Subgroups — C₂²×C₃×#4031 #14479654

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×C₃×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4031	C₂	1	24	yes	maximal, direct product factor
9	C₂²×#4031	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
11	C₂⁴×C₃×D₅	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×C₃×C₂²⋊D₅	—	2	8	no	—
15	C₂²×C₃×C₂²⋊D₅	C₂²	1	12	yes	—
16	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₁₀	—	2	8	no	—
20	C₂²×C₃×Dic₁₀	C₂²	1	12	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	12	yes	complemented
22	C₂×C₃×C₂²⋊Dic₅	C₂²	1	12	yes	complemented
23	C₂×C₃×#685	C₂²	1	12	yes	complemented
24	C₂×C₃×#685	C₂²	1	12	yes	complemented
25	C₂×C₃×C₄×Dic₅	C₂²	1	12	yes	complemented
26	C₃×#4031	C₂²	1	64	yes	direct product factor
27	C₂²×C₃×#124	—	5	1	no	maximal, Hall
28	C₂³×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic
29	C₂³×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂²×C₂²⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂²×#685	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×#685	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#4031	C₂×C₃	1	24	yes	direct product factor
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×C₃×D₅	—	2	4	no	—
42	C₂³×C₃×D₅	—	2	4	no	—
43	C₂³×C₃×D₅	—	2	4	no	—
44	C₂³×C₃×D₅	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×C₃×C₂²⋊D₅	—	2	48	no	—
50	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
51	C₂²×C₃×Dic₅	—	2	4	no	—
52	C₂²×C₃×Dic₅	—	2	4	no	—
53	C₂²×C₃×Dic₅	D₄	1	8	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
56	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
57	C₂×C₃×Dic₁₀	—	2	48	no	—
58	C₂×C₃×Dic₁₀	C₂³	1	16	yes	complemented
59	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
60	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
61	C₃×#685	C₂³	1	16	yes	complemented
62	C₃×#685	C₂³	1	16	yes	complemented
63	C₃×C₄×Dic₅	C₂³	1	16	yes	complemented
64	C₂³×C₃×Q₈	—	5	1	no	—
65	C₂³×C₃×D₄	—	5	1	no	—
66	C₂×C₃×#124	—	5	24	no	—
67	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
68	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
69	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
70	C₂²×C₃×C₂²⋊C₄	D₅	1	1	yes	characteristic, complemented
71	C₂²×C₃×C₄²	—	5	1	no	—
72	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₂²⋊D₅	—	2	8	no	—
77	C₂²×C₂²⋊D₅	C₂²×C₃	1	12	yes	—
78	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
79	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
80	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
81	C₂²×Dic₁₀	—	2	8	no	—
82	C₂²×Dic₁₀	C₂²×C₃	1	12	yes	complemented
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	12	yes	complemented
84	C₂×C₂²⋊Dic₅	C₂²×C₃	1	12	yes	complemented
85	C₂×#685	C₂²×C₃	1	12	yes	complemented
86	C₂×#685	C₂²×C₃	1	12	yes	complemented
87	C₂×C₄×Dic₅	C₂²×C₃	1	12	yes	complemented
88	#4031	C₂²×C₃	1	64	yes	direct product factor
89	C₂²×#124	—	5	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×C₃×D₅	—	2	12	no	—
100	C₂²×C₃×D₅	—	2	12	no	—
101	C₂²×C₃×D₅	—	2	12	no	—
102	C₂²×C₃×D₅	—	4	16	no	—
103	C₂²×C₃×D₅	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	C₃×C₂²⋊D₅	—	2	32	no	—
109	C₂×C₃×Dic₅	—	2	12	no	—
110	C₂×C₃×Dic₅	—	2	12	no	—
111	C₂×C₃×Dic₅	C₂×D₄	1	24	yes	—
112	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
113	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
114	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
115	C₃×Dic₁₀	—	2	32	no	—
116	C₂⁵×C₃	—	5	1	no	—
117	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
118	C₂²×C₃×Q₈	—	5	12	no	—
119	C₂²×C₃×Q₈	—	10	8	no	—
120	C₂²×C₃×D₄	—	5	12	no	—
121	C₂²×C₃×D₄	—	10	8	no	—
122	C₂³×C₃×C₄	—	5	1	no	—
123	C₂³×C₃×C₄	—	5	1	no	—
124	C₂³×C₃×C₄	—	5	1	no	—
125	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
126	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
127	C₃×#124	—	5	64	no	—
128	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
129	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
130	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
131	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	12	yes	complemented
132	C₂×C₃×C₄²	—	5	12	no	—
133	C₂⁴×C₅	—	2	4	no	—
134	C₂⁴×C₅	—	2	4	no	—
135	C₂⁴×C₅	—	2	4	no	—
136	C₂⁴×C₅	C₂³×C₃	1	6	yes	—
137	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₂³×D₅	—	2	4	no	—
139	C₂³×D₅	—	2	4	no	—
140	C₂³×D₅	—	2	4	no	—
141	C₂³×D₅	C₂³×C₃	1	6	yes	—
142	C₂²×C₄×C₅	—	2	4	no	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
146	C₂×C₂²⋊D₅	—	2	48	no	—
147	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
148	C₂²×Dic₅	—	2	4	no	—
149	C₂²×Dic₅	—	2	4	no	—
150	C₂²×Dic₅	C₃×D₄	1	8	yes	—
151	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
152	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
153	C₂²×Dic₅	C₂³×C₃	1	6	yes	—
154	C₂×Dic₁₀	—	2	48	no	—
155	C₂×Dic₁₀	C₂³×C₃	1	16	yes	complemented
156	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
157	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	complemented
158	#685	C₂³×C₃	1	16	yes	complemented
159	#685	C₂³×C₃	1	16	yes	complemented
160	C₄×Dic₅	C₂³×C₃	1	16	yes	complemented
161	C₂³×Q₈	—	5	1	no	—
162	C₂³×D₄	—	5	1	no	—
163	C₂×#124	—	5	24	no	—
164	C₂²×C₂²⋊C₄	—	5	1	no	—
165	C₂²×C₂²⋊C₄	—	5	1	no	—
166	C₂²×C₂²⋊C₄	—	5	1	no	—
167	C₂²×C₂²⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
168	C₂²×C₄²	—	5	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×C₃×D₅	—	2	4	no	—
179	C₂×C₃×D₅	—	2	4	no	—
180	C₂×C₃×D₅	—	2	4	no	—
181	C₂×C₃×D₅	—	4	24	no	—
182	C₃×C₄×C₅	—	2	4	no	—
183	C₃×C₄×C₅	—	2	4	no	—
184	C₃×Dic₅	—	2	4	no	—
185	C₃×Dic₅	—	2	4	no	—
186	C₃×Dic₅	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	—	5	6	no	—
191	C₂⁴×C₃	—	10	4	no	—
192	C₂⁴×C₃	—	10	4	no	—
193	C₂⁴×C₃	—	10	4	no	—
194	C₂⁴×C₃	C₂²×D₅	1	6	yes	—
195	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
196	C₂×C₃×Q₈	—	5	16	no	—
197	C₂×C₃×Q₈	—	10	48	no	—
198	C₂×C₃×D₄	—	5	16	no	—
199	C₂×C₃×D₄	—	10	48	no	—
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	5	8	no	—
203	C₂²×C₃×C₄	—	5	6	no	—
204	C₂²×C₃×C₄	—	5	6	no	—
205	C₂²×C₃×C₄	—	5	6	no	—
206	C₂²×C₃×C₄	—	10	4	no	—
207	C₂²×C₃×C₄	—	10	4	no	—
208	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
209	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
210	C₃×C₂²⋊C₄	—	5	16	no	—
211	C₃×C₂²⋊C₄	—	5	16	no	—
212	C₃×C₂²⋊C₄	—	5	16	no	—
213	C₃×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
214	C₃×C₄²	—	5	16	no	—
215	C₂³×C₅	—	2	12	no	—
216	C₂³×C₅	—	2	12	no	—
217	C₂³×C₅	—	2	12	no	—
218	C₂³×C₅	—	4	16	no	—
219	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
220	C₂³×C₅	C₃×#41	1	4	yes	—
221	C₂³×C₅	C₃×#41	1	4	yes	—
222	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
223	C₂³×C₅	C₂⁴×C₃	1	3	yes	—
224	C₂²×D₅	—	2	12	no	—
225	C₂²×D₅	—	2	12	no	—
226	C₂²×D₅	—	2	12	no	—
227	C₂²×D₅	—	4	16	no	—
228	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
229	C₂×C₄×C₅	—	2	12	no	—
230	C₂×C₄×C₅	—	2	12	no	—
231	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
232	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
233	C₂²⋊D₅	—	2	32	no	—
234	C₂×Dic₅	—	2	12	no	—
235	C₂×Dic₅	—	2	12	no	—
236	C₂×Dic₅	C₂×C₃×D₄	1	24	yes	—
237	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
238	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
239	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
240	Dic₁₀	—	2	32	no	—
241	C₂⁵	—	5	1	no	—
242	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
243	C₂²×Q₈	—	5	12	no	—
244	C₂²×Q₈	—	10	8	no	—
245	C₂²×D₄	—	5	12	no	—
246	C₂²×D₄	—	10	8	no	—
247	C₂³×C₄	—	5	1	no	—
248	C₂³×C₄	—	5	1	no	—
249	C₂³×C₄	—	5	1	no	—
250	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
252	#124	—	5	64	no	—
253	C₂×C₂²⋊C₄	—	5	12	no	—
254	C₂×C₂²⋊C₄	—	5	12	no	—
255	C₂×C₂²⋊C₄	—	5	12	no	—
256	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	12	yes	complemented
257	C₂×C₄²	—	5	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	C₃×D₅	—	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	—	5	4	no	—
269	C₂³×C₃	—	10	12	no	—
270	C₂³×C₃	—	10	12	no	—
271	C₂³×C₃	—	10	12	no	—
272	C₂³×C₃	—	20	16	no	—
273	C₂³×C₃	#709	1	4	yes	—
274	C₂³×C₃	D₄×D₅	1	4	yes	—
275	C₂³×C₃	#711	1	4	yes	—
276	C₂³×C₃	C₂³×D₅	1	4	yes	—
277	C₂³×C₃	C₂³×D₅	1	3	yes	—
278	C₃×Q₈	—	10	32	no	—
279	C₃×D₄	—	10	32	no	—
280	C₂×C₃×C₄	—	2	12	no	—
281	C₂×C₃×C₄	—	2	12	no	—
282	C₂×C₃×C₄	—	5	24	no	—
283	C₂×C₃×C₄	—	5	4	no	—
284	C₂×C₃×C₄	—	5	4	no	—
285	C₂×C₃×C₄	—	5	4	no	—
286	C₂×C₃×C₄	—	10	12	no	—
287	C₂×C₃×C₄	—	10	12	no	—
288	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
289	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
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	C₃×#124	1	16	yes	complemented
295	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
296	C₂²×C₅	C₂×C₃×#41	1	6	yes	—
297	C₂²×C₅	C₂×C₃×#41	1	6	yes	—
298	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
299	C₂×D₅	—	2	4	no	—
300	C₂×D₅	—	2	4	no	—
301	C₂×D₅	—	2	4	no	—
302	C₂×D₅	—	4	24	no	—
303	C₄×C₅	—	2	4	no	—
304	C₄×C₅	—	2	4	no	—
305	Dic₅	—	2	4	no	—
306	Dic₅	—	2	4	no	—
307	Dic₅	C₂²×C₃×D₄	1	8	yes	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	5	6	no	—
312	C₂⁴	—	10	4	no	—
313	C₂⁴	—	10	4	no	—
314	C₂⁴	—	10	4	no	—
315	C₂⁴	C₂²×C₃×D₅	1	6	yes	—
316	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
317	C₂×Q₈	—	5	16	no	—
318	C₂×Q₈	—	10	48	no	—
319	C₂×D₄	—	5	16	no	—
320	C₂×D₄	—	10	48	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	5	8	no	—
324	C₂²×C₄	—	5	6	no	—
325	C₂²×C₄	—	5	6	no	—
326	C₂²×C₄	—	5	6	no	—
327	C₂²×C₄	—	10	4	no	—
328	C₂²×C₄	—	10	4	no	—
329	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
330	C₂²×C₄	C₂²×C₃×D₅	1	6	yes	—
331	C₂²⋊C₄	—	5	16	no	—
332	C₂²⋊C₄	—	5	16	no	—
333	C₂²⋊C₄	—	5	16	no	—
334	C₂²⋊C₄	C₂²×C₃×D₅	1	16	yes	complemented
335	C₄²	—	5	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	—	10	4	no	—
342	C₂²×C₃	—	10	4	no	—
343	C₂²×C₃	—	10	4	no	—
344	C₂²×C₃	—	20	24	no	—
345	C₂²×C₃	#4031	1	16	yes	direct product factor
346	C₂²×C₃	C₂×#709	1	6	yes	—
347	C₂²×C₃	C₂×D₄×D₅	1	6	yes	—
348	C₂²×C₃	C₂×#711	1	6	yes	—
349	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
350	C₃×C₄	—	2	4	no	—
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	5	8	no	—
353	C₃×C₄	—	10	4	no	—
354	C₃×C₄	—	10	4	no	—
355	C₂×C₅	—	4	4	no	—
356	C₂×C₅	C₂×C₃×#124	1	12	yes	complemented
357	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
358	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
359	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
360	D₅	—	4	4	no	—
361	C₂³	—	2	12	no	—
362	C₂³	—	2	12	no	—
363	C₂³	—	2	12	no	—
364	C₂³	—	4	16	no	—
365	C₂³	—	5	4	no	—
366	C₂³	—	10	12	no	—
367	C₂³	—	10	12	no	—
368	C₂³	—	10	12	no	—
369	C₂³	—	20	16	no	—
370	C₂³	C₃×#709	1	4	yes	—
371	C₂³	C₃×D₄×D₅	1	4	yes	—
372	C₂³	C₃×#711	1	4	yes	—
373	C₂³	C₂³×C₃×D₅	1	4	yes	—
374	C₂³	C₂³×C₃×D₅	1	3	yes	—
375	Q₈	—	10	32	no	—
376	D₄	—	10	32	no	—
377	C₂×C₄	—	2	12	no	—
378	C₂×C₄	—	2	12	no	—
379	C₂×C₄	—	5	24	no	—
380	C₂×C₄	—	5	4	no	—
381	C₂×C₄	—	5	4	no	—
382	C₂×C₄	—	5	4	no	—
383	C₂×C₄	—	10	12	no	—
384	C₂×C₄	—	10	12	no	—
385	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
386	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
387	C₂×C₃	—	4	4	no	—
388	C₂×C₃	—	20	4	no	—
389	C₂×C₃	C₂×#4031	1	12	yes	direct product factor
390	C₂×C₃	C₂²×#709	1	1	yes	characteristic
391	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
392	C₂×C₃	C₂²×#711	1	1	yes	characteristic
393	C₅	C₂²×C₃×#124	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	4	24	no	—
398	C₂²	—	10	4	no	—
399	C₂²	—	10	4	no	—
400	C₂²	—	10	4	no	—
401	C₂²	—	20	24	no	—
402	C₂²	C₃×#4031	1	16	yes	direct product factor
403	C₂²	C₂×C₃×#709	1	6	yes	—
404	C₂²	C₂×C₃×D₄×D₅	1	6	yes	—
405	C₂²	C₂×C₃×#711	1	6	yes	—
406	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
407	C₄	—	2	4	no	—
408	C₄	—	2	4	no	—
409	C₄	—	5	8	no	—
410	C₄	—	10	4	no	—
411	C₄	—	10	4	no	—
412	C₃	C₂²×#4031	1	1	yes	characteristic, direct product factor, Sylow
413	C₂	—	4	4	no	—
414	C₂	—	20	4	no	—
415	C₂	C₂×C₃×#4031	1	12	yes	direct product factor
416	C₂	C₂²×C₃×#709	1	1	yes	characteristic
417	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
418	C₂	C₂²×C₃×#711	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂³×C₃×C₂²⋊D₅	C₂
hypercenter	C₂²×C₃×C₂²⋊C₄	D₅
hypocenter	C₅	C₂²×C₃×#124
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×Dic₁₀	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂²×C₃×C₂²⋊Dic₅	C₂	semidirect
5. C₂²×C₃×#685	C₂	semidirect
6. C₂²×C₃×#685	C₂	semidirect
7. C₂²×C₃×C₄×Dic₅	C₂	semidirect
8. C₂×C₃×#4031	C₂	direct (N × H)
9. C₂²×#4031	C₃	direct (N × H)
20. C₂²×C₃×Dic₁₀	C₂²	semidirect
21. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
22. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
23. C₂×C₃×#685	C₂²	semidirect
24. C₂×C₃×#685	C₂²	semidirect
25. C₂×C₃×C₄×Dic₅	C₂²	semidirect
26. C₃×#4031	C₂²	direct (N × H)
29. C₂³×Dic₁₀	C₂×C₃	semidirect
30. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
31. C₂²×C₂²⋊Dic₅	C₂×C₃	semidirect
32. C₂²×#685	C₂×C₃	semidirect
33. C₂²×#685	C₂×C₃	semidirect
34. C₂²×C₄×Dic₅	C₂×C₃	semidirect
35. C₂×#4031	C₂×C₃	direct (N × H)
58. C₂×C₃×Dic₁₀	C₂³	semidirect
59. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
60. C₃×C₂²⋊Dic₅	C₂³	semidirect
61. C₃×#685	C₂³	semidirect
62. C₃×#685	C₂³	semidirect
63. C₃×C₄×Dic₅	C₂³	semidirect
70. C₂²×C₃×C₂²⋊C₄	D₅	semidirect
82. C₂²×Dic₁₀	C₂²×C₃	semidirect
83. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
84. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
85. C₂×#685	C₂²×C₃	semidirect
86. C₂×#685	C₂²×C₃	semidirect
87. C₂×C₄×Dic₅	C₂²×C₃	semidirect
88. #4031	C₂²×C₃	direct (N × H)
131. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
155. C₂×Dic₁₀	C₂³×C₃	semidirect
156. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
157. C₂²⋊Dic₅	C₂³×C₃	semidirect
158. #685	C₂³×C₃	semidirect
159. #685	C₂³×C₃	semidirect
160. C₄×Dic₅	C₂³×C₃	semidirect
167. C₂²×C₂²⋊C₄	C₃×D₅	semidirect
173. C₂²×C₃×C₅	#124	semidirect
213. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
256. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
259. C₂×C₃×C₅	C₂×#124	semidirect
294. C₂²×C₅	C₃×#124	semidirect
334. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
336. C₃×C₅	C₂²×#124	semidirect
345. C₂²×C₃	#4031	direct (N × H)
356. C₂×C₅	C₂×C₃×#124	semidirect
389. C₂×C₃	C₂×#4031	direct (N × H)
393. C₅	C₂²×C₃×#124	semidirect
402. C₂²	C₃×#4031	direct (N × H)
412. C₃	C₂²×#4031	direct (N × H)
415. C₂	C₂×C₃×#4031	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×C₂²⋊D₅	2
C₂³×C₃×Dic₁₀	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂²×C₃×C₂²⋊Dic₅	2
C₂²×C₃×#685	2
C₂²×C₃×C₄×Dic₅	2
C₂×C₃×#4031	2
C₂²×#4031	3
C₂²×C₃×#124	5

Subgroups — C22×C3×#4031 #14479654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#4031 #14479654