidirect
3. C₂×C₃×Q₈×Dic₅	C₂	semidirect
4. #11755200	C₂	direct (N × H)
5. C₂×#91428	C₂	semidirect
6. C₂×#91418	C₂	semidirect
7. C₂×C₄×#1200	C₂	semidirect
8. C₂×#91347	C₂	semidirect
11. C₂×#6821	C₄	semidirect
17. C₅×Q₈×Dic₃	C₂²	semidirect
20. C₃×Q₈×Dic₅	C₂²	semidirect
26. #91428	C₂²	semidirect
27. #91418	C₂²	semidirect
28. C₄×#1200	C₂²	semidirect
29. #91347	C₂²	semidirect
33. C₂×Q₈×Dic₅	D₃	semidirect
40. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
44. #6821	C₂×C₄	semidirect
45. C₂×D₆₀	C₂×C₄	semidirect
47. C₂×C₄×D₁₅	C₂×C₄	semidirect
66. C₂×Q₈×Dic₃	D₅	semidirect
82. Q₈×Dic₅	C₂×D₃	semidirect
98. C₃×C₅×Q₈	C₂²×C₄	semidirect
103. D₆₀	C₂²×C₄	semidirect
104. C₄×D₁₅	C₂²×C₄	semidirect
106. C₂×C₅×Dic₃	#41	semidirect
110. C₂×C₃×Dic₅	#41	semidirect
125. Q₈×Dic₃	C₂×D₅	semidirect
136. C₂×C₅×Q₈	C₄×D₃	semidirect
179. C₃×Dic₅	C₂×#41	semidirect
181. C₅×Dic₃	C₂×#41	semidirect
183. C₂×C₃×Q₈	C₄×D₅	semidirect
212. C₅×Q₈	C₂×C₄×D₃	semidirect
222. C₂×Dic₅	#239	semidirect
249. C₂×C₃×C₅	C₄×#41	semidirect
259. C₃×Q₈	C₂×C₄×D₅	semidirect
269. C₂×Dic₃	#713	semidirect
289. Dic₅	C₂×#239	semidirect
292. C₂×Q₈	#1200	semidirect
315. C₃×C₅	C₂×C₄×#41	semidirect
329. Dic₃	C₂×#713	semidirect
330. C₂×C₅	C₄×#239	semidirect
340. Q₈	C₂×#1200	semidirect
357. C₂×C₃	C₄×#713	semidirect
362. C₅	C₂×C₄×#239	semidirect
377. C₃	C₂×C₄×#713	semidirect
379. C₂	#11755200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6821	2
C₂×C₅×Q₈×Dic₃	2
C₂×C₃×Q₈×Dic₅	2
#11755200	2
C₂×#91428	2
C₂×#91418	2
C₂×C₄×#1200	2
C₂×#91347	2
C₂×C₄×#713	3
C₂×C₄×#239	5

Subgroups — C2×#11755200 #14478941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11755200 #14478941