Subgroups — C₂×C₃×#66008 #14480378

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 576 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
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×#4086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66008	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4030	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#4028	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#66008	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	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	complemented
17	C₂×C₃×#713	—	2	8	no	—
18	C₂×C₃×#713	C₂²	1	8	yes	complemented
19	C₂×C₃×D₄×D₅	—	2	8	no	—
20	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
21	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
23	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×D₂₀	C₂²	1	4	yes	complemented
25	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
27	C₃×C₅×#124	C₂²	1	8	yes	complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4093	C₂²	1	8	yes	complemented
31	C₃×#4086	C₂²	1	8	yes	complemented
32	C₂×C₃×#685	C₂²	1	2	yes	—
33	C₂×C₃×#685	C₂²	1	4	yes	complemented
34	C₂×C₃×#683	C₂²	1	2	yes	complemented
35	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₃×#4030	C₂²	1	32	yes	complemented
37	C₃×#4028	C₂²	1	32	yes	complemented
38	C₃×#4020	C₂²	1	8	yes	complemented
39	C₃×#4018	C₂²	1	8	yes	complemented
40	C₂×C₃×#535	—	5	1	no	maximal, Hall
41	C₂²×#713	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#4093	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4086	C₂×C₃	1	1	yes	characteristic, complemented
46	#66008	C₂×C₃	1	16	yes	direct product factor
47	C₂×#4030	C₂×C₃	1	4	yes	complemented
48	C₂×#4028	C₂×C₃	1	4	yes	complemented
49	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4018	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	—	4	8	no	—
54	C₂³×C₃×D₅	C₂³	1	2	yes	—
55	C₂³×C₃×D₅	C₂³	1	2	yes	—
56	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
57	C₂³×C₃×D₅	C₂³	1	8	yes	—
58	C₂×C₃×C₅×Q₈	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
60	C₂×C₃×C₅×D₄	—	2	4	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
66	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
67	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
68	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	complemented
69	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
70	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
71	C₃×#713	—	2	32	no	—
72	C₃×D₄×D₅	—	2	32	no	—
73	C₂×C₃×D₂₀	—	2	8	no	—
74	C₂×C₃×D₂₀	—	2	4	no	—
75	C₂×C₃×D₂₀	—	2	4	no	—
76	C₂×C₃×D₂₀	—	4	8	no	—
77	C₂×C₃×D₂₀	C₂³	1	4	yes	—
78	C₂×C₃×D₂₀	C₂³	1	8	yes	—
79	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
80	C₂×C₃×D₂₀	C₂³	1	16	yes	complemented
81	C₂×C₃×C₄×D₅	—	2	8	no	—
82	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
83	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
84	C₂×C₃×C₄×D₅	C₂³	1	8	yes	complemented
85	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
86	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
87	C₃×#685	C₂³	1	8	yes	—
88	C₃×#685	C₂³	1	16	yes	complemented
89	C₃×#683	C₂³	1	8	yes	complemented
90	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
91	C₂²×C₃×#41	—	5	1	no	—
92	C₂³×C₃×D₄	—	5	1	no	—
93	C₃×#535	—	5	16	no	—
94	C₂×C₃×#127	—	5	1	no	—
95	C₂×C₃×#127	—	5	1	no	—
96	C₂×C₃×#124	—	5	1	no	—
97	C₂×C₃×#124	D₅	1	1	yes	characteristic, complemented
98	C₂×C₃×#121	—	5	4	no	—
99	C₂×C₃×#120	—	5	4	no	—
100	C₂×C₃×#117	—	5	1	no	—
101	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
102	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
105	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
106	C₂×#713	—	2	8	no	—
107	C₂×#713	C₂²×C₃	1	8	yes	complemented
108	C₂×D₄×D₅	—	2	8	no	—
109	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
110	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
111	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
112	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂²×D₂₀	C₂²×C₃	1	4	yes	complemented
114	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
116	C₅×#124	C₂²×C₃	1	8	yes	complemented
117	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
118	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
119	#4093	C₂²×C₃	1	8	yes	complemented
120	#4086	C₂²×C₃	1	8	yes	complemented
121	C₂×#685	C₂²×C₃	1	2	yes	—
122	C₂×#685	C₂²×C₃	1	4	yes	complemented
123	C₂×#683	C₂²×C₃	1	2	yes	complemented
124	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
125	#4030	C₂²×C₃	1	32	yes	complemented
126	#4028	C₂²×C₃	1	32	yes	complemented
127	#4020	C₂²×C₃	1	8	yes	complemented
128	#4018	C₂²×C₃	1	8	yes	complemented
129	C₂×#535	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	4	no	—
131	C₂³×C₃×C₅	—	2	8	no	—
132	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
133	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
134	C₂²×C₃×D₅	—	2	4	no	—
135	C₂²×C₃×D₅	—	2	4	no	—
136	C₂²×C₃×D₅	—	2	4	no	—
137	C₂²×C₃×D₅	—	2	8	no	—
138	C₂²×C₃×D₅	—	2	8	no	—
139	C₂²×C₃×D₅	—	2	16	no	—
140	C₂²×C₃×D₅	—	4	16	no	—
141	C₂²×C₃×D₅	—	4	32	no	—
142	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
143	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
144	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
145	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
146	C₃×C₅×Q₈	—	2	8	no	—
147	C₃×C₅×D₄	—	2	8	no	—
148	C₂×C₃×C₄×C₅	—	2	4	no	—
149	C₂×C₃×C₄×C₅	—	2	4	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
154	C₃×C₂²⋊D₅	—	2	16	no	—
155	C₃×C₂²⋊D₅	—	4	16	no	—
156	C₂×C₃×Dic₅	—	2	4	no	—
157	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
158	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
159	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
160	C₃×D₂₀	—	2	16	no	—
161	C₃×D₂₀	—	2	8	no	—
162	C₃×D₂₀	—	2	8	no	—
163	C₃×D₂₀	—	4	16	no	—
164	C₃×C₄×D₅	—	2	16	no	—
165	C₃×C₄×D₅	C₂×D₄	1	16	yes	complemented
166	C₂⁵×C₃	—	5	2	no	—
167	C₂×C₃×#41	—	5	8	no	—
168	C₂×C₃×#41	—	10	8	no	—
169	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
170	C₂²×C₃×D₄	—	5	2	no	—
171	C₂²×C₃×D₄	—	5	4	no	—
172	C₂²×C₃×D₄	—	5	8	no	—
173	C₂²×C₃×D₄	—	5	1	no	—
174	C₂²×C₃×D₄	—	5	2	no	—
175	C₂²×C₃×D₄	—	5	1	no	—
176	C₂²×C₃×D₄	—	5	4	no	—
177	C₂²×C₃×D₄	—	10	8	no	—
178	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
179	C₂³×C₃×C₄	—	5	1	no	—
180	C₂³×C₃×C₄	—	5	2	no	—
181	C₃×#127	—	5	8	no	—
182	C₃×#127	—	5	8	no	—
183	C₃×#124	—	5	8	no	—
184	C₃×#124	C₂×D₅	1	8	yes	complemented
185	C₃×#121	—	5	32	no	—
186	C₃×#120	—	5	32	no	—
187	C₃×#117	—	5	8	no	—
188	C₂×C₃×C₄⋊C₄	—	5	2	no	—
189	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
190	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
191	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	4	yes	complemented
192	C₂×C₃×C₄²	—	5	1	no	—
193	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
194	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
195	C₂³×D₅	—	2	8	no	—
196	C₂³×D₅	—	4	8	no	—
197	C₂³×D₅	C₂³×C₃	1	2	yes	—
198	C₂³×D₅	C₂³×C₃	1	2	yes	—
199	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
200	C₂³×D₅	C₂³×C₃	1	8	yes	—
201	C₂×C₅×Q₈	—	2	4	no	—
202	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	complemented
203	C₂×C₅×D₄	—	2	4	no	—
204	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
205	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₂²⋊D₅	—	2	8	no	—
209	C₂×C₂²⋊D₅	—	4	8	no	—
210	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
211	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	complemented
212	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
213	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
214	#713	—	2	32	no	—
215	D₄×D₅	—	2	32	no	—
216	C₂×D₂₀	—	2	8	no	—
217	C₂×D₂₀	—	2	4	no	—
218	C₂×D₂₀	—	2	4	no	—
219	C₂×D₂₀	—	4	8	no	—
220	C₂×D₂₀	C₂³×C₃	1	4	yes	—
221	C₂×D₂₀	C₂³×C₃	1	8	yes	—
222	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
223	C₂×D₂₀	C₂³×C₃	1	16	yes	complemented
224	C₂×C₄×D₅	—	2	8	no	—
225	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
226	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
227	C₂×C₄×D₅	C₂³×C₃	1	8	yes	complemented
228	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
229	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
230	#685	C₂³×C₃	1	8	yes	—
231	#685	C₂³×C₃	1	16	yes	complemented
232	#683	C₂³×C₃	1	8	yes	complemented
233	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
234	C₂²×#41	—	5	1	no	—
235	C₂³×D₄	—	5	1	no	—
236	#535	—	5	16	no	—
237	C₂×#127	—	5	1	no	—
238	C₂×#127	—	5	1	no	—
239	C₂×#124	—	5	1	no	—
240	C₂×#124	C₃×D₅	1	1	yes	characteristic, complemented
241	C₂×#121	—	5	4	no	—
242	C₂×#120	—	5	4	no	—
243	C₂×#117	—	5	1	no	—
244	C₂²×C₃×C₅	—	2	4	no	—
245	C₂²×C₃×C₅	—	2	8	no	—
246	C₂²×C₃×C₅	—	4	8	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
248	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
249	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
250	C₂×C₃×D₅	—	2	8	no	—
251	C₂×C₃×D₅	—	2	4	no	—
252	C₂×C₃×D₅	—	2	4	no	—
253	C₂×C₃×D₅	—	2	4	no	—
254	C₂×C₃×D₅	—	2	8	no	—
255	C₂×C₃×D₅	—	2	8	no	—
256	C₂×C₃×D₅	—	4	32	no	—
257	C₂×C₃×D₅	—	4	8	no	—
258	C₂×C₃×D₅	—	4	8	no	—
259	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
260	C₃×C₄×C₅	—	2	4	no	—
261	C₃×C₄×C₅	—	2	4	no	—
262	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
263	C₃×Dic₅	—	2	4	no	—
264	C₃×Dic₅	C₂²×D₄	1	4	yes	—
265	C₂⁴×C₃	—	5	1	no	—
266	C₂⁴×C₃	—	5	2	no	—
267	C₂⁴×C₃	—	5	2	no	—
268	C₂⁴×C₃	—	5	8	no	—
269	C₂⁴×C₃	—	10	8	no	—
270	C₂⁴×C₃	—	20	8	no	—
271	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
272	C₃×#41	—	10	32	no	—
273	C₂×C₃×Q₈	—	2	4	no	—
274	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	complemented
275	C₂×C₃×D₄	—	2	4	no	—
276	C₂×C₃×D₄	—	5	8	no	—
277	C₂×C₃×D₄	—	5	16	no	—
278	C₂×C₃×D₄	—	5	8	no	—
279	C₂×C₃×D₄	—	5	4	no	—
280	C₂×C₃×D₄	—	5	4	no	—
281	C₂×C₃×D₄	—	5	16	no	—
282	C₂×C₃×D₄	—	10	8	no	—
283	C₂×C₃×D₄	—	10	32	no	—
284	C₂×C₃×D₄	—	10	8	no	—
285	C₂×C₃×D₄	—	10	4	no	—
286	C₂×C₃×D₄	—	10	4	no	—
287	C₂×C₃×D₄	—	20	8	no	—
288	C₂×C₃×D₄	—	20	8	no	—
289	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	8	no	—
292	C₂²×C₃×C₄	—	5	4	no	—
293	C₂²×C₃×C₄	—	5	2	no	—
294	C₂²×C₃×C₄	—	5	8	no	—
295	C₂²×C₃×C₄	—	10	8	no	—
296	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
297	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
298	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
299	C₃×C₄⋊C₄	—	5	8	no	—
300	C₃×C₂²⋊C₄	—	5	8	no	—
301	C₃×C₂²⋊C₄	—	5	16	no	—
302	C₃×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
303	C₃×C₄²	—	5	4	no	—
304	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	2	8	no	—
307	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
308	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
309	C₂²×D₅	—	2	4	no	—
310	C₂²×D₅	—	2	4	no	—
311	C₂²×D₅	—	2	4	no	—
312	C₂²×D₅	—	2	8	no	—
313	C₂²×D₅	—	2	8	no	—
314	C₂²×D₅	—	2	16	no	—
315	C₂²×D₅	—	4	16	no	—
316	C₂²×D₅	—	4	32	no	—
317	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
318	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
319	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
320	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
321	C₅×Q₈	—	2	8	no	—
322	C₅×D₄	—	2	8	no	—
323	C₂×C₄×C₅	—	2	4	no	—
324	C₂×C₄×C₅	—	2	4	no	—
325	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
326	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
327	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
328	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
329	C₂²⋊D₅	—	2	16	no	—
330	C₂²⋊D₅	—	4	16	no	—
331	C₂×Dic₅	—	2	4	no	—
332	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
333	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
334	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
335	D₂₀	—	2	16	no	—
336	D₂₀	—	2	8	no	—
337	D₂₀	—	2	8	no	—
338	D₂₀	—	4	16	no	—
339	C₄×D₅	—	2	16	no	—
340	C₄×D₅	C₂×C₃×D₄	1	16	yes	complemented
341	C₂⁵	—	5	2	no	—
342	C₂×#41	—	5	8	no	—
343	C₂×#41	—	10	8	no	—
344	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
345	C₂²×D₄	—	5	2	no	—
346	C₂²×D₄	—	5	4	no	—
347	C₂²×D₄	—	5	8	no	—
348	C₂²×D₄	—	5	2	no	—
349	C₂²×D₄	—	5	1	no	—
350	C₂²×D₄	—	5	1	no	—
351	C₂²×D₄	—	5	4	no	—
352	C₂²×D₄	—	10	8	no	—
353	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
354	C₂³×C₄	—	5	1	no	—
355	C₂³×C₄	—	5	2	no	—
356	#127	—	5	8	no	—
357	#127	—	5	8	no	—
358	#124	—	5	8	no	—
359	#124	C₂×C₃×D₅	1	8	yes	complemented
360	#121	—	5	32	no	—
361	#120	—	5	32	no	—
362	#117	—	5	8	no	—
363	C₂×C₄⋊C₄	—	5	2	no	—
364	C₂×C₂²⋊C₄	—	5	2	no	—
365	C₂×C₂²⋊C₄	—	5	4	no	—
366	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
367	C₂×C₄²	—	5	1	no	—
368	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
369	C₂×C₃×C₅	—	4	4	no	—
370	C₂×C₃×C₅	#535	1	4	yes	complemented
371	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
372	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
373	C₃×D₅	—	2	4	no	—
374	C₃×D₅	—	4	4	no	—
375	C₃×D₅	—	4	4	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	8	no	—
378	C₂³×C₃	—	5	4	no	—
379	C₂³×C₃	—	5	2	no	—
380	C₂³×C₃	—	5	4	no	—
381	C₂³×C₃	—	5	4	no	—
382	C₂³×C₃	—	10	16	no	—
383	C₂³×C₃	—	10	4	no	—
384	C₂³×C₃	—	10	4	no	—
385	C₂³×C₃	—	10	4	no	—
386	C₂³×C₃	—	10	8	no	—
387	C₂³×C₃	—	10	8	no	—
388	C₂³×C₃	—	20	16	no	—
389	C₂³×C₃	—	20	32	no	—
390	C₂³×C₃	C₂³×D₅	1	4	yes	—
391	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
392	C₃×Q₈	—	2	8	no	—
393	C₃×D₄	—	2	8	no	—
394	C₃×D₄	—	10	16	no	—
395	C₃×D₄	—	10	16	no	—
396	C₃×D₄	—	10	8	no	—
397	C₃×D₄	—	10	8	no	—
398	C₃×D₄	—	20	16	no	—
399	C₃×D₄	—	20	16	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	5	4	no	—
403	C₂×C₃×C₄	—	5	2	no	—
404	C₂×C₃×C₄	—	5	16	no	—
405	C₂×C₃×C₄	—	5	4	no	—
406	C₂×C₃×C₄	—	10	16	no	—
407	C₂×C₃×C₄	—	10	4	no	—
408	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
409	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
410	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
411	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
412	C₂²×C₅	—	2	4	no	—
413	C₂²×C₅	—	2	8	no	—
414	C₂²×C₅	—	4	8	no	—
415	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
416	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
417	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
418	C₂×D₅	—	2	4	no	—
419	C₂×D₅	—	2	8	no	—
420	C₂×D₅	—	2	4	no	—
421	C₂×D₅	—	2	4	no	—
422	C₂×D₅	—	2	8	no	—
423	C₂×D₅	—	2	8	no	—
424	C₂×D₅	—	4	32	no	—
425	C₂×D₅	—	4	8	no	—
426	C₂×D₅	—	4	8	no	—
427	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
428	C₄×C₅	—	2	4	no	—
429	C₄×C₅	—	2	4	no	—
430	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
431	Dic₅	—	2	4	no	—
432	Dic₅	C₂²×C₃×D₄	1	4	yes	—
433	C₂⁴	—	5	1	no	—
434	C₂⁴	—	5	2	no	—
435	C₂⁴	—	5	2	no	—
436	C₂⁴	—	5	8	no	—
437	C₂⁴	—	10	8	no	—
438	C₂⁴	—	20	8	no	—
439	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
440	#41	—	10	32	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	complemented
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	5	8	no	—
445	C₂×D₄	—	5	16	no	—
446	C₂×D₄	—	5	8	no	—
447	C₂×D₄	—	5	4	no	—
448	C₂×D₄	—	5	4	no	—
449	C₂×D₄	—	5	16	no	—
450	C₂×D₄	—	10	8	no	—
451	C₂×D₄	—	10	32	no	—
452	C₂×D₄	—	10	8	no	—
453	C₂×D₄	—	10	4	no	—
454	C₂×D₄	—	10	4	no	—
455	C₂×D₄	—	20	8	no	—
456	C₂×D₄	—	20	8	no	—
457	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	8	no	—
460	C₂²×C₄	—	5	4	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	8	no	—
463	C₂²×C₄	—	10	8	no	—
464	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
465	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
466	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
467	C₄⋊C₄	—	5	8	no	—
468	C₂²⋊C₄	—	5	8	no	—
469	C₂²⋊C₄	—	5	16	no	—
470	C₂²⋊C₄	C₂²×C₃×D₅	1	16	yes	complemented
471	C₄²	—	5	4	no	—
472	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
473	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
474	C₂²×C₃	—	2	4	no	—
475	C₂²×C₃	—	2	8	no	—
476	C₂²×C₃	—	4	8	no	—
477	C₂²×C₃	—	5	4	no	—
478	C₂²×C₃	—	10	8	no	—
479	C₂²×C₃	—	10	4	no	—
480	C₂²×C₃	—	10	4	no	—
481	C₂²×C₃	—	10	4	no	—
482	C₂²×C₃	—	10	8	no	—
483	C₂²×C₃	—	10	8	no	—
484	C₂²×C₃	—	20	32	no	—
485	C₂²×C₃	—	20	8	no	—
486	C₂²×C₃	—	20	8	no	—
487	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
488	C₂²×C₃	#4149	1	4	yes	—
489	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
490	C₃×C₄	—	2	4	no	—
491	C₃×C₄	—	2	4	no	—
492	C₃×C₄	—	5	4	no	—
493	C₃×C₄	—	10	4	no	—
494	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
495	C₂×C₅	—	4	4	no	—
496	C₂×C₅	C₃×#535	1	4	yes	complemented
497	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
498	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
499	D₅	—	2	4	no	—
500	D₅	—	4	4	no	—
501	D₅	—	4	4	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	5	4	no	—
505	C₂³	—	5	2	no	—
506	C₂³	—	5	4	no	—
507	C₂³	—	5	4	no	—
508	C₂³	—	10	16	no	—
509	C₂³	—	10	4	no	—
510	C₂³	—	10	4	no	—
511	C₂³	—	10	4	no	—
512	C₂³	—	10	8	no	—
513	C₂³	—	10	8	no	—
514	C₂³	—	20	16	no	—
515	C₂³	—	20	32	no	—
516	C₂³	C₂³×C₃×D₅	1	4	yes	—
517	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
518	Q₈	—	2	8	no	—
519	D₄	—	2	8	no	—
520	D₄	—	10	16	no	—
521	D₄	—	10	16	no	—
522	D₄	—	10	8	no	—
523	D₄	—	10	8	no	—
524	D₄	—	20	16	no	—
525	D₄	—	20	16	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	5	4	no	—
529	C₂×C₄	—	5	2	no	—
530	C₂×C₄	—	5	16	no	—
531	C₂×C₄	—	5	4	no	—
532	C₂×C₄	—	10	16	no	—
533	C₂×C₄	—	10	4	no	—
534	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
535	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
536	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
537	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
538	C₂×C₃	—	4	4	no	—
539	C₂×C₃	—	10	4	no	—
540	C₂×C₃	—	20	4	no	—
541	C₂×C₃	—	20	4	no	—
542	C₂×C₃	#66008	1	4	yes	direct product factor
543	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
544	C₂×C₃	C₂×#4149	1	2	yes	—
545	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
546	C₂²	—	2	4	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	4	8	no	—
549	C₂²	—	5	4	no	—
550	C₂²	—	10	4	no	—
551	C₂²	—	10	8	no	—
552	C₂²	—	10	4	no	—
553	C₂²	—	10	4	no	—
554	C₂²	—	10	8	no	—
555	C₂²	—	10	8	no	—
556	C₂²	—	20	32	no	—
557	C₂²	—	20	8	no	—
558	C₂²	—	20	8	no	—
559	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
560	C₂²	C₃×#4149	1	4	yes	—
561	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
562	C₄	—	2	4	no	—
563	C₄	—	2	4	no	—
564	C₄	—	5	4	no	—
565	C₄	—	10	4	no	—
566	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
567	C₃	C₂×#66008	1	1	yes	characteristic, direct product factor, Sylow
568	C₂	—	4	4	no	—
569	C₂	—	10	4	no	—
570	C₂	—	20	4	no	—
571	C₂	—	20	4	no	—
572	C₂	C₃×#66008	1	4	yes	direct product factor
573	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
574	C₂	C₂×C₃×#4149	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
hypercenter	C₂×C₃×#124	D₅
hypocenter	C₅	C₂×C₃×#535
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×#713	C₂	semidirect
2. C₂²×C₃×D₄×D₅	C₂	semidirect
3. C₂×C₃×C₅×#124	C₂	semidirect
4. C₂×C₃×#4093	C₂	semidirect
5. C₂×C₃×#4086	C₂	semidirect
6. C₃×#66008	C₂	direct (N × H)
7. C₂×C₃×#4030	C₂	semidirect
8. C₂×C₃×#4028	C₂	semidirect
9. C₂×C₃×#4020	C₂	semidirect
10. C₂×C₃×#4018	C₂	semidirect
11. C₂×#66008	C₃	direct (N × H)
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
16. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
18. C₂×C₃×#713	C₂²	semidirect
20. C₂×C₃×D₄×D₅	C₂²	semidirect
23. C₂²×C₃×D₂₀	C₂²	semidirect
24. C₂²×C₃×D₂₀	C₂²	semidirect
26. C₂²×C₃×C₄×D₅	C₂²	semidirect
27. C₃×C₅×#124	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₄²×C₅	C₂²	semidirect
30. C₃×#4093	C₂²	semidirect
31. C₃×#4086	C₂²	semidirect
33. C₂×C₃×#685	C₂²	semidirect
34. C₂×C₃×#683	C₂²	semidirect
35. C₂×C₃×C₄×Dic₅	C₂²	semidirect
36. C₃×#4030	C₂²	semidirect
37. C₃×#4028	C₂²	semidirect
38. C₃×#4020	C₂²	semidirect
39. C₃×#4018	C₂²	semidirect
41. C₂²×#713	C₂×C₃	semidirect
42. C₂²×D₄×D₅	C₂×C₃	semidirect
43. C₂×C₅×#124	C₂×C₃	semidirect
44. C₂×#4093	C₂×C₃	semidirect
45. C₂×#4086	C₂×C₃	semidirect
46. #66008	C₂×C₃	direct (N × H)
47. C₂×#4030	C₂×C₃	semidirect
48. C₂×#4028	C₂×C₃	semidirect
49. C₂×#4020	C₂×C₃	semidirect
50. C₂×#4018	C₂×C₃	semidirect
59. C₂×C₃×C₅×Q₈	C₂³	semidirect
68. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
79. C₂×C₃×D₂₀	C₂³	semidirect
80. C₂×C₃×D₂₀	C₂³	semidirect
82. C₂×C₃×C₄×D₅	D₄	semidirect
84. C₂×C₃×C₄×D₅	C₂³	semidirect
85. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
86. C₃×C₄²×C₅	C₂³	semidirect
88. C₃×#685	C₂³	semidirect
89. C₃×#683	C₂³	semidirect
90. C₃×C₄×Dic₅	C₂³	semidirect
97. C₂×C₃×#124	D₅	semidirect
102. C₂²×C₅×Q₈	C₂²×C₃	semidirect
105. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
107. C₂×#713	C₂²×C₃	semidirect
109. C₂×D₄×D₅	C₂²×C₃	semidirect
112. C₂²×D₂₀	C₂²×C₃	semidirect
113. C₂²×D₂₀	C₂²×C₃	semidirect
115. C₂²×C₄×D₅	C₂²×C₃	semidirect
116. C₅×#124	C₂²×C₃	semidirect
117. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
118. C₂×C₄²×C₅	C₂²×C₃	semidirect
119. #4093	C₂²×C₃	semidirect
120. #4086	C₂²×C₃	semidirect
122. C₂×#685	C₂²×C₃	semidirect
123. C₂×#683	C₂²×C₃	semidirect
124. C₂×C₄×Dic₅	C₂²×C₃	semidirect
125. #4030	C₂²×C₃	semidirect
126. #4028	C₂²×C₃	semidirect
127. #4020	C₂²×C₃	semidirect
128. #4018	C₂²×C₃	semidirect
165. C₃×C₄×D₅	C₂×D₄	semidirect
169. C₂²×C₃×Q₈	C₂×D₅	semidirect
184. C₃×#124	C₂×D₅	semidirect
191. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
193. C₂×C₃×C₄²	C₂×D₅	semidirect
202. C₂×C₅×Q₈	C₂³×C₃	semidirect
211. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
222. C₂×D₂₀	C₂³×C₃	semidirect
223. C₂×D₂₀	C₂³×C₃	semidirect
225. C₂×C₄×D₅	C₃×D₄	semidirect
227. C₂×C₄×D₅	C₂³×C₃	semidirect
228. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
229. C₄²×C₅	C₂³×C₃	semidirect
231. #685	C₂³×C₃	semidirect
232. #683	C₂³×C₃	semidirect
233. C₄×Dic₅	C₂³×C₃	semidirect
240. C₂×#124	C₃×D₅	semidirect
274. C₂×C₃×Q₈	C₂²×D₅	semidirect
302. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
304. C₃×C₄²	C₂²×D₅	semidirect
340. C₄×D₅	C₂×C₃×D₄	semidirect
344. C₂²×Q₈	C₂×C₃×D₅	semidirect
359. #124	C₂×C₃×D₅	semidirect
366. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
368. C₂×C₄²	C₂×C₃×D₅	semidirect
370. C₂×C₃×C₅	#535	semidirect
442. C₂×Q₈	C₂²×C₃×D₅	semidirect
470. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
472. C₄²	C₂²×C₃×D₅	semidirect
473. C₃×C₅	C₂×#535	semidirect
496. C₂×C₅	C₃×#535	semidirect
542. C₂×C₃	#66008	direct (N × H)
545. C₅	C₂×C₃×#535	semidirect
567. C₃	C₂×#66008	direct (N × H)
572. C₂	C₃×#66008	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
C₂²×C₃×D₄×D₅	2
C₂×C₃×C₅×#124	2
C₂×C₃×#4093	2
C₂×C₃×#4086	2
C₃×#66008	2
C₂×C₃×#4030	2
C₂×C₃×#4028	2
C₂×C₃×#4020	2
C₂×C₃×#4018	2
C₂×#66008	3
C₂×C₃×#535	5

Subgroups — C2×C3×#66008 #14480378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66008 #14480378