Subgroups — C₂×C₃×#66017 #14495252

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4093	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4083	C₂	1	2	yes	maximal, complemented
4	C₃×#66017	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4031	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×#66017	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁴×C₃×D₅	C₂²	1	2	yes	complemented
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	—
13	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
15	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	complemented
16	C₃×C₅×#124	C₂²	1	8	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
20	C₃×#4093	C₂²	1	16	yes	complemented
21	C₃×#4083	C₂²	1	16	yes	complemented
22	C₂×C₃×#685	C₂²	1	4	yes	complemented
23	C₂×C₃×#685	C₂²	1	4	yes	complemented
24	C₂×C₃×#685	C₂²	1	4	yes	complemented
25	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
26	C₃×#4031	C₂²	1	32	yes	complemented
27	C₃×#4028	C₂²	1	32	yes	complemented
28	C₃×#4021	C₂²	1	16	yes	complemented
29	C₂×C₃×H(3,𝔽₄)	—	5	1	no	maximal, Hall
30	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#4093	C₂×C₃	1	2	yes	complemented
32	C₂×#4083	C₂×C₃	1	2	yes	complemented
33	#66017	C₂×C₃	1	16	yes	direct product factor
34	C₂×#4031	C₂×C₃	1	4	yes	complemented
35	C₂×#4028	C₂×C₃	1	4	yes	complemented
36	C₂×#4021	C₂×C₃	1	2	yes	complemented
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂³×C₃×D₅	—	4	4	no	—
39	C₂³×C₃×D₅	—	4	8	no	—
40	C₂³×C₃×D₅	C₂³	1	4	yes	—
41	C₂³×C₃×D₅	C₂³	1	8	yes	complemented
42	C₂×C₃×C₅×Q₈	—	4	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
44	C₂×C₃×C₅×D₄	—	4	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
50	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
52	C₂×C₃×D₂₀	—	4	4	no	—
53	C₂×C₃×D₂₀	—	4	4	no	—
54	C₂×C₃×D₂₀	C₂³	1	8	yes	—
55	C₂×C₃×D₂₀	C₂³	1	8	yes	—
56	C₂×C₃×Dic₁₀	—	4	4	no	—
57	C₂×C₃×Dic₁₀	C₂³	1	8	yes	complemented
58	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
59	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
60	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
61	C₃×#685	C₂³	1	16	yes	complemented
62	C₃×#685	C₂³	1	16	yes	complemented
63	C₃×#685	C₂³	1	16	yes	complemented
64	C₃×C₄×Dic₅	C₂³	1	8	yes	complemented
65	C₃×H(3,𝔽₄)	—	5	16	no	—
66	C₂×C₃×#124	—	5	2	no	—
67	C₂×C₃×#124	—	5	4	no	—
68	C₂×C₃×#124	—	5	2	no	—
69	C₂×C₃×#124	D₅	1	1	yes	characteristic, complemented
70	C₂×C₃×#120	—	5	2	no	—
71	C₂×C₃×#120	—	5	4	no	—
72	C₂⁴×D₅	C₂²×C₃	1	2	yes	complemented
73	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
76	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
77	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
78	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	complemented
79	C₅×#124	C₂²×C₃	1	8	yes	complemented
80	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
81	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
83	#4093	C₂²×C₃	1	16	yes	complemented
84	#4083	C₂²×C₃	1	16	yes	complemented
85	C₂×#685	C₂²×C₃	1	4	yes	complemented
86	C₂×#685	C₂²×C₃	1	4	yes	complemented
87	C₂×#685	C₂²×C₃	1	4	yes	complemented
88	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
89	#4031	C₂²×C₃	1	32	yes	complemented
90	#4028	C₂²×C₃	1	32	yes	complemented
91	#4021	C₂²×C₃	1	16	yes	complemented
92	C₂×H(3,𝔽₄)	—	5	1	no	Sylow
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	8	no	—
98	C₂²×C₃×D₅	—	2	8	no	—
99	C₂²×C₃×D₅	—	2	8	no	—
100	C₂²×C₃×D₅	—	4	8	no	—
101	C₂²×C₃×D₅	—	4	16	no	—
102	C₂²×C₃×D₅	—	4	32	no	—
103	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
104	C₃×C₅×Q₈	—	4	4	no	—
105	C₃×C₅×D₄	—	4	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
112	C₃×C₂²⋊D₅	—	4	16	no	—
113	C₂×C₃×Dic₅	—	2	8	no	—
114	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
115	C₃×D₂₀	—	4	8	no	—
116	C₃×D₂₀	—	4	8	no	—
117	C₃×Dic₁₀	—	4	8	no	—
118	C₂⁵×C₃	—	5	2	no	—
119	C₂²×C₃×Q₈	—	5	2	no	—
120	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
121	C₂²×C₃×D₄	—	5	4	no	—
122	C₂²×C₃×D₄	—	5	2	no	—
123	C₂²×C₃×D₄	—	5	2	no	—
124	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
125	C₃×#124	—	5	16	no	—
126	C₃×#124	—	5	32	no	—
127	C₃×#124	—	5	16	no	—
128	C₃×#124	C₂×D₅	1	8	yes	complemented
129	C₃×#120	—	5	16	no	—
130	C₃×#120	—	5	32	no	—
131	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
132	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
133	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
134	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
135	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	4	yes	complemented
136	C₂×C₃×C₄²	—	5	2	no	—
137	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
139	C₂³×D₅	—	4	4	no	—
140	C₂³×D₅	—	4	8	no	—
141	C₂³×D₅	C₂³×C₃	1	4	yes	—
142	C₂³×D₅	C₂³×C₃	1	8	yes	complemented
143	C₂×C₅×Q₈	—	4	2	no	—
144	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	complemented
145	C₂×C₅×D₄	—	4	2	no	—
146	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
147	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
150	C₂×C₂²⋊D₅	—	4	8	no	—
151	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
152	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
153	C₂×D₂₀	—	4	4	no	—
154	C₂×D₂₀	—	4	4	no	—
155	C₂×D₂₀	C₂³×C₃	1	8	yes	—
156	C₂×D₂₀	C₂³×C₃	1	8	yes	—
157	C₂×Dic₁₀	—	4	4	no	—
158	C₂×Dic₁₀	C₂³×C₃	1	8	yes	complemented
159	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	complemented
160	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
161	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
162	#685	C₂³×C₃	1	16	yes	complemented
163	#685	C₂³×C₃	1	16	yes	complemented
164	#685	C₂³×C₃	1	16	yes	complemented
165	C₄×Dic₅	C₂³×C₃	1	8	yes	complemented
166	H(3,𝔽₄)	—	5	16	no	—
167	C₂×#124	—	5	2	no	—
168	C₂×#124	—	5	4	no	—
169	C₂×#124	—	5	2	no	—
170	C₂×#124	C₃×D₅	1	1	yes	characteristic, complemented
171	C₂×#120	—	5	2	no	—
172	C₂×#120	—	5	4	no	—
173	C₂²×C₃×C₅	—	2	8	no	—
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	4	8	no	—
176	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
177	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
178	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
179	C₂×C₃×D₅	—	2	8	no	—
180	C₂×C₃×D₅	—	2	8	no	—
181	C₂×C₃×D₅	—	2	8	no	—
182	C₂×C₃×D₅	—	4	32	no	—
183	C₂×C₃×D₅	—	4	16	no	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	2	4	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₃×Dic₅	—	2	8	no	—
188	C₂⁴×C₃	—	5	4	no	—
189	C₂⁴×C₃	—	5	8	no	—
190	C₂⁴×C₃	—	20	4	no	—
191	C₂⁴×C₃	—	20	8	no	—
192	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
193	C₂×C₃×Q₈	—	4	2	no	—
194	C₂×C₃×Q₈	—	5	8	no	—
195	C₂×C₃×Q₈	—	20	4	no	—
196	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	complemented
197	C₂×C₃×D₄	—	4	2	no	—
198	C₂×C₃×D₄	—	5	16	no	—
199	C₂×C₃×D₄	—	5	8	no	—
200	C₂×C₃×D₄	—	5	8	no	—
201	C₂×C₃×D₄	—	20	4	no	—
202	C₂×C₃×D₄	—	20	4	no	—
203	C₂×C₃×D₄	—	20	8	no	—
204	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
205	C₂²×C₃×C₄	—	5	4	no	—
206	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
209	C₃×C₂²⋊C₄	—	5	8	no	—
210	C₃×C₂²⋊C₄	—	5	16	no	—
211	C₃×C₂²⋊C₄	—	5	16	no	—
212	C₃×C₂²⋊C₄	—	5	16	no	—
213	C₃×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
214	C₃×C₄²	—	5	8	no	—
215	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
216	C₂³×C₅	—	2	8	no	—
217	C₂³×C₅	—	2	4	no	—
218	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
219	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
220	C₂²×D₅	—	2	8	no	—
221	C₂²×D₅	—	2	8	no	—
222	C₂²×D₅	—	2	8	no	—
223	C₂²×D₅	—	4	8	no	—
224	C₂²×D₅	—	4	16	no	—
225	C₂²×D₅	—	4	32	no	—
226	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
227	C₅×Q₈	—	4	4	no	—
228	C₅×D₄	—	4	4	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	2	4	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
233	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
234	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
235	C₂²⋊D₅	—	4	16	no	—
236	C₂×Dic₅	—	2	8	no	—
237	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
238	D₂₀	—	4	8	no	—
239	D₂₀	—	4	8	no	—
240	Dic₁₀	—	4	8	no	—
241	C₂⁵	—	5	2	no	—
242	C₂²×Q₈	—	5	2	no	—
243	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
244	C₂²×D₄	—	5	4	no	—
245	C₂²×D₄	—	5	2	no	—
246	C₂²×D₄	—	5	2	no	—
247	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
248	#124	—	5	16	no	—
249	#124	—	5	32	no	—
250	#124	—	5	16	no	—
251	#124	C₂×C₃×D₅	1	8	yes	complemented
252	#120	—	5	16	no	—
253	#120	—	5	32	no	—
254	C₂×C₂²⋊C₄	—	5	2	no	—
255	C₂×C₂²⋊C₄	—	5	4	no	—
256	C₂×C₂²⋊C₄	—	5	4	no	—
257	C₂×C₂²⋊C₄	—	5	4	no	—
258	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
259	C₂×C₄²	—	5	2	no	—
260	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
261	C₂×C₃×C₅	—	4	4	no	—
262	C₂×C₃×C₅	H(3,𝔽₄)	1	4	yes	complemented
263	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
265	C₃×D₅	—	4	8	no	—
266	C₂³×C₃	—	2	4	no	—
267	C₂³×C₃	—	2	8	no	—
268	C₂³×C₃	—	5	8	no	—
269	C₂³×C₃	—	10	8	no	—
270	C₂³×C₃	—	10	8	no	—
271	C₂³×C₃	—	10	8	no	—
272	C₂³×C₃	—	20	8	no	—
273	C₂³×C₃	—	20	16	no	—
274	C₂³×C₃	—	20	32	no	—
275	C₂³×C₃	C₂³×D₅	1	4	yes	—
276	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
277	C₃×Q₈	—	4	4	no	—
278	C₃×Q₈	—	20	8	no	—
279	C₃×D₄	—	4	4	no	—
280	C₃×D₄	—	20	8	no	—
281	C₃×D₄	—	20	8	no	—
282	C₃×D₄	—	20	16	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	5	8	no	—
287	C₂×C₃×C₄	—	10	8	no	—
288	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
289	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
290	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
291	C₂²×C₅	—	2	8	no	—
292	C₂²×C₅	—	2	4	no	—
293	C₂²×C₅	—	4	8	no	—
294	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
296	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
297	C₂×D₅	—	2	8	no	—
298	C₂×D₅	—	2	8	no	—
299	C₂×D₅	—	2	8	no	—
300	C₂×D₅	—	4	32	no	—
301	C₂×D₅	—	4	16	no	—
302	C₄×C₅	—	2	4	no	—
303	C₄×C₅	—	2	4	no	—
304	C₄×C₅	—	2	2	no	—
305	Dic₅	—	2	8	no	—
306	C₂⁴	—	5	4	no	—
307	C₂⁴	—	5	8	no	—
308	C₂⁴	—	20	4	no	—
309	C₂⁴	—	20	8	no	—
310	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	5	8	no	—
313	C₂×Q₈	—	20	4	no	—
314	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	complemented
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	5	16	no	—
317	C₂×D₄	—	5	8	no	—
318	C₂×D₄	—	5	8	no	—
319	C₂×D₄	—	20	4	no	—
320	C₂×D₄	—	20	4	no	—
321	C₂×D₄	—	20	8	no	—
322	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
323	C₂²×C₄	—	5	4	no	—
324	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
327	C₂²⋊C₄	—	5	8	no	—
328	C₂²⋊C₄	—	5	16	no	—
329	C₂²⋊C₄	—	5	16	no	—
330	C₂²⋊C₄	—	5	16	no	—
331	C₂²⋊C₄	C₂²×C₃×D₅	1	16	yes	complemented
332	C₄²	—	5	8	no	—
333	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
334	C₃×C₅	C₂×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Hall
335	C₂²×C₃	—	2	4	no	—
336	C₂²×C₃	—	2	8	no	—
337	C₂²×C₃	—	4	8	no	—
338	C₂²×C₃	—	10	8	no	—
339	C₂²×C₃	—	10	8	no	—
340	C₂²×C₃	—	10	8	no	—
341	C₂²×C₃	—	20	32	no	—
342	C₂²×C₃	—	20	16	no	—
343	C₂²×C₃	#4144	1	2	yes	—
344	C₂²×C₃	#4149	1	4	yes	—
345	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	4	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	10	8	no	—
350	C₂×C₅	—	4	4	no	—
351	C₂×C₅	C₃×H(3,𝔽₄)	1	4	yes	complemented
352	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
354	D₅	—	4	8	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	5	8	no	—
358	C₂³	—	10	8	no	—
359	C₂³	—	10	8	no	—
360	C₂³	—	10	8	no	—
361	C₂³	—	20	8	no	—
362	C₂³	—	20	16	no	—
363	C₂³	—	20	32	no	—
364	C₂³	C₂³×C₃×D₅	1	4	yes	—
365	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
366	Q₈	—	4	4	no	—
367	Q₈	—	20	8	no	—
368	D₄	—	4	4	no	—
369	D₄	—	20	8	no	—
370	D₄	—	20	8	no	—
371	D₄	—	20	16	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	5	8	no	—
376	C₂×C₄	—	10	8	no	—
377	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
378	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
379	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
380	C₂×C₃	—	4	4	no	—
381	C₂×C₃	—	20	8	no	—
382	C₂×C₃	#66017	1	4	yes	direct product factor
383	C₂×C₃	C₂×#4144	1	1	yes	characteristic
384	C₂×C₃	C₂×#4149	1	2	yes	—
385	C₅	C₂×C₃×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	10	8	no	—
390	C₂²	—	10	8	no	—
391	C₂²	—	10	8	no	—
392	C₂²	—	20	32	no	—
393	C₂²	—	20	16	no	—
394	C₂²	C₃×#4144	1	2	yes	—
395	C₂²	C₃×#4149	1	4	yes	—
396	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	10	8	no	—
401	C₃	C₂×#66017	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	4	4	no	—
403	C₂	—	20	8	no	—
404	C₂	C₃×#66017	1	4	yes	direct product factor
405	C₂	C₂×C₃×#4144	1	1	yes	characteristic
406	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×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#124	D₅
hypocenter	C₅	C₂×C₃×H(3,𝔽₄)
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₃×#4093	C₂	semidirect
3. C₂×C₃×#4083	C₂	semidirect
4. C₃×#66017	C₂	direct (N × H)
5. C₂×C₃×#4031	C₂	semidirect
6. C₂×C₃×#4028	C₂	semidirect
7. C₂×C₃×#4021	C₂	semidirect
8. C₂×#66017	C₃	direct (N × H)
9. C₂⁴×C₃×D₅	C₂²	semidirect
10. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂²×C₃×Dic₁₀	C₂²	semidirect
16. C₃×C₅×#124	C₂²	semidirect
17. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₃×C₄²×C₅	C₂²	semidirect
19. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
20. C₃×#4093	C₂²	semidirect
21. C₃×#4083	C₂²	semidirect
22. C₂×C₃×#685	C₂²	semidirect
23. C₂×C₃×#685	C₂²	semidirect
24. C₂×C₃×#685	C₂²	semidirect
25. C₂×C₃×C₄×Dic₅	C₂²	semidirect
26. C₃×#4031	C₂²	semidirect
27. C₃×#4028	C₂²	semidirect
28. C₃×#4021	C₂²	semidirect
30. C₂×C₅×#124	C₂×C₃	semidirect
31. C₂×#4093	C₂×C₃	semidirect
32. C₂×#4083	C₂×C₃	semidirect
33. #66017	C₂×C₃	direct (N × H)
34. C₂×#4031	C₂×C₃	semidirect
35. C₂×#4028	C₂×C₃	semidirect
36. C₂×#4021	C₂×C₃	semidirect
41. C₂³×C₃×D₅	C₂³	semidirect
43. C₂×C₃×C₅×Q₈	C₂³	semidirect
57. C₂×C₃×Dic₁₀	C₂³	semidirect
58. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
59. C₃×C₄²×C₅	C₂³	semidirect
60. C₃×C₂²⋊Dic₅	C₂³	semidirect
61. C₃×#685	C₂³	semidirect
62. C₃×#685	C₂³	semidirect
63. C₃×#685	C₂³	semidirect
64. C₃×C₄×Dic₅	C₂³	semidirect
69. C₂×C₃×#124	D₅	semidirect
72. C₂⁴×D₅	C₂²×C₃	semidirect
73. C₂²×C₅×Q₈	C₂²×C₃	semidirect
78. C₂²×Dic₁₀	C₂²×C₃	semidirect
79. C₅×#124	C₂²×C₃	semidirect
80. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
81. C₂×C₄²×C₅	C₂²×C₃	semidirect
82. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
83. #4093	C₂²×C₃	semidirect
84. #4083	C₂²×C₃	semidirect
85. C₂×#685	C₂²×C₃	semidirect
86. C₂×#685	C₂²×C₃	semidirect
87. C₂×#685	C₂²×C₃	semidirect
88. C₂×C₄×Dic₅	C₂²×C₃	semidirect
89. #4031	C₂²×C₃	semidirect
90. #4028	C₂²×C₃	semidirect
91. #4021	C₂²×C₃	semidirect
120. C₂²×C₃×Q₈	C₂×D₅	semidirect
128. C₃×#124	C₂×D₅	semidirect
135. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
137. C₂×C₃×C₄²	C₂×D₅	semidirect
142. C₂³×D₅	C₂³×C₃	semidirect
144. C₂×C₅×Q₈	C₂³×C₃	semidirect
158. C₂×Dic₁₀	C₂³×C₃	semidirect
159. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
160. C₄²×C₅	C₂³×C₃	semidirect
161. C₂²⋊Dic₅	C₂³×C₃	semidirect
162. #685	C₂³×C₃	semidirect
163. #685	C₂³×C₃	semidirect
164. #685	C₂³×C₃	semidirect
165. C₄×Dic₅	C₂³×C₃	semidirect
170. C₂×#124	C₃×D₅	semidirect
196. C₂×C₃×Q₈	C₂²×D₅	semidirect
213. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
215. C₃×C₄²	C₂²×D₅	semidirect
243. C₂²×Q₈	C₂×C₃×D₅	semidirect
251. #124	C₂×C₃×D₅	semidirect
258. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
260. C₂×C₄²	C₂×C₃×D₅	semidirect
262. C₂×C₃×C₅	H(3,𝔽₄)	semidirect
314. C₂×Q₈	C₂²×C₃×D₅	semidirect
331. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
333. C₄²	C₂²×C₃×D₅	semidirect
334. C₃×C₅	C₂×H(3,𝔽₄)	semidirect
351. C₂×C₅	C₃×H(3,𝔽₄)	semidirect
382. C₂×C₃	#66017	direct (N × H)
385. C₅	C₂×C₃×H(3,𝔽₄)	semidirect
401. C₃	C₂×#66017	direct (N × H)
404. C₂	C₃×#66017	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×#124	2
C₂×C₃×#4093	2
C₂×C₃×#4083	2
C₃×#66017	2
C₂×C₃×#4031	2
C₂×C₃×#4028	2
C₂×C₃×#4021	2
C₂×#66017	3
C₂×C₃×H(3,𝔽₄)	5

Subgroups — C2×C3×#66017 #14495252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66017 #14495252