Subgroups — C₂×#11755149 #14479108

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 376 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	#11755149	C₂	1	16	yes	maximal, direct product factor
5	C₂×#91437	C₂	1	3	yes	maximal, complemented
6	C₂×#91428	C₂	1	3	yes	maximal, complemented
7	C₂×#91418	C₂	1	3	yes	maximal, complemented
8	C₂×#91386	C₂	1	3	yes	maximal, complemented
9	C₂×#65908	—	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	6	yes	—
16	C₅×Q₈×Dic₃	C₂²	1	8	yes	complemented
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	3	yes	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	3	yes	—
19	C₃×Q₈×Dic₅	C₂²	1	8	yes	complemented
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	—
22	C₂×#6669	C₂²	1	1	yes	characteristic
23	C₂×#6669	C₂²	1	3	yes	—
24	C₂×#6667	C₂²	1	3	yes	—
25	C₂×#6667	C₂²	1	3	yes	—
26	#91437	C₂²	1	24	yes	complemented
27	#91428	C₂²	1	24	yes	complemented
28	#91418	C₂²	1	24	yes	complemented
29	#91386	C₂²	1	24	yes	complemented
30	C₂×#5574	—	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	#65908	—	3	16	no	—
35	C₂×#4039	—	3	3	no	—
36	C₂×D₅×C₄⋊C₄	—	3	3	no	—
37	C₂×C₄×D₂₀	—	3	3	no	—
38	C₂×#4018	—	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	1	yes	characteristic
50	C₂²×C₅×Dic₃	C₂³	1	3	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
52	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
53	C₂×#1200	—	4	12	no	—
54	C₂×#1200	C₂³	1	24	yes	—
55	C₅×C₄⋊Dic₃	C₂³	1	12	yes	—
56	C₄×C₅×Dic₃	C₂³	1	12	yes	—
57	C₃×C₄⋊Dic₅	C₂³	1	12	yes	—
58	C₃×C₄×Dic₅	C₂³	1	12	yes	—
59	#6669	C₂³	1	12	yes	—
60	#6669	C₂³	1	4	yes	—
61	#6667	C₂³	1	12	yes	—
62	#6667	C₂³	1	12	yes	—
63	C₂²×#239	—	5	1	no	—
64	C₂×C₃×C₄×Q₈	—	5	1	no	—
65	C₂×Q₈×Dic₃	D₅	1	1	yes	characteristic, complemented
66	#5574	—	5	16	no	—
67	C₂×#893	—	5	3	no	—
68	C₂×D₃×C₄⋊C₄	—	5	3	no	—
69	C₂×C₄×D₁₂	—	5	3	no	—
70	C₂×#872	—	5	3	no	—
71	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
72	C₂×#713	—	3	16	no	—
73	C₂×#713	—	3	8	no	—
74	C₂²×D₂₀	—	3	3	no	—
75	C₂²×C₄×D₅	—	3	3	no	—
76	C₂²×C₄×D₅	—	3	6	no	—
77	C₄×C₅×Q₈	—	3	8	no	—
78	C₂×C₅×C₄⋊C₄	—	3	3	no	—
79	C₂×C₄²×C₅	—	3	3	no	—
80	Q₈×Dic₅	C₂×D₃	1	8	yes	complemented
81	C₂×#685	—	3	3	no	—
82	C₂×#685	—	3	3	no	—
83	C₂×C₄⋊Dic₅	C₂×D₃	1	3	yes	—
84	C₂×#683	—	3	1	no	—
85	C₂×#683	—	3	3	no	—
86	C₂×C₄×Dic₅	C₂×D₃	1	3	yes	—
87	#4039	—	3	24	no	—
88	D₅×C₄⋊C₄	—	3	24	no	—
89	C₄×D₂₀	—	3	24	no	—
90	#4018	—	3	24	no	—
91	C₂×#520	—	15	1	no	Sylow
92	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
93	C₂²×D₁₅	—	2	6	no	—
94	C₂²×D₁₅	—	2	6	no	—
95	C₂²×D₁₅	C₂²×C₄	1	12	yes	—
96	C₂²×D₁₅	C₂⁴	1	6	yes	—
97	C₃×C₅×Q₈	C₂²×C₄	1	16	yes	complemented
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	12	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
100	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
101	C₂×Dic₁₅	C₂⁴	1	2	yes	—
102	D₆₀	C₂²×C₄	1	48	yes	complemented
103	C₄×D₁₅	C₂²×C₄	1	48	yes	complemented
104	C₂×C₅×Dic₃	—	2	6	no	—
105	C₂×C₅×Dic₃	—	2	2	no	—
106	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
107	C₂×C₅×Dic₃	C₂⁴	1	6	yes	—
108	C₂×C₃×Dic₅	—	2	6	no	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
111	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
112	#1200	—	4	24	no	—
113	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
114	C₂×#239	—	5	16	no	—
115	C₂×#239	—	5	8	no	—
116	C₂²×D₁₂	—	5	3	no	—
117	C₂²×C₄×D₃	—	5	3	no	—
118	C₂²×C₄×D₃	—	5	6	no	—
119	C₃×C₄×Q₈	—	5	8	no	—
120	C₂×C₃×C₄⋊C₄	—	5	3	no	—
121	C₂×C₃×C₄²	—	5	3	no	—
122	Q₈×Dic₃	C₂×D₅	1	8	yes	complemented
123	C₂×(C₂×D₃)⋊C₄	—	5	3	no	—
124	C₂×(C₂×D₃)⋊C₄	—	5	3	no	—
125	C₂×C₄⋊Dic₃	C₂×D₅	1	3	yes	—
126	C₂×Dic₃⋊C₄	—	5	1	no	—
127	C₂×Dic₃⋊C₄	—	5	3	no	—
128	C₂×C₄×Dic₃	C₂×D₅	1	3	yes	—
129	#893	—	5	24	no	—
130	D₃×C₄⋊C₄	—	5	24	no	—
131	C₄×D₁₂	—	5	24	no	—
132	#872	—	5	24	no	—
133	C₂³×D₅	—	3	3	no	—
134	C₂×C₅×Q₈	C₄×D₃	1	8	yes	complemented
135	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
136	C₂²×C₄×C₅	—	3	1	no	—
137	C₂²×C₄×C₅	—	3	3	no	—
138	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
139	C₂²×Dic₅	—	3	1	no	—
140	C₂²×Dic₅	C₂²×D₃	1	3	yes	—
141	C₂²×Dic₅	C₂²×D₃	1	1	yes	characteristic
142	#713	—	3	64	no	—
143	C₂×D₂₀	—	3	24	no	—
144	C₂×D₂₀	—	3	12	no	—
145	C₂×C₄×D₅	—	3	24	no	—
146	C₂×C₄×D₅	—	3	12	no	—
147	C₂×C₄×D₅	—	3	24	no	—
148	C₂×C₄×D₅	—	12	12	no	—
149	C₅×C₄⋊C₄	—	3	12	no	—
150	C₄²×C₅	—	3	12	no	—
151	#685	—	3	12	no	—
152	#685	—	3	12	no	—
153	C₄⋊Dic₅	C₂²×D₃	1	12	yes	—
154	#683	—	3	4	no	—
155	#683	—	3	12	no	—
156	C₄×Dic₅	C₂²×D₃	1	12	yes	—
157	C₂²×#41	—	15	1	no	—
158	#520	—	15	16	no	—
159	C₂×C₄×Q₈	—	3	1	no	—
160	C₂×C₄×Q₈	—	5	1	no	—
161	C₂×C₄×D₄	—	15	3	no	—
162	C₂×C₄×D₄	—	15	3	no	—
163	C₂×#117	—	15	3	no	—
164	C₂²×C₄⋊C₄	—	15	3	no	—
165	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
166	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
167	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
168	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
169	C₂×D₁₅	—	2	24	no	—
170	C₂×D₁₅	—	2	6	no	—
171	C₂×D₁₅	—	2	6	no	—
172	C₂×D₁₅	C₂³×C₄	1	12	yes	—
173	C₃×C₄×C₅	C₂³×C₄	1	12	yes	—
174	Dic₁₅	C₂³×C₄	1	4	yes	—
175	C₃×Dic₅	—	2	6	no	—
176	C₃×Dic₅	—	2	2	no	—
177	C₅×Dic₃	—	2	6	no	—
178	C₅×Dic₃	—	2	2	no	—
179	C₂³×D₃	—	5	3	no	—
180	C₂×C₃×Q₈	C₄×D₅	1	8	yes	complemented
181	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
182	C₂²×C₃×C₄	—	5	1	no	—
183	C₂²×C₃×C₄	—	5	3	no	—
184	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
185	C₂²×Dic₃	—	5	1	no	—
186	C₂²×Dic₃	C₂²×D₅	1	1	yes	characteristic
187	C₂²×Dic₃	C₂²×D₅	1	3	yes	—
188	#239	—	5	64	no	—
189	C₂×D₁₂	—	5	24	no	—
190	C₂×D₁₂	—	5	12	no	—
191	C₂×C₄×D₃	—	5	24	no	—
192	C₂×C₄×D₃	—	5	12	no	—
193	C₂×C₄×D₃	—	5	24	no	—
194	C₂×C₄×D₃	—	20	12	no	—
195	C₃×C₄⋊C₄	—	5	12	no	—
196	C₃×C₄²	—	5	12	no	—
197	(C₂×D₃)⋊C₄	—	5	12	no	—
198	(C₂×D₃)⋊C₄	—	5	12	no	—
199	C₄⋊Dic₃	C₂²×D₅	1	12	yes	—
200	Dic₃⋊C₄	—	5	4	no	—
201	Dic₃⋊C₄	—	5	12	no	—
202	C₄×Dic₃	C₂²×D₅	1	12	yes	—
203	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
204	C₂²×D₅	—	3	12	no	—
205	C₂²×D₅	—	3	6	no	—
206	C₂²×D₅	—	6	6	no	—
207	C₂²×D₅	—	6	6	no	—
208	C₅×Q₈	C₂×C₄×D₃	1	16	yes	complemented
209	C₂×C₄×C₅	—	3	2	no	—
210	C₂×C₄×C₅	—	3	6	no	—
211	C₂×C₄×C₅	—	6	2	no	—
212	C₂×C₄×C₅	—	6	6	no	—
213	C₂×C₄×C₅	C₂×C₄×D₃	1	12	yes	—
214	C₂×C₄×C₅	C₂³×D₃	1	6	yes	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	2	6	no	—
217	C₂×Dic₅	—	3	4	no	—
218	C₂×Dic₅	—	3	2	no	—
219	C₂×Dic₅	C₂³×D₃	1	2	yes	—
220	C₂×Dic₅	C₂³×D₃	1	6	yes	—
221	D₂₀	—	3	48	no	—
222	C₄×D₅	—	3	48	no	—
223	C₄×D₅	—	12	24	no	—
224	C₂×#41	—	15	16	no	—
225	C₂×#41	—	15	8	no	—
226	C₂²×Q₈	D₃×D₅	1	1	yes	characteristic
227	C₂²×D₄	—	15	3	no	—
228	C₂³×C₄	—	15	6	no	—
229	C₂³×C₄	—	15	3	no	—
230	C₄×Q₈	—	3	8	no	—
231	C₄×Q₈	—	5	8	no	—
232	C₄×D₄	—	15	24	no	—
233	C₄×D₄	—	15	24	no	—
234	#117	—	15	24	no	—
235	C₂×C₄⋊C₄	—	3	3	no	—
236	C₂×C₄⋊C₄	—	5	3	no	—
237	C₂×C₄⋊C₄	—	15	24	no	—
238	C₂×C₄⋊C₄	—	15	3	no	—
239	C₂×C₄⋊C₄	—	15	1	no	—
240	C₂×C₂²⋊C₄	—	15	3	no	—
241	C₂×C₂²⋊C₄	—	15	3	no	—
242	C₂×C₄²	—	3	3	no	—
243	C₂×C₄²	—	5	3	no	—
244	C₂×C₃×C₅	#520	1	4	yes	complemented
245	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
248	D₁₅	—	2	12	no	—
249	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
250	C₂²×D₃	—	5	12	no	—
251	C₂²×D₃	—	5	6	no	—
252	C₂²×D₃	—	10	6	no	—
253	C₂²×D₃	—	10	6	no	—
254	C₃×Q₈	C₂×C₄×D₅	1	16	yes	complemented
255	C₂×C₃×C₄	—	5	2	no	—
256	C₂×C₃×C₄	—	5	6	no	—
257	C₂×C₃×C₄	—	10	2	no	—
258	C₂×C₃×C₄	—	10	6	no	—
259	C₂×C₃×C₄	C₂×C₄×D₅	1	12	yes	—
260	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
261	C₂×Dic₃	—	2	2	no	—
262	C₂×Dic₃	—	2	6	no	—
263	C₂×Dic₃	—	5	4	no	—
264	C₂×Dic₃	—	5	2	no	—
265	C₂×Dic₃	C₂³×D₅	1	2	yes	—
266	C₂×Dic₃	C₂³×D₅	1	6	yes	—
267	D₁₂	—	5	48	no	—
268	C₄×D₃	—	5	48	no	—
269	C₄×D₃	—	20	24	no	—
270	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
271	C₂²×C₅	#1007	1	2	yes	—
272	C₂²×C₅	#1009	1	2	yes	—
273	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
274	C₂×D₅	—	3	12	no	—
275	C₂×D₅	—	6	6	no	—
276	C₂×D₅	—	6	6	no	—
277	C₂×D₅	—	6	24	no	—
278	C₄×C₅	—	6	2	no	—
279	C₄×C₅	—	6	6	no	—
280	C₄×C₅	C₂²×C₄×D₃	1	12	yes	—
281	Dic₅	—	2	2	no	—
282	Dic₅	—	2	6	no	—
283	Dic₅	—	3	4	no	—
284	C₂⁴	—	15	3	no	—
285	#41	—	15	64	no	—
286	C₂×Q₈	#1200	1	8	yes	complemented
287	C₂×Q₈	C₂×D₃×D₅	1	4	yes	—
288	C₂×D₄	—	15	24	no	—
289	C₂×D₄	—	15	12	no	—
290	C₂²×C₄	—	3	1	no	—
291	C₂²×C₄	—	3	3	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	3	no	—
294	C₂²×C₄	—	15	24	no	—
295	C₂²×C₄	—	15	1	no	—
296	C₂²×C₄	—	15	24	no	—
297	C₂²×C₄	—	15	12	no	—
298	C₂²×C₄	—	60	12	no	—
299	C₂²×C₄	C₂×D₃×D₅	1	3	yes	—
300	C₄⋊C₄	—	3	12	no	—
301	C₄⋊C₄	—	5	12	no	—
302	C₄⋊C₄	—	15	12	no	—
303	C₄⋊C₄	—	15	4	no	—
304	C₂²⋊C₄	—	15	12	no	—
305	C₂²⋊C₄	—	15	12	no	—
306	C₄²	—	3	12	no	—
307	C₄²	—	5	12	no	—
308	C₃×C₅	C₂×#520	1	1	yes	characteristic, complemented, Hall
309	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
310	C₂²×C₃	#4147	1	2	yes	—
311	C₂²×C₃	#4149	1	2	yes	—
312	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
313	C₂×D₃	—	5	12	no	—
314	C₂×D₃	—	10	24	no	—
315	C₂×D₃	—	10	6	no	—
316	C₂×D₃	—	10	6	no	—
317	C₃×C₄	—	10	2	no	—
318	C₃×C₄	—	10	6	no	—
319	C₃×C₄	C₂²×C₄×D₅	1	12	yes	—
320	Dic₃	—	2	2	no	—
321	Dic₃	—	2	6	no	—
322	Dic₃	—	5	4	no	—
323	C₂×C₅	#5574	1	4	yes	complemented
324	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
325	C₂×C₅	C₂×#1007	1	1	yes	characteristic
326	C₂×C₅	C₂×#1009	1	1	yes	characteristic
327	D₅	—	6	12	no	—
328	C₂³	—	15	12	no	—
329	C₂³	—	15	6	no	—
330	C₂³	—	30	6	no	—
331	C₂³	—	30	6	no	—
332	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
333	Q₈	C₂×#1200	1	16	yes	complemented
334	D₄	—	15	48	no	—
335	C₂×C₄	—	3	2	no	—
336	C₂×C₄	—	3	6	no	—
337	C₂×C₄	—	5	2	no	—
338	C₂×C₄	—	5	6	no	—
339	C₂×C₄	—	6	2	no	—
340	C₂×C₄	—	6	6	no	—
341	C₂×C₄	—	10	2	no	—
342	C₂×C₄	—	10	6	no	—
343	C₂×C₄	—	15	4	no	—
344	C₂×C₄	—	15	2	no	—
345	C₂×C₄	—	15	48	no	—
346	C₂×C₄	—	60	24	no	—
347	C₂×C₄	C₂×#1200	1	12	yes	—
348	C₂×C₄	C₂²×D₃×D₅	1	6	yes	—
349	C₂×C₃	#65908	1	4	yes	complemented
350	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃	C₂×#4147	1	1	yes	characteristic
352	C₂×C₃	C₂×#4149	1	1	yes	characteristic
353	D₃	—	10	12	no	—
354	C₅	C₂×#5574	1	1	yes	characteristic, complemented, Sylow
355	C₂²	—	15	12	no	—
356	C₂²	—	30	24	no	—
357	C₂²	—	30	6	no	—
358	C₂²	—	30	6	no	—
359	C₂²	#92029	1	2	yes	—
360	C₂²	#92035	1	2	yes	—
361	C₂²	C₂²×#1200	1	2	yes	—
362	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
363	C₄	—	6	2	no	—
364	C₄	—	6	6	no	—
365	C₄	—	10	2	no	—
366	C₄	—	10	6	no	—
367	C₄	—	15	4	no	—
368	C₄	C₂²×#1200	1	12	yes	—
369	C₃	C₂×#65908	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	30	12	no	—
371	C₂	#11755149	1	4	yes	direct product factor
372	C₂	C₂×#92029	1	1	yes	characteristic
373	C₂	C₂×#92035	1	1	yes	characteristic
374	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×#520
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. #11755149	C₂	direct (N × H)
5. C₂×#91437	C₂	semidirect
6. C₂×#91428	C₂	semidirect
7. C₂×#91418	C₂	semidirect
8. C₂×#91386	C₂	semidirect
11. C₂×#6821	C₄	semidirect
16. C₅×Q₈×Dic₃	C₂²	semidirect
19. C₃×Q₈×Dic₅	C₂²	semidirect
26. #91437	C₂²	semidirect
27. #91428	C₂²	semidirect
28. #91418	C₂²	semidirect
29. #91386	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
65. C₂×Q₈×Dic₃	D₅	semidirect
80. Q₈×Dic₅	C₂×D₃	semidirect
97. C₃×C₅×Q₈	C₂²×C₄	semidirect
102. D₆₀	C₂²×C₄	semidirect
103. C₄×D₁₅	C₂²×C₄	semidirect
122. Q₈×Dic₃	C₂×D₅	semidirect
134. C₂×C₅×Q₈	C₄×D₃	semidirect
180. C₂×C₃×Q₈	C₄×D₅	semidirect
208. C₅×Q₈	C₂×C₄×D₃	semidirect
244. C₂×C₃×C₅	#520	semidirect
254. C₃×Q₈	C₂×C₄×D₅	semidirect
286. C₂×Q₈	#1200	semidirect
308. C₃×C₅	C₂×#520	semidirect
323. C₂×C₅	#5574	semidirect
333. Q₈	C₂×#1200	semidirect
349. C₂×C₃	#65908	semidirect
354. C₅	C₂×#5574	semidirect
369. C₃	C₂×#65908	semidirect
371. C₂	#11755149	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
#11755149	2
C₂×#91437	2
C₂×#91428	2
C₂×#91418	2
C₂×#91386	2
C₂×#65908	3
C₂×#5574	5

Subgroups — C2×#11755149 #14479108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11755149 #14479108