Subgroups — C₂×C₃×#65993 #14483248

Order 1920.

2656 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	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
5	C₃×#65993	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#4042	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4038	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4029	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4025	C₂	1	2	yes	maximal, complemented
11	C₂×#65993	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#123	C₂²	1	8	yes	complemented
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
26	C₃×#4083	C₂²	1	8	yes	—
27	C₃×#4082	C₂²	1	8	yes	complemented
28	C₃×C₄×C₂²⋊D₅	C₂²	1	16	yes	complemented
29	C₂×C₃×#685	C₂²	1	2	yes	—
30	C₂×C₃×#685	C₂²	1	2	yes	—
31	C₂×C₃×#685	C₂²	1	2	yes	—
32	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
33	C₂×C₃×#683	C₂²	1	2	yes	complemented
34	C₂×C₃×#683	C₂²	1	2	yes	complemented
35	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
36	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
37	C₃×#4042	C₂²	1	16	yes	complemented
38	C₃×#4038	C₂²	1	16	yes	complemented
39	C₃×#4029	C₂²	1	16	yes	complemented
40	C₃×D₅×C₂²⋊C₄	C₂²	1	16	yes	complemented
41	C₃×#4025	C₂²	1	16	yes	complemented
42	C₂×C₃×#551	—	5	1	no	maximal, Hall
43	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#4083	C₂×C₃	1	1	yes	characteristic
45	C₂×#4082	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
47	#65993	C₂×C₃	1	16	yes	direct product factor
48	C₂×#4042	C₂×C₃	1	2	yes	complemented
49	C₂×#4038	C₂×C₃	1	2	yes	complemented
50	C₂×#4029	C₂×C₃	1	2	yes	complemented
51	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
52	C₂×#4025	C₂×C₃	1	2	yes	complemented
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
55	C₂³×C₃×D₅	—	2	8	no	—
56	C₂³×C₃×D₅	—	4	2	no	—
57	C₂³×C₃×D₅	C₂³	1	4	yes	—
58	C₂³×C₃×D₅	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	—	4	2	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	—	4	2	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
66	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
67	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
68	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
69	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
70	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
71	C₂×C₃×C₄×D₅	—	2	8	no	—
72	C₂×C₃×C₄×D₅	—	4	4	no	—
73	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
74	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
75	C₂×C₃×Dic₁₀	—	4	2	no	—
76	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
77	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
78	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
80	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
81	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
82	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
83	C₃×#685	C₂³	1	8	yes	—
84	C₃×#685	C₂³	1	8	yes	—
85	C₃×#685	C₂³	1	8	yes	—
86	C₃×C₄⋊Dic₅	C₂³	1	8	yes	complemented
87	C₃×#683	C₂³	1	8	yes	complemented
88	C₃×#683	C₂³	1	8	yes	complemented
89	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
90	C₃×C₄×Dic₅	C₂³	1	8	yes	complemented
91	C₃×#551	—	5	16	no	—
92	C₂×C₃×#126	—	5	2	no	—
93	C₂×C₃×#124	—	5	1	no	—
94	C₂×C₃×#123	—	5	2	no	—
95	C₂×C₃×#123	D₅	1	1	yes	characteristic, complemented
96	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
97	C₂×C₃×#120	—	5	1	no	—
98	C₂×C₃×C₄×D₄	—	5	2	no	—
99	C₂×C₃×#117	—	5	2	no	—
100	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
101	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
105	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
106	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
107	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₅×#123	C₂²×C₃	1	8	yes	complemented
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
114	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
115	#4083	C₂²×C₃	1	8	yes	—
116	#4082	C₂²×C₃	1	8	yes	complemented
117	C₄×C₂²⋊D₅	C₂²×C₃	1	16	yes	complemented
118	C₂×#685	C₂²×C₃	1	2	yes	—
119	C₂×#685	C₂²×C₃	1	2	yes	—
120	C₂×#685	C₂²×C₃	1	2	yes	—
121	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
122	C₂×#683	C₂²×C₃	1	2	yes	complemented
123	C₂×#683	C₂²×C₃	1	2	yes	complemented
124	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
125	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
126	#4042	C₂²×C₃	1	16	yes	complemented
127	#4038	C₂²×C₃	1	16	yes	complemented
128	#4029	C₂²×C₃	1	16	yes	complemented
129	D₅×C₂²⋊C₄	C₂²×C₃	1	16	yes	complemented
130	#4025	C₂²×C₃	1	16	yes	complemented
131	C₂×#551	—	5	1	no	Sylow
132	C₂³×C₃×C₅	—	2	4	no	—
133	C₂³×C₃×C₅	—	2	4	no	—
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
137	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
138	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
139	C₂²×C₃×D₅	—	2	4	no	—
140	C₂²×C₃×D₅	—	2	4	no	—
141	C₂²×C₃×D₅	—	2	16	no	—
142	C₂²×C₃×D₅	—	4	4	no	—
143	C₂²×C₃×D₅	—	4	16	no	—
144	C₂²×C₃×D₅	#41	1	8	yes	—
145	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
146	C₃×C₅×D₄	—	4	4	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	4	no	—
150	C₂×C₃×C₄×C₅	—	4	4	no	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
154	C₃×C₂²⋊D₅	—	2	16	no	—
155	C₂×C₃×Dic₅	—	2	4	no	—
156	C₂×C₃×Dic₅	—	2	4	no	—
157	C₂×C₃×Dic₅	—	2	4	no	—
158	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
159	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
160	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
161	C₃×C₄×D₅	—	2	16	no	—
162	C₃×C₄×D₅	—	4	8	no	—
163	C₃×Dic₁₀	—	4	4	no	—
164	C₂⁵×C₃	—	5	1	no	—
165	C₂²×C₃×Q₈	—	5	1	no	—
166	C₂²×C₃×D₄	—	5	2	no	—
167	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
168	C₂³×C₃×C₄	—	5	2	no	—
169	C₂³×C₃×C₄	—	5	2	no	—
170	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
171	C₃×#126	—	5	16	no	—
172	C₃×#124	—	5	8	no	—
173	C₃×#123	—	5	16	no	—
174	C₃×#123	C₂×D₅	1	8	yes	complemented
175	C₃×C₂²⋊Q₈	—	5	16	no	—
176	C₃×#120	—	5	8	no	—
177	C₃×C₄×D₄	—	5	16	no	—
178	C₃×#117	—	5	16	no	—
179	C₂×C₃×C₄⋊C₄	—	5	2	no	—
180	C₂×C₃×C₄⋊C₄	—	5	2	no	—
181	C₂×C₃×C₄⋊C₄	—	5	2	no	—
182	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
183	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
184	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
185	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
186	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
187	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
188	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
189	C₂×C₃×C₂²⋊C₄	—	5	16	no	—
190	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
191	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
192	C₂×C₃×C₄²	—	5	1	no	—
193	C₂×C₃×C₄²	—	5	2	no	—
194	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
196	C₂³×D₅	—	2	8	no	—
197	C₂³×D₅	—	4	2	no	—
198	C₂³×D₅	C₂³×C₃	1	4	yes	—
199	C₂³×D₅	C₂³×C₃	1	2	yes	—
200	C₂×C₅×D₄	—	4	2	no	—
201	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
202	C₂²×C₄×C₅	—	4	2	no	—
203	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
204	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
205	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
207	C₂×C₂²⋊D₅	—	2	8	no	—
208	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
209	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
210	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
211	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
212	C₂×C₄×D₅	—	2	8	no	—
213	C₂×C₄×D₅	—	4	4	no	—
214	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
215	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
216	C₂×Dic₁₀	—	4	2	no	—
217	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
218	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
219	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
220	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
221	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
222	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
223	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
224	#685	C₂³×C₃	1	8	yes	—
225	#685	C₂³×C₃	1	8	yes	—
226	#685	C₂³×C₃	1	8	yes	—
227	C₄⋊Dic₅	C₂³×C₃	1	8	yes	complemented
228	#683	C₂³×C₃	1	8	yes	complemented
229	#683	C₂³×C₃	1	8	yes	complemented
230	C₄×Dic₅	C₂³×C₃	1	8	yes	complemented
231	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
232	#551	—	5	16	no	—
233	C₂×#126	—	5	2	no	—
234	C₂×#124	—	5	1	no	—
235	C₂×#123	—	5	2	no	—
236	C₂×#123	C₃×D₅	1	1	yes	characteristic, complemented
237	C₂×C₂²⋊Q₈	—	5	2	no	—
238	C₂×#120	—	5	1	no	—
239	C₂×C₄×D₄	—	5	2	no	—
240	C₂×#117	—	5	2	no	—
241	C₂²×C₂²⋊C₄	—	5	2	no	—
242	C₂²×C₃×C₅	—	2	4	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	2	2	no	—
246	C₂²×C₃×C₅	—	4	4	no	—
247	C₂²×C₃×C₅	—	4	4	no	—
248	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
249	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
250	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
251	C₂×C₃×D₅	—	2	16	no	—
252	C₂×C₃×D₅	—	2	4	no	—
253	C₂×C₃×D₅	—	2	4	no	—
254	C₂×C₃×D₅	—	4	16	no	—
255	C₂×C₃×D₅	C₂×#41	1	8	yes	—
256	C₃×C₄×C₅	—	2	4	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	—	2	4	no	—
259	C₃×Dic₅	—	2	4	no	—
260	C₃×Dic₅	—	2	4	no	—
261	C₃×Dic₅	—	2	4	no	—
262	C₂⁴×C₃	—	5	2	no	—
263	C₂⁴×C₃	—	5	4	no	—
264	C₂⁴×C₃	—	10	8	no	—
265	C₂⁴×C₃	—	20	2	no	—
266	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
267	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
268	C₂×C₃×Q₈	—	5	4	no	—
269	C₂×C₃×Q₈	—	20	2	no	—
270	C₂×C₃×D₄	—	4	2	no	—
271	C₂×C₃×D₄	—	5	8	no	—
272	C₂×C₃×D₄	—	10	8	no	—
273	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
274	C₂²×C₃×C₄	—	4	2	no	—
275	C₂²×C₃×C₄	—	5	2	no	—
276	C₂²×C₃×C₄	—	5	2	no	—
277	C₂²×C₃×C₄	—	5	2	no	—
278	C₂²×C₃×C₄	—	5	8	no	—
279	C₂²×C₃×C₄	—	5	8	no	—
280	C₂²×C₃×C₄	—	10	8	no	—
281	C₂²×C₃×C₄	—	20	4	no	—
282	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
283	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
284	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
285	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
286	C₃×C₄⋊C₄	—	5	8	no	—
287	C₃×C₄⋊C₄	—	5	8	no	—
288	C₃×C₄⋊C₄	—	5	8	no	—
289	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	complemented
290	C₃×C₂²⋊C₄	—	5	8	no	—
291	C₃×C₂²⋊C₄	—	5	4	no	—
292	C₃×C₂²⋊C₄	—	5	8	no	—
293	C₃×C₂²⋊C₄	—	5	8	no	—
294	C₃×C₂²⋊C₄	—	5	8	no	—
295	C₃×C₂²⋊C₄	—	5	8	no	—
296	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
297	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
298	C₃×C₄²	—	5	4	no	—
299	C₃×C₄²	—	5	8	no	—
300	C₂³×C₅	—	2	4	no	—
301	C₂³×C₅	—	2	4	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
305	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
306	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
307	C₂²×D₅	—	2	4	no	—
308	C₂²×D₅	—	2	4	no	—
309	C₂²×D₅	—	2	16	no	—
310	C₂²×D₅	—	4	4	no	—
311	C₂²×D₅	—	4	16	no	—
312	C₂²×D₅	C₃×#41	1	8	yes	—
313	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
314	C₅×D₄	—	4	4	no	—
315	C₂×C₄×C₅	—	2	4	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	4	no	—
318	C₂×C₄×C₅	—	4	4	no	—
319	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
320	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
321	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
322	C₂²⋊D₅	—	2	16	no	—
323	C₂×Dic₅	—	2	4	no	—
324	C₂×Dic₅	—	2	4	no	—
325	C₂×Dic₅	—	2	4	no	—
326	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
327	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
328	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
329	C₄×D₅	—	2	16	no	—
330	C₄×D₅	—	4	8	no	—
331	Dic₁₀	—	4	4	no	—
332	C₂⁵	—	5	1	no	—
333	C₂²×Q₈	—	5	1	no	—
334	C₂²×D₄	—	5	2	no	—
335	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
336	C₂³×C₄	—	5	2	no	—
337	C₂³×C₄	—	5	2	no	—
338	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
339	#126	—	5	16	no	—
340	#124	—	5	8	no	—
341	#123	—	5	16	no	—
342	#123	C₂×C₃×D₅	1	8	yes	complemented
343	C₂²⋊Q₈	—	5	16	no	—
344	#120	—	5	8	no	—
345	C₄×D₄	—	5	16	no	—
346	#117	—	5	16	no	—
347	C₂×C₄⋊C₄	—	5	2	no	—
348	C₂×C₄⋊C₄	—	5	2	no	—
349	C₂×C₄⋊C₄	—	5	2	no	—
350	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
351	C₂×C₂²⋊C₄	—	5	2	no	—
352	C₂×C₂²⋊C₄	—	5	1	no	—
353	C₂×C₂²⋊C₄	—	5	2	no	—
354	C₂×C₂²⋊C₄	—	5	2	no	—
355	C₂×C₂²⋊C₄	—	5	2	no	—
356	C₂×C₂²⋊C₄	—	5	2	no	—
357	C₂×C₂²⋊C₄	—	5	16	no	—
358	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
360	C₂×C₄²	—	5	1	no	—
361	C₂×C₄²	—	5	2	no	—
362	C₂×C₃×C₅	—	4	2	no	—
363	C₂×C₃×C₅	—	4	2	no	—
364	C₂×C₃×C₅	#551	1	4	yes	complemented
365	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
366	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₃×D₅	—	2	8	no	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	2	2	no	—
370	C₂³×C₃	—	2	4	no	—
371	C₂³×C₃	—	2	4	no	—
372	C₂³×C₃	—	5	8	no	—
373	C₂³×C₃	—	5	4	no	—
374	C₂³×C₃	—	10	16	no	—
375	C₂³×C₃	—	10	4	no	—
376	C₂³×C₃	—	10	4	no	—
377	C₂³×C₃	—	20	4	no	—
378	C₂³×C₃	—	20	16	no	—
379	C₂³×C₃	C₂³×D₅	1	2	yes	—
380	C₂³×C₃	C₂³×D₅	1	2	yes	—
381	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
382	C₃×Q₈	—	20	4	no	—
383	C₃×D₄	—	4	4	no	—
384	C₃×D₄	—	10	16	no	—
385	C₂×C₃×C₄	—	2	4	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	4	no	—
388	C₂×C₃×C₄	—	4	4	no	—
389	C₂×C₃×C₄	—	5	4	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	4	no	—
394	C₂×C₃×C₄	—	10	4	no	—
395	C₂×C₃×C₄	—	10	4	no	—
396	C₂×C₃×C₄	—	20	8	no	—
397	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
398	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
399	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
400	C₂²×C₅	—	2	4	no	—
401	C₂²×C₅	—	2	4	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	4	4	no	—
405	C₂²×C₅	—	4	4	no	—
406	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
407	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
409	C₂×D₅	—	2	4	no	—
410	C₂×D₅	—	2	4	no	—
411	C₂×D₅	—	2	16	no	—
412	C₂×D₅	—	4	16	no	—
413	C₂×D₅	C₂×C₃×#41	1	8	yes	—
414	C₄×C₅	—	2	4	no	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	4	no	—
417	Dic₅	—	2	4	no	—
418	Dic₅	—	2	4	no	—
419	Dic₅	—	2	4	no	—
420	C₂⁴	—	5	2	no	—
421	C₂⁴	—	5	4	no	—
422	C₂⁴	—	10	8	no	—
423	C₂⁴	—	20	2	no	—
424	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
425	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
426	C₂×Q₈	—	5	4	no	—
427	C₂×Q₈	—	20	2	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	5	8	no	—
430	C₂×D₄	—	10	8	no	—
431	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	5	2	no	—
434	C₂²×C₄	—	5	2	no	—
435	C₂²×C₄	—	5	2	no	—
436	C₂²×C₄	—	5	8	no	—
437	C₂²×C₄	—	5	8	no	—
438	C₂²×C₄	—	10	8	no	—
439	C₂²×C₄	—	20	4	no	—
440	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
442	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
443	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
444	C₄⋊C₄	—	5	8	no	—
445	C₄⋊C₄	—	5	8	no	—
446	C₄⋊C₄	—	5	8	no	—
447	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
448	C₂²⋊C₄	—	5	8	no	—
449	C₂²⋊C₄	—	5	8	no	—
450	C₂²⋊C₄	—	5	4	no	—
451	C₂²⋊C₄	—	5	8	no	—
452	C₂²⋊C₄	—	5	8	no	—
453	C₂²⋊C₄	—	5	8	no	—
454	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
455	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
456	C₄²	—	5	4	no	—
457	C₄²	—	5	8	no	—
458	C₃×C₅	C₂×#551	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	2	4	no	—
462	C₂²×C₃	—	2	4	no	—
463	C₂²×C₃	—	4	4	no	—
464	C₂²×C₃	—	4	4	no	—
465	C₂²×C₃	—	5	8	no	—
466	C₂²×C₃	—	10	16	no	—
467	C₂²×C₃	—	10	4	no	—
468	C₂²×C₃	—	10	4	no	—
469	C₂²×C₃	—	20	16	no	—
470	C₂²×C₃	#4144	1	2	yes	—
471	C₂²×C₃	D₅×#41	1	4	yes	—
472	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	4	no	—
476	C₃×C₄	—	10	4	no	—
477	C₃×C₄	—	10	4	no	—
478	C₃×C₄	—	10	4	no	—
479	C₂×C₅	—	4	2	no	—
480	C₂×C₅	—	4	2	no	—
481	C₂×C₅	C₃×#551	1	4	yes	complemented
482	C₂×C₅	C₂²×C₃×#41	1	2	yes	—
483	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
484	D₅	—	2	8	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	5	8	no	—
490	C₂³	—	5	4	no	—
491	C₂³	—	10	16	no	—
492	C₂³	—	10	4	no	—
493	C₂³	—	10	4	no	—
494	C₂³	—	20	4	no	—
495	C₂³	—	20	16	no	—
496	C₂³	C₂³×C₃×D₅	1	2	yes	—
497	C₂³	C₂³×C₃×D₅	1	2	yes	—
498	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
499	Q₈	—	20	4	no	—
500	D₄	—	4	4	no	—
501	D₄	—	10	16	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	5	4	no	—
507	C₂×C₄	—	5	4	no	—
508	C₂×C₄	—	5	4	no	—
509	C₂×C₄	—	10	16	no	—
510	C₂×C₄	—	10	4	no	—
511	C₂×C₄	—	10	4	no	—
512	C₂×C₄	—	10	4	no	—
513	C₂×C₄	—	20	8	no	—
514	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
515	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
516	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
517	C₂×C₃	—	4	2	no	—
518	C₂×C₃	—	4	2	no	—
519	C₂×C₃	—	10	8	no	—
520	C₂×C₃	#65993	1	4	yes	direct product factor
521	C₂×C₃	C₂×#4144	1	1	yes	characteristic
522	C₂×C₃	C₂×D₅×#41	1	2	yes	—
523	C₅	C₂×C₃×#551	1	1	yes	characteristic, complemented, Sylow
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	5	8	no	—
531	C₂²	—	10	4	no	—
532	C₂²	—	10	4	no	—
533	C₂²	—	10	16	no	—
534	C₂²	—	20	16	no	—
535	C₂²	C₃×#4144	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	2	no	—
540	C₄	—	2	4	no	—
541	C₄	—	10	4	no	—
542	C₄	—	10	4	no	—
543	C₄	—	10	4	no	—
544	C₃	C₂×#65993	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	4	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	10	8	no	—
548	C₂	C₃×#65993	1	4	yes	direct product factor
549	C₂	C₂×C₃×#4144	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×#123	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₃×#4083	C₂
hypercenter	C₂×C₃×#123	D₅
hypocenter	C₅	C₂×C₃×#551
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂×C₃×#4082	C₂	semidirect
4. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
5. C₃×#65993	C₂	direct (N × H)
6. C₂×C₃×#4042	C₂	semidirect
7. C₂×C₃×#4038	C₂	semidirect
8. C₂×C₃×#4029	C₂	semidirect
9. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
10. C₂×C₃×#4025	C₂	semidirect
11. C₂×#65993	C₃	direct (N × H)
14. C₂³×C₃×C₄×C₅	C₂²	semidirect
18. C₂²×C₃×Dic₁₀	C₂²	semidirect
19. C₃×C₅×#123	C₂²	semidirect
20. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
27. C₃×#4082	C₂²	semidirect
28. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
32. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
33. C₂×C₃×#683	C₂²	semidirect
34. C₂×C₃×#683	C₂²	semidirect
35. C₂×C₃×C₄×Dic₅	C₂²	semidirect
36. C₂×C₃×C₄×Dic₅	C₂²	semidirect
37. C₃×#4042	C₂²	semidirect
38. C₃×#4038	C₂²	semidirect
39. C₃×#4029	C₂²	semidirect
40. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
41. C₃×#4025	C₂²	semidirect
43. C₂×C₅×#123	C₂×C₃	semidirect
45. C₂×#4082	C₂×C₃	semidirect
46. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
47. #65993	C₂×C₃	direct (N × H)
48. C₂×#4042	C₂×C₃	semidirect
49. C₂×#4038	C₂×C₃	semidirect
50. C₂×#4029	C₂×C₃	semidirect
51. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
52. C₂×#4025	C₂×C₃	semidirect
65. C₂²×C₃×C₄×C₅	C₂³	semidirect
76. C₂×C₃×Dic₁₀	C₂³	semidirect
77. C₃×C₅×C₄⋊C₄	C₂³	semidirect
79. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
82. C₃×C₂²⋊Dic₅	C₂³	semidirect
86. C₃×C₄⋊Dic₅	C₂³	semidirect
87. C₃×#683	C₂³	semidirect
88. C₃×#683	C₂³	semidirect
89. C₃×C₄×Dic₅	C₂³	semidirect
90. C₃×C₄×Dic₅	C₂³	semidirect
95. C₂×C₃×#123	D₅	semidirect
103. C₂³×C₄×C₅	C₂²×C₃	semidirect
107. C₂²×Dic₁₀	C₂²×C₃	semidirect
108. C₅×#123	C₂²×C₃	semidirect
109. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
111. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
114. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
116. #4082	C₂²×C₃	semidirect
117. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
121. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
122. C₂×#683	C₂²×C₃	semidirect
123. C₂×#683	C₂²×C₃	semidirect
124. C₂×C₄×Dic₅	C₂²×C₃	semidirect
125. C₂×C₄×Dic₅	C₂²×C₃	semidirect
126. #4042	C₂²×C₃	semidirect
127. #4038	C₂²×C₃	semidirect
128. #4029	C₂²×C₃	semidirect
129. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
130. #4025	C₂²×C₃	semidirect
170. C₂³×C₃×C₄	C₂×D₅	semidirect
174. C₃×#123	C₂×D₅	semidirect
182. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
191. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
206. C₂²×C₄×C₅	C₂³×C₃	semidirect
217. C₂×Dic₁₀	C₂³×C₃	semidirect
218. C₅×C₄⋊C₄	C₂³×C₃	semidirect
220. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
223. C₂²⋊Dic₅	C₂³×C₃	semidirect
227. C₄⋊Dic₅	C₂³×C₃	semidirect
228. #683	C₂³×C₃	semidirect
229. #683	C₂³×C₃	semidirect
230. C₄×Dic₅	C₂³×C₃	semidirect
231. C₄×Dic₅	C₂³×C₃	semidirect
236. C₂×#123	C₃×D₅	semidirect
285. C₂²×C₃×C₄	C₂²×D₅	semidirect
289. C₃×C₄⋊C₄	C₂²×D₅	semidirect
297. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
338. C₂³×C₄	C₂×C₃×D₅	semidirect
342. #123	C₂×C₃×D₅	semidirect
350. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
359. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
364. C₂×C₃×C₅	#551	semidirect
443. C₂²×C₄	C₂²×C₃×D₅	semidirect
447. C₄⋊C₄	C₂²×C₃×D₅	semidirect
455. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
458. C₃×C₅	C₂×#551	semidirect
481. C₂×C₅	C₃×#551	semidirect
520. C₂×C₃	#65993	direct (N × H)
523. C₅	C₂×C₃×#551	semidirect
544. C₃	C₂×#65993	direct (N × H)
548. C₂	C₃×#65993	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×C₅×#123	2
C₂×C₃×#4083	2
C₂×C₃×#4082	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₃×#65993	2
C₂×C₃×#4042	2
C₂×C₃×#4038	2
C₂×C₃×#4029	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₂×C₃×#4025	2
C₂×#65993	3
C₂×C₃×#551	5

Subgroups — C2×C3×#65993 #14483248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65993 #14483248