Subgroups — C₂×C₃×#66060 #14482686

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#713	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4092	C₂	1	2	yes	maximal, complemented
4	C₃×#66060	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4041	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4040	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×D₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66060	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂×C₃×#713	—	2	16	no	—
13	C₂×C₃×#713	C₂²	1	16	yes	complemented
14	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
15	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
16	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
19	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
20	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×#4092	C₂²	1	16	yes	complemented
25	C₂×C₃×#685	C₂²	1	4	yes	—
26	C₂×C₃×#685	C₂²	1	2	yes	—
27	C₂×C₃×#685	C₂²	1	2	yes	—
28	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×#683	C₂²	1	4	yes	—
31	C₃×#4041	C₂²	1	16	yes	complemented
32	C₃×#4040	C₂²	1	32	yes	complemented
33	C₃×D₅×C₄⋊C₄	C₂²	1	16	yes	complemented
34	C₃×C₄×D₂₀	C₂²	1	8	yes	complemented
35	C₃×C₄×D₂₀	C₂²	1	8	yes	complemented
36	C₂×C₃×#547	—	5	1	no	maximal, Hall
37	C₂²×#713	C₂×C₃	1	2	yes	complemented
38	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#4092	C₂×C₃	1	2	yes	complemented
40	#66060	C₂×C₃	1	16	yes	direct product factor
41	C₂×#4041	C₂×C₃	1	2	yes	complemented
42	C₂×#4040	C₂×C₃	1	4	yes	complemented
43	C₂×D₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
44	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂³×C₃×D₅	C₂³	1	2	yes	—
47	C₂³×C₃×D₅	C₂³	1	2	yes	—
48	C₂×C₃×C₅×Q₈	—	2	8	no	—
49	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
56	C₃×#713	—	2	64	no	—
57	C₂×C₃×D₂₀	—	2	16	no	—
58	C₂×C₃×D₂₀	—	2	4	no	—
59	C₂×C₃×D₂₀	D₄	1	8	yes	complemented
60	C₂×C₃×D₂₀	C₂³	1	16	yes	—
61	C₂×C₃×D₂₀	C₂³	1	4	yes	—
62	C₂×C₃×D₂₀	C₂³	1	4	yes	—
63	C₂×C₃×C₄×D₅	—	2	16	no	—
64	C₂×C₃×C₄×D₅	—	2	8	no	—
65	C₂×C₃×C₄×D₅	—	2	8	no	—
66	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
67	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
68	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
71	C₃×C₄²×C₅	C₂³	1	4	yes	—
72	C₃×#685	C₂³	1	16	yes	—
73	C₃×#685	C₂³	1	8	yes	—
74	C₃×#685	C₂³	1	8	yes	—
75	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
76	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
77	C₃×#683	C₂³	1	16	yes	—
78	C₂²×C₃×#41	—	5	2	no	—
79	C₃×#547	—	5	16	no	—
80	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
81	C₂×C₃×#123	—	5	4	no	—
82	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
83	C₂×C₃×#121	—	5	2	no	—
84	C₂×C₃×C₄×D₄	—	5	1	no	—
85	C₂×C₃×C₄×D₄	—	5	1	no	—
86	C₂²×C₃×C₄⋊C₄	—	5	2	no	—
87	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
88	C₂×#713	—	2	16	no	—
89	C₂×#713	C₂²×C₃	1	16	yes	complemented
90	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
91	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
92	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
94	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
95	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
96	C₅×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	#4092	C₂²×C₃	1	16	yes	complemented
101	C₂×#685	C₂²×C₃	1	2	yes	—
102	C₂×#685	C₂²×C₃	1	2	yes	—
103	C₂×#685	C₂²×C₃	1	4	yes	—
104	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×#683	C₂²×C₃	1	4	yes	—
107	#4041	C₂²×C₃	1	16	yes	complemented
108	#4040	C₂²×C₃	1	32	yes	complemented
109	D₅×C₄⋊C₄	C₂²×C₃	1	16	yes	complemented
110	C₄×D₂₀	C₂²×C₃	1	8	yes	complemented
111	C₄×D₂₀	C₂²×C₃	1	8	yes	complemented
112	C₂×#547	—	5	1	no	Sylow
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	—	2	4	no	—
118	C₂²×C₃×D₅	—	2	4	no	—
119	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
120	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
121	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
122	C₃×C₅×Q₈	—	2	16	no	—
123	C₂×C₃×C₄×C₅	—	2	8	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
127	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
131	C₂×C₃×Dic₅	—	2	4	no	—
132	C₂×C₃×Dic₅	—	2	4	no	—
133	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
134	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
135	C₃×D₂₀	—	2	32	no	—
136	C₃×D₂₀	—	2	8	no	—
137	C₃×D₂₀	C₂×D₄	1	16	yes	complemented
138	C₃×C₄×D₅	—	2	32	no	—
139	C₃×C₄×D₅	—	2	16	no	—
140	C₃×C₄×D₅	—	2	16	no	—
141	C₂×C₃×#41	—	5	16	no	—
142	C₂×C₃×#41	—	10	16	no	—
143	C₂²×C₃×Q₈	C₂×D₅	1	2	yes	—
144	C₂²×C₃×D₄	—	5	1	no	—
145	C₂²×C₃×D₄	—	5	4	no	—
146	C₂²×C₃×D₄	—	5	1	no	—
147	C₂³×C₃×C₄	—	5	4	no	—
148	C₂³×C₃×C₄	—	5	2	no	—
149	C₂³×C₃×C₄	—	5	2	no	—
150	C₃×C₄⋊Q₈	C₂×D₅	1	8	yes	complemented
151	C₃×#123	—	5	32	no	—
152	C₃×C₂²⋊Q₈	—	5	16	no	—
153	C₃×#121	—	5	16	no	—
154	C₃×C₄×D₄	—	5	8	no	—
155	C₃×C₄×D₄	—	5	8	no	—
156	C₂×C₃×C₄⋊C₄	—	5	1	no	—
157	C₂×C₃×C₄⋊C₄	—	5	4	no	—
158	C₂×C₃×C₄⋊C₄	—	5	1	no	—
159	C₂×C₃×C₄⋊C₄	—	5	16	no	—
160	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
161	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
163	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
164	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
165	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
166	C₂³×D₅	C₂³×C₃	1	2	yes	—
167	C₂³×D₅	C₂³×C₃	1	2	yes	—
168	C₂×C₅×Q₈	—	2	8	no	—
169	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
175	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
176	#713	—	2	64	no	—
177	C₂×D₂₀	—	2	16	no	—
178	C₂×D₂₀	—	2	4	no	—
179	C₂×D₂₀	C₃×D₄	1	8	yes	complemented
180	C₂×D₂₀	C₂³×C₃	1	16	yes	—
181	C₂×D₂₀	C₂³×C₃	1	4	yes	—
182	C₂×D₂₀	C₂³×C₃	1	4	yes	—
183	C₂×C₄×D₅	—	2	16	no	—
184	C₂×C₄×D₅	—	2	8	no	—
185	C₂×C₄×D₅	—	2	8	no	—
186	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
187	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
188	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
189	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
190	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
191	C₄²×C₅	C₂³×C₃	1	4	yes	—
192	#685	C₂³×C₃	1	8	yes	—
193	#685	C₂³×C₃	1	8	yes	—
194	#685	C₂³×C₃	1	16	yes	—
195	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
196	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
197	#683	C₂³×C₃	1	16	yes	—
198	C₂²×#41	—	5	2	no	—
199	#547	—	5	16	no	—
200	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
201	C₂×#123	—	5	4	no	—
202	C₂×C₂²⋊Q₈	—	5	2	no	—
203	C₂×#121	—	5	2	no	—
204	C₂×C₄×D₄	—	5	1	no	—
205	C₂×C₄×D₄	—	5	1	no	—
206	C₂²×C₄⋊C₄	—	5	2	no	—
207	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
208	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
209	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
210	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
211	C₂×C₃×D₅	—	2	16	no	—
212	C₂×C₃×D₅	—	2	4	no	—
213	C₂×C₃×D₅	—	2	4	no	—
214	C₂×C₃×D₅	—	2	4	no	—
215	C₂×C₃×D₅	—	2	4	no	—
216	C₂×C₃×D₅	—	2	4	no	—
217	C₂×C₃×D₅	—	4	8	no	—
218	C₂×C₃×D₅	C₂²×D₄	1	8	yes	—
219	C₃×C₄×C₅	—	2	8	no	—
220	C₃×C₄×C₅	—	2	2	no	—
221	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
222	C₃×C₄×C₅	C₂×#41	1	4	yes	complemented
223	C₃×Dic₅	—	2	4	no	—
224	C₃×Dic₅	—	2	4	no	—
225	C₂⁴×C₃	—	5	2	no	—
226	C₂⁴×C₃	—	5	2	no	—
227	C₃×#41	—	10	64	no	—
228	C₂×C₃×Q₈	—	2	8	no	—
229	C₂×C₃×Q₈	C₂²×D₅	1	8	yes	—
230	C₂×C₃×D₄	—	5	8	no	—
231	C₂×C₃×D₄	—	5	4	no	—
232	C₂×C₃×D₄	—	5	4	no	—
233	C₂×C₃×D₄	—	5	16	no	—
234	C₂×C₃×D₄	—	10	16	no	—
235	C₂×C₃×D₄	—	10	4	no	—
236	C₂²×C₃×C₄	—	5	2	no	—
237	C₂²×C₃×C₄	—	5	2	no	—
238	C₂²×C₃×C₄	—	5	8	no	—
239	C₂²×C₃×C₄	—	5	16	no	—
240	C₂²×C₃×C₄	—	5	8	no	—
241	C₂²×C₃×C₄	—	10	16	no	—
242	C₂²×C₃×C₄	—	10	8	no	—
243	C₂²×C₃×C₄	—	10	8	no	—
244	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
246	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
248	C₃×C₄⋊C₄	—	5	16	no	—
249	C₃×C₄⋊C₄	—	5	4	no	—
250	C₃×C₄⋊C₄	—	5	4	no	—
251	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
252	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
253	C₃×C₂²⋊C₄	—	5	8	no	—
254	C₃×C₂²⋊C₄	—	5	8	no	—
255	C₃×C₂²⋊C₄	—	5	16	no	—
256	C₃×C₄²	C₂²×D₅	1	4	yes	—
257	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
258	C₂²×D₅	—	2	4	no	—
259	C₂²×D₅	—	2	4	no	—
260	C₂²×D₅	—	2	4	no	—
261	C₂²×D₅	—	2	4	no	—
262	C₂²×D₅	—	2	4	no	—
263	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
264	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
265	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
266	C₅×Q₈	—	2	16	no	—
267	C₂×C₄×C₅	—	2	8	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
270	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
271	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
272	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
274	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
275	C₂×Dic₅	—	2	4	no	—
276	C₂×Dic₅	—	2	4	no	—
277	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
278	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
279	D₂₀	—	2	32	no	—
280	D₂₀	—	2	8	no	—
281	D₂₀	C₂×C₃×D₄	1	16	yes	complemented
282	C₄×D₅	—	2	32	no	—
283	C₄×D₅	—	2	16	no	—
284	C₄×D₅	—	2	16	no	—
285	C₂×#41	—	5	16	no	—
286	C₂×#41	—	10	16	no	—
287	C₂²×Q₈	C₂×C₃×D₅	1	2	yes	—
288	C₂²×D₄	—	5	1	no	—
289	C₂²×D₄	—	5	1	no	—
290	C₂²×D₄	—	5	4	no	—
291	C₂³×C₄	—	5	2	no	—
292	C₂³×C₄	—	5	4	no	—
293	C₂³×C₄	—	5	2	no	—
294	C₄⋊Q₈	C₂×C₃×D₅	1	8	yes	complemented
295	#123	—	5	32	no	—
296	C₂²⋊Q₈	—	5	16	no	—
297	#121	—	5	16	no	—
298	C₄×D₄	—	5	8	no	—
299	C₄×D₄	—	5	8	no	—
300	C₂×C₄⋊C₄	—	5	1	no	—
301	C₂×C₄⋊C₄	—	5	4	no	—
302	C₂×C₄⋊C₄	—	5	1	no	—
303	C₂×C₄⋊C₄	—	5	16	no	—
304	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
305	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
306	C₂×C₂²⋊C₄	—	5	2	no	—
307	C₂×C₂²⋊C₄	—	5	2	no	—
308	C₂×C₂²⋊C₄	—	5	4	no	—
309	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
310	C₂×C₃×C₅	#547	1	4	yes	complemented
311	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
312	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
313	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₃×D₅	—	2	8	no	—
315	C₃×D₅	—	4	4	no	—
316	C₂³×C₃	—	5	8	no	—
317	C₂³×C₃	—	5	4	no	—
318	C₂³×C₃	—	5	4	no	—
319	C₂³×C₃	—	10	4	no	—
320	C₂³×C₃	—	10	4	no	—
321	C₂³×C₃	—	10	4	no	—
322	C₂³×C₃	—	10	4	no	—
323	C₂³×C₃	—	10	4	no	—
324	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
325	C₃×Q₈	—	2	16	no	—
326	C₃×D₄	—	5	16	no	—
327	C₃×D₄	—	10	32	no	—
328	C₃×D₄	—	10	8	no	—
329	C₂×C₃×C₄	—	2	8	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	5	4	no	—
332	C₂×C₃×C₄	—	5	4	no	—
333	C₂×C₃×C₄	—	10	32	no	—
334	C₂×C₃×C₄	—	10	4	no	—
335	C₂×C₃×C₄	—	10	4	no	—
336	C₂×C₃×C₄	—	10	16	no	—
337	C₂×C₃×C₄	—	10	16	no	—
338	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
339	C₂×C₃×C₄	#713	1	4	yes	complemented
340	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
341	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
342	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
343	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
344	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
345	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
346	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
347	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
348	C₂×D₅	—	2	4	no	—
349	C₂×D₅	—	2	4	no	—
350	C₂×D₅	—	2	16	no	—
351	C₂×D₅	—	2	4	no	—
352	C₂×D₅	—	2	4	no	—
353	C₂×D₅	—	2	4	no	—
354	C₂×D₅	—	4	8	no	—
355	C₂×D₅	C₂²×C₃×D₄	1	8	yes	—
356	C₄×C₅	—	2	8	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
359	C₄×C₅	C₂×C₃×#41	1	4	yes	complemented
360	Dic₅	—	2	4	no	—
361	Dic₅	—	2	4	no	—
362	C₂⁴	—	5	2	no	—
363	C₂⁴	—	5	2	no	—
364	#41	—	10	64	no	—
365	C₂×Q₈	—	2	8	no	—
366	C₂×Q₈	C₂²×C₃×D₅	1	8	yes	—
367	C₂×D₄	—	5	8	no	—
368	C₂×D₄	—	5	4	no	—
369	C₂×D₄	—	5	4	no	—
370	C₂×D₄	—	5	16	no	—
371	C₂×D₄	—	10	16	no	—
372	C₂×D₄	—	10	4	no	—
373	C₂²×C₄	—	5	2	no	—
374	C₂²×C₄	—	5	2	no	—
375	C₂²×C₄	—	5	8	no	—
376	C₂²×C₄	—	5	16	no	—
377	C₂²×C₄	—	5	8	no	—
378	C₂²×C₄	—	10	16	no	—
379	C₂²×C₄	—	10	8	no	—
380	C₂²×C₄	—	10	8	no	—
381	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
383	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
385	C₄⋊C₄	—	5	4	no	—
386	C₄⋊C₄	—	5	16	no	—
387	C₄⋊C₄	—	5	4	no	—
388	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
389	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
390	C₂²⋊C₄	—	5	8	no	—
391	C₂²⋊C₄	—	5	8	no	—
392	C₂²⋊C₄	—	5	16	no	—
393	C₄²	C₂²×C₃×D₅	1	4	yes	—
394	C₃×C₅	C₂×#547	1	1	yes	characteristic, complemented, Hall
395	C₂²×C₃	—	5	8	no	—
396	C₂²×C₃	—	10	16	no	—
397	C₂²×C₃	—	10	4	no	—
398	C₂²×C₃	—	10	4	no	—
399	C₂²×C₃	—	10	4	no	—
400	C₂²×C₃	—	10	4	no	—
401	C₂²×C₃	—	10	4	no	—
402	C₂²×C₃	—	20	8	no	—
403	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
404	C₂²×C₃	C₂×#713	1	2	yes	—
405	C₂²×C₃	#4147	1	2	yes	—
406	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
407	C₃×C₄	—	2	8	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	10	4	no	—
410	C₃×C₄	—	10	4	no	—
411	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
412	C₃×C₄	C₂×#713	1	4	yes	complemented
413	C₂×C₅	C₃×#547	1	4	yes	complemented
414	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
415	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
416	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
417	D₅	—	2	8	no	—
418	D₅	—	4	4	no	—
419	C₂³	—	5	8	no	—
420	C₂³	—	5	4	no	—
421	C₂³	—	5	4	no	—
422	C₂³	—	10	4	no	—
423	C₂³	—	10	4	no	—
424	C₂³	—	10	4	no	—
425	C₂³	—	10	4	no	—
426	C₂³	—	10	4	no	—
427	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
428	Q₈	—	2	16	no	—
429	D₄	—	5	16	no	—
430	D₄	—	10	32	no	—
431	D₄	—	10	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	5	4	no	—
435	C₂×C₄	—	5	4	no	—
436	C₂×C₄	—	10	32	no	—
437	C₂×C₄	—	10	4	no	—
438	C₂×C₄	—	10	4	no	—
439	C₂×C₄	—	10	16	no	—
440	C₂×C₄	—	10	16	no	—
441	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
442	C₂×C₄	C₃×#713	1	4	yes	complemented
443	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
444	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
445	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
446	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
447	C₂×C₃	—	10	8	no	—
448	C₂×C₃	—	20	4	no	—
449	C₂×C₃	#66060	1	4	yes	direct product factor
450	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
451	C₂×C₃	C₂²×#713	1	1	yes	characteristic
452	C₂×C₃	C₂×#4147	1	1	yes	characteristic
453	C₅	C₂×C₃×#547	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	5	8	no	—
455	C₂²	—	10	4	no	—
456	C₂²	—	10	4	no	—
457	C₂²	—	10	16	no	—
458	C₂²	—	10	4	no	—
459	C₂²	—	10	4	no	—
460	C₂²	—	10	4	no	—
461	C₂²	—	20	8	no	—
462	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
463	C₂²	C₂×C₃×#713	1	2	yes	—
464	C₂²	C₃×#4147	1	2	yes	—
465	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
466	C₄	—	2	8	no	—
467	C₄	—	2	2	no	—
468	C₄	—	10	4	no	—
469	C₄	—	10	4	no	—
470	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
471	C₄	C₂×C₃×#713	1	4	yes	complemented
472	C₃	C₂×#66060	1	1	yes	characteristic, direct product factor, Sylow
473	C₂	—	10	8	no	—
474	C₂	—	20	4	no	—
475	C₂	C₃×#66060	1	4	yes	direct product factor
476	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
477	C₂	C₂²×C₃×#713	1	1	yes	characteristic
478	C₂	C₂×C₃×#4147	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×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#547
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#713	C₂	semidirect
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃×#4092	C₂	semidirect
4. C₃×#66060	C₂	direct (N × H)
5. C₂×C₃×#4041	C₂	semidirect
6. C₂×C₃×#4040	C₂	semidirect
7. C₂×C₃×D₅×C₄⋊C₄	C₂	semidirect
8. C₂×C₃×C₄×D₂₀	C₂	semidirect
9. C₂×C₃×C₄×D₂₀	C₂	semidirect
10. C₂×#66060	C₃	direct (N × H)
13. C₂×C₃×#713	C₂²	semidirect
20. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×#4092	C₂²	semidirect
31. C₃×#4041	C₂²	semidirect
32. C₃×#4040	C₂²	semidirect
33. C₃×D₅×C₄⋊C₄	C₂²	semidirect
34. C₃×C₄×D₂₀	C₂²	semidirect
35. C₃×C₄×D₂₀	C₂²	semidirect
37. C₂²×#713	C₂×C₃	semidirect
38. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
39. C₂×#4092	C₂×C₃	semidirect
40. #66060	C₂×C₃	direct (N × H)
41. C₂×#4041	C₂×C₃	semidirect
42. C₂×#4040	C₂×C₃	semidirect
43. C₂×D₅×C₄⋊C₄	C₂×C₃	semidirect
44. C₂×C₄×D₂₀	C₂×C₃	semidirect
45. C₂×C₄×D₂₀	C₂×C₃	semidirect
59. C₂×C₃×D₂₀	D₄	semidirect
80. C₂×C₃×C₄⋊Q₈	D₅	semidirect
89. C₂×#713	C₂²×C₃	semidirect
96. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
100. #4092	C₂²×C₃	semidirect
107. #4041	C₂²×C₃	semidirect
108. #4040	C₂²×C₃	semidirect
109. D₅×C₄⋊C₄	C₂²×C₃	semidirect
110. C₄×D₂₀	C₂²×C₃	semidirect
111. C₄×D₂₀	C₂²×C₃	semidirect
126. C₂×C₃×C₄×C₅	#41	semidirect
137. C₃×D₂₀	C₂×D₄	semidirect
150. C₃×C₄⋊Q₈	C₂×D₅	semidirect
179. C₂×D₂₀	C₃×D₄	semidirect
200. C₂×C₄⋊Q₈	C₃×D₅	semidirect
222. C₃×C₄×C₅	C₂×#41	semidirect
270. C₂×C₄×C₅	C₃×#41	semidirect
281. D₂₀	C₂×C₃×D₄	semidirect
294. C₄⋊Q₈	C₂×C₃×D₅	semidirect
310. C₂×C₃×C₅	#547	semidirect
339. C₂×C₃×C₄	#713	semidirect
359. C₄×C₅	C₂×C₃×#41	semidirect
394. C₃×C₅	C₂×#547	semidirect
412. C₃×C₄	C₂×#713	semidirect
413. C₂×C₅	C₃×#547	semidirect
442. C₂×C₄	C₃×#713	semidirect
449. C₂×C₃	#66060	direct (N × H)
453. C₅	C₂×C₃×#547	semidirect
471. C₄	C₂×C₃×#713	semidirect
472. C₃	C₂×#66060	direct (N × H)
475. C₂	C₃×#66060	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×#713	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₃×#4092	2
C₃×#66060	2
C₂×C₃×#4041	2
C₂×C₃×#4040	2
C₂×C₃×D₅×C₄⋊C₄	2
C₂×C₃×C₄×D₂₀	2
C₂×#66060	3
C₂×C₃×#547	5

Subgroups — C2×C3×#66060 #14482686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66060 #14482686