Subgroups — C₂²×C₅×#924 #14479420

Order 1920.

3680 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#217	C₂	1	2	yes	maximal
4	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#924	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₂²×C₅×C₂²⋊Q₈	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	—	2	8	no	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	12	yes	—
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
14	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
15	C₂²×C₅×Dic₆	—	2	8	no	—
16	C₂²×C₅×Dic₆	C₂²	1	12	yes	complemented
17	C₂×C₅×#217	C₂²	1	24	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	12	yes	complemented
19	C₅×#924	C₂²	1	64	yes	direct product factor
20	C₂×C₅×Dic₃⋊C₄	C₂²	1	24	yes	complemented
21	C₂²×#924	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₅×Q₈	—	3	1	no	—
23	C₂⁴×C₄×C₅	D₃	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊Q₈	—	3	24	no	—
25	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
26	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
27	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
28	C₂⁴×C₃×C₅	—	2	4	no	—
29	C₂⁴×C₃×C₅	—	2	4	no	—
30	C₂⁴×C₃×C₅	Q₈	1	8	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	6	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	48	no	—
35	C₂²×C₃×C₄×C₅	D₄	1	8	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	16	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
39	C₂²×C₅×Dic₃	—	2	8	no	—
40	C₂²×C₅×Dic₃	—	2	8	no	—
41	C₂²×C₅×Dic₃	C₂³	1	12	yes	—
42	C₂²×C₅×Dic₃	C₂³	1	12	yes	—
43	C₂×C₅×Dic₆	—	2	48	no	—
44	C₂×C₅×Dic₆	C₂³	1	16	yes	complemented
45	C₅×#217	C₂³	1	32	yes	—
46	C₅×C₄⋊Dic₃	C₂³	1	16	yes	complemented
47	C₅×Dic₃⋊C₄	C₂³	1	32	yes	complemented
48	C₂⁴×C₃×C₄	C₂×C₅	1	1	yes	characteristic
49	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
50	C₂²×#217	C₂×C₅	1	2	yes	—
51	C₂²×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
52	C₂×#924	C₂×C₅	1	24	yes	direct product factor
53	C₂²×Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
54	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
55	C₂²×C₅×Q₈	—	3	12	no	—
56	C₂²×C₅×Q₈	—	6	8	no	—
57	C₂³×C₄×C₅	—	2	8	no	—
58	C₂³×C₄×C₅	—	3	2	no	—
59	C₂³×C₄×C₅	—	3	2	no	—
60	C₂³×C₄×C₅	C₂×D₃	1	12	yes	—
61	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
63	C₅×C₂²⋊Q₈	—	3	64	no	—
64	C₂×C₅×C₄⋊C₄	—	3	24	no	—
65	C₂×C₅×C₄⋊C₄	—	3	12	no	—
66	C₂×C₅×C₂²⋊C₄	—	3	24	no	—
67	C₂²×C₂²⋊Q₈	—	3	1	no	Sylow
68	C₂³×C₃×C₅	—	2	32	no	—
69	C₂³×C₃×C₅	—	2	12	no	—
70	C₂³×C₃×C₅	—	2	12	no	—
71	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
72	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
73	C₂³×C₃×C₅	C₂×Q₈	1	24	yes	complemented
74	C₂³×C₃×C₅	#41	1	4	yes	—
75	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
76	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
77	C₂×C₃×C₄×C₅	—	2	12	no	—
78	C₂×C₃×C₄×C₅	—	2	32	no	—
79	C₂×C₃×C₄×C₅	C₂×D₄	1	24	yes	—
80	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
81	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
82	C₂×C₅×Dic₃	—	2	24	no	—
83	C₂×C₅×Dic₃	—	2	24	no	—
84	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
85	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
86	C₅×Dic₆	—	2	32	no	—
87	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
88	C₂³×C₃×C₄	—	2	8	no	—
89	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
90	C₂³×C₃×C₄	C₂²×C₅	1	12	yes	—
91	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
92	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
93	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
94	C₂²×Dic₆	—	2	8	no	—
95	C₂²×Dic₆	C₂²×C₅	1	12	yes	complemented
96	C₂×#217	C₂²×C₅	1	24	yes	—
97	C₂×C₄⋊Dic₃	C₂²×C₅	1	12	yes	complemented
98	#924	C₂²×C₅	1	64	yes	direct product factor
99	C₂×Dic₃⋊C₄	C₂²×C₅	1	24	yes	complemented
100	C₂⁴×C₅	—	2	4	no	—
101	C₂⁴×C₅	—	2	4	no	—
102	C₂⁴×C₅	Dic₆	1	8	yes	complemented
103	C₂⁴×C₅	C₂²×D₃	1	6	yes	—
104	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
105	C₂×C₅×Q₈	—	3	16	no	—
106	C₂×C₅×Q₈	—	6	48	no	—
107	C₂²×C₄×C₅	—	2	4	no	—
108	C₂²×C₄×C₅	—	2	48	no	—
109	C₂²×C₄×C₅	—	3	12	no	—
110	C₂²×C₄×C₅	—	3	12	no	—
111	C₂²×C₄×C₅	—	6	8	no	—
112	C₂²×C₄×C₅	—	6	8	no	—
113	C₂²×C₄×C₅	#67	1	8	yes	—
114	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
115	C₂²×C₄×C₅	C₂²×D₃	1	16	yes	—
116	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
117	C₅×C₄⋊C₄	—	3	32	no	—
118	C₅×C₄⋊C₄	—	3	16	no	—
119	C₅×C₂²⋊C₄	—	3	32	no	—
120	C₂³×Q₈	—	3	1	no	—
121	C₂⁴×C₄	C₅×D₃	1	1	yes	characteristic
122	C₂×C₂²⋊Q₈	—	3	24	no	—
123	C₂²×C₄⋊C₄	—	3	2	no	—
124	C₂²×C₄⋊C₄	—	3	1	no	—
125	C₂²×C₂²⋊C₄	—	3	2	no	—
126	C₂²×C₃×C₅	—	2	48	no	—
127	C₂²×C₃×C₅	—	2	4	no	—
128	C₂²×C₃×C₅	—	2	4	no	—
129	C₂²×C₃×C₅	C₂²⋊Q₈	1	16	yes	complemented
130	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
131	C₂²×C₃×C₅	C₂²×Q₈	1	6	yes	—
132	C₂²×C₃×C₅	C₂²×Q₈	1	8	yes	complemented
133	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
134	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
135	C₃×C₄×C₅	—	2	4	no	—
136	C₃×C₄×C₅	C₂²×D₄	1	8	yes	—
137	C₅×Dic₃	—	2	8	no	—
138	C₅×Dic₃	—	2	8	no	—
139	C₂⁴×C₃	—	2	4	no	—
140	C₂⁴×C₃	—	2	4	no	—
141	C₂⁴×C₃	C₅×Q₈	1	8	yes	complemented
142	C₂⁴×C₃	C₂³×C₅	1	6	yes	—
143	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
144	C₂²×C₃×C₄	—	2	4	no	—
145	C₂²×C₃×C₄	—	2	48	no	—
146	C₂²×C₃×C₄	C₅×D₄	1	8	yes	—
147	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
148	C₂²×C₃×C₄	C₂³×C₅	1	16	yes	—
149	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
150	C₂²×Dic₃	—	2	8	no	—
151	C₂²×Dic₃	—	2	8	no	—
152	C₂²×Dic₃	C₂³×C₅	1	12	yes	—
153	C₂²×Dic₃	C₂³×C₅	1	12	yes	—
154	C₂×Dic₆	—	2	48	no	—
155	C₂×Dic₆	C₂³×C₅	1	16	yes	complemented
156	#217	C₂³×C₅	1	32	yes	—
157	C₄⋊Dic₃	C₂³×C₅	1	16	yes	complemented
158	Dic₃⋊C₄	C₂³×C₅	1	32	yes	complemented
159	C₂³×C₅	—	2	32	no	—
160	C₂³×C₅	—	2	12	no	—
161	C₂³×C₅	—	2	12	no	—
162	C₂³×C₅	C₂×Dic₆	1	4	yes	—
163	C₂³×C₅	C₂×Dic₆	1	24	yes	complemented
164	C₂³×C₅	#235	1	4	yes	—
165	C₂³×C₅	C₂×#67	1	4	yes	—
166	C₂³×C₅	C₂³×D₃	1	4	yes	—
167	C₂³×C₅	C₂³×D₃	1	3	yes	—
168	C₅×Q₈	—	6	32	no	—
169	C₂×C₄×C₅	—	2	12	no	—
170	C₂×C₄×C₅	—	2	32	no	—
171	C₂×C₄×C₅	—	3	8	no	—
172	C₂×C₄×C₅	—	3	8	no	—
173	C₂×C₄×C₅	—	6	24	no	—
174	C₂×C₄×C₅	—	6	24	no	—
175	C₂×C₄×C₅	C₂×#67	1	24	yes	—
176	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
177	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
178	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
179	C₂²×Q₈	—	3	12	no	—
180	C₂²×Q₈	—	6	8	no	—
181	C₂³×C₄	—	2	8	no	—
182	C₂³×C₄	—	3	2	no	—
183	C₂³×C₄	—	3	2	no	—
184	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
185	C₂³×C₄	C₂×C₅×D₃	1	12	yes	—
186	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
187	C₂²⋊Q₈	—	3	64	no	—
188	C₂×C₄⋊C₄	—	3	24	no	—
189	C₂×C₄⋊C₄	—	3	12	no	—
190	C₂×C₂²⋊C₄	—	3	24	no	—
191	C₂×C₃×C₅	—	2	8	no	—
192	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	12	yes	complemented
193	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
195	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
196	C₂³×C₃	—	2	32	no	—
197	C₂³×C₃	—	2	12	no	—
198	C₂³×C₃	—	2	12	no	—
199	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
200	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
201	C₂³×C₃	C₂×C₅×Q₈	1	24	yes	complemented
202	C₂³×C₃	C₅×#41	1	4	yes	—
203	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
204	C₂³×C₃	C₂⁴×C₅	1	3	yes	—
205	C₂×C₃×C₄	—	2	12	no	—
206	C₂×C₃×C₄	—	2	32	no	—
207	C₂×C₃×C₄	C₂×C₅×D₄	1	24	yes	—
208	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
209	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
210	C₂×Dic₃	—	2	24	no	—
211	C₂×Dic₃	—	2	24	no	—
212	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
213	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
214	Dic₆	—	2	32	no	—
215	C₂²×C₅	—	2	4	no	—
216	C₂²×C₅	—	2	4	no	—
217	C₂²×C₅	—	2	48	no	—
218	C₂²×C₅	#924	1	16	yes	direct product factor
219	C₂²×C₅	C₂²×Dic₆	1	6	yes	—
220	C₂²×C₅	C₂²×Dic₆	1	8	yes	complemented
221	C₂²×C₅	C₂×#235	1	6	yes	—
222	C₂²×C₅	C₂²×#67	1	6	yes	—
223	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
224	C₄×C₅	—	2	4	no	—
225	C₄×C₅	—	6	8	no	—
226	C₄×C₅	—	6	8	no	—
227	C₄×C₅	C₂²×#67	1	8	yes	—
228	C₂⁴	—	2	4	no	—
229	C₂⁴	—	2	4	no	—
230	C₂⁴	C₅×Dic₆	1	8	yes	complemented
231	C₂⁴	C₂²×C₅×D₃	1	6	yes	—
232	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
233	C₂×Q₈	—	3	16	no	—
234	C₂×Q₈	—	6	48	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	48	no	—
237	C₂²×C₄	—	3	12	no	—
238	C₂²×C₄	—	3	12	no	—
239	C₂²×C₄	—	6	8	no	—
240	C₂²×C₄	—	6	8	no	—
241	C₂²×C₄	C₅×#67	1	8	yes	—
242	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
243	C₂²×C₄	C₂²×C₅×D₃	1	16	yes	—
244	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
245	C₄⋊C₄	—	3	32	no	—
246	C₄⋊C₄	—	3	16	no	—
247	C₂²⋊C₄	—	3	32	no	—
248	C₃×C₅	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
249	C₂²×C₃	—	2	48	no	—
250	C₂²×C₃	—	2	4	no	—
251	C₂²×C₃	—	2	4	no	—
252	C₂²×C₃	C₅×C₂²⋊Q₈	1	16	yes	complemented
253	C₂²×C₃	C₂²×C₅×D₄	1	6	yes	—
254	C₂²×C₃	C₂²×C₅×Q₈	1	6	yes	—
255	C₂²×C₃	C₂²×C₅×Q₈	1	8	yes	complemented
256	C₂²×C₃	C₂×C₅×#41	1	6	yes	—
257	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
258	C₃×C₄	—	2	4	no	—
259	C₃×C₄	C₂²×C₅×D₄	1	8	yes	—
260	Dic₃	—	2	8	no	—
261	Dic₃	—	2	8	no	—
262	C₂×C₅	—	2	8	no	—
263	C₂×C₅	C₂×#924	1	12	yes	direct product factor
264	C₂×C₅	C₂³×Dic₆	1	1	yes	characteristic
265	C₂×C₅	C₂²×#235	1	1	yes	characteristic
266	C₂×C₅	C₂³×#67	1	1	yes	characteristic
267	C₂³	—	2	32	no	—
268	C₂³	—	2	12	no	—
269	C₂³	—	2	12	no	—
270	C₂³	C₂×C₅×Dic₆	1	4	yes	—
271	C₂³	C₂×C₅×Dic₆	1	24	yes	complemented
272	C₂³	C₅×#235	1	4	yes	—
273	C₂³	C₂×C₅×#67	1	4	yes	—
274	C₂³	C₂³×C₅×D₃	1	4	yes	—
275	C₂³	C₂³×C₅×D₃	1	3	yes	—
276	Q₈	—	6	32	no	—
277	C₂×C₄	—	2	12	no	—
278	C₂×C₄	—	2	32	no	—
279	C₂×C₄	—	3	8	no	—
280	C₂×C₄	—	3	8	no	—
281	C₂×C₄	—	6	24	no	—
282	C₂×C₄	—	6	24	no	—
283	C₂×C₄	C₂×C₅×#67	1	24	yes	—
284	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
285	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
286	C₂×C₃	—	2	8	no	—
287	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	12	yes	complemented
288	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
289	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
290	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
291	C₅	C₂²×#924	1	1	yes	characteristic, direct product factor, Sylow
292	C₂²	—	2	4	no	—
293	C₂²	—	2	4	no	—
294	C₂²	—	2	48	no	—
295	C₂²	C₅×#924	1	16	yes	direct product factor
296	C₂²	C₂²×C₅×Dic₆	1	6	yes	—
297	C₂²	C₂²×C₅×Dic₆	1	8	yes	complemented
298	C₂²	C₂×C₅×#235	1	6	yes	—
299	C₂²	C₂²×C₅×#67	1	6	yes	—
300	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
301	C₄	—	2	4	no	—
302	C₄	—	6	8	no	—
303	C₄	—	6	8	no	—
304	C₄	C₂²×C₅×#67	1	8	yes	—
305	C₃	C₂²×C₅×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
306	C₂	—	2	8	no	—
307	C₂	C₂×C₅×#924	1	12	yes	direct product factor
308	C₂	C₂³×C₅×Dic₆	1	1	yes	characteristic
309	C₂	C₂²×C₅×#235	1	1	yes	characteristic
310	C₂	C₂³×C₅×#67	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Dic₆	C₂	semidirect
4. C₂²×C₅×C₄⋊Dic₃	C₂	semidirect
5. C₂×C₅×#924	C₂	direct (N × H)
6. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
16. C₂²×C₅×Dic₆	C₂²	semidirect
18. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
19. C₅×#924	C₂²	direct (N × H)
20. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
21. C₂²×#924	C₅	direct (N × H)
30. C₂⁴×C₃×C₅	Q₈	semidirect
44. C₂×C₅×Dic₆	C₂³	semidirect
46. C₅×C₄⋊Dic₃	C₂³	semidirect
47. C₅×Dic₃⋊C₄	C₂³	semidirect
49. C₂³×Dic₆	C₂×C₅	semidirect
51. C₂²×C₄⋊Dic₃	C₂×C₅	semidirect
52. C₂×#924	C₂×C₅	direct (N × H)
53. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
73. C₂³×C₃×C₅	C₂×Q₈	semidirect
95. C₂²×Dic₆	C₂²×C₅	semidirect
97. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
98. #924	C₂²×C₅	direct (N × H)
99. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
102. C₂⁴×C₅	Dic₆	semidirect
129. C₂²×C₃×C₅	C₂²⋊Q₈	semidirect
132. C₂²×C₃×C₅	C₂²×Q₈	semidirect
141. C₂⁴×C₃	C₅×Q₈	semidirect
155. C₂×Dic₆	C₂³×C₅	semidirect
157. C₄⋊Dic₃	C₂³×C₅	semidirect
158. Dic₃⋊C₄	C₂³×C₅	semidirect
163. C₂³×C₅	C₂×Dic₆	semidirect
192. C₂×C₃×C₅	C₂×C₂²⋊Q₈	semidirect
201. C₂³×C₃	C₂×C₅×Q₈	semidirect
218. C₂²×C₅	#924	direct (N × H)
220. C₂²×C₅	C₂²×Dic₆	semidirect
230. C₂⁴	C₅×Dic₆	semidirect
248. C₃×C₅	C₂²×C₂²⋊Q₈	semidirect
252. C₂²×C₃	C₅×C₂²⋊Q₈	semidirect
255. C₂²×C₃	C₂²×C₅×Q₈	semidirect
263. C₂×C₅	C₂×#924	direct (N × H)
271. C₂³	C₂×C₅×Dic₆	semidirect
287. C₂×C₃	C₂×C₅×C₂²⋊Q₈	semidirect
291. C₅	C₂²×#924	direct (N × H)
295. C₂²	C₅×#924	direct (N × H)
297. C₂²	C₂²×C₅×Dic₆	semidirect
305. C₃	C₂²×C₅×C₂²⋊Q₈	semidirect
307. C₂	C₂×C₅×#924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₄×C₅	2
C₂³×C₅×Dic₆	2
C₂²×C₅×#217	2
C₂²×C₅×C₄⋊Dic₃	2
C₂×C₅×#924	2
C₂²×C₅×Dic₃⋊C₄	2
C₂²×C₅×C₂²⋊Q₈	3
C₂²×#924	5

Subgroups — C22×C5×#924 #14479420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#924 #14479420