Subgroups — C₂×C₃×D₅×#124 #14479651

Order 1920.

3760 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4082	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₅×#124	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4031	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₅×#124	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
16	C₂×C₃×Q₈×D₅	—	2	8	no	—
17	C₂×C₃×Q₈×D₅	C₂²	1	8	yes	complemented
18	C₂×C₃×D₄×D₅	—	2	8	no	—
19	C₂×C₃×D₄×D₅	C₂²	1	8	yes	—
20	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
22	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
23	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	complemented
26	C₃×C₅×#124	C₂²	1	8	yes	complemented
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	complemented
30	C₃×#4093	C₂²	1	8	yes	complemented
31	C₃×#4082	C₂²	1	8	yes	complemented
32	C₂×C₃×#685	C₂²	1	4	yes	complemented
33	C₂×C₃×#685	C₂²	1	4	yes	complemented
34	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
36	C₃×#4031	C₂²	1	32	yes	complemented
37	C₃×D₅×C₂²⋊C₄	C₂²	1	32	yes	complemented
38	C₃×#4021	C₂²	1	8	yes	complemented
39	C₃×C₄²×D₅	C₂²	1	8	yes	complemented
40	C₂²×C₃×#124	—	5	1	no	maximal, Hall
41	C₂²×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic
43	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#4093	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4082	C₂×C₃	1	1	yes	characteristic, complemented
46	D₅×#124	C₂×C₃	1	16	yes	direct product factor
47	C₂×#4031	C₂×C₃	1	4	yes	complemented
48	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
49	C₂×#4021	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂³×C₃×D₅	—	2	8	no	—
53	C₂³×C₃×D₅	—	2	16	no	—
54	C₂³×C₃×D₅	C₂³	1	2	yes	—
55	C₂³×C₃×D₅	C₂³	1	8	yes	—
56	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×Q₈	—	2	4	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
65	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
66	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
67	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
68	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
69	C₃×Q₈×D₅	—	2	32	no	—
70	C₃×D₄×D₅	—	2	32	no	—
71	C₂×C₃×D₂₀	—	2	4	no	—
72	C₂×C₃×D₂₀	C₂³	1	4	yes	—
73	C₂×C₃×C₄×D₅	—	2	8	no	—
74	C₂×C₃×C₄×D₅	—	2	8	no	—
75	C₂×C₃×C₄×D₅	D₄	1	8	yes	—
76	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
77	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
78	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
79	C₂×C₃×Dic₁₀	—	2	4	no	—
80	C₂×C₃×Dic₁₀	—	2	8	no	—
81	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
82	C₂×C₃×Dic₁₀	C₂³	1	8	yes	complemented
83	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
84	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
85	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
86	C₃×#685	C₂³	1	16	yes	complemented
87	C₃×#685	C₂³	1	16	yes	complemented
88	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
89	C₃×C₄×Dic₅	C₂³	1	8	yes	complemented
90	C₂³×C₃×Q₈	—	5	1	no	—
91	C₂³×C₃×D₄	—	5	1	no	—
92	C₂×C₃×#124	—	5	1	no	—
93	C₂×C₃×#124	—	5	1	no	—
94	C₂×C₃×#124	—	5	16	no	—
95	C₂×C₃×#124	—	5	4	no	—
96	C₂×C₃×#124	—	5	1	no	—
97	C₂×C₃×#124	D₅	1	1	yes	characteristic, direct product factor
98	C₂²×C₃×C₂²⋊C₄	—	5	4	no	—
99	C₂²×C₃×C₄²	—	5	1	no	—
100	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
101	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
104	C₂×Q₈×D₅	—	2	8	no	—
105	C₂×Q₈×D₅	C₂²×C₃	1	8	yes	complemented
106	C₂×D₄×D₅	—	2	8	no	—
107	C₂×D₄×D₅	C₂²×C₃	1	8	yes	—
108	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
110	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
111	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
112	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	complemented
114	C₅×#124	C₂²×C₃	1	8	yes	complemented
115	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
116	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	complemented
118	#4093	C₂²×C₃	1	8	yes	complemented
119	#4082	C₂²×C₃	1	8	yes	complemented
120	C₂×#685	C₂²×C₃	1	4	yes	complemented
121	C₂×#685	C₂²×C₃	1	4	yes	complemented
122	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
123	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
124	#4031	C₂²×C₃	1	32	yes	complemented
125	D₅×C₂²⋊C₄	C₂²×C₃	1	32	yes	complemented
126	#4021	C₂²×C₃	1	8	yes	complemented
127	C₄²×D₅	C₂²×C₃	1	8	yes	complemented
128	C₂²×#124	—	5	1	no	Sylow
129	C₂³×C₃×C₅	—	2	4	no	—
130	C₂³×C₃×C₅	—	2	8	no	—
131	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
132	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
133	C₂²×C₃×D₅	—	2	4	no	—
134	C₂²×C₃×D₅	—	2	8	no	—
135	C₂²×C₃×D₅	—	2	16	no	—
136	C₂²×C₃×D₅	—	2	32	no	—
137	C₂²×C₃×D₅	—	4	32	no	—
138	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
139	C₂²×C₃×D₅	#41	1	8	yes	—
140	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
141	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
142	C₃×C₅×Q₈	—	2	8	no	—
143	C₃×C₅×D₄	—	2	8	no	—
144	C₂×C₃×C₄×C₅	—	2	4	no	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
150	C₃×C₂²⋊D₅	—	2	16	no	—
151	C₂×C₃×Dic₅	—	2	4	no	—
152	C₂×C₃×Dic₅	—	2	4	no	—
153	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
154	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
155	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
156	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
157	C₃×D₂₀	—	2	8	no	—
158	C₃×C₄×D₅	—	2	16	no	—
159	C₃×C₄×D₅	—	2	16	no	—
160	C₃×C₄×D₅	C₂×D₄	1	16	yes	—
161	C₃×Dic₁₀	—	2	8	no	—
162	C₃×Dic₁₀	—	2	16	no	—
163	C₂⁵×C₃	—	5	2	no	—
164	C₂²×C₃×Q₈	—	5	8	no	—
165	C₂²×C₃×Q₈	—	5	2	no	—
166	C₂²×C₃×Q₈	—	5	1	no	—
167	C₂²×C₃×Q₈	—	10	8	no	—
168	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×D₄	—	5	2	no	—
170	C₂²×C₃×D₄	—	5	8	no	—
171	C₂²×C₃×D₄	—	5	1	no	—
172	C₂²×C₃×D₄	—	10	8	no	—
173	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
174	C₂³×C₃×C₄	—	5	1	no	—
175	C₂³×C₃×C₄	—	5	2	no	—
176	C₂³×C₃×C₄	—	5	2	no	—
177	C₃×#124	—	5	8	no	—
178	C₃×#124	—	5	8	no	—
179	C₃×#124	—	5	32	no	—
180	C₃×#124	—	5	8	no	—
181	C₃×#124	C₂×D₅	1	8	yes	direct product factor
182	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
183	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
184	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
185	C₂×C₃×C₂²⋊C₄	—	5	32	no	—
186	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	4	yes	complemented
187	C₂×C₃×C₄²	—	5	2	no	—
188	C₂×C₃×C₄²	—	5	1	no	—
189	C₂×C₃×C₄²	—	5	8	no	—
190	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
191	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
192	C₂³×D₅	—	2	8	no	—
193	C₂³×D₅	—	2	16	no	—
194	C₂³×D₅	C₂³×C₃	1	2	yes	—
195	C₂³×D₅	C₂³×C₃	1	8	yes	—
196	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×Q₈	—	2	4	no	—
198	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	complemented
199	C₂×C₅×D₄	—	2	4	no	—
200	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
201	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
202	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
203	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₂²⋊D₅	—	2	8	no	—
205	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
206	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
207	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
208	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
209	Q₈×D₅	—	2	32	no	—
210	D₄×D₅	—	2	32	no	—
211	C₂×D₂₀	—	2	4	no	—
212	C₂×D₂₀	C₂³×C₃	1	4	yes	—
213	C₂×C₄×D₅	—	2	8	no	—
214	C₂×C₄×D₅	—	2	8	no	—
215	C₂×C₄×D₅	C₃×D₄	1	8	yes	—
216	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
217	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
218	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
219	C₂×Dic₁₀	—	2	4	no	—
220	C₂×Dic₁₀	—	2	8	no	—
221	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
222	C₂×Dic₁₀	C₂³×C₃	1	8	yes	complemented
223	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
224	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
225	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	complemented
226	#685	C₂³×C₃	1	16	yes	complemented
227	#685	C₂³×C₃	1	16	yes	complemented
228	C₄×Dic₅	C₂³×C₃	1	8	yes	complemented
229	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
230	C₂³×Q₈	—	5	1	no	—
231	C₂³×D₄	—	5	1	no	—
232	C₂×#124	—	5	1	no	—
233	C₂×#124	—	5	1	no	—
234	C₂×#124	—	5	16	no	—
235	C₂×#124	—	5	4	no	—
236	C₂×#124	—	5	1	no	—
237	C₂×#124	C₃×D₅	1	1	yes	characteristic, direct product factor
238	C₂²×C₂²⋊C₄	—	5	4	no	—
239	C₂²×C₄²	—	5	1	no	—
240	C₂²×C₃×C₅	—	2	4	no	—
241	C₂²×C₃×C₅	—	2	8	no	—
242	C₂²×C₃×C₅	—	4	8	no	—
243	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
244	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
245	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
246	C₂×C₃×D₅	—	2	4	no	—
247	C₂×C₃×D₅	—	2	8	no	—
248	C₂×C₃×D₅	—	4	8	no	—
249	C₂×C₃×D₅	—	4	32	no	—
250	C₂×C₃×D₅	#124	1	16	yes	direct product factor
251	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
252	C₂×C₃×D₅	C₂×#41	1	8	yes	—
253	C₃×C₄×C₅	—	2	4	no	—
254	C₃×C₄×C₅	—	2	4	no	—
255	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
256	C₃×Dic₅	—	2	4	no	—
257	C₃×Dic₅	—	2	4	no	—
258	C₃×Dic₅	C₂²×D₄	1	4	yes	—
259	C₂⁴×C₃	—	5	1	no	—
260	C₂⁴×C₃	—	5	8	no	—
261	C₂⁴×C₃	—	5	2	no	—
262	C₂⁴×C₃	—	10	16	no	—
263	C₂⁴×C₃	—	10	8	no	—
264	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
265	C₂×C₃×Q₈	—	2	4	no	—
266	C₂×C₃×Q₈	—	5	8	no	—
267	C₂×C₃×Q₈	—	5	4	no	—
268	C₂×C₃×Q₈	—	10	8	no	—
269	C₂×C₃×Q₈	—	10	32	no	—
270	C₂×C₃×Q₈	—	10	4	no	—
271	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	complemented
272	C₂×C₃×D₄	—	2	4	no	—
273	C₂×C₃×D₄	—	5	8	no	—
274	C₂×C₃×D₄	—	5	4	no	—
275	C₂×C₃×D₄	—	10	32	no	—
276	C₂×C₃×D₄	—	10	8	no	—
277	C₂×C₃×D₄	—	10	4	no	—
278	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
279	C₂²×C₃×C₄	—	5	1	no	—
280	C₂²×C₃×C₄	—	5	8	no	—
281	C₂²×C₃×C₄	—	5	4	no	—
282	C₂²×C₃×C₄	—	5	2	no	—
283	C₂²×C₃×C₄	—	5	2	no	—
284	C₂²×C₃×C₄	—	5	8	no	—
285	C₂²×C₃×C₄	—	5	8	no	—
286	C₂²×C₃×C₄	—	10	8	no	—
287	C₂²×C₃×C₄	—	10	8	no	—
288	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
289	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
290	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	—	5	16	no	—
292	C₃×C₂²⋊C₄	—	5	16	no	—
293	C₃×C₂²⋊C₄	—	5	16	no	—
294	C₃×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
295	C₃×C₄²	—	5	8	no	—
296	C₃×C₄²	—	5	4	no	—
297	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
298	C₂³×C₅	—	2	4	no	—
299	C₂³×C₅	—	2	8	no	—
300	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
301	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
302	C₂²×D₅	—	2	4	no	—
303	C₂²×D₅	—	2	8	no	—
304	C₂²×D₅	—	2	16	no	—
305	C₂²×D₅	—	2	32	no	—
306	C₂²×D₅	—	4	32	no	—
307	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
308	C₂²×D₅	C₃×#41	1	8	yes	—
309	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
310	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
311	C₅×Q₈	—	2	8	no	—
312	C₅×D₄	—	2	8	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	2	4	no	—
315	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
316	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
317	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
318	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
319	C₂²⋊D₅	—	2	16	no	—
320	C₂×Dic₅	—	2	4	no	—
321	C₂×Dic₅	—	2	4	no	—
322	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
323	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
324	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
325	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
326	D₂₀	—	2	8	no	—
327	C₄×D₅	—	2	16	no	—
328	C₄×D₅	—	2	16	no	—
329	C₄×D₅	C₂×C₃×D₄	1	16	yes	—
330	Dic₁₀	—	2	8	no	—
331	Dic₁₀	—	2	16	no	—
332	C₂⁵	—	5	2	no	—
333	C₂²×Q₈	—	5	8	no	—
334	C₂²×Q₈	—	5	2	no	—
335	C₂²×Q₈	—	5	1	no	—
336	C₂²×Q₈	—	10	8	no	—
337	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
338	C₂²×D₄	—	5	2	no	—
339	C₂²×D₄	—	5	8	no	—
340	C₂²×D₄	—	5	1	no	—
341	C₂²×D₄	—	10	8	no	—
342	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
343	C₂³×C₄	—	5	1	no	—
344	C₂³×C₄	—	5	2	no	—
345	C₂³×C₄	—	5	2	no	—
346	#124	—	5	8	no	—
347	#124	—	5	8	no	—
348	#124	—	5	32	no	—
349	#124	—	5	8	no	—
350	#124	C₂×C₃×D₅	1	8	yes	direct product factor
351	C₂×C₂²⋊C₄	—	5	4	no	—
352	C₂×C₂²⋊C₄	—	5	4	no	—
353	C₂×C₂²⋊C₄	—	5	4	no	—
354	C₂×C₂²⋊C₄	—	5	32	no	—
355	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
356	C₂×C₄²	—	5	2	no	—
357	C₂×C₄²	—	5	1	no	—
358	C₂×C₄²	—	5	8	no	—
359	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
360	C₂×C₃×C₅	—	4	4	no	—
361	C₂×C₃×C₅	C₂×#124	1	4	yes	complemented
362	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
363	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
364	C₃×D₅	—	4	4	no	—
365	C₃×D₅	C₂×#124	1	8	yes	direct product factor
366	C₂³×C₃	—	2	4	no	—
367	C₂³×C₃	—	2	8	no	—
368	C₂³×C₃	—	5	4	no	—
369	C₂³×C₃	—	5	8	no	—
370	C₂³×C₃	—	5	2	no	—
371	C₂³×C₃	—	5	4	no	—
372	C₂³×C₃	—	10	16	no	—
373	C₂³×C₃	—	10	32	no	—
374	C₂³×C₃	—	10	4	no	—
375	C₂³×C₃	—	10	8	no	—
376	C₂³×C₃	—	20	32	no	—
377	C₂³×C₃	C₂³×D₅	1	4	yes	—
378	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
379	C₃×Q₈	—	2	8	no	—
380	C₃×Q₈	—	10	16	no	—
381	C₃×Q₈	—	10	8	no	—
382	C₃×D₄	—	2	8	no	—
383	C₃×D₄	—	10	16	no	—
384	C₃×D₄	—	10	8	no	—
385	C₂×C₃×C₄	—	2	4	no	—
386	C₂×C₃×C₄	—	2	4	no	—
387	C₂×C₃×C₄	—	5	4	no	—
388	C₂×C₃×C₄	—	5	2	no	—
389	C₂×C₃×C₄	—	5	16	no	—
390	C₂×C₃×C₄	—	5	4	no	—
391	C₂×C₃×C₄	—	5	4	no	—
392	C₂×C₃×C₄	—	10	16	no	—
393	C₂×C₃×C₄	—	10	16	no	—
394	C₂×C₃×C₄	—	10	4	no	—
395	C₂×C₃×C₄	—	10	4	no	—
396	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
397	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
398	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
399	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
400	C₂²×C₅	—	2	4	no	—
401	C₂²×C₅	—	2	8	no	—
402	C₂²×C₅	—	4	8	no	—
403	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
404	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
405	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
406	C₂×D₅	—	2	4	no	—
407	C₂×D₅	—	2	8	no	—
408	C₂×D₅	—	4	8	no	—
409	C₂×D₅	—	4	32	no	—
410	C₂×D₅	C₃×#124	1	16	yes	direct product factor
411	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
412	C₂×D₅	C₂×C₃×#41	1	8	yes	—
413	C₄×C₅	—	2	4	no	—
414	C₄×C₅	—	2	4	no	—
415	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
416	Dic₅	—	2	4	no	—
417	Dic₅	—	2	4	no	—
418	Dic₅	C₂²×C₃×D₄	1	4	yes	—
419	C₂⁴	—	5	1	no	—
420	C₂⁴	—	5	8	no	—
421	C₂⁴	—	5	2	no	—
422	C₂⁴	—	10	8	no	—
423	C₂⁴	—	10	16	no	—
424	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	5	8	no	—
427	C₂×Q₈	—	5	4	no	—
428	C₂×Q₈	—	10	8	no	—
429	C₂×Q₈	—	10	32	no	—
430	C₂×Q₈	—	10	4	no	—
431	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	complemented
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	5	8	no	—
434	C₂×D₄	—	5	4	no	—
435	C₂×D₄	—	10	32	no	—
436	C₂×D₄	—	10	8	no	—
437	C₂×D₄	—	10	4	no	—
438	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	8	no	—
441	C₂²×C₄	—	5	4	no	—
442	C₂²×C₄	—	5	2	no	—
443	C₂²×C₄	—	5	2	no	—
444	C₂²×C₄	—	5	8	no	—
445	C₂²×C₄	—	5	8	no	—
446	C₂²×C₄	—	10	8	no	—
447	C₂²×C₄	—	10	8	no	—
448	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
449	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
450	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
451	C₂²⋊C₄	—	5	16	no	—
452	C₂²⋊C₄	—	5	16	no	—
453	C₂²⋊C₄	—	5	16	no	—
454	C₂²⋊C₄	C₂²×C₃×D₅	1	16	yes	complemented
455	C₄²	—	5	8	no	—
456	C₄²	—	5	4	no	—
457	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
458	C₃×C₅	C₂²×#124	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	4	no	—
460	C₂²×C₃	—	2	8	no	—
461	C₂²×C₃	—	4	8	no	—
462	C₂²×C₃	—	5	16	no	—
463	C₂²×C₃	—	5	4	no	—
464	C₂²×C₃	—	5	8	no	—
465	C₂²×C₃	—	10	4	no	—
466	C₂²×C₃	—	10	8	no	—
467	C₂²×C₃	—	20	32	no	—
468	C₂²×C₃	—	20	8	no	—
469	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
470	C₂²×C₃	D₅×#41	1	4	yes	—
471	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
472	C₃×C₄	—	2	4	no	—
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	—	5	4	no	—
475	C₃×C₄	—	10	4	no	—
476	C₃×C₄	—	10	4	no	—
477	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
478	C₂×C₅	—	4	4	no	—
479	C₂×C₅	C₂×C₃×#124	1	4	yes	complemented
480	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
481	C₂×C₅	C₂²×C₃×#41	1	2	yes	—
482	D₅	—	4	4	no	—
483	D₅	C₂×C₃×#124	1	8	yes	direct product factor
484	C₂³	—	2	4	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	5	4	no	—
487	C₂³	—	5	8	no	—
488	C₂³	—	5	2	no	—
489	C₂³	—	5	4	no	—
490	C₂³	—	10	16	no	—
491	C₂³	—	10	32	no	—
492	C₂³	—	10	4	no	—
493	C₂³	—	10	8	no	—
494	C₂³	—	20	32	no	—
495	C₂³	C₂³×C₃×D₅	1	4	yes	—
496	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
497	Q₈	—	2	8	no	—
498	Q₈	—	10	16	no	—
499	Q₈	—	10	8	no	—
500	D₄	—	2	8	no	—
501	D₄	—	10	16	no	—
502	D₄	—	10	8	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	5	4	no	—
506	C₂×C₄	—	5	2	no	—
507	C₂×C₄	—	5	16	no	—
508	C₂×C₄	—	5	4	no	—
509	C₂×C₄	—	5	4	no	—
510	C₂×C₄	—	10	16	no	—
511	C₂×C₄	—	10	16	no	—
512	C₂×C₄	—	10	4	no	—
513	C₂×C₄	—	10	4	no	—
514	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
515	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
516	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
517	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
518	C₂×C₃	—	4	4	no	—
519	C₂×C₃	—	5	8	no	—
520	C₂×C₃	—	20	4	no	—
521	C₂×C₃	D₅×#124	1	4	yes	direct product factor
522	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
523	C₂×C₃	C₂×D₅×#41	1	2	yes	—
524	C₅	C₂²×C₃×#124	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	2	4	no	—
526	C₂²	—	2	8	no	—
527	C₂²	—	4	8	no	—
528	C₂²	—	5	4	no	—
529	C₂²	—	5	8	no	—
530	C₂²	—	5	16	no	—
531	C₂²	—	10	4	no	—
532	C₂²	—	10	8	no	—
533	C₂²	—	20	32	no	—
534	C₂²	—	20	8	no	—
535	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
536	C₂²	C₃×D₅×#41	1	4	yes	—
537	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
538	C₄	—	2	4	no	—
539	C₄	—	2	4	no	—
540	C₄	—	5	4	no	—
541	C₄	—	10	4	no	—
542	C₄	—	10	4	no	—
543	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
544	C₃	C₂×D₅×#124	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	4	4	no	—
546	C₂	—	5	8	no	—
547	C₂	—	20	4	no	—
548	C₂	C₃×D₅×#124	1	4	yes	direct product factor
549	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
550	C₂	C₂×C₃×D₅×#41	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×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₄×D₅	C₂
hypercenter	C₂×C₃×#124	D₅
hypocenter	C₅	C₂²×C₃×#124
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×D₅	C₂	semidirect
3. C₂×C₃×C₅×#124	C₂	semidirect
4. C₂×C₃×#4093	C₂	semidirect
5. C₂×C₃×#4082	C₂	semidirect
6. C₃×D₅×#124	C₂	direct (N × H)
7. C₂×C₃×#4031	C₂	semidirect
8. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
9. C₂×C₃×#4021	C₂	semidirect
10. C₂×C₃×C₄²×D₅	C₂	semidirect
11. C₂×D₅×#124	C₃	direct (N × H)
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₂×C₃×Q₈×D₅	C₂²	semidirect
24. C₂²×C₃×Dic₁₀	C₂²	semidirect
25. C₂²×C₃×Dic₁₀	C₂²	semidirect
26. C₃×C₅×#124	C₂²	semidirect
27. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
30. C₃×#4093	C₂²	semidirect
31. C₃×#4082	C₂²	semidirect
32. C₂×C₃×#685	C₂²	semidirect
33. C₂×C₃×#685	C₂²	semidirect
34. C₂×C₃×C₄×Dic₅	C₂²	semidirect
35. C₂×C₃×C₄×Dic₅	C₂²	semidirect
36. C₃×#4031	C₂²	semidirect
37. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
38. C₃×#4021	C₂²	semidirect
39. C₃×C₄²×D₅	C₂²	semidirect
41. C₂²×Q₈×D₅	C₂×C₃	semidirect
43. C₂×C₅×#124	C₂×C₃	semidirect
44. C₂×#4093	C₂×C₃	semidirect
45. C₂×#4082	C₂×C₃	semidirect
46. D₅×#124	C₂×C₃	direct (N × H)
47. C₂×#4031	C₂×C₃	semidirect
48. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
49. C₂×#4021	C₂×C₃	semidirect
50. C₂×C₄²×D₅	C₂×C₃	semidirect
58. C₂×C₃×C₅×Q₈	C₂³	semidirect
81. C₂×C₃×Dic₁₀	C₂³	semidirect
82. C₂×C₃×Dic₁₀	C₂³	semidirect
83. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
84. C₃×C₄²×C₅	C₂³	semidirect
85. C₃×C₂²⋊Dic₅	C₂³	semidirect
86. C₃×#685	C₂³	semidirect
87. C₃×#685	C₂³	semidirect
88. C₃×C₄×Dic₅	C₂³	semidirect
89. C₃×C₄×Dic₅	C₂³	semidirect
97. C₂×C₃×#124	D₅	direct (N × H)
101. C₂²×C₅×Q₈	C₂²×C₃	semidirect
105. C₂×Q₈×D₅	C₂²×C₃	semidirect
112. C₂²×Dic₁₀	C₂²×C₃	semidirect
113. C₂²×Dic₁₀	C₂²×C₃	semidirect
114. C₅×#124	C₂²×C₃	semidirect
115. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
116. C₂×C₄²×C₅	C₂²×C₃	semidirect
117. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
118. #4093	C₂²×C₃	semidirect
119. #4082	C₂²×C₃	semidirect
120. C₂×#685	C₂²×C₃	semidirect
121. C₂×#685	C₂²×C₃	semidirect
122. C₂×C₄×Dic₅	C₂²×C₃	semidirect
123. C₂×C₄×Dic₅	C₂²×C₃	semidirect
124. #4031	C₂²×C₃	semidirect
125. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
126. #4021	C₂²×C₃	semidirect
127. C₄²×D₅	C₂²×C₃	semidirect
168. C₂²×C₃×Q₈	C₂×D₅	semidirect
181. C₃×#124	C₂×D₅	direct (N × H)
186. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
190. C₂×C₃×C₄²	C₂×D₅	semidirect
198. C₂×C₅×Q₈	C₂³×C₃	semidirect
221. C₂×Dic₁₀	C₂³×C₃	semidirect
222. C₂×Dic₁₀	C₂³×C₃	semidirect
223. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
224. C₄²×C₅	C₂³×C₃	semidirect
225. C₂²⋊Dic₅	C₂³×C₃	semidirect
226. #685	C₂³×C₃	semidirect
227. #685	C₂³×C₃	semidirect
228. C₄×Dic₅	C₂³×C₃	semidirect
229. C₄×Dic₅	C₂³×C₃	semidirect
237. C₂×#124	C₃×D₅	direct (N × H)
250. C₂×C₃×D₅	#124	direct (N × H)
271. C₂×C₃×Q₈	C₂²×D₅	semidirect
294. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
297. C₃×C₄²	C₂²×D₅	semidirect
337. C₂²×Q₈	C₂×C₃×D₅	semidirect
350. #124	C₂×C₃×D₅	direct (N × H)
355. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
359. C₂×C₄²	C₂×C₃×D₅	semidirect
361. C₂×C₃×C₅	C₂×#124	semidirect
365. C₃×D₅	C₂×#124	direct (N × H)
410. C₂×D₅	C₃×#124	direct (N × H)
431. C₂×Q₈	C₂²×C₃×D₅	semidirect
454. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
457. C₄²	C₂²×C₃×D₅	semidirect
458. C₃×C₅	C₂²×#124	semidirect
479. C₂×C₅	C₂×C₃×#124	semidirect
483. D₅	C₂×C₃×#124	direct (N × H)
521. C₂×C₃	D₅×#124	direct (N × H)
524. C₅	C₂²×C₃×#124	semidirect
544. C₃	C₂×D₅×#124	direct (N × H)
548. C₂	C₃×D₅×#124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Q₈×D₅	2
C₂²×C₃×D₄×D₅	2
C₂×C₃×C₅×#124	2
C₂×C₃×#4093	2
C₂×C₃×#4082	2
C₃×D₅×#124	2
C₂×C₃×#4031	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₂×C₃×#4021	2
C₂×C₃×C₄²×D₅	2
C₂×D₅×#124	3
C₂²×C₃×#124	5

Subgroups — C2×C3×D5×#124 #14479651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×#124 #14479651