Subgroups — C₂×C₃×#65887 #14482976

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4086	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4076	C₂	1	2	yes	maximal, complemented
5	C₃×#65887	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×#4039	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4030	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65887	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×C₂²⋊D₅	C₂²	1	4	yes	—
15	C₂×C₃×#709	—	2	16	no	—
16	C₂×C₃×#709	C₂²	1	16	yes	complemented
17	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
18	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
19	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
20	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
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	C₃×#4086	C₂²	1	16	yes	complemented
27	C₃×#4076	C₂²	1	16	yes	complemented
28	C₂×C₃×#685	C₂²	1	4	yes	—
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×#683	C₂²	1	2	yes	—
31	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
32	C₃×#4039	C₂²	1	16	yes	complemented
33	C₃×#4030	C₂²	1	32	yes	complemented
34	C₃×#4020	C₂²	1	8	yes	complemented
35	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
36	C₂×C₃×#550	—	5	1	no	maximal, Hall
37	C₂²×#709	C₂×C₃	1	2	yes	complemented
38	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#4086	C₂×C₃	1	2	yes	complemented
40	C₂×#4076	C₂×C₃	1	2	yes	complemented
41	#65887	C₂×C₃	1	16	yes	direct product factor
42	C₂×#4039	C₂×C₃	1	2	yes	complemented
43	C₂×#4030	C₂×C₃	1	4	yes	complemented
44	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
47	C₂³×C₃×D₅	C₂³	1	4	yes	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
50	C₂²×C₃×C₄×C₅	—	2	8	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
57	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
58	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
59	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
60	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
61	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
62	C₃×#709	—	2	64	no	—
63	C₂×C₃×D₂₀	—	2	8	no	—
64	C₂×C₃×D₂₀	—	2	8	no	—
65	C₂×C₃×D₂₀	—	4	4	no	—
66	C₂×C₃×D₂₀	C₂³	1	8	yes	—
67	C₂×C₃×D₂₀	C₂³	1	8	yes	—
68	C₂×C₃×D₂₀	C₂³	1	8	yes	—
69	C₂×C₃×C₄×D₅	—	2	16	no	—
70	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
71	C₂×C₃×Dic₁₀	D₄	1	8	yes	complemented
72	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₃×C₄²×C₅	C₂³	1	4	yes	—
76	C₃×#685	C₂³	1	16	yes	—
77	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
78	C₃×#683	C₂³	1	8	yes	—
79	C₃×C₄×Dic₅	C₂³	1	8	yes	—
80	C₂²×C₃×#41	—	5	2	no	—
81	C₃×#550	—	5	16	no	—
82	C₂×C₃×#127	—	5	2	no	—
83	C₂×C₃×#127	—	5	1	no	—
84	C₂×C₃×#121	—	5	2	no	—
85	C₂×C₃×#121	—	5	4	no	—
86	C₂×C₃×C₄×Q₈	—	5	1	no	—
87	C₂×C₃×C₄×D₄	—	5	2	no	—
88	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
89	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
91	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
92	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
93	C₂×#709	—	2	16	no	—
94	C₂×#709	C₂²×C₃	1	16	yes	complemented
95	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
96	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
97	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
98	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
99	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×D₄	C₂²×C₃	1	8	yes	complemented
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
104	#4086	C₂²×C₃	1	16	yes	complemented
105	#4076	C₂²×C₃	1	16	yes	complemented
106	C₂×#685	C₂²×C₃	1	4	yes	—
107	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
108	C₂×#683	C₂²×C₃	1	2	yes	—
109	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
110	#4039	C₂²×C₃	1	16	yes	complemented
111	#4030	C₂²×C₃	1	32	yes	complemented
112	#4020	C₂²×C₃	1	8	yes	complemented
113	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
114	C₂×#550	—	5	1	no	Sylow
115	C₂³×C₃×C₅	—	2	4	no	—
116	C₂³×C₃×C₅	—	2	4	no	—
117	C₂³×C₃×C₅	—	2	4	no	—
118	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
119	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
120	C₂²×C₃×D₅	—	2	8	no	—
121	C₂²×C₃×D₅	—	2	8	no	—
122	C₂²×C₃×D₅	—	2	8	no	—
123	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
124	C₃×C₅×D₄	—	2	8	no	—
125	C₂×C₃×C₄×C₅	—	2	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	16	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
130	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
134	C₃×C₂²⋊D₅	—	2	32	no	—
135	C₃×C₂²⋊D₅	—	4	16	no	—
136	C₂×C₃×Dic₅	—	2	4	no	—
137	C₂×C₃×Dic₅	C₂×D₄	1	8	yes	—
138	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
139	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
140	C₃×D₂₀	—	2	16	no	—
141	C₃×D₂₀	—	2	16	no	—
142	C₃×D₂₀	—	4	8	no	—
143	C₃×C₄×D₅	—	2	32	no	—
144	C₃×Dic₁₀	C₂×D₄	1	16	yes	complemented
145	C₂×C₃×#41	—	5	16	no	—
146	C₂×C₃×#41	—	10	16	no	—
147	C₂²×C₃×Q₈	—	5	1	no	—
148	C₂²×C₃×D₄	—	5	4	no	—
149	C₂²×C₃×D₄	—	5	4	no	—
150	C₂²×C₃×D₄	—	5	2	no	—
151	C₂²×C₃×D₄	—	5	2	no	—
152	C₂²×C₃×D₄	—	5	2	no	—
153	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
154	C₂³×C₃×C₄	—	5	4	no	—
155	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
156	C₃×#127	—	5	16	no	—
157	C₃×#127	—	5	8	no	—
158	C₃×#121	—	5	16	no	—
159	C₃×#121	—	5	32	no	—
160	C₃×C₄×Q₈	—	5	8	no	—
161	C₃×C₄×D₄	—	5	16	no	—
162	C₃×C₄×D₄	C₂×D₅	1	8	yes	complemented
163	C₂×C₃×C₄⋊C₄	—	5	2	no	—
164	C₂×C₃×C₄⋊C₄	—	5	1	no	—
165	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
166	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
167	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
168	C₂×C₃×C₄²	—	5	2	no	—
169	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
170	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
171	C₂³×D₅	C₂³×C₃	1	4	yes	—
172	C₂×C₅×D₄	—	2	4	no	—
173	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
174	C₂²×C₄×C₅	—	2	8	no	—
175	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
177	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
178	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₂²⋊D₅	—	2	16	no	—
181	C₂×C₂²⋊D₅	—	4	8	no	—
182	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
183	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
184	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
185	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
186	#709	—	2	64	no	—
187	C₂×D₂₀	—	2	8	no	—
188	C₂×D₂₀	—	2	8	no	—
189	C₂×D₂₀	—	4	4	no	—
190	C₂×D₂₀	C₂³×C₃	1	8	yes	—
191	C₂×D₂₀	C₂³×C₃	1	8	yes	—
192	C₂×D₂₀	C₂³×C₃	1	8	yes	—
193	C₂×C₄×D₅	—	2	16	no	—
194	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
195	C₂×Dic₁₀	C₃×D₄	1	8	yes	complemented
196	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
197	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
198	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
199	C₄²×C₅	C₂³×C₃	1	4	yes	—
200	#685	C₂³×C₃	1	16	yes	—
201	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
202	#683	C₂³×C₃	1	8	yes	—
203	C₄×Dic₅	C₂³×C₃	1	8	yes	—
204	C₂²×#41	—	5	2	no	—
205	#550	—	5	16	no	—
206	C₂×#127	—	5	2	no	—
207	C₂×#127	—	5	1	no	—
208	C₂×#121	—	5	2	no	—
209	C₂×#121	—	5	4	no	—
210	C₂×C₄×Q₈	—	5	1	no	—
211	C₂×C₄×D₄	—	5	2	no	—
212	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
213	C₂²×C₃×C₅	—	2	4	no	—
214	C₂²×C₃×C₅	—	2	4	no	—
215	C₂²×C₃×C₅	—	2	4	no	—
216	C₂²×C₃×C₅	—	4	8	no	—
217	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
218	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
219	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
220	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
221	C₂×C₃×D₅	—	2	8	no	—
222	C₂×C₃×D₅	—	2	8	no	—
223	C₂×C₃×D₅	—	2	8	no	—
224	C₂×C₃×D₅	—	4	16	no	—
225	C₃×C₄×C₅	—	2	4	no	—
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
228	C₃×C₄×C₅	C₂×#41	1	4	yes	complemented
229	C₃×Dic₅	—	2	4	no	—
230	C₃×Dic₅	C₂²×D₄	1	8	yes	—
231	C₂⁴×C₃	—	5	4	no	—
232	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
233	C₃×#41	—	10	64	no	—
234	C₂×C₃×Q₈	—	5	8	no	—
235	C₂×C₃×Q₈	—	5	4	no	—
236	C₂×C₃×D₄	—	2	4	no	—
237	C₂×C₃×D₄	—	5	16	no	—
238	C₂×C₃×D₄	—	5	16	no	—
239	C₂×C₃×D₄	—	5	8	no	—
240	C₂×C₃×D₄	—	5	8	no	—
241	C₂×C₃×D₄	—	5	8	no	—
242	C₂×C₃×D₄	—	10	16	no	—
243	C₂×C₃×D₄	—	10	8	no	—
244	C₂×C₃×D₄	—	10	8	no	—
245	C₂×C₃×D₄	—	20	4	no	—
246	C₂×C₃×D₄	—	20	8	no	—
247	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
248	C₂²×C₃×C₄	—	2	8	no	—
249	C₂²×C₃×C₄	—	5	2	no	—
250	C₂²×C₃×C₄	—	5	2	no	—
251	C₂²×C₃×C₄	—	5	16	no	—
252	C₂²×C₃×C₄	—	10	16	no	—
253	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
254	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
256	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
258	C₃×C₄⋊C₄	—	5	8	no	—
259	C₃×C₄⋊C₄	—	5	4	no	—
260	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
261	C₃×C₂²⋊C₄	—	5	16	no	—
262	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
263	C₃×C₄²	—	5	8	no	—
264	C₃×C₄²	C₂²×D₅	1	4	yes	—
265	C₂³×C₅	—	2	4	no	—
266	C₂³×C₅	—	2	4	no	—
267	C₂³×C₅	—	2	4	no	—
268	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
269	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
270	C₂²×D₅	—	2	8	no	—
271	C₂²×D₅	—	2	8	no	—
272	C₂²×D₅	—	2	8	no	—
273	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
274	C₅×D₄	—	2	8	no	—
275	C₂×C₄×C₅	—	2	4	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	16	no	—
278	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
279	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
280	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
281	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
282	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
283	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
284	C₂²⋊D₅	—	2	32	no	—
285	C₂²⋊D₅	—	4	16	no	—
286	C₂×Dic₅	—	2	4	no	—
287	C₂×Dic₅	C₂×C₃×D₄	1	8	yes	—
288	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
289	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
290	D₂₀	—	2	16	no	—
291	D₂₀	—	2	16	no	—
292	D₂₀	—	4	8	no	—
293	C₄×D₅	—	2	32	no	—
294	Dic₁₀	C₂×C₃×D₄	1	16	yes	complemented
295	C₂×#41	—	5	16	no	—
296	C₂×#41	—	10	16	no	—
297	C₂²×Q₈	—	5	1	no	—
298	C₂²×D₄	—	5	4	no	—
299	C₂²×D₄	—	5	4	no	—
300	C₂²×D₄	—	5	2	no	—
301	C₂²×D₄	—	5	2	no	—
302	C₂²×D₄	—	5	2	no	—
303	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
304	C₂³×C₄	—	5	4	no	—
305	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
306	#127	—	5	16	no	—
307	#127	—	5	8	no	—
308	#121	—	5	16	no	—
309	#121	—	5	32	no	—
310	C₄×Q₈	—	5	8	no	—
311	C₄×D₄	—	5	16	no	—
312	C₄×D₄	C₂×C₃×D₅	1	8	yes	complemented
313	C₂×C₄⋊C₄	—	5	2	no	—
314	C₂×C₄⋊C₄	—	5	1	no	—
315	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	5	4	no	—
317	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
318	C₂×C₄²	—	5	2	no	—
319	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
320	C₂×C₃×C₅	—	4	4	no	—
321	C₂×C₃×C₅	#550	1	4	yes	complemented
322	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₃×D₅	—	4	8	no	—
326	C₂³×C₃	—	2	4	no	—
327	C₂³×C₃	—	2	4	no	—
328	C₂³×C₃	—	2	4	no	—
329	C₂³×C₃	—	5	8	no	—
330	C₂³×C₃	—	10	8	no	—
331	C₂³×C₃	—	10	8	no	—
332	C₂³×C₃	—	10	8	no	—
333	C₂³×C₃	C₂³×D₅	1	4	yes	—
334	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
335	C₃×Q₈	—	5	16	no	—
336	C₃×D₄	—	2	8	no	—
337	C₃×D₄	—	10	32	no	—
338	C₃×D₄	—	10	16	no	—
339	C₃×D₄	—	10	16	no	—
340	C₃×D₄	—	20	8	no	—
341	C₃×D₄	—	20	16	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	16	no	—
345	C₂×C₃×C₄	—	5	8	no	—
346	C₂×C₃×C₄	—	5	4	no	—
347	C₂×C₃×C₄	—	5	4	no	—
348	C₂×C₃×C₄	—	10	32	no	—
349	C₂×C₃×C₄	—	10	4	no	—
350	C₂×C₃×C₄	#709	1	4	yes	complemented
351	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
352	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
353	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
354	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
355	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
356	C₂²×C₅	—	2	4	no	—
357	C₂²×C₅	—	2	4	no	—
358	C₂²×C₅	—	2	4	no	—
359	C₂²×C₅	—	4	8	no	—
360	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
361	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
362	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
363	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
364	C₂×D₅	—	2	8	no	—
365	C₂×D₅	—	2	8	no	—
366	C₂×D₅	—	2	8	no	—
367	C₂×D₅	—	4	16	no	—
368	C₄×C₅	—	2	4	no	—
369	C₄×C₅	—	2	2	no	—
370	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
371	C₄×C₅	C₂×C₃×#41	1	4	yes	complemented
372	Dic₅	—	2	4	no	—
373	Dic₅	C₂²×C₃×D₄	1	8	yes	—
374	C₂⁴	—	5	4	no	—
375	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
376	#41	—	10	64	no	—
377	C₂×Q₈	—	5	8	no	—
378	C₂×Q₈	—	5	4	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	5	16	no	—
381	C₂×D₄	—	5	16	no	—
382	C₂×D₄	—	5	8	no	—
383	C₂×D₄	—	5	8	no	—
384	C₂×D₄	—	5	8	no	—
385	C₂×D₄	—	10	16	no	—
386	C₂×D₄	—	10	8	no	—
387	C₂×D₄	—	10	8	no	—
388	C₂×D₄	—	20	4	no	—
389	C₂×D₄	—	20	8	no	—
390	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	5	2	no	—
393	C₂²×C₄	—	5	2	no	—
394	C₂²×C₄	—	5	16	no	—
395	C₂²×C₄	—	10	16	no	—
396	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
398	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
399	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
401	C₄⋊C₄	—	5	8	no	—
402	C₄⋊C₄	—	5	4	no	—
403	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
404	C₂²⋊C₄	—	5	16	no	—
405	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
406	C₄²	—	5	8	no	—
407	C₄²	C₂²×C₃×D₅	1	4	yes	—
408	C₃×C₅	C₂×#550	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	2	4	no	—
411	C₂²×C₃	—	2	4	no	—
412	C₂²×C₃	—	4	8	no	—
413	C₂²×C₃	—	10	8	no	—
414	C₂²×C₃	—	10	8	no	—
415	C₂²×C₃	—	10	8	no	—
416	C₂²×C₃	—	20	16	no	—
417	C₂²×C₃	C₂×#709	1	2	yes	—
418	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
419	C₂²×C₃	#4149	1	2	yes	—
420	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
421	C₃×C₄	—	2	4	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	5	8	no	—
424	C₃×C₄	—	10	4	no	—
425	C₃×C₄	C₂×#709	1	4	yes	complemented
426	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
427	C₂×C₅	—	4	4	no	—
428	C₂×C₅	C₃×#550	1	4	yes	complemented
429	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
430	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
431	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
432	D₅	—	4	8	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	5	8	no	—
437	C₂³	—	10	8	no	—
438	C₂³	—	10	8	no	—
439	C₂³	—	10	8	no	—
440	C₂³	C₂³×C₃×D₅	1	4	yes	—
441	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
442	Q₈	—	5	16	no	—
443	D₄	—	2	8	no	—
444	D₄	—	10	32	no	—
445	D₄	—	10	16	no	—
446	D₄	—	10	16	no	—
447	D₄	—	20	8	no	—
448	D₄	—	20	16	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	16	no	—
452	C₂×C₄	—	5	8	no	—
453	C₂×C₄	—	5	4	no	—
454	C₂×C₄	—	5	4	no	—
455	C₂×C₄	—	10	32	no	—
456	C₂×C₄	—	10	4	no	—
457	C₂×C₄	C₃×#709	1	4	yes	complemented
458	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
459	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
460	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
461	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
462	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
463	C₂×C₃	—	4	4	no	—
464	C₂×C₃	—	20	8	no	—
465	C₂×C₃	#65887	1	4	yes	direct product factor
466	C₂×C₃	C₂²×#709	1	1	yes	characteristic
467	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
468	C₂×C₃	C₂×#4149	1	1	yes	characteristic
469	C₅	C₂×C₃×#550	1	1	yes	characteristic, complemented, Sylow
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	10	8	no	—
475	C₂²	—	10	8	no	—
476	C₂²	—	10	8	no	—
477	C₂²	—	20	16	no	—
478	C₂²	C₂×C₃×#709	1	2	yes	—
479	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
480	C₂²	C₃×#4149	1	2	yes	—
481	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	2	2	no	—
484	C₄	—	5	8	no	—
485	C₄	—	10	4	no	—
486	C₄	C₂×C₃×#709	1	4	yes	complemented
487	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
488	C₃	C₂×#65887	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	4	4	no	—
490	C₂	—	20	8	no	—
491	C₂	C₃×#65887	1	4	yes	direct product factor
492	C₂	C₂²×C₃×#709	1	1	yes	characteristic
493	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
494	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×#550
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. C₂²×C₃×#709	C₂	semidirect
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₃×#4086	C₂	semidirect
4. C₂×C₃×#4076	C₂	semidirect
5. C₃×#65887	C₂	direct (N × H)
6. C₂×C₃×#4039	C₂	semidirect
7. C₂×C₃×#4030	C₂	semidirect
8. C₂×C₃×#4020	C₂	semidirect
9. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
10. C₂×#65887	C₃	direct (N × H)
16. C₂×C₃×#709	C₂²	semidirect
22. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₃×#4086	C₂²	semidirect
27. C₃×#4076	C₂²	semidirect
32. C₃×#4039	C₂²	semidirect
33. C₃×#4030	C₂²	semidirect
34. C₃×#4020	C₂²	semidirect
35. C₃×C₄×Dic₁₀	C₂²	semidirect
37. C₂²×#709	C₂×C₃	semidirect
38. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
39. C₂×#4086	C₂×C₃	semidirect
40. C₂×#4076	C₂×C₃	semidirect
41. #65887	C₂×C₃	direct (N × H)
42. C₂×#4039	C₂×C₃	semidirect
43. C₂×#4030	C₂×C₃	semidirect
44. C₂×#4020	C₂×C₃	semidirect
45. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
71. C₂×C₃×Dic₁₀	D₄	semidirect
88. C₂×C₃×C₄×D₄	D₅	semidirect
94. C₂×#709	C₂²×C₃	semidirect
100. C₄×C₅×D₄	C₂²×C₃	semidirect
104. #4086	C₂²×C₃	semidirect
105. #4076	C₂²×C₃	semidirect
110. #4039	C₂²×C₃	semidirect
111. #4030	C₂²×C₃	semidirect
112. #4020	C₂²×C₃	semidirect
113. C₄×Dic₁₀	C₂²×C₃	semidirect
129. C₂×C₃×C₄×C₅	#41	semidirect
144. C₃×Dic₁₀	C₂×D₄	semidirect
162. C₃×C₄×D₄	C₂×D₅	semidirect
195. C₂×Dic₁₀	C₃×D₄	semidirect
212. C₂×C₄×D₄	C₃×D₅	semidirect
228. C₃×C₄×C₅	C₂×#41	semidirect
279. C₂×C₄×C₅	C₃×#41	semidirect
294. Dic₁₀	C₂×C₃×D₄	semidirect
312. C₄×D₄	C₂×C₃×D₅	semidirect
321. C₂×C₃×C₅	#550	semidirect
350. C₂×C₃×C₄	#709	semidirect
371. C₄×C₅	C₂×C₃×#41	semidirect
408. C₃×C₅	C₂×#550	semidirect
425. C₃×C₄	C₂×#709	semidirect
428. C₂×C₅	C₃×#550	semidirect
457. C₂×C₄	C₃×#709	semidirect
465. C₂×C₃	#65887	direct (N × H)
469. C₅	C₂×C₃×#550	semidirect
486. C₄	C₂×C₃×#709	semidirect
488. C₃	C₂×#65887	direct (N × H)
491. C₂	C₃×#65887	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×#709	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₃×#4086	2
C₂×C₃×#4076	2
C₃×#65887	2
C₂×C₃×#4039	2
C₂×C₃×#4030	2
C₂×C₃×#4020	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#65887	3
C₂×C₃×#550	5

Subgroups — C2×C3×#65887 #14482976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65887 #14482976