Subgroups — C₂×C₃×#66139 #14480375

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	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4099	C₂	1	4	yes	maximal, complemented
4	C₃×#66139	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4086	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4084	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4082	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66139	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	—	2	8	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂²×C₃×C₂²⋊D₅	C₂²	1	8	yes	complemented
18	C₂×C₃×#709	—	2	8	no	—
19	C₂×C₃×#709	C₂²	1	8	yes	complemented
20	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
22	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
23	C₃×#4099	C₂²	1	32	yes	complemented
24	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Dic₅	C₂²	1	8	yes	complemented
26	C₃×#4086	C₂²	1	16	yes	complemented
27	C₃×#4084	C₂²	1	32	yes	complemented
28	C₃×#4082	C₂²	1	16	yes	complemented
29	C₃×#4072	C₂²	1	8	yes	complemented
30	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
32	C₂×C₃×#535	—	5	1	no	maximal, Hall
33	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×#709	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#4099	C₂×C₃	1	4	yes	complemented
36	#66139	C₂×C₃	1	16	yes	direct product factor
37	C₂×#4086	C₂×C₃	1	2	yes	complemented
38	C₂×#4084	C₂×C₃	1	4	yes	complemented
39	C₂×#4082	C₂×C₃	1	2	yes	complemented
40	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	—	2	8	no	—
42	C₂⁴×C₃×C₅	—	4	8	no	—
43	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
44	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
45	C₂⁴×C₃×C₅	C₂³	1	8	yes	—
46	C₂³×C₃×D₅	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	8	no	—
48	C₂×C₃×C₅×D₄	—	2	8	no	—
49	C₂×C₃×C₅×D₄	—	2	32	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
51	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
56	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
57	C₂×C₃×C₂²⋊D₅	—	4	16	no	—
58	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
59	C₂×C₃×C₂²⋊D₅	C₂³	1	32	yes	complemented
60	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
61	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
62	C₃×#709	—	2	32	no	—
63	C₂×C₃×D₂₀	—	2	4	no	—
64	C₂×C₃×D₂₀	C₂³	1	4	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×C₂²⋊Dic₅	C₂³	1	8	yes	—
70	C₃×C₂²⋊Dic₅	C₂³	1	32	yes	complemented
71	C₃×C₄⋊Dic₅	C₂³	1	8	yes	complemented
72	C₃×C₄×Dic₅	C₂³	1	8	yes	complemented
73	C₂²×C₃×#41	—	5	1	no	—
74	C₂³×C₃×D₄	D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
81	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
82	C₂²×C₅×D₄	—	2	8	no	—
83	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
84	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
85	C₂²×C₅×D₄	C₂²×C₃	1	8	yes	complemented
86	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
88	C₂²×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
89	C₂×#709	—	2	8	no	—
90	C₂×#709	C₂²×C₃	1	8	yes	complemented
91	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
93	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
94	#4099	C₂²×C₃	1	32	yes	complemented
95	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
96	C₂×C₂²⋊Dic₅	C₂²×C₃	1	8	yes	complemented
97	#4086	C₂²×C₃	1	16	yes	complemented
98	#4084	C₂²×C₃	1	32	yes	complemented
99	#4082	C₂²×C₃	1	16	yes	complemented
100	#4072	C₂²×C₃	1	8	yes	complemented
101	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
102	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
103	C₂×#535	—	5	1	no	Sylow
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	16	no	—
106	C₂³×C₃×C₅	—	2	8	no	—
107	C₂³×C₃×C₅	—	2	16	no	—
108	C₂³×C₃×C₅	—	4	16	no	—
109	C₂³×C₃×C₅	—	4	32	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
111	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
112	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₂²×C₃×D₅	—	2	4	no	—
115	C₂²×C₃×D₅	—	2	8	no	—
116	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
117	C₃×C₅×D₄	—	2	16	no	—
118	C₃×C₅×D₄	—	2	16	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
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	C₃×C₂²⋊D₅	—	4	32	no	—
126	C₂×C₃×Dic₅	—	2	4	no	—
127	C₂×C₃×Dic₅	—	2	8	no	—
128	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
129	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
130	C₃×D₂₀	—	2	8	no	—
131	C₃×C₄×D₅	—	2	16	no	—
132	C₃×Dic₁₀	—	2	8	no	—
133	C₂⁵×C₃	C₂×D₅	1	2	yes	—
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	—	2	8	no	—
138	C₂²×C₃×D₄	—	5	2	no	—
139	C₂²×C₃×D₄	—	5	8	no	—
140	C₂²×C₃×D₄	—	5	1	no	—
141	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
142	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
143	C₂²×C₃×D₄	C₂×D₅	1	8	yes	complemented
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	—	5	8	no	—
151	C₂×C₃×C₄⋊C₄	—	5	2	no	—
152	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
153	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
154	C₂×C₃×C₄²	—	5	2	no	—
155	C₂⁴×C₅	—	2	8	no	—
156	C₂⁴×C₅	—	4	8	no	—
157	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
158	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
159	C₂⁴×C₅	C₂³×C₃	1	8	yes	—
160	C₂³×D₅	C₂³×C₃	1	2	yes	—
161	C₂×C₅×D₄	—	2	8	no	—
162	C₂×C₅×D₄	—	2	8	no	—
163	C₂×C₅×D₄	—	2	32	no	—
164	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
165	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
166	C₂²×C₄×C₅	C₃×D₄	1	8	yes	complemented
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
170	C₂×C₂²⋊D₅	—	2	8	no	—
171	C₂×C₂²⋊D₅	—	4	16	no	—
172	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
173	C₂×C₂²⋊D₅	C₂³×C₃	1	32	yes	complemented
174	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
175	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
176	#709	—	2	32	no	—
177	C₂×D₂₀	—	2	4	no	—
178	C₂×D₂₀	C₂³×C₃	1	4	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	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
184	C₂²⋊Dic₅	C₂³×C₃	1	32	yes	complemented
185	C₄⋊Dic₅	C₂³×C₃	1	8	yes	complemented
186	C₄×Dic₅	C₂³×C₃	1	8	yes	complemented
187	C₂²×#41	—	5	1	no	—
188	C₂³×D₄	C₃×D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
195	C₂²×C₃×C₅	—	2	8	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	—	2	8	no	—
198	C₂²×C₃×C₅	—	2	16	no	—
199	C₂²×C₃×C₅	—	4	32	no	—
200	C₂²×C₃×C₅	—	4	16	no	—
201	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
202	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
203	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
204	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
205	C₂×C₃×D₅	—	2	4	no	—
206	C₂×C₃×D₅	—	2	8	no	—
207	C₂×C₃×D₅	—	4	8	no	—
208	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
209	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
210	C₃×Dic₅	—	2	4	no	—
211	C₃×Dic₅	—	2	8	no	—
212	C₂⁴×C₃	—	2	8	no	—
213	C₂⁴×C₃	—	4	8	no	—
214	C₂⁴×C₃	—	5	2	no	—
215	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
216	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
217	C₂⁴×C₃	C₂²×D₅	1	8	yes	—
218	C₃×#41	—	10	32	no	—
219	C₂×C₃×Q₈	—	5	4	no	—
220	C₂×C₃×Q₈	—	10	4	no	—
221	C₂×C₃×D₄	—	2	8	no	—
222	C₂×C₃×D₄	—	2	8	no	—
223	C₂×C₃×D₄	—	2	32	no	—
224	C₂×C₃×D₄	—	5	8	no	—
225	C₂×C₃×D₄	—	5	32	no	—
226	C₂×C₃×D₄	—	5	4	no	—
227	C₂×C₃×D₄	—	10	8	no	—
228	C₂×C₃×D₄	—	10	4	no	—
229	C₂×C₃×D₄	—	20	16	no	—
230	C₂×C₃×D₄	C₂²×D₅	1	8	yes	—
231	C₂×C₃×D₄	C₂²×D₅	1	8	yes	—
232	C₂²×C₃×C₄	—	5	4	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	5	8	no	—
235	C₂²×C₃×C₄	—	10	8	no	—
236	C₂²×C₃×C₄	C₂²⋊D₅	1	8	yes	complemented
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	—	5	8	no	—
241	C₃×C₂²⋊C₄	—	5	8	no	—
242	C₃×C₂²⋊C₄	—	5	32	no	—
243	C₃×C₄²	—	5	8	no	—
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	—	2	16	no	—
246	C₂³×C₅	—	2	8	no	—
247	C₂³×C₅	—	2	16	no	—
248	C₂³×C₅	—	4	16	no	—
249	C₂³×C₅	—	4	32	no	—
250	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
251	C₂³×C₅	C₂⁴×C₃	1	8	yes	—
252	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
253	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
254	C₂²×D₅	—	2	4	no	—
255	C₂²×D₅	—	2	8	no	—
256	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
257	C₅×D₄	—	2	16	no	—
258	C₅×D₄	—	2	16	no	—
259	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
260	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
261	C₂×C₄×C₅	C₂×C₃×D₄	1	16	yes	complemented
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	C₂²⋊D₅	—	4	32	no	—
266	C₂×Dic₅	—	2	4	no	—
267	C₂×Dic₅	—	2	8	no	—
268	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
269	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
270	D₂₀	—	2	8	no	—
271	C₄×D₅	—	2	16	no	—
272	Dic₁₀	—	2	8	no	—
273	C₂⁵	C₂×C₃×D₅	1	2	yes	—
274	C₂×#41	—	5	8	no	—
275	C₂×#41	—	10	8	no	—
276	C₂²×Q₈	—	5	1	no	—
277	C₂²×D₄	—	2	8	no	—
278	C₂²×D₄	—	5	2	no	—
279	C₂²×D₄	—	5	8	no	—
280	C₂²×D₄	—	5	1	no	—
281	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
282	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
283	C₂²×D₄	C₂×C₃×D₅	1	8	yes	complemented
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	—	5	8	no	—
291	C₂×C₄⋊C₄	—	5	2	no	—
292	C₂×C₂²⋊C₄	—	5	2	no	—
293	C₂×C₂²⋊C₄	—	5	8	no	—
294	C₂×C₄²	—	5	2	no	—
295	C₂×C₃×C₅	—	2	4	no	—
296	C₂×C₃×C₅	—	4	8	no	—
297	C₂×C₃×C₅	#535	1	4	yes	complemented
298	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
300	C₃×D₅	—	4	4	no	—
301	C₂³×C₃	—	2	4	no	—
302	C₂³×C₃	—	2	16	no	—
303	C₂³×C₃	—	2	16	no	—
304	C₂³×C₃	—	2	8	no	—
305	C₂³×C₃	—	4	16	no	—
306	C₂³×C₃	—	4	32	no	—
307	C₂³×C₃	—	5	4	no	—
308	C₂³×C₃	—	10	8	no	—
309	C₂³×C₃	—	10	4	no	—
310	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
311	C₂³×C₃	C₂³×D₅	1	8	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	—	2	16	no	—
316	C₃×D₄	—	2	16	no	—
317	C₃×D₄	—	10	16	no	—
318	C₃×D₄	—	10	8	no	—
319	C₃×D₄	—	20	32	no	—
320	C₂×C₃×C₄	—	5	8	no	—
321	C₂×C₃×C₄	—	5	4	no	—
322	C₂×C₃×C₄	—	10	8	no	—
323	C₂×C₃×C₄	—	10	4	no	—
324	C₂×C₃×C₄	—	10	16	no	—
325	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
326	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
327	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	16	yes	complemented
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	—	2	8	no	—
333	C₂²×C₅	—	2	16	no	—
334	C₂²×C₅	—	4	32	no	—
335	C₂²×C₅	—	4	16	no	—
336	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
337	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
338	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
339	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
340	C₂×D₅	—	2	4	no	—
341	C₂×D₅	—	2	8	no	—
342	C₂×D₅	—	4	8	no	—
343	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
344	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
345	Dic₅	—	2	4	no	—
346	Dic₅	—	2	8	no	—
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	4	8	no	—
349	C₂⁴	—	5	2	no	—
350	C₂⁴	C₂²×C₃×D₅	1	4	yes	—
351	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
352	C₂⁴	C₂²×C₃×D₅	1	8	yes	—
353	#41	—	10	32	no	—
354	C₂×Q₈	—	5	4	no	—
355	C₂×Q₈	—	10	4	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	32	no	—
359	C₂×D₄	—	5	8	no	—
360	C₂×D₄	—	5	32	no	—
361	C₂×D₄	—	5	4	no	—
362	C₂×D₄	—	10	8	no	—
363	C₂×D₄	—	10	4	no	—
364	C₂×D₄	—	20	16	no	—
365	C₂×D₄	C₂²×C₃×D₅	1	8	yes	—
366	C₂×D₄	C₂²×C₃×D₅	1	8	yes	—
367	C₂²×C₄	—	5	4	no	—
368	C₂²×C₄	—	5	2	no	—
369	C₂²×C₄	—	5	8	no	—
370	C₂²×C₄	—	10	8	no	—
371	C₂²×C₄	C₃×C₂²⋊D₅	1	8	yes	complemented
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	—	5	8	no	—
376	C₂²⋊C₄	—	5	8	no	—
377	C₂²⋊C₄	—	5	32	no	—
378	C₄²	—	5	8	no	—
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	—	2	16	no	—
383	C₂²×C₃	—	2	8	no	—
384	C₂²×C₃	—	4	32	no	—
385	C₂²×C₃	—	4	16	no	—
386	C₂²×C₃	—	10	8	no	—
387	C₂²×C₃	—	10	4	no	—
388	C₂²×C₃	—	20	8	no	—
389	C₂²×C₃	#4144	1	4	yes	—
390	C₂²×C₃	C₂²×C₂²⋊D₅	1	4	yes	—
391	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
392	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
393	C₃×C₄	—	10	8	no	—
394	C₃×C₄	—	10	4	no	—
395	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
396	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	4	8	no	—
399	C₂×C₅	C₃×#535	1	4	yes	complemented
400	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
401	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
402	D₅	—	4	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	16	no	—
405	C₂³	—	2	16	no	—
406	C₂³	—	2	8	no	—
407	C₂³	—	4	16	no	—
408	C₂³	—	4	32	no	—
409	C₂³	—	5	4	no	—
410	C₂³	—	10	8	no	—
411	C₂³	—	10	4	no	—
412	C₂³	C₂×C₃×C₂²⋊D₅	1	4	yes	—
413	C₂³	C₂³×C₃×D₅	1	8	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	—	2	16	no	—
418	D₄	—	2	16	no	—
419	D₄	—	10	16	no	—
420	D₄	—	10	8	no	—
421	D₄	—	20	32	no	—
422	C₂×C₄	—	5	8	no	—
423	C₂×C₄	—	5	4	no	—
424	C₂×C₄	—	10	8	no	—
425	C₂×C₄	—	10	4	no	—
426	C₂×C₄	—	10	16	no	—
427	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
428	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
429	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	16	yes	complemented
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	—	4	8	no	—
434	C₂×C₃	—	20	4	no	—
435	C₂×C₃	#66139	1	4	yes	direct product factor
436	C₂×C₃	C₂×#4144	1	2	yes	—
437	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
438	C₅	C₂×C₃×#535	1	1	yes	characteristic, complemented, Sylow
439	C₂²	—	2	8	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	16	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	4	32	no	—
444	C₂²	—	4	16	no	—
445	C₂²	—	10	8	no	—
446	C₂²	—	10	4	no	—
447	C₂²	—	20	8	no	—
448	C₂²	C₃×#4144	1	4	yes	—
449	C₂²	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
450	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
451	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
452	C₄	—	10	8	no	—
453	C₄	—	10	4	no	—
454	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
455	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	—
456	C₃	C₂×#66139	1	1	yes	characteristic, direct product factor, Sylow
457	C₂	—	2	4	no	—
458	C₂	—	4	8	no	—
459	C₂	—	20	4	no	—
460	C₂	C₃×#66139	1	4	yes	direct product factor
461	C₂	C₂×C₃×#4144	1	2	yes	—
462	C₂	C₂³×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂³×C₃×D₄	D₅
hypocenter	C₅	C₂×C₃×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂²×C₃×#709	C₂	semidirect
3. C₂×C₃×#4099	C₂	semidirect
4. C₃×#66139	C₂	direct (N × H)
5. C₂×C₃×#4086	C₂	semidirect
6. C₂×C₃×#4084	C₂	semidirect
7. C₂×C₃×#4082	C₂	semidirect
8. C₂×C₃×#4072	C₂	semidirect
9. C₂×#66139	C₃	direct (N × H)
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
19. C₂×C₃×#709	C₂²	semidirect
20. C₂²×C₃×D₂₀	C₂²	semidirect
21. C₂²×C₃×C₄×D₅	C₂²	semidirect
22. C₂²×C₃×Dic₁₀	C₂²	semidirect
23. C₃×#4099	C₂²	semidirect
25. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
26. C₃×#4086	C₂²	semidirect
27. C₃×#4084	C₂²	semidirect
28. C₃×#4082	C₂²	semidirect
29. C₃×#4072	C₂²	semidirect
30. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
31. C₂×C₃×C₄×Dic₅	C₂²	semidirect
33. C₂³×C₅×D₄	C₂×C₃	semidirect
34. C₂²×#709	C₂×C₃	semidirect
35. C₂×#4099	C₂×C₃	semidirect
36. #66139	C₂×C₃	direct (N × H)
37. C₂×#4086	C₂×C₃	semidirect
38. C₂×#4084	C₂×C₃	semidirect
39. C₂×#4082	C₂×C₃	semidirect
40. C₂×#4072	C₂×C₃	semidirect
52. C₂²×C₃×C₄×C₅	D₄	semidirect
59. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
64. C₂×C₃×D₂₀	C₂³	semidirect
66. C₂×C₃×C₄×D₅	C₂³	semidirect
68. C₂×C₃×Dic₁₀	C₂³	semidirect
70. C₃×C₂²⋊Dic₅	C₂³	semidirect
71. C₃×C₄⋊Dic₅	C₂³	semidirect
72. C₃×C₄×Dic₅	C₂³	semidirect
74. C₂³×C₃×D₄	D₅	semidirect
85. C₂²×C₅×D₄	C₂²×C₃	semidirect
88. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
90. C₂×#709	C₂²×C₃	semidirect
91. C₂²×D₂₀	C₂²×C₃	semidirect
92. C₂²×C₄×D₅	C₂²×C₃	semidirect
93. C₂²×Dic₁₀	C₂²×C₃	semidirect
94. #4099	C₂²×C₃	semidirect
96. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
97. #4086	C₂²×C₃	semidirect
98. #4084	C₂²×C₃	semidirect
99. #4082	C₂²×C₃	semidirect
100. #4072	C₂²×C₃	semidirect
101. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
102. C₂×C₄×Dic₅	C₂²×C₃	semidirect
121. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
143. C₂²×C₃×D₄	C₂×D₅	semidirect
166. C₂²×C₄×C₅	C₃×D₄	semidirect
173. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
178. C₂×D₂₀	C₂³×C₃	semidirect
180. C₂×C₄×D₅	C₂³×C₃	semidirect
182. C₂×Dic₁₀	C₂³×C₃	semidirect
184. C₂²⋊Dic₅	C₂³×C₃	semidirect
185. C₄⋊Dic₅	C₂³×C₃	semidirect
186. C₄×Dic₅	C₂³×C₃	semidirect
188. C₂³×D₄	C₃×D₅	semidirect
236. C₂²×C₃×C₄	C₂²⋊D₅	semidirect
261. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
283. C₂²×D₄	C₂×C₃×D₅	semidirect
297. C₂×C₃×C₅	#535	semidirect
327. C₂×C₃×C₄	C₂×C₂²⋊D₅	semidirect
371. C₂²×C₄	C₃×C₂²⋊D₅	semidirect
379. C₃×C₅	C₂×#535	semidirect
399. C₂×C₅	C₃×#535	semidirect
429. C₂×C₄	C₂×C₃×C₂²⋊D₅	semidirect
435. C₂×C₃	#66139	direct (N × H)
438. C₅	C₂×C₃×#535	semidirect
456. C₃	C₂×#66139	direct (N × H)
460. C₂	C₃×#66139	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂²×C₃×#709	2
C₂×C₃×#4099	2
C₃×#66139	2
C₂×C₃×#4086	2
C₂×C₃×#4084	2
C₂×C₃×#4082	2
C₂×C₃×#4072	2
C₂×#66139	3
C₂×C₃×#535	5

Subgroups — C2×C3×#66139 #14480375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66139 #14480375