Subgroups — C₂×C₃×#66045 #14495191

Order 1920.

2688 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×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66045	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4041	C₂	1	3	yes	maximal, complemented
4	C₂×C₃×#4040	C₂	1	3	yes	maximal, complemented
5	C₂×C₃×#4030	C₂	1	3	yes	maximal, complemented
6	C₂×C₃×#4028	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#4022	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66045	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	C₂²	1	3	yes	—
12	C₂²×C₃×D₂₀	C₂²	1	3	yes	—
13	C₂²×C₃×D₂₀	C₂²	1	3	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	3	yes	complemented
15	C₂²×C₃×C₄×D₅	C₂²	1	3	yes	complemented
16	C₃×C₅×#126	C₂²	1	8	yes	complemented
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	complemented
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#685	C₂²	1	3	yes	—
21	C₂×C₃×#685	C₂²	1	3	yes	—
22	C₂×C₃×#685	C₂²	1	3	yes	complemented
23	C₂×C₃×#683	C₂²	1	3	yes	complemented
24	C₃×#4041	C₂²	1	24	yes	complemented
25	C₃×#4040	C₂²	1	24	yes	complemented
26	C₃×#4030	C₂²	1	24	yes	complemented
27	C₃×#4028	C₂²	1	24	yes	complemented
28	C₃×#4022	C₂²	1	8	yes	complemented
29	C₃×#4020	C₂²	1	8	yes	complemented
30	C₂×C₃×#560	—	5	1	no	maximal, Hall
31	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
32	#66045	C₂×C₃	1	16	yes	direct product factor
33	C₂×#4041	C₂×C₃	1	3	yes	complemented
34	C₂×#4040	C₂×C₃	1	3	yes	complemented
35	C₂×#4030	C₂×C₃	1	3	yes	complemented
36	C₂×#4028	C₂×C₃	1	3	yes	complemented
37	C₂×#4022	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
40	C₂³×C₃×D₅	—	4	6	no	—
41	C₂³×C₃×D₅	C₂³	1	3	yes	—
42	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
43	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
44	C₂³×C₃×D₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
47	C₂×C₃×C₂²⋊D₅	—	4	6	no	—
48	C₂×C₃×C₂²⋊D₅	C₂³	1	12	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
50	C₂×C₃×D₂₀	—	4	6	no	—
51	C₂×C₃×D₂₀	—	4	6	no	—
52	C₂×C₃×D₂₀	—	4	6	no	—
53	C₂×C₃×D₂₀	C₂³	1	12	yes	—
54	C₂×C₃×D₂₀	C₂³	1	12	yes	—
55	C₂×C₃×D₂₀	C₂³	1	12	yes	complemented
56	C₂×C₃×C₄×D₅	—	4	6	no	—
57	C₂×C₃×C₄×D₅	C₂³	1	12	yes	complemented
58	C₃×C₅×C₄⋊C₄	C₂³	1	12	yes	complemented
59	C₃×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
60	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
61	C₃×#685	C₂³	1	12	yes	—
62	C₃×#685	C₂³	1	12	yes	—
63	C₃×#685	C₂³	1	12	yes	complemented
64	C₃×#683	C₂³	1	12	yes	complemented
65	C₃×#560	—	5	16	no	—
66	C₂×C₃×#127	—	5	1	no	—
67	C₂×C₃×#126	—	5	1	no	—
68	C₂×C₃×#126	D₅	1	1	yes	characteristic, complemented
69	C₂×C₃×#123	—	5	3	no	—
70	C₂×C₃×#121	—	5	3	no	—
71	C₂×C₃×#121	—	5	3	no	—
72	C₂×C₃×#120	—	5	3	no	—
73	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₂²⋊D₅	C₂²×C₃	1	3	yes	—
75	C₂²×D₂₀	C₂²×C₃	1	3	yes	—
76	C₂²×D₂₀	C₂²×C₃	1	3	yes	—
77	C₂²×D₂₀	C₂²×C₃	1	3	yes	complemented
78	C₂²×C₄×D₅	C₂²×C₃	1	3	yes	complemented
79	C₅×#126	C₂²×C₃	1	8	yes	complemented
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
82	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
83	C₂×#685	C₂²×C₃	1	3	yes	—
84	C₂×#685	C₂²×C₃	1	3	yes	—
85	C₂×#685	C₂²×C₃	1	3	yes	complemented
86	C₂×#683	C₂²×C₃	1	3	yes	complemented
87	#4041	C₂²×C₃	1	24	yes	complemented
88	#4040	C₂²×C₃	1	24	yes	complemented
89	#4030	C₂²×C₃	1	24	yes	complemented
90	#4028	C₂²×C₃	1	24	yes	complemented
91	#4022	C₂²×C₃	1	8	yes	complemented
92	#4020	C₂²×C₃	1	8	yes	complemented
93	C₂×#560	—	5	1	no	Sylow
94	C₂³×C₃×C₅	—	2	6	no	—
95	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	6	no	—
98	C₂²×C₃×D₅	—	2	6	no	—
99	C₂²×C₃×D₅	—	2	6	no	—
100	C₂²×C₃×D₅	—	2	6	no	—
101	C₂²×C₃×D₅	—	2	6	no	—
102	C₂²×C₃×D₅	—	4	12	no	—
103	C₂²×C₃×D₅	—	4	16	no	—
104	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
105	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
106	C₂²×C₃×D₅	C₂⁴	1	6	yes	—
107	C₂×C₃×C₄×C₅	—	2	6	no	—
108	C₂×C₃×C₄×C₅	—	2	6	no	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
111	C₃×C₂²⋊D₅	—	4	12	no	—
112	C₂×C₃×Dic₅	—	2	6	no	—
113	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
114	C₃×D₂₀	—	4	12	no	—
115	C₃×D₂₀	—	4	12	no	—
116	C₃×D₂₀	—	4	12	no	—
117	C₃×C₄×D₅	—	4	12	no	—
118	C₂⁵×C₃	—	5	1	no	—
119	C₂²×C₃×D₄	—	5	3	no	—
120	C₂²×C₃×D₄	—	5	3	no	—
121	C₂²×C₃×D₄	—	5	3	no	—
122	C₂²×C₃×D₄	—	5	3	no	—
123	C₂³×C₃×C₄	—	5	3	no	—
124	C₃×#127	—	5	8	no	—
125	C₃×#126	—	5	8	no	—
126	C₃×#126	C₂×D₅	1	8	yes	complemented
127	C₃×#123	—	5	24	no	—
128	C₃×#121	—	5	24	no	—
129	C₃×#121	—	5	24	no	—
130	C₃×#120	—	5	24	no	—
131	C₂×C₃×C₄⋊C₄	—	5	3	no	—
132	C₂×C₃×C₄⋊C₄	C₂×D₅	1	3	yes	complemented
133	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
134	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
135	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
136	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	3	yes	—
137	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂³×D₅	—	4	6	no	—
140	C₂³×D₅	C₂³×C₃	1	3	yes	—
141	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
142	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
143	C₂³×D₅	C₂³×C₃	1	4	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
145	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
146	C₂×C₂²⋊D₅	—	4	6	no	—
147	C₂×C₂²⋊D₅	C₂³×C₃	1	12	yes	—
148	C₂²×Dic₅	C₂³×C₃	1	3	yes	—
149	C₂×D₂₀	—	4	6	no	—
150	C₂×D₂₀	—	4	6	no	—
151	C₂×D₂₀	—	4	6	no	—
152	C₂×D₂₀	C₂³×C₃	1	12	yes	—
153	C₂×D₂₀	C₂³×C₃	1	12	yes	—
154	C₂×D₂₀	C₂³×C₃	1	12	yes	complemented
155	C₂×C₄×D₅	—	4	6	no	—
156	C₂×C₄×D₅	C₂³×C₃	1	12	yes	complemented
157	C₅×C₄⋊C₄	C₂³×C₃	1	12	yes	complemented
158	C₅×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
159	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
160	#685	C₂³×C₃	1	12	yes	—
161	#685	C₂³×C₃	1	12	yes	—
162	#685	C₂³×C₃	1	12	yes	complemented
163	#683	C₂³×C₃	1	12	yes	complemented
164	#560	—	5	16	no	—
165	C₂×#127	—	5	1	no	—
166	C₂×#126	—	5	1	no	—
167	C₂×#126	C₃×D₅	1	1	yes	characteristic, complemented
168	C₂×#123	—	5	3	no	—
169	C₂×#121	—	5	3	no	—
170	C₂×#121	—	5	3	no	—
171	C₂×#120	—	5	3	no	—
172	C₂²×C₃×C₅	—	2	6	no	—
173	C₂²×C₃×C₅	—	4	4	no	—
174	C₂²×C₃×C₅	H(5,𝔽₂)	1	6	yes	—
175	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
176	C₂×C₃×D₅	—	2	6	no	—
177	C₂×C₃×D₅	—	2	6	no	—
178	C₂×C₃×D₅	—	2	6	no	—
179	C₂×C₃×D₅	—	2	6	no	—
180	C₂×C₃×D₅	—	2	6	no	—
181	C₂×C₃×D₅	—	4	16	no	—
182	C₂×C₃×D₅	—	4	12	no	—
183	C₂×C₃×D₅	—	4	4	no	—
184	C₂×C₃×D₅	—	4	4	no	—
185	C₃×C₄×C₅	—	2	6	no	—
186	C₃×C₄×C₅	—	2	6	no	—
187	C₃×Dic₅	—	2	6	no	—
188	C₂⁴×C₃	—	5	1	no	—
189	C₂⁴×C₃	—	5	1	no	—
190	C₂⁴×C₃	—	5	3	no	—
191	C₂⁴×C₃	—	5	4	no	—
192	C₂⁴×C₃	—	20	6	no	—
193	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
194	C₂×C₃×D₄	—	5	12	no	—
195	C₂×C₃×D₄	—	5	12	no	—
196	C₂×C₃×D₄	—	5	12	no	—
197	C₂×C₃×D₄	—	5	12	no	—
198	C₂×C₃×D₄	—	20	6	no	—
199	C₂×C₃×D₄	—	20	6	no	—
200	C₂×C₃×D₄	—	20	6	no	—
201	C₂×C₃×D₄	—	20	6	no	—
202	C₂²×C₃×C₄	—	5	3	no	—
203	C₂²×C₃×C₄	—	5	12	no	—
204	C₂²×C₃×C₄	—	20	6	no	—
205	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
206	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
207	C₃×C₄⋊C₄	—	5	12	no	—
208	C₃×C₄⋊C₄	C₂²×D₅	1	12	yes	complemented
209	C₃×C₂²⋊C₄	—	5	12	no	—
210	C₃×C₂²⋊C₄	—	5	12	no	—
211	C₃×C₂²⋊C₄	—	5	12	no	—
212	C₃×C₂²⋊C₄	C₂²×D₅	1	12	yes	—
213	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
214	C₂³×C₅	—	2	6	no	—
215	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
216	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
217	C₂²×D₅	—	2	6	no	—
218	C₂²×D₅	—	2	6	no	—
219	C₂²×D₅	—	2	6	no	—
220	C₂²×D₅	—	2	6	no	—
221	C₂²×D₅	—	2	6	no	—
222	C₂²×D₅	—	4	12	no	—
223	C₂²×D₅	—	4	16	no	—
224	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
225	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
226	C₂²×D₅	C₂⁴×C₃	1	6	yes	—
227	C₂×C₄×C₅	—	2	6	no	—
228	C₂×C₄×C₅	—	2	6	no	—
229	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
230	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
231	C₂²⋊D₅	—	4	12	no	—
232	C₂×Dic₅	—	2	6	no	—
233	C₂×Dic₅	C₂⁴×C₃	1	6	yes	—
234	D₂₀	—	4	12	no	—
235	D₂₀	—	4	12	no	—
236	D₂₀	—	4	12	no	—
237	C₄×D₅	—	4	12	no	—
238	C₂⁵	—	5	1	no	—
239	C₂²×D₄	—	5	3	no	—
240	C₂²×D₄	—	5	3	no	—
241	C₂²×D₄	—	5	3	no	—
242	C₂²×D₄	—	5	3	no	—
243	C₂³×C₄	—	5	3	no	—
244	#127	—	5	8	no	—
245	#126	—	5	8	no	—
246	#126	C₂×C₃×D₅	1	8	yes	complemented
247	#123	—	5	24	no	—
248	#121	—	5	24	no	—
249	#121	—	5	24	no	—
250	#120	—	5	24	no	—
251	C₂×C₄⋊C₄	—	5	3	no	—
252	C₂×C₄⋊C₄	C₂×C₃×D₅	1	3	yes	complemented
253	C₂×C₂²⋊C₄	—	5	3	no	—
254	C₂×C₂²⋊C₄	—	5	3	no	—
255	C₂×C₂²⋊C₄	—	5	3	no	—
256	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	3	yes	—
257	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
258	C₂×C₃×C₅	—	4	2	no	—
259	C₂×C₃×C₅	#560	1	4	yes	complemented
260	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	3	yes	—
261	C₃×D₅	—	4	6	no	—
262	C₃×D₅	—	4	2	no	—
263	C₃×D₅	—	4	2	no	—
264	C₂³×C₃	—	2	6	no	—
265	C₂³×C₃	—	5	2	no	—
266	C₂³×C₃	—	5	2	no	—
267	C₂³×C₃	—	5	6	no	—
268	C₂³×C₃	—	10	6	no	—
269	C₂³×C₃	—	10	6	no	—
270	C₂³×C₃	—	10	6	no	—
271	C₂³×C₃	—	10	6	no	—
272	C₂³×C₃	—	10	6	no	—
273	C₂³×C₃	—	20	12	no	—
274	C₂³×C₃	—	20	16	no	—
275	C₂³×C₃	C₂³×D₅	1	2	yes	—
276	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
277	C₃×D₄	—	20	12	no	—
278	C₃×D₄	—	20	12	no	—
279	C₃×D₄	—	20	12	no	—
280	C₃×D₄	—	20	12	no	—
281	C₂×C₃×C₄	—	2	6	no	—
282	C₂×C₃×C₄	—	2	6	no	—
283	C₂×C₃×C₄	—	5	6	no	—
284	C₂×C₃×C₄	—	10	6	no	—
285	C₂×C₃×C₄	—	20	12	no	—
286	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
287	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
288	C₂²×C₅	—	2	6	no	—
289	C₂²×C₅	—	4	4	no	—
290	C₂²×C₅	C₃×H(5,𝔽₂)	1	6	yes	—
291	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
292	C₂×D₅	—	2	6	no	—
293	C₂×D₅	—	2	6	no	—
294	C₂×D₅	—	2	6	no	—
295	C₂×D₅	—	2	6	no	—
296	C₂×D₅	—	2	6	no	—
297	C₂×D₅	—	4	16	no	—
298	C₂×D₅	—	4	12	no	—
299	C₂×D₅	—	4	4	no	—
300	C₂×D₅	—	4	4	no	—
301	C₄×C₅	—	2	6	no	—
302	C₄×C₅	—	2	6	no	—
303	Dic₅	—	2	6	no	—
304	C₂⁴	—	5	1	no	—
305	C₂⁴	—	5	1	no	—
306	C₂⁴	—	5	3	no	—
307	C₂⁴	—	5	4	no	—
308	C₂⁴	—	20	6	no	—
309	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
310	C₂×D₄	—	5	12	no	—
311	C₂×D₄	—	5	12	no	—
312	C₂×D₄	—	5	12	no	—
313	C₂×D₄	—	5	12	no	—
314	C₂×D₄	—	20	6	no	—
315	C₂×D₄	—	20	6	no	—
316	C₂×D₄	—	20	6	no	—
317	C₂×D₄	—	20	6	no	—
318	C₂²×C₄	—	5	3	no	—
319	C₂²×C₄	—	5	12	no	—
320	C₂²×C₄	—	20	6	no	—
321	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
322	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
323	C₄⋊C₄	—	5	12	no	—
324	C₄⋊C₄	C₂²×C₃×D₅	1	12	yes	complemented
325	C₂²⋊C₄	—	5	12	no	—
326	C₂²⋊C₄	—	5	12	no	—
327	C₂²⋊C₄	—	5	12	no	—
328	C₂²⋊C₄	C₂²×C₃×D₅	1	12	yes	—
329	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
330	C₃×C₅	C₂×#560	1	1	yes	characteristic, complemented, Hall
331	C₂²×C₃	—	2	6	no	—
332	C₂²×C₃	—	4	4	no	—
333	C₂²×C₃	—	10	6	no	—
334	C₂²×C₃	—	10	6	no	—
335	C₂²×C₃	—	10	6	no	—
336	C₂²×C₃	—	10	6	no	—
337	C₂²×C₃	—	10	6	no	—
338	C₂²×C₃	—	20	16	no	—
339	C₂²×C₃	—	20	12	no	—
340	C₂²×C₃	—	20	4	no	—
341	C₂²×C₃	—	20	4	no	—
342	C₂²×C₃	#4149	1	6	yes	—
343	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
344	C₃×C₄	—	2	6	no	—
345	C₃×C₄	—	2	6	no	—
346	C₃×C₄	—	10	6	no	—
347	C₂×C₅	—	4	2	no	—
348	C₂×C₅	C₃×#560	1	4	yes	complemented
349	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	3	yes	—
350	D₅	—	4	2	no	—
351	D₅	—	4	2	no	—
352	D₅	—	4	6	no	—
353	C₂³	—	2	6	no	—
354	C₂³	—	5	2	no	—
355	C₂³	—	5	2	no	—
356	C₂³	—	5	6	no	—
357	C₂³	—	10	6	no	—
358	C₂³	—	10	6	no	—
359	C₂³	—	10	6	no	—
360	C₂³	—	10	6	no	—
361	C₂³	—	10	6	no	—
362	C₂³	—	20	12	no	—
363	C₂³	—	20	16	no	—
364	C₂³	C₂³×C₃×D₅	1	2	yes	—
365	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
366	D₄	—	20	12	no	—
367	D₄	—	20	12	no	—
368	D₄	—	20	12	no	—
369	D₄	—	20	12	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	5	6	no	—
373	C₂×C₄	—	10	6	no	—
374	C₂×C₄	—	20	12	no	—
375	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
376	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
377	C₂×C₃	—	4	2	no	—
378	C₂×C₃	—	20	2	no	—
379	C₂×C₃	—	20	2	no	—
380	C₂×C₃	—	20	6	no	—
381	C₂×C₃	#66045	1	4	yes	direct product factor
382	C₂×C₃	C₂×#4149	1	3	yes	—
383	C₅	C₂×C₃×#560	1	1	yes	characteristic, complemented, Sylow
384	C₂²	—	2	6	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	10	6	no	—
387	C₂²	—	10	6	no	—
388	C₂²	—	10	6	no	—
389	C₂²	—	10	6	no	—
390	C₂²	—	10	6	no	—
391	C₂²	—	20	16	no	—
392	C₂²	—	20	4	no	—
393	C₂²	—	20	4	no	—
394	C₂²	—	20	12	no	—
395	C₂²	C₃×#4149	1	6	yes	—
396	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
397	C₄	—	2	6	no	—
398	C₄	—	2	6	no	—
399	C₄	—	10	6	no	—
400	C₃	C₂×#66045	1	1	yes	characteristic, direct product factor, Sylow
401	C₂	—	4	2	no	—
402	C₂	—	20	2	no	—
403	C₂	—	20	2	no	—
404	C₂	—	20	6	no	—
405	C₂	C₃×#66045	1	4	yes	direct product factor
406	C₂	C₂×C₃×#4149	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#126	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#126	D₅
hypocenter	C₅	C₂×C₃×#560
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#126

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#126	C₂	semidirect
2. C₃×#66045	C₂	direct (N × H)
3. C₂×C₃×#4041	C₂	semidirect
4. C₂×C₃×#4040	C₂	semidirect
5. C₂×C₃×#4030	C₂	semidirect
6. C₂×C₃×#4028	C₂	semidirect
7. C₂×C₃×#4022	C₂	semidirect
8. C₂×C₃×#4020	C₂	semidirect
9. C₂×#66045	C₃	direct (N × H)
14. C₂²×C₃×D₂₀	C₂²	semidirect
15. C₂²×C₃×C₄×D₅	C₂²	semidirect
16. C₃×C₅×#126	C₂²	semidirect
17. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₂×C₃×C₄²×C₅	C₂²	semidirect
22. C₂×C₃×#685	C₂²	semidirect
23. C₂×C₃×#683	C₂²	semidirect
24. C₃×#4041	C₂²	semidirect
25. C₃×#4040	C₂²	semidirect
26. C₃×#4030	C₂²	semidirect
27. C₃×#4028	C₂²	semidirect
28. C₃×#4022	C₂²	semidirect
29. C₃×#4020	C₂²	semidirect
31. C₂×C₅×#126	C₂×C₃	semidirect
32. #66045	C₂×C₃	direct (N × H)
33. C₂×#4041	C₂×C₃	semidirect
34. C₂×#4040	C₂×C₃	semidirect
35. C₂×#4030	C₂×C₃	semidirect
36. C₂×#4028	C₂×C₃	semidirect
37. C₂×#4022	C₂×C₃	semidirect
38. C₂×#4020	C₂×C₃	semidirect
55. C₂×C₃×D₂₀	C₂³	semidirect
57. C₂×C₃×C₄×D₅	C₂³	semidirect
58. C₃×C₅×C₄⋊C₄	C₂³	semidirect
60. C₃×C₄²×C₅	C₂³	semidirect
63. C₃×#685	C₂³	semidirect
64. C₃×#683	C₂³	semidirect
68. C₂×C₃×#126	D₅	semidirect
77. C₂²×D₂₀	C₂²×C₃	semidirect
78. C₂²×C₄×D₅	C₂²×C₃	semidirect
79. C₅×#126	C₂²×C₃	semidirect
80. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
82. C₂×C₄²×C₅	C₂²×C₃	semidirect
85. C₂×#685	C₂²×C₃	semidirect
86. C₂×#683	C₂²×C₃	semidirect
87. #4041	C₂²×C₃	semidirect
88. #4040	C₂²×C₃	semidirect
89. #4030	C₂²×C₃	semidirect
90. #4028	C₂²×C₃	semidirect
91. #4022	C₂²×C₃	semidirect
92. #4020	C₂²×C₃	semidirect
126. C₃×#126	C₂×D₅	semidirect
132. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
137. C₂×C₃×C₄²	C₂×D₅	semidirect
154. C₂×D₂₀	C₂³×C₃	semidirect
156. C₂×C₄×D₅	C₂³×C₃	semidirect
157. C₅×C₄⋊C₄	C₂³×C₃	semidirect
159. C₄²×C₅	C₂³×C₃	semidirect
162. #685	C₂³×C₃	semidirect
163. #683	C₂³×C₃	semidirect
167. C₂×#126	C₃×D₅	semidirect
208. C₃×C₄⋊C₄	C₂²×D₅	semidirect
213. C₃×C₄²	C₂²×D₅	semidirect
246. #126	C₂×C₃×D₅	semidirect
252. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
257. C₂×C₄²	C₂×C₃×D₅	semidirect
259. C₂×C₃×C₅	#560	semidirect
324. C₄⋊C₄	C₂²×C₃×D₅	semidirect
329. C₄²	C₂²×C₃×D₅	semidirect
330. C₃×C₅	C₂×#560	semidirect
348. C₂×C₅	C₃×#560	semidirect
381. C₂×C₃	#66045	direct (N × H)
383. C₅	C₂×C₃×#560	semidirect
400. C₃	C₂×#66045	direct (N × H)
405. C₂	C₃×#66045	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×#126	2
C₃×#66045	2
C₂×C₃×#4041	2
C₂×C₃×#4040	2
C₂×C₃×#4030	2
C₂×C₃×#4028	2
C₂×C₃×#4022	2
C₂×C₃×#4020	2
C₂×#66045	3
C₂×C₃×#560	5

Subgroups — C2×C3×#66045 #14495191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66045 #14495191