Subgroups — C₂²×C₅×#885 #14479653

Order 1920.

3760 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#885	C₂	1	24	yes	maximal, direct product factor
9	C₂²×C₅×#124	—	3	1	no	maximal, Hall
10	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
11	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#67	—	2	8	no	—
15	C₂²×C₅×#67	C₂²	1	12	yes	—
16	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₆	—	2	8	no	—
20	C₂²×C₅×Dic₆	C₂²	1	12	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	12	yes	complemented
22	C₂×C₅×#217	C₂²	1	12	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	12	yes	complemented
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	12	yes	complemented
25	C₂×C₄×C₅×Dic₃	C₂²	1	12	yes	complemented
26	C₅×#885	C₂²	1	64	yes	direct product factor
27	C₂²×#885	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂³×C₅×Q₈	—	3	1	no	—
29	C₂³×C₅×D₄	—	3	1	no	—
30	C₂×C₅×#124	—	3	24	no	—
31	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
32	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
33	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
34	C₂²×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
35	C₂²×C₄²×C₅	—	3	1	no	—
36	C₂⁴×C₃×C₅	—	2	4	no	—
37	C₂⁴×C₃×C₅	—	2	4	no	—
38	C₂⁴×C₃×C₅	—	2	4	no	—
39	C₂⁴×C₃×C₅	C₂³	1	6	yes	—
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂³×C₅×D₃	—	2	4	no	—
42	C₂³×C₅×D₃	—	2	4	no	—
43	C₂³×C₅×D₃	—	2	4	no	—
44	C₂³×C₅×D₃	C₂³	1	6	yes	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	2	4	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
49	C₂×C₅×#67	—	2	48	no	—
50	C₂×C₅×#67	C₂³	1	16	yes	—
51	C₂²×C₅×Dic₃	—	2	4	no	—
52	C₂²×C₅×Dic₃	—	2	4	no	—
53	C₂²×C₅×Dic₃	D₄	1	8	yes	—
54	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
56	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
57	C₂×C₅×Dic₆	—	2	48	no	—
58	C₂×C₅×Dic₆	C₂³	1	16	yes	complemented
59	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
60	C₅×#217	C₂³	1	16	yes	complemented
61	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
62	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
63	C₄×C₅×Dic₃	C₂³	1	16	yes	complemented
64	C₂³×#67	C₂×C₅	1	1	yes	characteristic
65	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×#217	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#885	C₂×C₅	1	24	yes	direct product factor
72	C₂⁵×C₅	—	3	1	no	—
73	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₅×Q₈	—	3	12	no	—
75	C₂²×C₅×Q₈	—	6	8	no	—
76	C₂²×C₅×D₄	—	3	12	no	—
77	C₂²×C₅×D₄	—	6	8	no	—
78	C₂³×C₄×C₅	—	3	1	no	—
79	C₂³×C₄×C₅	—	3	1	no	—
80	C₂³×C₄×C₅	—	3	1	no	—
81	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
82	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
83	C₅×#124	—	3	64	no	—
84	C₂×C₅×C₂²⋊C₄	—	3	12	no	—
85	C₂×C₅×C₂²⋊C₄	—	3	12	no	—
86	C₂×C₅×C₂²⋊C₄	—	3	12	no	—
87	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	12	yes	complemented
88	C₂×C₄²×C₅	—	3	12	no	—
89	C₂²×#124	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	12	no	—
91	C₂³×C₃×C₅	—	2	12	no	—
92	C₂³×C₃×C₅	—	2	12	no	—
93	C₂³×C₃×C₅	—	4	16	no	—
94	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
95	C₂³×C₃×C₅	#41	1	4	yes	—
96	C₂³×C₃×C₅	#41	1	4	yes	—
97	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
98	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
99	C₂²×C₅×D₃	—	2	12	no	—
100	C₂²×C₅×D₃	—	2	12	no	—
101	C₂²×C₅×D₃	—	2	12	no	—
102	C₂²×C₅×D₃	—	4	16	no	—
103	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
104	C₂×C₃×C₄×C₅	—	2	12	no	—
105	C₂×C₃×C₄×C₅	—	2	12	no	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
107	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
108	C₅×#67	—	2	32	no	—
109	C₂×C₅×Dic₃	—	2	12	no	—
110	C₂×C₅×Dic₃	—	2	12	no	—
111	C₂×C₅×Dic₃	C₂×D₄	1	24	yes	—
112	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
113	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
114	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
115	C₅×Dic₆	—	2	32	no	—
116	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
117	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
120	C₂²×#67	—	2	8	no	—
121	C₂²×#67	C₂²×C₅	1	12	yes	—
122	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
123	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
124	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
125	C₂²×Dic₆	—	2	8	no	—
126	C₂²×Dic₆	C₂²×C₅	1	12	yes	complemented
127	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	12	yes	complemented
128	C₂×#217	C₂²×C₅	1	12	yes	complemented
129	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	12	yes	complemented
130	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	12	yes	complemented
131	C₂×C₄×Dic₃	C₂²×C₅	1	12	yes	complemented
132	#885	C₂²×C₅	1	64	yes	direct product factor
133	C₂⁴×C₅	—	2	4	no	—
134	C₂⁴×C₅	—	2	4	no	—
135	C₂⁴×C₅	—	2	4	no	—
136	C₂⁴×C₅	—	3	6	no	—
137	C₂⁴×C₅	—	6	4	no	—
138	C₂⁴×C₅	—	6	4	no	—
139	C₂⁴×C₅	—	6	4	no	—
140	C₂⁴×C₅	C₂²×D₃	1	6	yes	—
141	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₂×C₅×Q₈	—	3	16	no	—
143	C₂×C₅×Q₈	—	6	48	no	—
144	C₂×C₅×D₄	—	3	16	no	—
145	C₂×C₅×D₄	—	6	48	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	3	8	no	—
149	C₂²×C₄×C₅	—	3	6	no	—
150	C₂²×C₄×C₅	—	3	6	no	—
151	C₂²×C₄×C₅	—	3	6	no	—
152	C₂²×C₄×C₅	—	6	4	no	—
153	C₂²×C₄×C₅	—	6	4	no	—
154	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
155	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
156	C₅×C₂²⋊C₄	—	3	16	no	—
157	C₅×C₂²⋊C₄	—	3	16	no	—
158	C₅×C₂²⋊C₄	—	3	16	no	—
159	C₅×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
160	C₄²×C₅	—	3	16	no	—
161	C₂³×Q₈	—	3	1	no	—
162	C₂³×D₄	—	3	1	no	—
163	C₂×#124	—	3	24	no	—
164	C₂²×C₂²⋊C₄	—	3	1	no	—
165	C₂²×C₂²⋊C₄	—	3	1	no	—
166	C₂²×C₂²⋊C₄	—	3	1	no	—
167	C₂²×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
168	C₂²×C₄²	—	3	1	no	—
169	C₂²×C₃×C₅	—	2	4	no	—
170	C₂²×C₃×C₅	—	2	4	no	—
171	C₂²×C₃×C₅	—	2	4	no	—
172	C₂²×C₃×C₅	—	4	24	no	—
173	C₂²×C₃×C₅	#124	1	16	yes	complemented
174	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
175	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
176	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
177	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
178	C₂×C₅×D₃	—	2	4	no	—
179	C₂×C₅×D₃	—	2	4	no	—
180	C₂×C₅×D₃	—	2	4	no	—
181	C₂×C₅×D₃	—	4	24	no	—
182	C₃×C₄×C₅	—	2	4	no	—
183	C₃×C₄×C₅	—	2	4	no	—
184	C₅×Dic₃	—	2	4	no	—
185	C₅×Dic₃	—	2	4	no	—
186	C₅×Dic₃	C₂²×D₄	1	8	yes	—
187	C₂⁴×C₃	—	2	4	no	—
188	C₂⁴×C₃	—	2	4	no	—
189	C₂⁴×C₃	—	2	4	no	—
190	C₂⁴×C₃	C₂³×C₅	1	6	yes	—
191	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
192	C₂³×D₃	—	2	4	no	—
193	C₂³×D₃	—	2	4	no	—
194	C₂³×D₃	—	2	4	no	—
195	C₂³×D₃	C₂³×C₅	1	6	yes	—
196	C₂²×C₃×C₄	—	2	4	no	—
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
199	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
200	C₂×#67	—	2	48	no	—
201	C₂×#67	C₂³×C₅	1	16	yes	—
202	C₂²×Dic₃	—	2	4	no	—
203	C₂²×Dic₃	—	2	4	no	—
204	C₂²×Dic₃	C₅×D₄	1	8	yes	—
205	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
206	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
207	C₂²×Dic₃	C₂³×C₅	1	6	yes	—
208	C₂×Dic₆	—	2	48	no	—
209	C₂×Dic₆	C₂³×C₅	1	16	yes	complemented
210	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	complemented
211	#217	C₂³×C₅	1	16	yes	complemented
212	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
213	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
214	C₄×Dic₃	C₂³×C₅	1	16	yes	complemented
215	C₂³×C₅	—	2	12	no	—
216	C₂³×C₅	—	2	12	no	—
217	C₂³×C₅	—	2	12	no	—
218	C₂³×C₅	—	3	4	no	—
219	C₂³×C₅	—	4	16	no	—
220	C₂³×C₅	—	6	12	no	—
221	C₂³×C₅	—	6	12	no	—
222	C₂³×C₅	—	6	12	no	—
223	C₂³×C₅	—	12	16	no	—
224	C₂³×C₅	#235	1	4	yes	—
225	C₂³×C₅	D₃×D₄	1	4	yes	—
226	C₂³×C₅	#237	1	4	yes	—
227	C₂³×C₅	C₂³×D₃	1	4	yes	—
228	C₂³×C₅	C₂³×D₃	1	3	yes	—
229	C₅×Q₈	—	6	32	no	—
230	C₅×D₄	—	6	32	no	—
231	C₂×C₄×C₅	—	2	12	no	—
232	C₂×C₄×C₅	—	2	12	no	—
233	C₂×C₄×C₅	—	3	24	no	—
234	C₂×C₄×C₅	—	3	4	no	—
235	C₂×C₄×C₅	—	3	4	no	—
236	C₂×C₄×C₅	—	3	4	no	—
237	C₂×C₄×C₅	—	6	12	no	—
238	C₂×C₄×C₅	—	6	12	no	—
239	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
240	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
241	C₂⁵	—	3	1	no	—
242	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
243	C₂²×Q₈	—	3	12	no	—
244	C₂²×Q₈	—	6	8	no	—
245	C₂²×D₄	—	3	12	no	—
246	C₂²×D₄	—	6	8	no	—
247	C₂³×C₄	—	3	1	no	—
248	C₂³×C₄	—	3	1	no	—
249	C₂³×C₄	—	3	1	no	—
250	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
252	#124	—	3	64	no	—
253	C₂×C₂²⋊C₄	—	3	12	no	—
254	C₂×C₂²⋊C₄	—	3	12	no	—
255	C₂×C₂²⋊C₄	—	3	12	no	—
256	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	12	yes	complemented
257	C₂×C₄²	—	3	12	no	—
258	C₂×C₃×C₅	—	4	4	no	—
259	C₂×C₃×C₅	C₂×#124	1	12	yes	complemented
260	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
261	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
262	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
263	C₅×D₃	—	4	4	no	—
264	C₂³×C₃	—	2	12	no	—
265	C₂³×C₃	—	2	12	no	—
266	C₂³×C₃	—	2	12	no	—
267	C₂³×C₃	—	4	16	no	—
268	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
269	C₂³×C₃	C₅×#41	1	4	yes	—
270	C₂³×C₃	C₅×#41	1	4	yes	—
271	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
272	C₂³×C₃	C₂⁴×C₅	1	3	yes	—
273	C₂²×D₃	—	2	12	no	—
274	C₂²×D₃	—	2	12	no	—
275	C₂²×D₃	—	2	12	no	—
276	C₂²×D₃	—	4	16	no	—
277	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
278	C₂×C₃×C₄	—	2	12	no	—
279	C₂×C₃×C₄	—	2	12	no	—
280	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
281	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
282	#67	—	2	32	no	—
283	C₂×Dic₃	—	2	12	no	—
284	C₂×Dic₃	—	2	12	no	—
285	C₂×Dic₃	C₂×C₅×D₄	1	24	yes	—
286	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
287	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
288	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
289	Dic₆	—	2	32	no	—
290	C₂²×C₅	—	2	4	no	—
291	C₂²×C₅	—	2	4	no	—
292	C₂²×C₅	—	2	4	no	—
293	C₂²×C₅	—	4	24	no	—
294	C₂²×C₅	—	6	4	no	—
295	C₂²×C₅	—	6	4	no	—
296	C₂²×C₅	—	6	4	no	—
297	C₂²×C₅	—	12	24	no	—
298	C₂²×C₅	#885	1	16	yes	direct product factor
299	C₂²×C₅	C₂×#235	1	6	yes	—
300	C₂²×C₅	C₂×D₃×D₄	1	6	yes	—
301	C₂²×C₅	C₂×#237	1	6	yes	—
302	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
303	C₄×C₅	—	2	4	no	—
304	C₄×C₅	—	2	4	no	—
305	C₄×C₅	—	3	8	no	—
306	C₄×C₅	—	6	4	no	—
307	C₄×C₅	—	6	4	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	3	6	no	—
312	C₂⁴	—	6	4	no	—
313	C₂⁴	—	6	4	no	—
314	C₂⁴	—	6	4	no	—
315	C₂⁴	C₂²×C₅×D₃	1	6	yes	—
316	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₂×Q₈	—	3	16	no	—
318	C₂×Q₈	—	6	48	no	—
319	C₂×D₄	—	3	16	no	—
320	C₂×D₄	—	6	48	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	3	8	no	—
324	C₂²×C₄	—	3	6	no	—
325	C₂²×C₄	—	3	6	no	—
326	C₂²×C₄	—	3	6	no	—
327	C₂²×C₄	—	6	4	no	—
328	C₂²×C₄	—	6	4	no	—
329	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
330	C₂²×C₄	C₂²×C₅×D₃	1	6	yes	—
331	C₂²⋊C₄	—	3	16	no	—
332	C₂²⋊C₄	—	3	16	no	—
333	C₂²⋊C₄	—	3	16	no	—
334	C₂²⋊C₄	C₂²×C₅×D₃	1	16	yes	complemented
335	C₄²	—	3	16	no	—
336	C₃×C₅	C₂²×#124	1	1	yes	characteristic, complemented, Hall
337	C₂²×C₃	—	2	4	no	—
338	C₂²×C₃	—	2	4	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	4	24	no	—
341	C₂²×C₃	C₅×#124	1	16	yes	complemented
342	C₂²×C₃	C₂²×C₅×D₄	1	6	yes	—
343	C₂²×C₃	C₂×C₅×#41	1	6	yes	—
344	C₂²×C₃	C₂×C₅×#41	1	6	yes	—
345	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
346	C₂×D₃	—	2	4	no	—
347	C₂×D₃	—	2	4	no	—
348	C₂×D₃	—	2	4	no	—
349	C₂×D₃	—	4	24	no	—
350	C₃×C₄	—	2	4	no	—
351	C₃×C₄	—	2	4	no	—
352	Dic₃	—	2	4	no	—
353	Dic₃	—	2	4	no	—
354	Dic₃	C₂²×C₅×D₄	1	8	yes	—
355	C₂×C₅	—	4	4	no	—
356	C₂×C₅	—	12	4	no	—
357	C₂×C₅	C₂×#885	1	12	yes	direct product factor
358	C₂×C₅	C₂²×#235	1	1	yes	characteristic
359	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
360	C₂×C₅	C₂²×#237	1	1	yes	characteristic
361	C₂³	—	2	12	no	—
362	C₂³	—	2	12	no	—
363	C₂³	—	2	12	no	—
364	C₂³	—	3	4	no	—
365	C₂³	—	4	16	no	—
366	C₂³	—	6	12	no	—
367	C₂³	—	6	12	no	—
368	C₂³	—	6	12	no	—
369	C₂³	—	12	16	no	—
370	C₂³	C₅×#235	1	4	yes	—
371	C₂³	C₅×D₃×D₄	1	4	yes	—
372	C₂³	C₅×#237	1	4	yes	—
373	C₂³	C₂³×C₅×D₃	1	4	yes	—
374	C₂³	C₂³×C₅×D₃	1	3	yes	—
375	Q₈	—	6	32	no	—
376	D₄	—	6	32	no	—
377	C₂×C₄	—	2	12	no	—
378	C₂×C₄	—	2	12	no	—
379	C₂×C₄	—	3	24	no	—
380	C₂×C₄	—	3	4	no	—
381	C₂×C₄	—	3	4	no	—
382	C₂×C₄	—	3	4	no	—
383	C₂×C₄	—	6	12	no	—
384	C₂×C₄	—	6	12	no	—
385	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
386	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	C₂×C₅×#124	1	12	yes	complemented
389	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
390	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
391	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
392	D₃	—	4	4	no	—
393	C₅	C₂²×#885	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	4	24	no	—
398	C₂²	—	6	4	no	—
399	C₂²	—	6	4	no	—
400	C₂²	—	6	4	no	—
401	C₂²	—	12	24	no	—
402	C₂²	C₅×#885	1	16	yes	direct product factor
403	C₂²	C₂×C₅×#235	1	6	yes	—
404	C₂²	C₂×C₅×D₃×D₄	1	6	yes	—
405	C₂²	C₂×C₅×#237	1	6	yes	—
406	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
407	C₄	—	2	4	no	—
408	C₄	—	2	4	no	—
409	C₄	—	3	8	no	—
410	C₄	—	6	4	no	—
411	C₄	—	6	4	no	—
412	C₃	C₂²×C₅×#124	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	4	4	no	—
414	C₂	—	12	4	no	—
415	C₂	C₂×C₅×#885	1	12	yes	direct product factor
416	C₂	C₂²×C₅×#235	1	1	yes	characteristic
417	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
418	C₂	C₂²×C₅×#237	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂³×C₅×#67	C₂
hypercenter	C₂²×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₂²×C₅×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₅×Dic₆	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂²×C₅×#217	C₂	semidirect
5. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₂²×C₄×C₅×Dic₃	C₂	semidirect
8. C₂×C₅×#885	C₂	direct (N × H)
20. C₂²×C₅×Dic₆	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₂×C₅×#217	C₂²	semidirect
23. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₂×C₄×C₅×Dic₃	C₂²	semidirect
26. C₅×#885	C₂²	direct (N × H)
27. C₂²×#885	C₅	direct (N × H)
34. C₂²×C₅×C₂²⋊C₄	D₃	semidirect
58. C₂×C₅×Dic₆	C₂³	semidirect
59. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
60. C₅×#217	C₂³	semidirect
61. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
62. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
63. C₄×C₅×Dic₃	C₂³	semidirect
65. C₂³×Dic₆	C₂×C₅	semidirect
66. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
67. C₂²×#217	C₂×C₅	semidirect
68. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
69. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
70. C₂²×C₄×Dic₃	C₂×C₅	semidirect
71. C₂×#885	C₂×C₅	direct (N × H)
87. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
126. C₂²×Dic₆	C₂²×C₅	semidirect
127. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
128. C₂×#217	C₂²×C₅	semidirect
129. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
130. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
131. C₂×C₄×Dic₃	C₂²×C₅	semidirect
132. #885	C₂²×C₅	direct (N × H)
159. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
167. C₂²×C₂²⋊C₄	C₅×D₃	semidirect
173. C₂²×C₃×C₅	#124	semidirect
209. C₂×Dic₆	C₂³×C₅	semidirect
210. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
211. #217	C₂³×C₅	semidirect
212. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
213. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
214. C₄×Dic₃	C₂³×C₅	semidirect
256. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
259. C₂×C₃×C₅	C₂×#124	semidirect
298. C₂²×C₅	#885	direct (N × H)
334. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
336. C₃×C₅	C₂²×#124	semidirect
341. C₂²×C₃	C₅×#124	semidirect
357. C₂×C₅	C₂×#885	direct (N × H)
388. C₂×C₃	C₂×C₅×#124	semidirect
393. C₅	C₂²×#885	direct (N × H)
402. C₂²	C₅×#885	direct (N × H)
412. C₃	C₂²×C₅×#124	semidirect
415. C₂	C₂×C₅×#885	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×C₅×#67	2
C₂³×C₅×Dic₆	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂²×C₅×#217	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₂²×C₄×C₅×Dic₃	2
C₂×C₅×#885	2
C₂²×C₅×#124	3
C₂²×#885	5

Subgroups — C22×C5×#885 #14479653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#885 #14479653