Subgroups — C₂×C₃×#65897 #14483923

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4084	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4076	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4072	C₂	1	2	yes	maximal, complemented
5	C₃×#65897	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#4038	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4031	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65897	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
13	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
16	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
22	C₃×#4084	C₂²	1	16	yes	complemented
23	C₃×#4076	C₂²	1	16	yes	complemented
24	C₂×C₃×#685	C₂²	1	4	yes	—
25	C₂×C₃×#685	C₂²	1	2	yes	—
26	C₃×#4072	C₂²	1	16	yes	complemented
27	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
30	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
31	C₃×#4038	C₂²	1	16	yes	complemented
32	C₃×#4031	C₂²	1	32	yes	complemented
33	C₃×C₄×D₂₀	C₂²	1	8	yes	complemented
34	C₃×#4015	C₂²	1	8	yes	complemented
35	C₂×C₃×#555	—	5	1	no	maximal, Hall
36	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4084	C₂×C₃	1	2	yes	complemented
38	C₂×#4076	C₂×C₃	1	2	yes	complemented
39	C₂×#4072	C₂×C₃	1	2	yes	complemented
40	#65897	C₂×C₃	1	16	yes	direct product factor
41	C₂×#4038	C₂×C₃	1	2	yes	complemented
42	C₂×#4031	C₂×C₃	1	4	yes	complemented
43	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#4015	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂³×C₃×D₅	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	—	2	8	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
56	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
58	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
59	C₂×C₃×D₂₀	—	2	4	no	—
60	C₂×C₃×D₂₀	C₂³	1	4	yes	—
61	C₂×C₃×C₄×D₅	—	2	8	no	—
62	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
63	C₂×C₃×Dic₁₀	—	4	4	no	—
64	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
66	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
67	C₃×C₄²×C₅	C₂³	1	4	yes	—
68	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	—
69	C₃×#685	C₂³	1	8	yes	—
70	C₃×#685	C₂³	1	16	yes	—
71	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
72	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
73	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
74	C₃×C₄×Dic₅	C₂³	1	16	yes	—
75	C₃×#555	—	5	16	no	—
76	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
77	C₂×C₃×#124	—	5	4	no	—
78	C₂×C₃×#121	—	5	2	no	—
79	C₂×C₃×#121	—	5	2	no	—
80	C₂×C₃×C₄×D₄	—	5	1	no	—
81	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
82	C₂×C₃×#117	—	5	2	no	—
83	C₂×C₃×#117	—	5	2	no	—
84	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
86	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
87	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
89	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
90	C₄×C₅×D₄	C₂²×C₃	1	8	yes	complemented
91	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
95	#4084	C₂²×C₃	1	16	yes	complemented
96	#4076	C₂²×C₃	1	16	yes	complemented
97	C₂×#685	C₂²×C₃	1	2	yes	—
98	C₂×#685	C₂²×C₃	1	4	yes	—
99	#4072	C₂²×C₃	1	16	yes	complemented
100	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
101	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
102	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
104	#4038	C₂²×C₃	1	16	yes	complemented
105	#4031	C₂²×C₃	1	32	yes	complemented
106	C₄×D₂₀	C₂²×C₃	1	8	yes	complemented
107	#4015	C₂²×C₃	1	8	yes	complemented
108	C₂×#555	—	5	1	no	Sylow
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	4	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₂²×C₃×D₅	—	2	4	no	—
115	C₂²×C₃×D₅	—	2	4	no	—
116	C₂²×C₃×D₅	—	2	4	no	—
117	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
118	C₃×C₅×D₄	—	2	8	no	—
119	C₂×C₃×C₄×C₅	—	2	4	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	16	no	—
122	C₂×C₃×C₄×C₅	#41	1	4	yes	—
123	C₂×C₃×C₄×C₅	#41	1	4	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
128	C₃×C₂²⋊D₅	—	4	16	no	—
129	C₂×C₃×Dic₅	—	2	4	no	—
130	C₂×C₃×Dic₅	—	2	8	no	—
131	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
132	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
133	C₃×D₂₀	—	2	8	no	—
134	C₃×C₄×D₅	—	2	16	no	—
135	C₃×Dic₁₀	—	4	8	no	—
136	C₂²×C₃×Q₈	—	5	2	no	—
137	C₂²×C₃×D₄	—	5	4	no	—
138	C₂²×C₃×D₄	—	5	1	no	—
139	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
140	C₂³×C₃×C₄	—	5	2	no	—
141	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
142	C₃×C₄⋊Q₈	—	5	8	no	—
143	C₃×#124	—	5	32	no	—
144	C₃×#121	—	5	16	no	—
145	C₃×#121	—	5	16	no	—
146	C₃×C₄×D₄	—	5	8	no	—
147	C₃×C₄×D₄	C₂×D₅	1	8	yes	complemented
148	C₃×#117	—	5	16	no	—
149	C₃×#117	—	5	16	no	—
150	C₂×C₃×C₄⋊C₄	—	5	1	no	—
151	C₂×C₃×C₄⋊C₄	—	5	2	no	—
152	C₂×C₃×C₄⋊C₄	—	5	2	no	—
153	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
155	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
156	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
157	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
158	C₂×C₃×C₄²	—	5	4	no	—
159	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
160	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
161	C₂³×D₅	C₂³×C₃	1	2	yes	—
162	C₂×C₅×D₄	—	2	4	no	—
163	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
164	C₂²×C₄×C₅	—	2	8	no	—
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₂²⋊D₅	—	4	8	no	—
171	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
172	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
173	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
174	C₂×D₂₀	—	2	4	no	—
175	C₂×D₂₀	C₂³×C₃	1	4	yes	—
176	C₂×C₄×D₅	—	2	8	no	—
177	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
178	C₂×Dic₁₀	—	4	4	no	—
179	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
180	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
181	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
182	C₄²×C₅	C₂³×C₃	1	4	yes	—
183	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	—
184	#685	C₂³×C₃	1	8	yes	—
185	#685	C₂³×C₃	1	16	yes	—
186	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
187	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
188	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
189	C₄×Dic₅	C₂³×C₃	1	16	yes	—
190	#555	—	5	16	no	—
191	C₂×C₄⋊Q₈	—	5	1	no	—
192	C₂×#124	—	5	4	no	—
193	C₂×#121	—	5	2	no	—
194	C₂×#121	—	5	2	no	—
195	C₂×C₄×D₄	—	5	1	no	—
196	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
197	C₂×#117	—	5	2	no	—
198	C₂×#117	—	5	2	no	—
199	C₂²×C₃×C₅	—	2	4	no	—
200	C₂²×C₃×C₅	—	2	4	no	—
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	4	8	no	—
203	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
204	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
205	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
206	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
207	C₂×C₃×D₅	—	2	4	no	—
208	C₂×C₃×D₅	—	2	4	no	—
209	C₂×C₃×D₅	—	2	4	no	—
210	C₂×C₃×D₅	—	4	8	no	—
211	C₃×C₄×C₅	—	2	4	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	C₂×#41	1	4	yes	—
214	C₃×C₄×C₅	C₂×#41	1	4	yes	—
215	C₃×Dic₅	—	2	4	no	—
216	C₃×Dic₅	—	2	8	no	—
217	C₂⁴×C₃	—	5	2	no	—
218	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
219	C₂×C₃×Q₈	—	5	8	no	—
220	C₂×C₃×Q₈	—	20	4	no	—
221	C₂×C₃×D₄	—	2	4	no	—
222	C₂×C₃×D₄	—	5	16	no	—
223	C₂×C₃×D₄	—	5	4	no	—
224	C₂×C₃×D₄	—	10	4	no	—
225	C₂×C₃×D₄	—	20	8	no	—
226	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
227	C₂²×C₃×C₄	—	2	8	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	—	5	4	no	—
230	C₂²×C₃×C₄	—	5	8	no	—
231	C₂²×C₃×C₄	—	10	8	no	—
232	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
233	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
234	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
237	C₃×C₄⋊C₄	—	5	4	no	—
238	C₃×C₄⋊C₄	—	5	8	no	—
239	C₃×C₄⋊C₄	—	5	8	no	—
240	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
241	C₃×C₂²⋊C₄	—	5	16	no	—
242	C₃×C₂²⋊C₄	—	5	16	no	—
243	C₃×C₂²⋊C₄	—	5	8	no	—
244	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
245	C₃×C₄²	—	5	16	no	—
246	C₃×C₄²	C₂²×D₅	1	4	yes	—
247	C₂³×C₅	—	2	4	no	—
248	C₂³×C₅	—	2	4	no	—
249	C₂³×C₅	—	2	4	no	—
250	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
251	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
252	C₂²×D₅	—	2	4	no	—
253	C₂²×D₅	—	2	4	no	—
254	C₂²×D₅	—	2	4	no	—
255	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
256	C₅×D₄	—	2	8	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	16	no	—
260	C₂×C₄×C₅	C₃×#41	1	4	yes	—
261	C₂×C₄×C₅	C₃×#41	1	4	yes	—
262	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
263	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
264	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
265	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
266	C₂²⋊D₅	—	4	16	no	—
267	C₂×Dic₅	—	2	4	no	—
268	C₂×Dic₅	—	2	8	no	—
269	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
270	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
271	D₂₀	—	2	8	no	—
272	C₄×D₅	—	2	16	no	—
273	Dic₁₀	—	4	8	no	—
274	C₂²×Q₈	—	5	2	no	—
275	C₂²×D₄	—	5	4	no	—
276	C₂²×D₄	—	5	1	no	—
277	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
278	C₂³×C₄	—	5	2	no	—
279	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
280	C₄⋊Q₈	—	5	8	no	—
281	#124	—	5	32	no	—
282	#121	—	5	16	no	—
283	#121	—	5	16	no	—
284	C₄×D₄	—	5	8	no	—
285	C₄×D₄	C₂×C₃×D₅	1	8	yes	complemented
286	#117	—	5	16	no	—
287	#117	—	5	16	no	—
288	C₂×C₄⋊C₄	—	5	1	no	—
289	C₂×C₄⋊C₄	—	5	2	no	—
290	C₂×C₄⋊C₄	—	5	2	no	—
291	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	5	4	no	—
293	C₂×C₂²⋊C₄	—	5	4	no	—
294	C₂×C₂²⋊C₄	—	5	2	no	—
295	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
296	C₂×C₄²	—	5	4	no	—
297	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
298	C₂×C₃×C₅	—	4	4	no	—
299	C₂×C₃×C₅	#555	1	4	yes	complemented
300	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₃×D₅	—	4	4	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	—	2	4	no	—
306	C₂³×C₃	—	2	4	no	—
307	C₂³×C₃	—	5	4	no	—
308	C₂³×C₃	—	10	4	no	—
309	C₂³×C₃	—	10	4	no	—
310	C₂³×C₃	—	10	4	no	—
311	C₂³×C₃	C₂³×D₅	1	4	yes	—
312	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
313	C₃×Q₈	—	20	8	no	—
314	C₃×D₄	—	2	8	no	—
315	C₃×D₄	—	10	8	no	—
316	C₃×D₄	—	20	16	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	16	no	—
320	C₂×C₃×C₄	—	5	4	no	—
321	C₂×C₃×C₄	—	5	8	no	—
322	C₂×C₃×C₄	—	10	4	no	—
323	C₂×C₃×C₄	—	10	8	no	—
324	C₂×C₃×C₄	—	10	16	no	—
325	C₂×C₃×C₄	#709	1	4	yes	—
326	C₂×C₃×C₄	#711	1	4	yes	—
327	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
328	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
329	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
330	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
331	C₂²×C₅	—	2	4	no	—
332	C₂²×C₅	—	2	4	no	—
333	C₂²×C₅	—	2	4	no	—
334	C₂²×C₅	—	4	8	no	—
335	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
336	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
337	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
338	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
339	C₂×D₅	—	2	4	no	—
340	C₂×D₅	—	2	4	no	—
341	C₂×D₅	—	2	4	no	—
342	C₂×D₅	—	4	8	no	—
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	C₂×C₃×#41	1	4	yes	—
346	C₄×C₅	C₂×C₃×#41	1	4	yes	—
347	Dic₅	—	2	4	no	—
348	Dic₅	—	2	8	no	—
349	C₂⁴	—	5	2	no	—
350	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
351	C₂×Q₈	—	5	8	no	—
352	C₂×Q₈	—	20	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	5	16	no	—
355	C₂×D₄	—	5	4	no	—
356	C₂×D₄	—	10	4	no	—
357	C₂×D₄	—	20	8	no	—
358	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	5	2	no	—
361	C₂²×C₄	—	5	4	no	—
362	C₂²×C₄	—	5	8	no	—
363	C₂²×C₄	—	10	8	no	—
364	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
365	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
367	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
369	C₄⋊C₄	—	5	4	no	—
370	C₄⋊C₄	—	5	8	no	—
371	C₄⋊C₄	—	5	8	no	—
372	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
373	C₂²⋊C₄	—	5	16	no	—
374	C₂²⋊C₄	—	5	16	no	—
375	C₂²⋊C₄	—	5	8	no	—
376	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
377	C₄²	—	5	16	no	—
378	C₄²	C₂²×C₃×D₅	1	4	yes	—
379	C₃×C₅	C₂×#555	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	2	4	no	—
383	C₂²×C₃	—	4	8	no	—
384	C₂²×C₃	—	10	4	no	—
385	C₂²×C₃	—	10	4	no	—
386	C₂²×C₃	—	10	4	no	—
387	C₂²×C₃	—	20	8	no	—
388	C₂²×C₃	C₂×#709	1	2	yes	—
389	C₂²×C₃	C₂×#711	1	2	yes	—
390	C₂²×C₃	#4149	1	2	yes	—
391	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	10	4	no	—
395	C₃×C₄	—	10	8	no	—
396	C₃×C₄	C₂×#709	1	4	yes	—
397	C₃×C₄	C₂×#711	1	4	yes	—
398	C₂×C₅	—	4	4	no	—
399	C₂×C₅	C₃×#555	1	4	yes	complemented
400	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
401	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
402	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
403	D₅	—	4	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	5	4	no	—
408	C₂³	—	10	4	no	—
409	C₂³	—	10	4	no	—
410	C₂³	—	10	4	no	—
411	C₂³	C₂³×C₃×D₅	1	4	yes	—
412	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
413	Q₈	—	20	8	no	—
414	D₄	—	2	8	no	—
415	D₄	—	10	8	no	—
416	D₄	—	20	16	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	16	no	—
420	C₂×C₄	—	5	4	no	—
421	C₂×C₄	—	5	8	no	—
422	C₂×C₄	—	10	4	no	—
423	C₂×C₄	—	10	8	no	—
424	C₂×C₄	—	10	16	no	—
425	C₂×C₄	C₃×#709	1	4	yes	—
426	C₂×C₄	C₃×#711	1	4	yes	—
427	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
428	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
429	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
430	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
431	C₂×C₃	—	4	4	no	—
432	C₂×C₃	—	20	4	no	—
433	C₂×C₃	#65897	1	4	yes	direct product factor
434	C₂×C₃	C₂²×#709	1	1	yes	characteristic
435	C₂×C₃	C₂²×#711	1	1	yes	characteristic
436	C₂×C₃	C₂×#4149	1	1	yes	characteristic
437	C₅	C₂×C₃×#555	1	1	yes	characteristic, complemented, Sylow
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	10	4	no	—
443	C₂²	—	10	4	no	—
444	C₂²	—	10	4	no	—
445	C₂²	—	20	8	no	—
446	C₂²	C₂×C₃×#709	1	2	yes	—
447	C₂²	C₂×C₃×#711	1	2	yes	—
448	C₂²	C₃×#4149	1	2	yes	—
449	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	10	4	no	—
453	C₄	—	10	8	no	—
454	C₄	C₂×C₃×#709	1	4	yes	—
455	C₄	C₂×C₃×#711	1	4	yes	—
456	C₃	C₂×#65897	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	4	4	no	—
458	C₂	—	20	4	no	—
459	C₂	C₃×#65897	1	4	yes	direct product factor
460	C₂	C₂²×C₃×#709	1	1	yes	characteristic
461	C₂	C₂²×C₃×#711	1	1	yes	characteristic
462	C₂	C₂×C₃×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₂×C₃×#555
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₂×C₃×#4084	C₂	semidirect
3. C₂×C₃×#4076	C₂	semidirect
4. C₂×C₃×#4072	C₂	semidirect
5. C₃×#65897	C₂	direct (N × H)
6. C₂×C₃×#4038	C₂	semidirect
7. C₂×C₃×#4031	C₂	semidirect
8. C₂×C₃×C₄×D₂₀	C₂	semidirect
9. C₂×C₃×#4015	C₂	semidirect
10. C₂×#65897	C₃	direct (N × H)
17. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₃×#4084	C₂²	semidirect
23. C₃×#4076	C₂²	semidirect
26. C₃×#4072	C₂²	semidirect
31. C₃×#4038	C₂²	semidirect
32. C₃×#4031	C₂²	semidirect
33. C₃×C₄×D₂₀	C₂²	semidirect
34. C₃×#4015	C₂²	semidirect
36. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
37. C₂×#4084	C₂×C₃	semidirect
38. C₂×#4076	C₂×C₃	semidirect
39. C₂×#4072	C₂×C₃	semidirect
40. #65897	C₂×C₃	direct (N × H)
41. C₂×#4038	C₂×C₃	semidirect
42. C₂×#4031	C₂×C₃	semidirect
43. C₂×C₄×D₂₀	C₂×C₃	semidirect
44. C₂×#4015	C₂×C₃	semidirect
81. C₂×C₃×C₄×D₄	D₅	semidirect
90. C₄×C₅×D₄	C₂²×C₃	semidirect
95. #4084	C₂²×C₃	semidirect
96. #4076	C₂²×C₃	semidirect
99. #4072	C₂²×C₃	semidirect
104. #4038	C₂²×C₃	semidirect
105. #4031	C₂²×C₃	semidirect
106. C₄×D₂₀	C₂²×C₃	semidirect
107. #4015	C₂²×C₃	semidirect
147. C₃×C₄×D₄	C₂×D₅	semidirect
196. C₂×C₄×D₄	C₃×D₅	semidirect
285. C₄×D₄	C₂×C₃×D₅	semidirect
299. C₂×C₃×C₅	#555	semidirect
379. C₃×C₅	C₂×#555	semidirect
399. C₂×C₅	C₃×#555	semidirect
433. C₂×C₃	#65897	direct (N × H)
437. C₅	C₂×C₃×#555	semidirect
456. C₃	C₂×#65897	direct (N × H)
459. C₂	C₃×#65897	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂×C₃×#4084	2
C₂×C₃×#4076	2
C₂×C₃×#4072	2
C₃×#65897	2
C₂×C₃×#4038	2
C₂×C₃×#4031	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×#4015	2
C₂×#65897	3
C₂×C₃×#555	5

Subgroups — C2×C3×#65897 #14483923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65897 #14483923