Subgroups — C₂×C₃×#66065 #14481203

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 344 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	C₂×C₃×#4092	C₂	1	2	yes	maximal
3	C₂×C₃×Q₈×Dic₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66065	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4044	C₂	1	4	yes	maximal
6	C₂×C₃×#4035	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
8	C₂×C₃×#4016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66065	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×#4092	C₂²	1	16	yes	—
16	C₃×Q₈×Dic₅	C₂²	1	16	yes	complemented
17	C₂×C₃×#685	C₂²	1	4	yes	—
18	C₂×C₃×#685	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×#683	C₂²	1	4	yes	—
22	C₂×C₃×#683	C₂²	1	4	yes	—
23	C₂×C₃×#683	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#4044	C₂²	1	32	yes	—
27	C₃×#4035	C₂²	1	32	yes	complemented
28	C₃×#4018	C₂²	1	8	yes	—
29	C₃×#4016	C₂²	1	8	yes	complemented
30	C₂×C₃×#541	—	5	1	no	maximal, Hall
31	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#4092	C₂×C₃	1	2	yes	—
33	C₂×Q₈×Dic₅	C₂×C₃	1	2	yes	complemented
34	#66065	C₂×C₃	1	16	yes	direct product factor
35	C₂×#4044	C₂×C₃	1	4	yes	—
36	C₂×#4035	C₂×C₃	1	4	yes	complemented
37	C₂×#4018	C₂×C₃	1	1	yes	characteristic
38	C₂×#4016	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₅×Q₈	—	2	8	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
47	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
48	C₂×C₃×C₄×D₅	—	2	4	no	—
49	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
50	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
51	C₃×C₄²×C₅	C₂³	1	4	yes	—
52	C₃×#685	C₂³	1	16	yes	—
53	C₃×#685	C₂³	1	8	yes	—
54	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
55	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
56	C₃×#683	C₂³	1	16	yes	—
57	C₃×#683	C₂³	1	16	yes	—
58	C₃×#683	C₂³	1	8	yes	—
59	C₃×C₄×Dic₅	C₂³	1	4	yes	—
60	C₃×C₄×Dic₅	C₂³	1	16	yes	—
61	C₃×#541	—	5	16	no	—
62	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
63	C₂×C₃×#126	—	5	4	no	—
64	C₂×C₃×#125	—	5	4	no	—
65	C₂×C₃×#125	—	5	1	no	—
66	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
67	C₂×C₃×C₄×Q₈	—	5	2	no	—
68	C₂×C₃×#117	—	5	1	no	—
69	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
70	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
71	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
74	#4092	C₂²×C₃	1	16	yes	—
75	Q₈×Dic₅	C₂²×C₃	1	16	yes	complemented
76	C₂×#685	C₂²×C₃	1	2	yes	—
77	C₂×#685	C₂²×C₃	1	4	yes	—
78	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
79	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
80	C₂×#683	C₂²×C₃	1	4	yes	—
81	C₂×#683	C₂²×C₃	1	2	yes	—
82	C₂×#683	C₂²×C₃	1	4	yes	—
83	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
85	#4044	C₂²×C₃	1	32	yes	—
86	#4035	C₂²×C₃	1	32	yes	complemented
87	#4018	C₂²×C₃	1	8	yes	—
88	#4016	C₂²×C₃	1	8	yes	complemented
89	C₂×#541	—	5	1	no	Sylow
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₂²×C₃×D₅	—	2	4	no	—
93	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
94	C₃×C₅×Q₈	—	2	16	no	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	#41	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	—	2	4	no	—
103	C₂×C₃×Dic₅	—	2	8	no	—
104	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
105	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
106	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
107	C₃×C₄×D₅	—	2	8	no	—
108	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
109	C₂³×C₃×C₄	—	5	1	no	—
110	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
111	C₃×#126	—	5	32	no	—
112	C₃×#125	—	5	32	no	—
113	C₃×#125	—	5	8	no	—
114	C₃×C₂²⋊Q₈	—	5	16	no	—
115	C₃×C₄×Q₈	—	5	16	no	—
116	C₃×#117	—	5	8	no	—
117	C₂×C₃×C₄⋊C₄	—	5	2	no	—
118	C₂×C₃×C₄⋊C₄	—	5	2	no	—
119	C₂×C₃×C₄⋊C₄	—	5	4	no	—
120	C₂×C₃×C₄⋊C₄	—	5	4	no	—
121	C₂×C₃×C₄⋊C₄	—	5	4	no	—
122	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₂×C₃×C₄²	—	5	4	no	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₅×Q₈	—	2	8	no	—
130	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
132	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
133	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
135	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
136	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
137	C₂×C₄×D₅	—	2	4	no	—
138	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
139	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
140	C₄²×C₅	C₂³×C₃	1	4	yes	—
141	#685	C₂³×C₃	1	8	yes	—
142	#685	C₂³×C₃	1	16	yes	—
143	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
144	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
145	#683	C₂³×C₃	1	16	yes	—
146	#683	C₂³×C₃	1	8	yes	—
147	#683	C₂³×C₃	1	16	yes	—
148	C₄×Dic₅	C₂³×C₃	1	4	yes	—
149	C₄×Dic₅	C₂³×C₃	1	16	yes	—
150	#541	—	5	16	no	—
151	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
152	C₂×#126	—	5	4	no	—
153	C₂×#125	—	5	4	no	—
154	C₂×#125	—	5	1	no	—
155	C₂×C₂²⋊Q₈	—	5	2	no	—
156	C₂×C₄×Q₈	—	5	2	no	—
157	C₂×#117	—	5	1	no	—
158	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
159	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
160	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×D₅	—	2	2	no	—
162	C₂×C₃×D₅	—	2	4	no	—
163	C₂×C₃×D₅	—	4	4	no	—
164	C₃×C₄×C₅	—	2	8	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	C₂×#41	1	4	yes	—
167	C₃×Dic₅	—	2	2	no	—
168	C₃×Dic₅	—	2	4	no	—
169	C₃×Dic₅	—	2	8	no	—
170	C₂⁴×C₃	—	5	1	no	—
171	C₂×C₃×Q₈	—	2	8	no	—
172	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
173	C₂²×C₃×C₄	—	5	2	no	—
174	C₂²×C₃×C₄	—	5	4	no	—
175	C₂²×C₃×C₄	—	5	1	no	—
176	C₂²×C₃×C₄	—	5	4	no	—
177	C₂²×C₃×C₄	—	10	4	no	—
178	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
179	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
180	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	5	8	no	—
182	C₃×C₄⋊C₄	—	5	16	no	—
183	C₃×C₄⋊C₄	—	5	16	no	—
184	C₃×C₄⋊C₄	—	5	8	no	—
185	C₃×C₄⋊C₄	—	5	16	no	—
186	C₃×C₄⋊C₄	C₂²×D₅	1	16	yes	—
187	C₃×C₂²⋊C₄	—	5	8	no	—
188	C₃×C₂²⋊C₄	—	5	16	no	—
189	C₃×C₄²	—	5	4	no	—
190	C₃×C₄²	—	5	16	no	—
191	C₃×C₄²	C₂²×D₅	1	4	yes	—
192	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
193	C₂²×D₅	—	2	2	no	—
194	C₂²×D₅	—	2	4	no	—
195	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
196	C₅×Q₈	—	2	16	no	—
197	C₂×C₄×C₅	—	2	8	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	C₃×#41	1	4	yes	—
200	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
201	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
202	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
203	C₂×Dic₅	—	2	2	no	—
204	C₂×Dic₅	—	2	4	no	—
205	C₂×Dic₅	—	2	8	no	—
206	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
207	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
208	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
209	C₄×D₅	—	2	8	no	—
210	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
211	C₂³×C₄	—	5	1	no	—
212	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
213	#126	—	5	32	no	—
214	#125	—	5	32	no	—
215	#125	—	5	8	no	—
216	C₂²⋊Q₈	—	5	16	no	—
217	C₄×Q₈	—	5	16	no	—
218	#117	—	5	8	no	—
219	C₂×C₄⋊C₄	—	5	2	no	—
220	C₂×C₄⋊C₄	—	5	2	no	—
221	C₂×C₄⋊C₄	—	5	4	no	—
222	C₂×C₄⋊C₄	—	5	4	no	—
223	C₂×C₄⋊C₄	—	5	4	no	—
224	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	—
225	C₂×C₂²⋊C₄	—	5	2	no	—
226	C₂×C₂²⋊C₄	—	5	4	no	—
227	C₂×C₄²	—	5	1	no	—
228	C₂×C₄²	—	5	4	no	—
229	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
230	C₂×C₃×C₅	#541	1	4	yes	complemented
231	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
233	C₃×D₅	—	4	2	no	—
234	C₂³×C₃	—	5	2	no	—
235	C₂³×C₃	—	10	2	no	—
236	C₂³×C₃	—	10	4	no	—
237	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
238	C₃×Q₈	—	2	16	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	5	4	no	—
242	C₂×C₃×C₄	—	5	8	no	—
243	C₂×C₃×C₄	—	5	2	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	10	4	no	—
246	C₂×C₃×C₄	—	10	8	no	—
247	C₂×C₃×C₄	—	10	8	no	—
248	C₂×C₃×C₄	#711	1	4	yes	—
249	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
250	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
251	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
252	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
253	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
254	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
255	C₂×D₅	—	2	2	no	—
256	C₂×D₅	—	2	4	no	—
257	C₂×D₅	—	4	4	no	—
258	C₄×C₅	—	2	8	no	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	C₂×C₃×#41	1	4	yes	—
261	Dic₅	—	2	2	no	—
262	Dic₅	—	2	4	no	—
263	Dic₅	—	2	8	no	—
264	C₂⁴	—	5	1	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
267	C₂²×C₄	—	5	2	no	—
268	C₂²×C₄	—	5	4	no	—
269	C₂²×C₄	—	5	1	no	—
270	C₂²×C₄	—	5	4	no	—
271	C₂²×C₄	—	10	4	no	—
272	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
273	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
274	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
275	C₄⋊C₄	—	5	8	no	—
276	C₄⋊C₄	—	5	8	no	—
277	C₄⋊C₄	—	5	16	no	—
278	C₄⋊C₄	—	5	16	no	—
279	C₄⋊C₄	—	5	16	no	—
280	C₄⋊C₄	C₂²×C₃×D₅	1	16	yes	—
281	C₂²⋊C₄	—	5	8	no	—
282	C₂²⋊C₄	—	5	16	no	—
283	C₄²	—	5	4	no	—
284	C₄²	—	5	16	no	—
285	C₄²	C₂²×C₃×D₅	1	4	yes	—
286	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	10	2	no	—
288	C₂²×C₃	—	10	4	no	—
289	C₂²×C₃	—	20	4	no	—
290	C₂²×C₃	C₂×#711	1	2	yes	—
291	C₂²×C₃	#4147	1	4	yes	—
292	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
293	C₃×C₄	—	2	8	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	10	2	no	—
296	C₃×C₄	—	10	4	no	—
297	C₃×C₄	—	10	8	no	—
298	C₃×C₄	C₂×#711	1	4	yes	—
299	C₂×C₅	C₃×#541	1	4	yes	complemented
300	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
301	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
302	D₅	—	4	2	no	—
303	C₂³	—	5	2	no	—
304	C₂³	—	10	2	no	—
305	C₂³	—	10	4	no	—
306	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
307	Q₈	—	2	16	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	5	4	no	—
311	C₂×C₄	—	5	8	no	—
312	C₂×C₄	—	5	2	no	—
313	C₂×C₄	—	10	2	no	—
314	C₂×C₄	—	10	4	no	—
315	C₂×C₄	—	10	8	no	—
316	C₂×C₄	—	10	8	no	—
317	C₂×C₄	C₃×#711	1	4	yes	—
318	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
319	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
320	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
321	C₂×C₃	—	20	2	no	—
322	C₂×C₃	#66065	1	4	yes	direct product factor
323	C₂×C₃	C₂²×#711	1	1	yes	characteristic
324	C₂×C₃	C₂×#4147	1	2	yes	—
325	C₅	C₂×C₃×#541	1	1	yes	characteristic, complemented, Sylow
326	C₂²	—	10	2	no	—
327	C₂²	—	10	4	no	—
328	C₂²	—	20	4	no	—
329	C₂²	C₂×C₃×#711	1	2	yes	—
330	C₂²	C₃×#4147	1	4	yes	—
331	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
332	C₄	—	2	8	no	—
333	C₄	—	2	4	no	—
334	C₄	—	10	2	no	—
335	C₄	—	10	4	no	—
336	C₄	—	10	8	no	—
337	C₄	C₂×C₃×#711	1	4	yes	—
338	C₃	C₂×#66065	1	1	yes	characteristic, direct product factor, Sylow
339	C₂	—	20	2	no	—
340	C₂	C₃×#66065	1	4	yes	direct product factor
341	C₂	C₂²×C₃×#711	1	1	yes	characteristic
342	C₂	C₂×C₃×#4147	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×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
3. C₂×C₃×Q₈×Dic₅	C₂	semidirect
4. C₃×#66065	C₂	direct (N × H)
6. C₂×C₃×#4035	C₂	semidirect
8. C₂×C₃×#4016	C₂	semidirect
9. C₂×#66065	C₃	direct (N × H)
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
16. C₃×Q₈×Dic₅	C₂²	semidirect
27. C₃×#4035	C₂²	semidirect
29. C₃×#4016	C₂²	semidirect
31. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
33. C₂×Q₈×Dic₅	C₂×C₃	semidirect
34. #66065	C₂×C₃	direct (N × H)
36. C₂×#4035	C₂×C₃	semidirect
38. C₂×#4016	C₂×C₃	semidirect
62. C₂×C₃×C₄⋊Q₈	D₅	semidirect
71. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
75. Q₈×Dic₅	C₂²×C₃	semidirect
86. #4035	C₂²×C₃	semidirect
88. #4016	C₂²×C₃	semidirect
110. C₃×C₄⋊Q₈	C₂×D₅	semidirect
151. C₂×C₄⋊Q₈	C₃×D₅	semidirect
212. C₄⋊Q₈	C₂×C₃×D₅	semidirect
230. C₂×C₃×C₅	#541	semidirect
286. C₃×C₅	C₂×#541	semidirect
299. C₂×C₅	C₃×#541	semidirect
322. C₂×C₃	#66065	direct (N × H)
325. C₅	C₂×C₃×#541	semidirect
338. C₃	C₂×#66065	direct (N × H)
340. C₂	C₃×#66065	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
C₂×C₃×#4092	2
C₂×C₃×Q₈×Dic₅	2
C₃×#66065	2
C₂×C₃×#4044	2
C₂×C₃×#4035	2
C₂×C₃×#4018	2
C₂×C₃×#4016	2
C₂×#66065	3
C₂×C₃×#541	5

Subgroups — C2×C3×#66065 #14481203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66065 #14481203