Subgroups — C₂×C₃×#65893 #14484703

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 608 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×#4086	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4075	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
6	C₃×#65893	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4031	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4029	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65893	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
20	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
21	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
27	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
28	C₃×#4086	C₂²	1	8	yes	—
29	C₃×#4082	C₂²	1	8	yes	complemented
30	C₃×#4075	C₂²	1	16	yes	complemented
31	C₃×C₄×C₂²⋊D₅	C₂²	1	16	yes	complemented
32	C₂×C₃×#685	C₂²	1	2	yes	—
33	C₂×C₃×#685	C₂²	1	2	yes	—
34	C₂×C₃×#685	C₂²	1	2	yes	—
35	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
36	C₂×C₃×#683	C₂²	1	1	yes	characteristic
37	C₂×C₃×#683	C₂²	1	1	yes	characteristic
38	C₂×C₃×#683	C₂²	1	2	yes	—
39	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
40	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
42	C₃×#4039	C₂²	1	8	yes	complemented
43	C₃×#4033	C₂²	1	8	yes	complemented
44	C₃×#4031	C₂²	1	16	yes	complemented
45	C₃×#4029	C₂²	1	16	yes	complemented
46	C₃×#4021	C₂²	1	8	yes	complemented
47	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
48	C₂×C₃×#559	—	5	1	no	maximal, Hall
49	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4086	C₂×C₃	1	1	yes	characteristic
51	C₂×#4082	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#4075	C₂×C₃	1	2	yes	complemented
53	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
54	#65893	C₂×C₃	1	16	yes	direct product factor
55	C₂×#4039	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#4033	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#4031	C₂×C₃	1	2	yes	complemented
58	C₂×#4029	C₂×C₃	1	2	yes	complemented
59	C₂×#4021	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
62	C₂³×C₃×D₅	C₂³	1	2	yes	—
63	C₂×C₃×C₅×D₄	—	2	4	no	—
64	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
65	C₂²×C₃×C₄×C₅	—	4	4	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
72	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
73	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
74	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
75	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
76	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×D₂₀	—	2	4	no	—
81	C₂×C₃×D₂₀	C₂³	1	4	yes	—
82	C₂×C₃×C₄×D₅	—	4	4	no	—
83	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
84	C₂×C₃×Dic₁₀	—	2	4	no	—
85	C₂×C₃×Dic₁₀	—	2	4	no	—
86	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
87	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
90	C₃×C₄²×C₅	C₂³	1	4	yes	—
91	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
92	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
93	C₃×#685	C₂³	1	8	yes	—
94	C₃×#685	C₂³	1	8	yes	—
95	C₃×#685	C₂³	1	8	yes	—
96	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
97	C₃×#683	C₂³	1	4	yes	—
98	C₃×#683	C₂³	1	4	yes	—
99	C₃×#683	C₂³	1	8	yes	—
100	C₃×C₄×Dic₅	C₂³	1	4	yes	—
101	C₃×C₄×Dic₅	C₂³	1	4	yes	—
102	C₃×C₄×Dic₅	C₂³	1	8	yes	—
103	C₃×#559	—	5	16	no	—
104	C₂×C₃×#127	—	5	1	no	—
105	C₂×C₃×#124	—	5	1	no	—
106	C₂×C₃×#124	—	5	2	no	—
107	C₂×C₃×#124	—	5	1	no	—
108	C₂×C₃×#123	—	5	2	no	—
109	C₂×C₃×#123	—	5	2	no	—
110	C₂×C₃×C₄×Q₈	—	5	1	no	—
111	C₂×C₃×C₄×Q₈	—	5	1	no	—
112	C₂×C₃×C₄×D₄	—	5	2	no	—
113	C₂×C₃×C₄×D₄	—	5	1	no	—
114	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
115	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
116	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
117	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
118	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
119	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
121	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
122	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
123	C₄×C₅×D₄	C₂²×C₃	1	8	yes	complemented
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
126	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
128	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
129	#4086	C₂²×C₃	1	8	yes	—
130	#4082	C₂²×C₃	1	8	yes	complemented
131	#4075	C₂²×C₃	1	16	yes	complemented
132	C₄×C₂²⋊D₅	C₂²×C₃	1	16	yes	complemented
133	C₂×#685	C₂²×C₃	1	2	yes	—
134	C₂×#685	C₂²×C₃	1	2	yes	—
135	C₂×#685	C₂²×C₃	1	2	yes	—
136	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
137	C₂×#683	C₂²×C₃	1	1	yes	characteristic
138	C₂×#683	C₂²×C₃	1	1	yes	characteristic
139	C₂×#683	C₂²×C₃	1	2	yes	—
140	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
143	#4039	C₂²×C₃	1	8	yes	complemented
144	#4033	C₂²×C₃	1	8	yes	complemented
145	#4031	C₂²×C₃	1	16	yes	complemented
146	#4029	C₂²×C₃	1	16	yes	complemented
147	#4021	C₂²×C₃	1	8	yes	complemented
148	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
149	C₂×#559	—	5	1	no	Sylow
150	C₂³×C₃×C₅	—	2	4	no	—
151	C₂³×C₃×C₅	—	2	4	no	—
152	C₂³×C₃×C₅	—	2	4	no	—
153	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
154	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
155	C₂²×C₃×D₅	—	2	4	no	—
156	C₂²×C₃×D₅	—	2	4	no	—
157	C₂²×C₃×D₅	—	2	4	no	—
158	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
159	C₃×C₅×D₄	—	2	8	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	4	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	4	8	no	—
164	C₂×C₃×C₄×C₅	#41	1	4	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
168	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
169	C₃×C₂²⋊D₅	—	2	16	no	—
170	C₃×C₂²⋊D₅	—	4	8	no	—
171	C₂×C₃×Dic₅	—	2	4	no	—
172	C₂×C₃×Dic₅	—	2	2	no	—
173	C₂×C₃×Dic₅	—	2	2	no	—
174	C₂×C₃×Dic₅	—	2	2	no	—
175	C₂×C₃×Dic₅	#41	1	4	yes	—
176	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
177	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
178	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
179	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
180	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
181	C₃×D₂₀	—	2	8	no	—
182	C₃×C₄×D₅	—	4	8	no	—
183	C₃×Dic₁₀	—	2	8	no	—
184	C₃×Dic₁₀	—	2	8	no	—
185	C₂²×C₃×Q₈	—	5	1	no	—
186	C₂²×C₃×Q₈	—	5	1	no	—
187	C₂²×C₃×D₄	—	5	2	no	—
188	C₂²×C₃×D₄	—	5	2	no	—
189	C₂²×C₃×D₄	—	5	1	no	—
190	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
191	C₂³×C₃×C₄	—	5	2	no	—
192	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
193	C₃×#127	—	5	8	no	—
194	C₃×#124	—	5	8	no	—
195	C₃×#124	—	5	16	no	—
196	C₃×#124	—	5	8	no	—
197	C₃×#123	—	5	16	no	—
198	C₃×#123	—	5	16	no	—
199	C₃×C₄×Q₈	—	5	8	no	—
200	C₃×C₄×Q₈	—	5	8	no	—
201	C₃×C₄×D₄	—	5	16	no	—
202	C₃×C₄×D₄	—	5	8	no	—
203	C₃×C₄×D₄	C₂×D₅	1	8	yes	complemented
204	C₂×C₃×C₄⋊C₄	—	5	1	no	—
205	C₂×C₃×C₄⋊C₄	—	5	2	no	—
206	C₂×C₃×C₄⋊C₄	—	5	1	no	—
207	C₂×C₃×C₄⋊C₄	—	5	1	no	—
208	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
209	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
210	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
211	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
212	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
213	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
214	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
215	C₂×C₃×C₄²	—	5	2	no	—
216	C₂×C₃×C₄²	—	5	1	no	—
217	C₂×C₃×C₄²	—	5	1	no	—
218	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
219	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
220	C₂³×D₅	C₂³×C₃	1	2	yes	—
221	C₂×C₅×D₄	—	2	4	no	—
222	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
223	C₂²×C₄×C₅	—	4	4	no	—
224	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
227	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
228	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₂²⋊D₅	—	2	8	no	—
230	C₂×C₂²⋊D₅	—	4	4	no	—
231	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
232	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
233	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
234	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
235	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
236	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
237	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
238	C₂×D₂₀	—	2	4	no	—
239	C₂×D₂₀	C₂³×C₃	1	4	yes	—
240	C₂×C₄×D₅	—	4	4	no	—
241	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
242	C₂×Dic₁₀	—	2	4	no	—
243	C₂×Dic₁₀	—	2	4	no	—
244	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
245	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
246	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
247	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
248	C₄²×C₅	C₂³×C₃	1	4	yes	—
249	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
250	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
251	#685	C₂³×C₃	1	8	yes	—
252	#685	C₂³×C₃	1	8	yes	—
253	#685	C₂³×C₃	1	8	yes	—
254	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
255	#683	C₂³×C₃	1	4	yes	—
256	#683	C₂³×C₃	1	4	yes	—
257	#683	C₂³×C₃	1	8	yes	—
258	C₄×Dic₅	C₂³×C₃	1	4	yes	—
259	C₄×Dic₅	C₂³×C₃	1	4	yes	—
260	C₄×Dic₅	C₂³×C₃	1	8	yes	—
261	#559	—	5	16	no	—
262	C₂×#127	—	5	1	no	—
263	C₂×#124	—	5	1	no	—
264	C₂×#124	—	5	2	no	—
265	C₂×#124	—	5	1	no	—
266	C₂×#123	—	5	2	no	—
267	C₂×#123	—	5	2	no	—
268	C₂×C₄×Q₈	—	5	1	no	—
269	C₂×C₄×Q₈	—	5	1	no	—
270	C₂×C₄×D₄	—	5	2	no	—
271	C₂×C₄×D₄	—	5	1	no	—
272	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
273	C₂²×C₃×C₅	—	2	4	no	—
274	C₂²×C₃×C₅	—	2	4	no	—
275	C₂²×C₃×C₅	—	2	4	no	—
276	C₂²×C₃×C₅	—	4	8	no	—
277	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
278	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
279	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
280	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
281	C₂×C₃×D₅	—	2	4	no	—
282	C₂×C₃×D₅	—	2	4	no	—
283	C₂×C₃×D₅	—	2	4	no	—
284	C₂×C₃×D₅	—	4	8	no	—
285	C₃×C₄×C₅	—	2	2	no	—
286	C₃×C₄×C₅	—	2	4	no	—
287	C₃×C₄×C₅	—	2	2	no	—
288	C₃×C₄×C₅	C₂×#41	1	4	yes	—
289	C₃×Dic₅	—	2	4	no	—
290	C₃×Dic₅	—	2	2	no	—
291	C₃×Dic₅	—	2	2	no	—
292	C₃×Dic₅	—	2	2	no	—
293	C₃×Dic₅	C₂×#41	1	4	yes	—
294	C₂⁴×C₃	—	5	2	no	—
295	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
296	C₂×C₃×Q₈	—	5	4	no	—
297	C₂×C₃×Q₈	—	5	4	no	—
298	C₂×C₃×Q₈	—	10	4	no	—
299	C₂×C₃×Q₈	—	10	4	no	—
300	C₂×C₃×D₄	—	2	4	no	—
301	C₂×C₃×D₄	—	5	8	no	—
302	C₂×C₃×D₄	—	5	8	no	—
303	C₂×C₃×D₄	—	5	4	no	—
304	C₂×C₃×D₄	—	10	8	no	—
305	C₂×C₃×D₄	—	10	4	no	—
306	C₂×C₃×D₄	—	20	4	no	—
307	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
308	C₂²×C₃×C₄	—	4	4	no	—
309	C₂²×C₃×C₄	—	5	1	no	—
310	C₂²×C₃×C₄	—	5	2	no	—
311	C₂²×C₃×C₄	—	5	1	no	—
312	C₂²×C₃×C₄	—	5	1	no	—
313	C₂²×C₃×C₄	—	5	1	no	—
314	C₂²×C₃×C₄	—	5	8	no	—
315	C₂²×C₃×C₄	—	20	4	no	—
316	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
317	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
320	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
321	C₃×C₄⋊C₄	—	5	4	no	—
322	C₃×C₄⋊C₄	—	5	8	no	—
323	C₃×C₄⋊C₄	—	5	4	no	—
324	C₃×C₄⋊C₄	—	5	4	no	—
325	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
326	C₃×C₂²⋊C₄	—	5	8	no	—
327	C₃×C₂²⋊C₄	—	5	8	no	—
328	C₃×C₂²⋊C₄	—	5	8	no	—
329	C₃×C₂²⋊C₄	—	5	8	no	—
330	C₃×C₂²⋊C₄	—	5	8	no	—
331	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
332	C₃×C₄²	—	5	8	no	—
333	C₃×C₄²	—	5	4	no	—
334	C₃×C₄²	—	5	4	no	—
335	C₃×C₄²	C₂²×D₅	1	4	yes	—
336	C₂³×C₅	—	2	4	no	—
337	C₂³×C₅	—	2	4	no	—
338	C₂³×C₅	—	2	4	no	—
339	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
340	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
341	C₂²×D₅	—	2	4	no	—
342	C₂²×D₅	—	2	4	no	—
343	C₂²×D₅	—	2	4	no	—
344	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
345	C₅×D₄	—	2	8	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	4	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	4	8	no	—
350	C₂×C₄×C₅	C₃×#41	1	4	yes	—
351	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
352	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
353	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
354	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
355	C₂²⋊D₅	—	2	16	no	—
356	C₂²⋊D₅	—	4	8	no	—
357	C₂×Dic₅	—	2	4	no	—
358	C₂×Dic₅	—	2	2	no	—
359	C₂×Dic₅	—	2	2	no	—
360	C₂×Dic₅	—	2	2	no	—
361	C₂×Dic₅	C₃×#41	1	4	yes	—
362	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
363	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
364	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
365	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
366	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
367	D₂₀	—	2	8	no	—
368	C₄×D₅	—	4	8	no	—
369	Dic₁₀	—	2	8	no	—
370	Dic₁₀	—	2	8	no	—
371	C₂²×Q₈	—	5	1	no	—
372	C₂²×Q₈	—	5	1	no	—
373	C₂²×D₄	—	5	2	no	—
374	C₂²×D₄	—	5	2	no	—
375	C₂²×D₄	—	5	1	no	—
376	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
377	C₂³×C₄	—	5	2	no	—
378	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
379	#127	—	5	8	no	—
380	#124	—	5	8	no	—
381	#124	—	5	16	no	—
382	#124	—	5	8	no	—
383	#123	—	5	16	no	—
384	#123	—	5	16	no	—
385	C₄×Q₈	—	5	8	no	—
386	C₄×Q₈	—	5	8	no	—
387	C₄×D₄	—	5	16	no	—
388	C₄×D₄	—	5	8	no	—
389	C₄×D₄	C₂×C₃×D₅	1	8	yes	complemented
390	C₂×C₄⋊C₄	—	5	1	no	—
391	C₂×C₄⋊C₄	—	5	2	no	—
392	C₂×C₄⋊C₄	—	5	1	no	—
393	C₂×C₄⋊C₄	—	5	1	no	—
394	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	5	2	no	—
396	C₂×C₂²⋊C₄	—	5	2	no	—
397	C₂×C₂²⋊C₄	—	5	2	no	—
398	C₂×C₂²⋊C₄	—	5	2	no	—
399	C₂×C₂²⋊C₄	—	5	2	no	—
400	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
401	C₂×C₄²	—	5	2	no	—
402	C₂×C₄²	—	5	1	no	—
403	C₂×C₄²	—	5	1	no	—
404	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
405	C₂×C₃×C₅	—	4	4	no	—
406	C₂×C₃×C₅	#559	1	4	yes	complemented
407	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
408	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
409	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₃×D₅	—	4	4	no	—
411	C₂³×C₃	—	2	4	no	—
412	C₂³×C₃	—	2	4	no	—
413	C₂³×C₃	—	2	4	no	—
414	C₂³×C₃	—	5	4	no	—
415	C₂³×C₃	—	10	4	no	—
416	C₂³×C₃	—	10	4	no	—
417	C₂³×C₃	—	10	4	no	—
418	C₂³×C₃	C₂³×D₅	1	4	yes	—
419	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
420	C₃×Q₈	—	10	8	no	—
421	C₃×Q₈	—	10	8	no	—
422	C₃×D₄	—	2	8	no	—
423	C₃×D₄	—	10	16	no	—
424	C₃×D₄	—	10	8	no	—
425	C₃×D₄	—	20	8	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	2	4	no	—
428	C₂×C₃×C₄	—	2	2	no	—
429	C₂×C₃×C₄	—	4	8	no	—
430	C₂×C₃×C₄	—	5	4	no	—
431	C₂×C₃×C₄	—	5	2	no	—
432	C₂×C₃×C₄	—	5	4	no	—
433	C₂×C₃×C₄	—	5	2	no	—
434	C₂×C₃×C₄	—	5	2	no	—
435	C₂×C₃×C₄	—	5	2	no	—
436	C₂×C₃×C₄	—	10	4	no	—
437	C₂×C₃×C₄	—	10	2	no	—
438	C₂×C₃×C₄	—	10	2	no	—
439	C₂×C₃×C₄	—	10	2	no	—
440	C₂×C₃×C₄	—	20	8	no	—
441	C₂×C₃×C₄	#709	1	4	yes	—
442	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
443	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
444	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
445	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
446	C₂²×C₅	—	2	4	no	—
447	C₂²×C₅	—	2	4	no	—
448	C₂²×C₅	—	2	4	no	—
449	C₂²×C₅	—	4	8	no	—
450	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
451	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
452	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
454	C₂×D₅	—	2	4	no	—
455	C₂×D₅	—	2	4	no	—
456	C₂×D₅	—	2	4	no	—
457	C₂×D₅	—	4	8	no	—
458	C₄×C₅	—	2	2	no	—
459	C₄×C₅	—	2	4	no	—
460	C₄×C₅	—	2	2	no	—
461	C₄×C₅	C₂×C₃×#41	1	4	yes	—
462	Dic₅	—	2	4	no	—
463	Dic₅	—	2	2	no	—
464	Dic₅	—	2	2	no	—
465	Dic₅	—	2	2	no	—
466	Dic₅	C₂×C₃×#41	1	4	yes	—
467	C₂⁴	—	5	2	no	—
468	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
469	C₂×Q₈	—	5	4	no	—
470	C₂×Q₈	—	5	4	no	—
471	C₂×Q₈	—	10	4	no	—
472	C₂×Q₈	—	10	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	5	8	no	—
475	C₂×D₄	—	5	8	no	—
476	C₂×D₄	—	5	4	no	—
477	C₂×D₄	—	10	8	no	—
478	C₂×D₄	—	10	4	no	—
479	C₂×D₄	—	20	4	no	—
480	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	8	no	—
488	C₂²×C₄	—	20	4	no	—
489	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
490	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
491	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
492	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
493	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
494	C₄⋊C₄	—	5	4	no	—
495	C₄⋊C₄	—	5	8	no	—
496	C₄⋊C₄	—	5	4	no	—
497	C₄⋊C₄	—	5	4	no	—
498	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
499	C₂²⋊C₄	—	5	8	no	—
500	C₂²⋊C₄	—	5	8	no	—
501	C₂²⋊C₄	—	5	8	no	—
502	C₂²⋊C₄	—	5	8	no	—
503	C₂²⋊C₄	—	5	8	no	—
504	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
505	C₄²	—	5	8	no	—
506	C₄²	—	5	4	no	—
507	C₄²	—	5	4	no	—
508	C₄²	C₂²×C₃×D₅	1	4	yes	—
509	C₃×C₅	C₂×#559	1	1	yes	characteristic, complemented, Hall
510	C₂²×C₃	—	2	4	no	—
511	C₂²×C₃	—	2	4	no	—
512	C₂²×C₃	—	2	4	no	—
513	C₂²×C₃	—	4	8	no	—
514	C₂²×C₃	—	10	4	no	—
515	C₂²×C₃	—	10	4	no	—
516	C₂²×C₃	—	10	4	no	—
517	C₂²×C₃	—	20	8	no	—
518	C₂²×C₃	C₂×#709	1	2	yes	—
519	C₂²×C₃	#4144	1	2	yes	—
520	C₂²×C₃	D₅×#41	1	2	yes	—
521	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	—	2	4	no	—
524	C₃×C₄	—	2	2	no	—
525	C₃×C₄	—	5	4	no	—
526	C₃×C₄	—	10	4	no	—
527	C₃×C₄	—	10	2	no	—
528	C₃×C₄	—	10	2	no	—
529	C₃×C₄	—	10	2	no	—
530	C₃×C₄	C₂×#709	1	4	yes	—
531	C₂×C₅	—	4	4	no	—
532	C₂×C₅	C₃×#559	1	4	yes	complemented
533	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
534	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
535	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
536	D₅	—	4	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	5	4	no	—
541	C₂³	—	10	4	no	—
542	C₂³	—	10	4	no	—
543	C₂³	—	10	4	no	—
544	C₂³	C₂³×C₃×D₅	1	4	yes	—
545	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
546	Q₈	—	10	8	no	—
547	Q₈	—	10	8	no	—
548	D₄	—	2	8	no	—
549	D₄	—	10	16	no	—
550	D₄	—	10	8	no	—
551	D₄	—	20	8	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	5	4	no	—
557	C₂×C₄	—	5	2	no	—
558	C₂×C₄	—	5	4	no	—
559	C₂×C₄	—	5	2	no	—
560	C₂×C₄	—	5	2	no	—
561	C₂×C₄	—	5	2	no	—
562	C₂×C₄	—	10	4	no	—
563	C₂×C₄	—	10	2	no	—
564	C₂×C₄	—	10	2	no	—
565	C₂×C₄	—	10	2	no	—
566	C₂×C₄	—	20	8	no	—
567	C₂×C₄	C₃×#709	1	4	yes	—
568	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
569	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
570	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
571	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
572	C₂×C₃	—	4	4	no	—
573	C₂×C₃	—	20	4	no	—
574	C₂×C₃	#65893	1	4	yes	direct product factor
575	C₂×C₃	C₂²×#709	1	1	yes	characteristic
576	C₂×C₃	C₂×#4144	1	1	yes	characteristic
577	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
578	C₅	C₂×C₃×#559	1	1	yes	characteristic, complemented, Sylow
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	10	4	no	—
584	C₂²	—	10	4	no	—
585	C₂²	—	10	4	no	—
586	C₂²	—	20	8	no	—
587	C₂²	C₂×C₃×#709	1	2	yes	—
588	C₂²	C₃×#4144	1	2	yes	—
589	C₂²	C₃×D₅×#41	1	2	yes	—
590	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	2	no	—
594	C₄	—	5	4	no	—
595	C₄	—	10	4	no	—
596	C₄	—	10	2	no	—
597	C₄	—	10	2	no	—
598	C₄	—	10	2	no	—
599	C₄	C₂×C₃×#709	1	4	yes	—
600	C₃	C₂×#65893	1	1	yes	characteristic, direct product factor, Sylow
601	C₂	—	4	4	no	—
602	C₂	—	20	4	no	—
603	C₂	C₃×#65893	1	4	yes	direct product factor
604	C₂	C₂²×C₃×#709	1	1	yes	characteristic
605	C₂	C₂×C₃×#4144	1	1	yes	characteristic
606	C₂	C₂×C₃×D₅×#41	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
prime radical	C₂×C₃×#4086	C₂
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₂×C₃×#559
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
3. C₂×C₃×#4082	C₂	semidirect
4. C₂×C₃×#4075	C₂	semidirect
5. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
6. C₃×#65893	C₂	direct (N × H)
7. C₂×C₃×#4039	C₂	semidirect
8. C₂×C₃×#4033	C₂	semidirect
9. C₂×C₃×#4031	C₂	semidirect
10. C₂×C₃×#4029	C₂	semidirect
11. C₂×C₃×#4021	C₂	semidirect
12. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
13. C₂×#65893	C₃	direct (N × H)
22. C₃×C₄×C₅×D₄	C₂²	semidirect
29. C₃×#4082	C₂²	semidirect
30. C₃×#4075	C₂²	semidirect
31. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
42. C₃×#4039	C₂²	semidirect
43. C₃×#4033	C₂²	semidirect
44. C₃×#4031	C₂²	semidirect
45. C₃×#4029	C₂²	semidirect
46. C₃×#4021	C₂²	semidirect
47. C₃×C₄×Dic₁₀	C₂²	semidirect
49. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
51. C₂×#4082	C₂×C₃	semidirect
52. C₂×#4075	C₂×C₃	semidirect
53. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
54. #65893	C₂×C₃	direct (N × H)
55. C₂×#4039	C₂×C₃	semidirect
56. C₂×#4033	C₂×C₃	semidirect
57. C₂×#4031	C₂×C₃	semidirect
58. C₂×#4029	C₂×C₃	semidirect
59. C₂×#4021	C₂×C₃	semidirect
60. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
114. C₂×C₃×C₄×D₄	D₅	semidirect
123. C₄×C₅×D₄	C₂²×C₃	semidirect
130. #4082	C₂²×C₃	semidirect
131. #4075	C₂²×C₃	semidirect
132. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
143. #4039	C₂²×C₃	semidirect
144. #4033	C₂²×C₃	semidirect
145. #4031	C₂²×C₃	semidirect
146. #4029	C₂²×C₃	semidirect
147. #4021	C₂²×C₃	semidirect
148. C₄×Dic₁₀	C₂²×C₃	semidirect
203. C₃×C₄×D₄	C₂×D₅	semidirect
272. C₂×C₄×D₄	C₃×D₅	semidirect
389. C₄×D₄	C₂×C₃×D₅	semidirect
406. C₂×C₃×C₅	#559	semidirect
509. C₃×C₅	C₂×#559	semidirect
532. C₂×C₅	C₃×#559	semidirect
574. C₂×C₃	#65893	direct (N × H)
578. C₅	C₂×C₃×#559	semidirect
600. C₃	C₂×#65893	direct (N × H)
603. C₂	C₃×#65893	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×#4086	2
C₂×C₃×#4082	2
C₂×C₃×#4075	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₃×#65893	2
C₂×C₃×#4039	2
C₂×C₃×#4033	2
C₂×C₃×#4031	2
C₂×C₃×#4029	2
C₂×C₃×#4021	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#65893	3
C₂×C₃×#559	5

Subgroups — C2×C3×#65893 #14484703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65893 #14484703