Subgroups — C₂×C₃×#65859 #14480381

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 464 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	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65859	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4041	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4028	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4021	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4020	C₂	1	2	yes	maximal, complemented
9	C₂×#65859	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
13	C₂×C₃×#709	—	2	8	no	—
14	C₂×C₃×#709	C₂²	1	8	yes	complemented
15	C₂²×C₃×D₂₀	—	2	8	no	—
16	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
17	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
18	C₂²×C₃×D₂₀	C₂²	1	8	yes	complemented
19	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×D₂₀	C₂²	1	8	yes	complemented
21	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
22	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#117	C₂²	1	8	yes	complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
27	C₂×C₃×#685	C₂²	1	8	yes	complemented
28	C₃×#4041	C₂²	1	32	yes	complemented
29	C₃×#4028	C₂²	1	32	yes	complemented
30	C₃×#4021	C₂²	1	16	yes	complemented
31	C₃×#4020	C₂²	1	16	yes	complemented
32	C₂×C₃×#535	—	5	1	no	maximal, Hall
33	C₂²×#709	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
36	#65859	C₂×C₃	1	16	yes	direct product factor
37	C₂×#4041	C₂×C₃	1	4	yes	complemented
38	C₂×#4028	C₂×C₃	1	4	yes	complemented
39	C₂×#4021	C₂×C₃	1	2	yes	complemented
40	C₂×#4020	C₂×C₃	1	2	yes	complemented
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂³×C₃×D₅	—	2	8	no	—
43	C₂³×C₃×D₅	—	4	8	no	—
44	C₂³×C₃×D₅	C₂³	1	2	yes	—
45	C₂³×C₃×D₅	C₂³	1	4	yes	—
46	C₂³×C₃×D₅	C₂³	1	8	yes	—
47	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
48	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
52	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
53	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₃×#709	—	2	32	no	—
56	C₂×C₃×D₂₀	—	2	8	no	—
57	C₂×C₃×D₂₀	—	2	8	no	—
58	C₂×C₃×D₂₀	—	2	4	no	—
59	C₂×C₃×D₂₀	—	2	32	no	—
60	C₂×C₃×D₂₀	—	4	16	no	—
61	C₂×C₃×D₂₀	C₂³	1	8	yes	—
62	C₂×C₃×D₂₀	C₂³	1	8	yes	—
63	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
64	C₂×C₃×D₂₀	C₂³	1	32	yes	complemented
65	C₂×C₃×C₄×D₅	—	2	8	no	—
66	C₂×C₃×C₄×D₅	C₂³	1	8	yes	complemented
67	C₂×C₃×Dic₁₀	—	2	4	no	—
68	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
69	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
70	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₃×C₄²×C₅	C₂³	1	8	yes	complemented
72	C₃×#685	C₂³	1	32	yes	complemented
73	C₂²×C₃×#41	—	5	1	no	—
74	C₂³×C₃×D₄	—	5	1	no	—
75	C₃×#535	—	5	16	no	—
76	C₂×C₃×#127	—	5	2	no	—
77	C₂×C₃×#124	—	5	2	no	—
78	C₂×C₃×#121	—	5	4	no	—
79	C₂×C₃×#120	—	5	4	no	—
80	C₂×C₃×#117	D₅	1	1	yes	characteristic, complemented
81	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
82	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
84	C₂×#709	—	2	8	no	—
85	C₂×#709	C₂²×C₃	1	8	yes	complemented
86	C₂²×D₂₀	—	2	8	no	—
87	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
88	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
89	C₂²×D₂₀	C₂²×C₃	1	8	yes	complemented
90	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
91	C₂²×D₂₀	C₂²×C₃	1	8	yes	complemented
92	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
93	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
94	C₅×#117	C₂²×C₃	1	8	yes	complemented
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
98	C₂×#685	C₂²×C₃	1	8	yes	complemented
99	#4041	C₂²×C₃	1	32	yes	complemented
100	#4028	C₂²×C₃	1	32	yes	complemented
101	#4021	C₂²×C₃	1	16	yes	complemented
102	#4020	C₂²×C₃	1	16	yes	complemented
103	C₂×#535	—	5	1	no	Sylow
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
106	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
107	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
108	C₂²×C₃×D₅	—	2	4	no	—
109	C₂²×C₃×D₅	—	2	16	no	—
110	C₂²×C₃×D₅	—	2	8	no	—
111	C₂²×C₃×D₅	—	2	8	no	—
112	C₂²×C₃×D₅	—	2	16	no	—
113	C₂²×C₃×D₅	—	4	16	no	—
114	C₂²×C₃×D₅	—	4	32	no	—
115	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
116	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
117	C₂×C₃×C₄×C₅	—	2	8	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
121	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₃×C₂²⋊D₅	—	2	16	no	—
125	C₂×C₃×Dic₅	—	2	4	no	—
126	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
127	C₃×D₂₀	—	2	16	no	—
128	C₃×D₂₀	—	2	16	no	—
129	C₃×D₂₀	—	2	8	no	—
130	C₃×D₂₀	—	4	32	no	—
131	C₃×C₄×D₅	—	2	16	no	—
132	C₃×Dic₁₀	—	2	8	no	—
133	C₂⁵×C₃	—	5	2	no	—
134	C₂×C₃×#41	—	5	8	no	—
135	C₂×C₃×#41	—	10	8	no	—
136	C₂²×C₃×Q₈	—	5	1	no	—
137	C₂²×C₃×D₄	—	5	2	no	—
138	C₂²×C₃×D₄	—	5	2	no	—
139	C₂²×C₃×D₄	—	5	2	no	—
140	C₂²×C₃×D₄	—	5	8	no	—
141	C₂²×C₃×D₄	—	5	1	no	—
142	C₂²×C₃×D₄	—	5	8	no	—
143	C₂²×C₃×D₄	—	10	8	no	—
144	C₂³×C₃×C₄	—	5	2	no	—
145	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
146	C₃×#127	—	5	16	no	—
147	C₃×#124	—	5	16	no	—
148	C₃×#121	—	5	32	no	—
149	C₃×#120	—	5	32	no	—
150	C₃×#117	C₂×D₅	1	8	yes	complemented
151	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
152	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
153	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
154	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
155	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂³×D₅	—	2	8	no	—
157	C₂³×D₅	—	4	8	no	—
158	C₂³×D₅	C₂³×C₃	1	2	yes	—
159	C₂³×D₅	C₂³×C₃	1	4	yes	—
160	C₂³×D₅	C₂³×C₃	1	8	yes	—
161	C₂²×C₄×C₅	C₃×D₄	1	8	yes	complemented
162	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
163	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
166	C₂×C₂²⋊D₅	—	2	8	no	—
167	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
168	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
169	#709	—	2	32	no	—
170	C₂×D₂₀	—	2	8	no	—
171	C₂×D₂₀	—	2	8	no	—
172	C₂×D₂₀	—	2	4	no	—
173	C₂×D₂₀	—	2	32	no	—
174	C₂×D₂₀	—	4	16	no	—
175	C₂×D₂₀	C₂³×C₃	1	8	yes	—
176	C₂×D₂₀	C₂³×C₃	1	8	yes	—
177	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
178	C₂×D₂₀	C₂³×C₃	1	32	yes	complemented
179	C₂×C₄×D₅	—	2	8	no	—
180	C₂×C₄×D₅	C₂³×C₃	1	8	yes	complemented
181	C₂×Dic₁₀	—	2	4	no	—
182	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
183	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
184	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
185	C₄²×C₅	C₂³×C₃	1	8	yes	complemented
186	#685	C₂³×C₃	1	32	yes	complemented
187	C₂²×#41	—	5	1	no	—
188	C₂³×D₄	—	5	1	no	—
189	#535	—	5	16	no	—
190	C₂×#127	—	5	2	no	—
191	C₂×#124	—	5	2	no	—
192	C₂×#121	—	5	4	no	—
193	C₂×#120	—	5	4	no	—
194	C₂×#117	C₃×D₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	—	2	8	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
198	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
200	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
201	C₂×C₃×D₅	—	2	4	no	—
202	C₂×C₃×D₅	—	2	8	no	—
203	C₂×C₃×D₅	—	2	8	no	—
204	C₂×C₃×D₅	—	2	16	no	—
205	C₂×C₃×D₅	—	4	32	no	—
206	C₂×C₃×D₅	—	4	8	no	—
207	C₂×C₃×D₅	—	4	16	no	—
208	C₃×C₄×C₅	—	2	8	no	—
209	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
210	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
211	C₃×Dic₅	—	2	4	no	—
212	C₂⁴×C₃	—	5	4	no	—
213	C₂⁴×C₃	—	5	2	no	—
214	C₂⁴×C₃	—	5	8	no	—
215	C₂⁴×C₃	—	10	8	no	—
216	C₂⁴×C₃	—	20	8	no	—
217	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
218	C₃×#41	—	10	32	no	—
219	C₂×C₃×Q₈	—	5	4	no	—
220	C₂×C₃×Q₈	—	10	4	no	—
221	C₂×C₃×D₄	—	5	8	no	—
222	C₂×C₃×D₄	—	5	8	no	—
223	C₂×C₃×D₄	—	5	8	no	—
224	C₂×C₃×D₄	—	5	4	no	—
225	C₂×C₃×D₄	—	5	32	no	—
226	C₂×C₃×D₄	—	10	8	no	—
227	C₂×C₃×D₄	—	10	8	no	—
228	C₂×C₃×D₄	—	10	8	no	—
229	C₂×C₃×D₄	—	10	4	no	—
230	C₂×C₃×D₄	—	10	32	no	—
231	C₂×C₃×D₄	—	20	16	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	8	no	—
234	C₂²×C₃×C₄	—	10	8	no	—
235	C₂²×C₃×C₄	D₂₀	1	8	yes	complemented
236	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
240	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	complemented
241	C₃×C₂²⋊C₄	—	5	32	no	—
242	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
243	C₃×C₄²	C₂²×D₅	1	8	yes	complemented
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
246	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
247	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
248	C₂²×D₅	—	2	4	no	—
249	C₂²×D₅	—	2	16	no	—
250	C₂²×D₅	—	2	8	no	—
251	C₂²×D₅	—	2	8	no	—
252	C₂²×D₅	—	2	16	no	—
253	C₂²×D₅	—	4	16	no	—
254	C₂²×D₅	—	4	32	no	—
255	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
256	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
257	C₂×C₄×C₅	—	2	8	no	—
258	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
259	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
260	C₂×C₄×C₅	C₂×C₃×D₄	1	16	yes	complemented
261	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
262	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
263	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
264	C₂²⋊D₅	—	2	16	no	—
265	C₂×Dic₅	—	2	4	no	—
266	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
267	D₂₀	—	2	16	no	—
268	D₂₀	—	2	16	no	—
269	D₂₀	—	2	8	no	—
270	D₂₀	—	4	32	no	—
271	C₄×D₅	—	2	16	no	—
272	Dic₁₀	—	2	8	no	—
273	C₂⁵	—	5	2	no	—
274	C₂×#41	—	5	8	no	—
275	C₂×#41	—	10	8	no	—
276	C₂²×Q₈	—	5	1	no	—
277	C₂²×D₄	—	5	2	no	—
278	C₂²×D₄	—	5	2	no	—
279	C₂²×D₄	—	5	2	no	—
280	C₂²×D₄	—	5	1	no	—
281	C₂²×D₄	—	5	8	no	—
282	C₂²×D₄	—	5	8	no	—
283	C₂²×D₄	—	10	8	no	—
284	C₂³×C₄	—	5	2	no	—
285	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
286	#127	—	5	16	no	—
287	#124	—	5	16	no	—
288	#121	—	5	32	no	—
289	#120	—	5	32	no	—
290	#117	C₂×C₃×D₅	1	8	yes	complemented
291	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
292	C₂×C₂²⋊C₄	—	5	8	no	—
293	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
294	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
295	C₂×C₃×C₅	—	2	4	no	—
296	C₂×C₃×C₅	#535	1	4	yes	complemented
297	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
298	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
299	C₃×D₅	—	4	4	no	—
300	C₃×D₅	—	4	8	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	5	8	no	—
303	C₂³×C₃	—	5	4	no	—
304	C₂³×C₃	—	10	4	no	—
305	C₂³×C₃	—	10	16	no	—
306	C₂³×C₃	—	10	8	no	—
307	C₂³×C₃	—	10	8	no	—
308	C₂³×C₃	—	10	16	no	—
309	C₂³×C₃	—	20	16	no	—
310	C₂³×C₃	—	20	32	no	—
311	C₂³×C₃	C₂×D₂₀	1	4	yes	—
312	C₂³×C₃	C₂³×D₅	1	2	yes	—
313	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
314	C₃×Q₈	—	10	8	no	—
315	C₃×D₄	—	10	16	no	—
316	C₃×D₄	—	10	16	no	—
317	C₃×D₄	—	10	16	no	—
318	C₃×D₄	—	10	8	no	—
319	C₃×D₄	—	20	32	no	—
320	C₂×C₃×C₄	—	2	8	no	—
321	C₂×C₃×C₄	—	5	4	no	—
322	C₂×C₃×C₄	—	10	4	no	—
323	C₂×C₃×C₄	—	10	16	no	—
324	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
325	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
326	C₂×C₃×C₄	C₂×D₂₀	1	16	yes	complemented
327	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
328	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
329	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
330	C₂²×C₅	—	2	4	no	—
331	C₂²×C₅	—	2	8	no	—
332	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
333	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
334	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
335	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
336	C₂×D₅	—	2	4	no	—
337	C₂×D₅	—	2	8	no	—
338	C₂×D₅	—	2	8	no	—
339	C₂×D₅	—	2	16	no	—
340	C₂×D₅	—	4	32	no	—
341	C₂×D₅	—	4	8	no	—
342	C₂×D₅	—	4	16	no	—
343	C₄×C₅	—	2	8	no	—
344	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
345	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
346	Dic₅	—	2	4	no	—
347	C₂⁴	—	5	4	no	—
348	C₂⁴	—	5	2	no	—
349	C₂⁴	—	5	8	no	—
350	C₂⁴	—	10	8	no	—
351	C₂⁴	—	20	8	no	—
352	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
353	#41	—	10	32	no	—
354	C₂×Q₈	—	5	4	no	—
355	C₂×Q₈	—	10	4	no	—
356	C₂×D₄	—	5	8	no	—
357	C₂×D₄	—	5	8	no	—
358	C₂×D₄	—	5	8	no	—
359	C₂×D₄	—	5	4	no	—
360	C₂×D₄	—	5	32	no	—
361	C₂×D₄	—	10	8	no	—
362	C₂×D₄	—	10	8	no	—
363	C₂×D₄	—	10	8	no	—
364	C₂×D₄	—	10	4	no	—
365	C₂×D₄	—	10	32	no	—
366	C₂×D₄	—	20	16	no	—
367	C₂²×C₄	—	5	2	no	—
368	C₂²×C₄	—	5	8	no	—
369	C₂²×C₄	—	10	8	no	—
370	C₂²×C₄	C₃×D₂₀	1	8	yes	complemented
371	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
372	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
375	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
376	C₂²⋊C₄	—	5	32	no	—
377	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
378	C₄²	C₂²×C₃×D₅	1	8	yes	complemented
379	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	4	no	—
382	C₂²×C₃	—	10	4	no	—
383	C₂²×C₃	—	10	8	no	—
384	C₂²×C₃	—	10	8	no	—
385	C₂²×C₃	—	10	16	no	—
386	C₂²×C₃	—	20	32	no	—
387	C₂²×C₃	—	20	8	no	—
388	C₂²×C₃	—	20	16	no	—
389	C₂²×C₃	C₂²×D₂₀	1	4	yes	—
390	C₂²×C₃	C₂²×D₂₀	1	2	yes	—
391	C₂²×C₃	#4149	1	4	yes	—
392	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
393	C₃×C₄	—	2	8	no	—
394	C₃×C₄	—	10	4	no	—
395	C₃×C₄	C₂²×D₂₀	1	4	yes	—
396	C₃×C₄	C₂²×D₂₀	1	4	yes	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	C₃×#535	1	4	yes	complemented
399	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
400	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
401	D₅	—	4	8	no	—
402	D₅	—	4	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	5	8	no	—
405	C₂³	—	5	4	no	—
406	C₂³	—	10	4	no	—
407	C₂³	—	10	16	no	—
408	C₂³	—	10	8	no	—
409	C₂³	—	10	8	no	—
410	C₂³	—	10	16	no	—
411	C₂³	—	20	16	no	—
412	C₂³	—	20	32	no	—
413	C₂³	C₂×C₃×D₂₀	1	4	yes	—
414	C₂³	C₂³×C₃×D₅	1	2	yes	—
415	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
416	Q₈	—	10	8	no	—
417	D₄	—	10	16	no	—
418	D₄	—	10	16	no	—
419	D₄	—	10	16	no	—
420	D₄	—	10	8	no	—
421	D₄	—	20	32	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	5	4	no	—
424	C₂×C₄	—	10	4	no	—
425	C₂×C₄	—	10	16	no	—
426	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
427	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
428	C₂×C₄	C₂×C₃×D₂₀	1	16	yes	complemented
429	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
430	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
431	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	20	8	no	—
434	C₂×C₃	—	20	4	no	—
435	C₂×C₃	#65859	1	4	yes	direct product factor
436	C₂×C₃	C₂³×D₂₀	1	1	yes	characteristic
437	C₂×C₃	C₂×#4149	1	2	yes	—
438	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
439	C₂²	—	2	8	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	10	4	no	—
442	C₂²	—	10	8	no	—
443	C₂²	—	10	8	no	—
444	C₂²	—	10	16	no	—
445	C₂²	—	20	32	no	—
446	C₂²	—	20	16	no	—
447	C₂²	—	20	8	no	—
448	C₂²	C₂²×C₃×D₂₀	1	4	yes	—
449	C₂²	C₂²×C₃×D₂₀	1	2	yes	—
450	C₂²	C₃×#4149	1	4	yes	—
451	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
452	C₄	—	2	8	no	—
453	C₄	—	10	4	no	—
454	C₄	C₂²×C₃×D₂₀	1	4	yes	—
455	C₄	C₂²×C₃×D₂₀	1	4	yes	—
456	C₃	C₂×#65859	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	2	4	no	—
458	C₂	—	20	8	no	—
459	C₂	—	20	4	no	—
460	C₂	C₃×#65859	1	4	yes	direct product factor
461	C₂	C₂³×C₃×D₂₀	1	1	yes	characteristic
462	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×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₂×C₃×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#709	C₂	semidirect
2. C₂³×C₃×D₂₀	C₂	semidirect
3. C₂×C₃×C₅×#117	C₂	semidirect
4. C₃×#65859	C₂	direct (N × H)
5. C₂×C₃×#4041	C₂	semidirect
6. C₂×C₃×#4028	C₂	semidirect
7. C₂×C₃×#4021	C₂	semidirect
8. C₂×C₃×#4020	C₂	semidirect
9. C₂×#65859	C₃	direct (N × H)
14. C₂×C₃×#709	C₂²	semidirect
18. C₂²×C₃×D₂₀	C₂²	semidirect
19. C₂²×C₃×D₂₀	C₂²	semidirect
20. C₂²×C₃×D₂₀	C₂²	semidirect
21. C₂²×C₃×C₄×D₅	C₂²	semidirect
22. C₂²×C₃×Dic₁₀	C₂²	semidirect
23. C₃×C₅×#117	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
27. C₂×C₃×#685	C₂²	semidirect
28. C₃×#4041	C₂²	semidirect
29. C₃×#4028	C₂²	semidirect
30. C₃×#4021	C₂²	semidirect
31. C₃×#4020	C₂²	semidirect
33. C₂²×#709	C₂×C₃	semidirect
34. C₂³×D₂₀	C₂×C₃	semidirect
35. C₂×C₅×#117	C₂×C₃	semidirect
36. #65859	C₂×C₃	direct (N × H)
37. C₂×#4041	C₂×C₃	semidirect
38. C₂×#4028	C₂×C₃	semidirect
39. C₂×#4021	C₂×C₃	semidirect
40. C₂×#4020	C₂×C₃	semidirect
47. C₂²×C₃×C₄×C₅	D₄	semidirect
63. C₂×C₃×D₂₀	C₂³	semidirect
64. C₂×C₃×D₂₀	C₂³	semidirect
66. C₂×C₃×C₄×D₅	C₂³	semidirect
68. C₂×C₃×Dic₁₀	C₂³	semidirect
69. C₃×C₅×C₄⋊C₄	C₂³	semidirect
71. C₃×C₄²×C₅	C₂³	semidirect
72. C₃×#685	C₂³	semidirect
80. C₂×C₃×#117	D₅	semidirect
85. C₂×#709	C₂²×C₃	semidirect
89. C₂²×D₂₀	C₂²×C₃	semidirect
90. C₂²×D₂₀	C₂²×C₃	semidirect
91. C₂²×D₂₀	C₂²×C₃	semidirect
92. C₂²×C₄×D₅	C₂²×C₃	semidirect
93. C₂²×Dic₁₀	C₂²×C₃	semidirect
94. C₅×#117	C₂²×C₃	semidirect
95. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
97. C₂×C₄²×C₅	C₂²×C₃	semidirect
98. C₂×#685	C₂²×C₃	semidirect
99. #4041	C₂²×C₃	semidirect
100. #4028	C₂²×C₃	semidirect
101. #4021	C₂²×C₃	semidirect
102. #4020	C₂²×C₃	semidirect
120. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
150. C₃×#117	C₂×D₅	semidirect
151. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
154. C₂×C₃×C₄²	C₂×D₅	semidirect
161. C₂²×C₄×C₅	C₃×D₄	semidirect
177. C₂×D₂₀	C₂³×C₃	semidirect
178. C₂×D₂₀	C₂³×C₃	semidirect
180. C₂×C₄×D₅	C₂³×C₃	semidirect
182. C₂×Dic₁₀	C₂³×C₃	semidirect
183. C₅×C₄⋊C₄	C₂³×C₃	semidirect
185. C₄²×C₅	C₂³×C₃	semidirect
186. #685	C₂³×C₃	semidirect
194. C₂×#117	C₃×D₅	semidirect
235. C₂²×C₃×C₄	D₂₀	semidirect
240. C₃×C₄⋊C₄	C₂²×D₅	semidirect
243. C₃×C₄²	C₂²×D₅	semidirect
260. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
290. #117	C₂×C₃×D₅	semidirect
291. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
294. C₂×C₄²	C₂×C₃×D₅	semidirect
296. C₂×C₃×C₅	#535	semidirect
326. C₂×C₃×C₄	C₂×D₂₀	semidirect
370. C₂²×C₄	C₃×D₂₀	semidirect
375. C₄⋊C₄	C₂²×C₃×D₅	semidirect
378. C₄²	C₂²×C₃×D₅	semidirect
379. C₃×C₅	C₂×#535	semidirect
398. C₂×C₅	C₃×#535	semidirect
428. C₂×C₄	C₂×C₃×D₂₀	semidirect
435. C₂×C₃	#65859	direct (N × H)
438. C₅	C₂×C₃×#535	semidirect
456. C₃	C₂×#65859	direct (N × H)
460. C₂	C₃×#65859	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
C₂³×C₃×D₂₀	2
C₂×C₃×C₅×#117	2
C₃×#65859	2
C₂×C₃×#4041	2
C₂×C₃×#4028	2
C₂×C₃×#4021	2
C₂×C₃×#4020	2
C₂×#65859	3
C₂×C₃×#535	5

Subgroups — C2×C3×#65859 #14480381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65859 #14480381