Subgroups — C₂²×C₃×#3966 #14411886

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₂²⋊Dic₅	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#3966	C₂	1	12	yes	maximal, direct product factor
4	C₂²×#3966	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁵×C₃×C₅	C₄	1	1	yes	characteristic, complemented
6	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₅×D₄	—	2	2	no	—
8	C₂²×C₃×C₅×D₄	—	2	6	no	—
9	C₂²×C₃×C₅×D₄	C₄	1	6	yes	complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	6	yes	—
11	C₂³×C₃×C₄×C₅	C₄	1	1	yes	characteristic, complemented
12	C₂³×C₃×Dic₅	—	2	2	no	—
13	C₂×C₃×C₂²⋊Dic₅	—	2	6	no	—
14	C₂×C₃×C₂²⋊Dic₅	C₂²	1	12	yes	complemented
15	C₃×#3966	C₂²	1	16	yes	direct product factor
16	C₂²×C₃×#99	—	5	1	no	maximal, Hall
17	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₂²⋊Dic₅	C₂×C₃	1	2	yes	complemented
19	C₂×#3966	C₂×C₃	1	12	yes	direct product factor
20	C₂⁴×C₃×C₅	—	2	3	no	—
21	C₂⁴×C₃×C₅	—	2	1	no	—
22	C₂⁴×C₃×C₅	—	4	4	no	—
23	C₂⁴×C₃×C₅	—	4	4	no	—
24	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂⁴×C₃×C₅	C₂×C₄	1	3	yes	—
26	C₂⁴×C₃×C₅	C₂×C₄	1	6	yes	complemented
27	C₂⁴×C₃×C₅	D₄	1	2	yes	—
28	C₂⁴×C₃×C₅	D₄	1	6	yes	—
29	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
30	C₂×C₃×C₅×D₄	—	2	12	no	—
31	C₂×C₃×C₅×D₄	—	2	12	no	—
32	C₂×C₃×C₅×D₄	—	2	12	no	—
33	C₂×C₃×C₅×D₄	—	2	12	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	12	yes	complemented
35	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	—	2	3	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	6	yes	complemented
39	C₂²×C₃×Dic₅	—	2	12	no	—
40	C₂²×C₃×Dic₅	—	4	8	no	—
41	C₃×C₂²⋊Dic₅	—	2	12	no	—
42	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
43	C₂³×C₃×D₄	D₅	1	1	yes	characteristic
44	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
45	C₂×C₃×#99	—	5	12	no	—
46	C₂⁵×C₅	C₃×C₄	1	1	yes	characteristic, complemented
47	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₅×D₄	—	2	2	no	—
49	C₂²×C₅×D₄	—	2	6	no	—
50	C₂²×C₅×D₄	C₃×C₄	1	6	yes	complemented
51	C₂²×C₅×D₄	C₂²×C₃	1	6	yes	—
52	C₂³×C₄×C₅	C₃×C₄	1	1	yes	characteristic, complemented
53	C₂³×Dic₅	—	2	2	no	—
54	C₂×C₂²⋊Dic₅	—	2	6	no	—
55	C₂×C₂²⋊Dic₅	C₂²×C₃	1	12	yes	complemented
56	#3966	C₂²×C₃	1	16	yes	direct product factor
57	C₂²×#99	—	5	1	no	Sylow
58	C₂³×C₃×C₅	—	2	8	no	—
59	C₂³×C₃×C₅	—	2	4	no	—
60	C₂³×C₃×C₅	—	2	6	no	—
61	C₂³×C₃×C₅	—	2	6	no	—
62	C₂³×C₃×C₅	—	4	6	no	—
63	C₂³×C₃×C₅	—	4	12	no	—
64	C₂³×C₃×C₅	—	4	6	no	—
65	C₂³×C₃×C₅	—	4	12	no	—
66	C₂³×C₃×C₅	—	4	12	no	—
67	C₂³×C₃×C₅	—	4	4	no	—
68	C₂³×C₃×C₅	C₂²⋊C₄	1	3	yes	—
69	C₂³×C₃×C₅	C₂²⋊C₄	1	6	yes	—
70	C₂³×C₃×C₅	C₂²⋊C₄	1	6	yes	—
71	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
72	C₂³×C₃×C₅	C₂²×C₄	1	3	yes	—
73	C₂³×C₃×C₅	C₂²×C₄	1	3	yes	—
74	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	complemented
75	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
76	C₂³×C₃×C₅	C₂×D₄	1	6	yes	—
77	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
78	C₃×C₅×D₄	—	2	24	no	—
79	C₃×C₅×D₄	—	2	8	no	—
80	C₂×C₃×C₄×C₅	—	2	6	no	—
81	C₂×C₃×C₄×C₅	—	2	6	no	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	complemented
83	C₂×C₃×Dic₅	—	2	8	no	—
84	C₂×C₃×Dic₅	—	4	24	no	—
85	C₂⁵×C₃	Dic₅	1	1	yes	characteristic, complemented
86	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
87	C₂²×C₃×D₄	—	2	6	no	—
88	C₂²×C₃×D₄	—	2	2	no	—
89	C₂²×C₃×D₄	Dic₅	1	6	yes	complemented
90	C₂²×C₃×D₄	C₂×D₅	1	6	yes	—
91	C₂³×C₃×C₄	—	10	2	no	—
92	C₂³×C₃×C₄	Dic₅	1	1	yes	characteristic, complemented
93	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
94	C₂×C₃×C₂²⋊C₄	—	10	6	no	—
95	C₃×#99	—	5	16	no	—
96	C₂⁴×C₅	—	2	3	no	—
97	C₂⁴×C₅	—	2	1	no	—
98	C₂⁴×C₅	—	4	4	no	—
99	C₂⁴×C₅	—	4	4	no	—
100	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
101	C₂⁴×C₅	C₂×C₃×C₄	1	3	yes	—
102	C₂⁴×C₅	C₂×C₃×C₄	1	6	yes	complemented
103	C₂⁴×C₅	C₃×D₄	1	2	yes	—
104	C₂⁴×C₅	C₃×D₄	1	6	yes	—
105	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
106	C₂×C₅×D₄	—	2	12	no	—
107	C₂×C₅×D₄	—	2	12	no	—
108	C₂×C₅×D₄	—	2	12	no	—
109	C₂×C₅×D₄	—	2	12	no	—
110	C₂×C₅×D₄	C₂×C₃×C₄	1	12	yes	complemented
111	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
112	C₂²×C₄×C₅	—	2	3	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	C₂×C₃×C₄	1	6	yes	complemented
115	C₂²×Dic₅	—	2	12	no	—
116	C₂²×Dic₅	—	4	8	no	—
117	C₂²⋊Dic₅	—	2	12	no	—
118	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
119	C₂³×D₄	C₃×D₅	1	1	yes	characteristic
120	C₂²×C₂²⋊C₄	—	5	2	no	—
121	C₂×#99	—	5	12	no	—
122	C₂²×C₃×C₅	—	2	12	no	—
123	C₂²×C₃×C₅	—	2	6	no	—
124	C₂²×C₃×C₅	—	2	6	no	—
125	C₂²×C₃×C₅	—	2	12	no	—
126	C₂²×C₃×C₅	—	2	4	no	—
127	C₂²×C₃×C₅	—	4	6	no	—
128	C₂²×C₃×C₅	—	4	3	no	—
129	C₂²×C₃×C₅	—	4	6	no	—
130	C₂²×C₃×C₅	—	4	1	no	—
131	C₂²×C₃×C₅	—	4	4	no	—
132	C₂²×C₃×C₅	—	4	12	no	—
133	C₂²×C₃×C₅	—	4	12	no	—
134	C₂²×C₃×C₅	#99	1	4	yes	complemented
135	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
136	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
137	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
138	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
139	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
140	C₃×C₄×C₅	—	2	4	no	—
141	C₃×Dic₅	—	4	8	no	—
142	C₂⁴×C₃	—	2	3	no	—
143	C₂⁴×C₃	—	2	1	no	—
144	C₂⁴×C₃	—	4	4	no	—
145	C₂⁴×C₃	—	4	4	no	—
146	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
147	C₂⁴×C₃	C₂×Dic₅	1	3	yes	—
148	C₂⁴×C₃	C₂×Dic₅	1	6	yes	complemented
149	C₂⁴×C₃	C₂²⋊D₅	1	2	yes	—
150	C₂⁴×C₃	C₂²⋊D₅	1	6	yes	—
151	C₂⁴×C₃	C₂²×D₅	1	3	yes	—
152	C₂×C₃×D₄	—	2	12	no	—
153	C₂×C₃×D₄	—	2	12	no	—
154	C₂×C₃×D₄	—	2	12	no	—
155	C₂×C₃×D₄	—	2	12	no	—
156	C₂×C₃×D₄	C₂×Dic₅	1	12	yes	complemented
157	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
158	C₂²×C₃×C₄	—	2	3	no	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	—	10	12	no	—
161	C₂²×C₃×C₄	—	20	8	no	—
162	C₂²×C₃×C₄	C₂×Dic₅	1	6	yes	complemented
163	C₃×C₂²⋊C₄	—	5	8	no	—
164	C₃×C₂²⋊C₄	—	10	12	no	—
165	C₂³×C₅	—	2	8	no	—
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	—	2	6	no	—
168	C₂³×C₅	—	2	6	no	—
169	C₂³×C₅	—	4	6	no	—
170	C₂³×C₅	—	4	12	no	—
171	C₂³×C₅	—	4	6	no	—
172	C₂³×C₅	—	4	12	no	—
173	C₂³×C₅	—	4	12	no	—
174	C₂³×C₅	—	4	4	no	—
175	C₂³×C₅	C₃×C₂²⋊C₄	1	3	yes	—
176	C₂³×C₅	C₃×C₂²⋊C₄	1	6	yes	—
177	C₂³×C₅	C₃×C₂²⋊C₄	1	6	yes	—
178	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
179	C₂³×C₅	C₂²×C₃×C₄	1	3	yes	—
180	C₂³×C₅	C₂²×C₃×C₄	1	3	yes	—
181	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	complemented
182	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
183	C₂³×C₅	C₂×C₃×D₄	1	6	yes	—
184	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
185	C₅×D₄	—	2	24	no	—
186	C₅×D₄	—	2	8	no	—
187	C₂×C₄×C₅	—	2	6	no	—
188	C₂×C₄×C₅	—	2	6	no	—
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	complemented
190	C₂×Dic₅	—	2	8	no	—
191	C₂×Dic₅	—	4	24	no	—
192	C₂⁵	C₃×Dic₅	1	1	yes	characteristic, complemented
193	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
194	C₂²×D₄	—	2	2	no	—
195	C₂²×D₄	—	2	6	no	—
196	C₂²×D₄	C₃×Dic₅	1	6	yes	complemented
197	C₂²×D₄	C₂×C₃×D₅	1	6	yes	—
198	C₂³×C₄	—	10	2	no	—
199	C₂³×C₄	C₃×Dic₅	1	1	yes	characteristic, complemented
200	C₂×C₂²⋊C₄	—	5	12	no	—
201	C₂×C₂²⋊C₄	—	10	6	no	—
202	#99	—	5	16	no	—
203	C₂×C₃×C₅	—	2	2	no	—
204	C₂×C₃×C₅	—	2	3	no	—
205	C₂×C₃×C₅	—	2	1	no	—
206	C₂×C₃×C₅	—	2	6	no	—
207	C₂×C₃×C₅	—	4	4	no	—
208	C₂×C₃×C₅	C₂×#99	1	6	yes	complemented
209	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×C₃	—	2	8	no	—
211	C₂³×C₃	—	2	4	no	—
212	C₂³×C₃	—	2	6	no	—
213	C₂³×C₃	—	2	6	no	—
214	C₂³×C₃	—	4	6	no	—
215	C₂³×C₃	—	4	12	no	—
216	C₂³×C₃	—	4	6	no	—
217	C₂³×C₃	—	4	12	no	—
218	C₂³×C₃	—	4	12	no	—
219	C₂³×C₃	—	4	4	no	—
220	C₂³×C₃	C₂²⋊Dic₅	1	3	yes	—
221	C₂³×C₃	C₂²⋊Dic₅	1	6	yes	—
222	C₂³×C₃	C₂²⋊Dic₅	1	6	yes	—
223	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
224	C₂³×C₃	C₂²×Dic₅	1	3	yes	—
225	C₂³×C₃	C₂²×Dic₅	1	3	yes	—
226	C₂³×C₃	C₂²×Dic₅	1	4	yes	complemented
227	C₂³×C₃	C₂×C₂²⋊D₅	1	6	yes	—
228	C₂³×C₃	C₂×C₂²⋊D₅	1	6	yes	—
229	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
230	C₃×D₄	—	2	24	no	—
231	C₃×D₄	—	2	8	no	—
232	C₂×C₃×C₄	—	2	6	no	—
233	C₂×C₃×C₄	—	2	6	no	—
234	C₂×C₃×C₄	—	10	8	no	—
235	C₂×C₃×C₄	—	20	24	no	—
236	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	complemented
237	C₂²×C₅	—	2	12	no	—
238	C₂²×C₅	—	2	6	no	—
239	C₂²×C₅	—	2	6	no	—
240	C₂²×C₅	—	2	12	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	4	6	no	—
243	C₂²×C₅	—	4	3	no	—
244	C₂²×C₅	—	4	6	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	—	4	4	no	—
247	C₂²×C₅	—	4	12	no	—
248	C₂²×C₅	—	4	12	no	—
249	C₂²×C₅	C₃×#99	1	4	yes	complemented
250	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
251	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
252	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
253	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
254	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
255	C₄×C₅	—	2	4	no	—
256	Dic₅	—	4	8	no	—
257	C₂⁴	—	2	3	no	—
258	C₂⁴	—	2	1	no	—
259	C₂⁴	—	4	4	no	—
260	C₂⁴	—	4	4	no	—
261	C₂⁴	C₂×C₃×Dic₅	1	1	yes	characteristic
262	C₂⁴	C₂×C₃×Dic₅	1	3	yes	—
263	C₂⁴	C₂×C₃×Dic₅	1	6	yes	complemented
264	C₂⁴	C₃×C₂²⋊D₅	1	2	yes	—
265	C₂⁴	C₃×C₂²⋊D₅	1	6	yes	—
266	C₂⁴	C₂²×C₃×D₅	1	3	yes	—
267	C₂×D₄	—	2	12	no	—
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	—	2	12	no	—
270	C₂×D₄	—	2	12	no	—
271	C₂×D₄	C₂×C₃×Dic₅	1	12	yes	complemented
272	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
273	C₂²×C₄	—	2	3	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	10	12	no	—
276	C₂²×C₄	—	20	8	no	—
277	C₂²×C₄	C₂×C₃×Dic₅	1	6	yes	complemented
278	C₂²⋊C₄	—	5	8	no	—
279	C₂²⋊C₄	—	10	12	no	—
280	C₃×C₅	C₂²×#99	1	1	yes	characteristic, complemented, Hall
281	C₂²×C₃	—	2	12	no	—
282	C₂²×C₃	—	2	6	no	—
283	C₂²×C₃	—	2	6	no	—
284	C₂²×C₃	—	2	12	no	—
285	C₂²×C₃	—	2	4	no	—
286	C₂²×C₃	—	4	6	no	—
287	C₂²×C₃	—	4	3	no	—
288	C₂²×C₃	—	4	6	no	—
289	C₂²×C₃	—	4	1	no	—
290	C₂²×C₃	—	4	4	no	—
291	C₂²×C₃	—	4	12	no	—
292	C₂²×C₃	—	4	12	no	—
293	C₂²×C₃	#3966	1	4	yes	direct product factor
294	C₂²×C₃	C₂×C₂²⋊Dic₅	1	3	yes	—
295	C₂²×C₃	C₂×C₂²⋊Dic₅	1	6	yes	—
296	C₂²×C₃	C₂×C₂²⋊Dic₅	1	3	yes	—
297	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
298	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
299	C₃×C₄	—	2	4	no	—
300	C₃×C₄	—	20	8	no	—
301	C₂×C₅	—	2	2	no	—
302	C₂×C₅	—	2	3	no	—
303	C₂×C₅	—	2	1	no	—
304	C₂×C₅	—	2	6	no	—
305	C₂×C₅	—	4	4	no	—
306	C₂×C₅	C₂×C₃×#99	1	6	yes	complemented
307	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₂³	—	2	8	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	6	no	—
311	C₂³	—	2	6	no	—
312	C₂³	—	4	6	no	—
313	C₂³	—	4	12	no	—
314	C₂³	—	4	6	no	—
315	C₂³	—	4	12	no	—
316	C₂³	—	4	12	no	—
317	C₂³	—	4	4	no	—
318	C₂³	C₃×C₂²⋊Dic₅	1	3	yes	—
319	C₂³	C₃×C₂²⋊Dic₅	1	6	yes	—
320	C₂³	C₃×C₂²⋊Dic₅	1	6	yes	—
321	C₂³	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
322	C₂³	C₂²×C₃×Dic₅	1	3	yes	—
323	C₂³	C₂²×C₃×Dic₅	1	3	yes	—
324	C₂³	C₂²×C₃×Dic₅	1	4	yes	complemented
325	C₂³	C₂×C₃×C₂²⋊D₅	1	6	yes	—
326	C₂³	C₂×C₃×C₂²⋊D₅	1	6	yes	—
327	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
328	D₄	—	2	24	no	—
329	D₄	—	2	8	no	—
330	C₂×C₄	—	2	6	no	—
331	C₂×C₄	—	2	6	no	—
332	C₂×C₄	—	10	8	no	—
333	C₂×C₄	—	20	24	no	—
334	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	complemented
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	—	2	3	no	—
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	2	6	no	—
339	C₂×C₃	—	4	4	no	—
340	C₂×C₃	C₂×#3966	1	6	yes	direct product factor
341	C₂×C₃	C₂²×C₂²⋊Dic₅	1	1	yes	characteristic
342	C₅	C₂²×C₃×#99	1	1	yes	characteristic, complemented, Sylow
343	C₂²	—	2	12	no	—
344	C₂²	—	2	6	no	—
345	C₂²	—	2	6	no	—
346	C₂²	—	2	12	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	4	6	no	—
349	C₂²	—	4	3	no	—
350	C₂²	—	4	6	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	12	no	—
354	C₂²	—	4	12	no	—
355	C₂²	C₃×#3966	1	4	yes	direct product factor
356	C₂²	C₂×C₃×C₂²⋊Dic₅	1	3	yes	—
357	C₂²	C₂×C₃×C₂²⋊Dic₅	1	6	yes	—
358	C₂²	C₂×C₃×C₂²⋊Dic₅	1	3	yes	—
359	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
360	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
361	C₄	—	2	4	no	—
362	C₄	—	20	8	no	—
363	C₃	C₂²×#3966	1	1	yes	characteristic, direct product factor, Sylow
364	C₂	—	2	2	no	—
365	C₂	—	2	3	no	—
366	C₂	—	2	1	no	—
367	C₂	—	2	6	no	—
368	C₂	—	4	4	no	—
369	C₂	C₂×C₃×#3966	1	6	yes	direct product factor
370	C₂	C₂²×C₃×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²⋊Dic₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting, prime radical	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂³×C₃×D₄	D₅
hypocenter	C₅	C₂²×C₃×#99
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂⁵×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₂²⋊Dic₅	C₂	semidirect
3. C₂×C₃×#3966	C₂	direct (N × H)
4. C₂²×#3966	C₃	direct (N × H)
5. C₂⁵×C₃×C₅	C₄	semidirect
9. C₂²×C₃×C₅×D₄	C₄	semidirect
11. C₂³×C₃×C₄×C₅	C₄	semidirect
14. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
15. C₃×#3966	C₂²	direct (N × H)
18. C₂²×C₂²⋊Dic₅	C₂×C₃	semidirect
19. C₂×#3966	C₂×C₃	direct (N × H)
26. C₂⁴×C₃×C₅	C₂×C₄	semidirect
34. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
38. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
42. C₃×C₂²⋊Dic₅	C₂³	semidirect
46. C₂⁵×C₅	C₃×C₄	semidirect
50. C₂²×C₅×D₄	C₃×C₄	semidirect
52. C₂³×C₄×C₅	C₃×C₄	semidirect
55. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
56. #3966	C₂²×C₃	direct (N × H)
74. C₂³×C₃×C₅	C₂²×C₄	semidirect
82. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
85. C₂⁵×C₃	Dic₅	semidirect
89. C₂²×C₃×D₄	Dic₅	semidirect
92. C₂³×C₃×C₄	Dic₅	semidirect
102. C₂⁴×C₅	C₂×C₃×C₄	semidirect
110. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
114. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
118. C₂²⋊Dic₅	C₂³×C₃	semidirect
134. C₂²×C₃×C₅	#99	semidirect
148. C₂⁴×C₃	C₂×Dic₅	semidirect
156. C₂×C₃×D₄	C₂×Dic₅	semidirect
162. C₂²×C₃×C₄	C₂×Dic₅	semidirect
181. C₂³×C₅	C₂²×C₃×C₄	semidirect
189. C₂×C₄×C₅	C₂²×C₃×C₄	semidirect
192. C₂⁵	C₃×Dic₅	semidirect
196. C₂²×D₄	C₃×Dic₅	semidirect
199. C₂³×C₄	C₃×Dic₅	semidirect
208. C₂×C₃×C₅	C₂×#99	semidirect
226. C₂³×C₃	C₂²×Dic₅	semidirect
236. C₂×C₃×C₄	C₂²×Dic₅	semidirect
249. C₂²×C₅	C₃×#99	semidirect
263. C₂⁴	C₂×C₃×Dic₅	semidirect
271. C₂×D₄	C₂×C₃×Dic₅	semidirect
277. C₂²×C₄	C₂×C₃×Dic₅	semidirect
280. C₃×C₅	C₂²×#99	semidirect
293. C₂²×C₃	#3966	direct (N × H)
306. C₂×C₅	C₂×C₃×#99	semidirect
324. C₂³	C₂²×C₃×Dic₅	semidirect
334. C₂×C₄	C₂²×C₃×Dic₅	semidirect
340. C₂×C₃	C₂×#3966	direct (N × H)
342. C₅	C₂²×C₃×#99	semidirect
355. C₂²	C₃×#3966	direct (N × H)
363. C₃	C₂²×#3966	direct (N × H)
369. C₂	C₂×C₃×#3966	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂²×C₃×C₂²⋊Dic₅	2
C₂×C₃×#3966	2
C₂²×#3966	3
C₂²×C₃×#99	5

Subgroups — C22×C3×#3966 #14411886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#3966 #14411886