Subgroups — C₂×C₃×#66168 #14482970

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#713	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66168	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×Q₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4086	C₂	1	3	yes	maximal, complemented
6	C₂×C₃×#4084	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#4076	C₂	1	3	yes	maximal, complemented
8	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	3	yes	maximal, complemented
9	C₂×#66168	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	—	2	8	no	—
11	C₂×C₃×C₅×#41	C₂²	1	8	yes	complemented
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₄	C₂²	1	3	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	3	yes	—
15	C₂²×C₃×C₂²⋊D₅	C₂²	1	3	yes	—
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	6	yes	—
17	C₂×C₃×#713	—	2	8	no	—
18	C₂×C₃×#713	C₂²	1	8	yes	complemented
19	C₂²×C₃×D₂₀	C₂²	1	3	yes	—
20	C₂²×C₃×C₄×D₅	C₂²	1	3	yes	—
21	C₂×C₃×C₂²⋊Dic₅	C₂²	1	3	yes	—
22	C₃×Q₈×Dic₅	C₂²	1	8	yes	complemented
23	C₃×#4086	C₂²	1	24	yes	complemented
24	C₃×#4084	C₂²	1	24	yes	complemented
25	C₃×#4076	C₂²	1	24	yes	complemented
26	C₃×C₄×C₂²⋊D₅	C₂²	1	24	yes	complemented
27	C₂×C₃×#685	C₂²	1	3	yes	—
28	C₂×C₃×C₄⋊Dic₅	C₂²	1	3	yes	—
29	C₂×C₃×#683	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	—
31	C₂×C₃×#550	—	5	1	no	maximal, Hall
32	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂²×#713	C₂×C₃	1	1	yes	characteristic, complemented
34	#66168	C₂×C₃	1	16	yes	direct product factor
35	C₂×Q₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#4086	C₂×C₃	1	3	yes	complemented
37	C₂×#4084	C₂×C₃	1	3	yes	complemented
38	C₂×#4076	C₂×C₃	1	3	yes	complemented
39	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	3	yes	complemented
40	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
41	C₂³×C₃×D₅	C₂³	1	3	yes	—
42	C₃×C₅×#41	—	2	32	no	—
43	C₂×C₃×C₅×Q₈	D₄	1	8	yes	complemented
44	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
45	C₂×C₃×C₅×D₄	—	2	12	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	12	yes	—
47	C₂²×C₃×C₄×C₅	—	2	12	no	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	12	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
51	C₂×C₃×C₂²⋊D₅	—	2	12	no	—
52	C₂×C₃×C₂²⋊D₅	—	4	12	no	—
53	C₂×C₃×C₂²⋊D₅	C₂³	1	12	yes	—
54	C₂×C₃×C₂²⋊D₅	C₂³	1	24	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₃×#713	—	2	32	no	—
59	C₂×C₃×D₂₀	—	2	12	no	—
60	C₂×C₃×D₂₀	C₂³	1	12	yes	—
61	C₂×C₃×C₄×D₅	—	2	12	no	—
62	C₂×C₃×C₄×D₅	C₂³	1	12	yes	—
63	C₃×C₂²⋊Dic₅	C₂³	1	12	yes	—
64	C₃×#685	C₂³	1	12	yes	—
65	C₃×C₄⋊Dic₅	C₂³	1	12	yes	—
66	C₃×#683	C₂³	1	4	yes	—
67	C₃×C₄×Dic₅	C₂³	1	12	yes	—
68	C₂²×C₃×#41	—	5	1	no	—
69	C₂²×C₃×#41	D₅	1	1	yes	characteristic, complemented
70	C₃×#550	—	5	16	no	—
71	C₂×C₃×#127	—	5	3	no	—
72	C₂×C₃×#121	—	5	3	no	—
73	C₂×C₃×#121	—	5	3	no	—
74	C₂×C₃×C₄×Q₈	—	5	1	no	—
75	C₂×C₃×C₄×D₄	—	5	3	no	—
76	C₂×C₅×#41	—	2	8	no	—
77	C₂×C₅×#41	C₂²×C₃	1	8	yes	complemented
78	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	C₂²×C₃	1	3	yes	—
80	C₂³×C₄×C₅	C₂²×C₃	1	3	yes	—
81	C₂²×C₂²⋊D₅	C₂²×C₃	1	3	yes	—
82	C₂²×C₂²⋊D₅	C₂²×C₃	1	6	yes	—
83	C₂×#713	—	2	8	no	—
84	C₂×#713	C₂²×C₃	1	8	yes	complemented
85	C₂²×D₂₀	C₂²×C₃	1	3	yes	—
86	C₂²×C₄×D₅	C₂²×C₃	1	3	yes	—
87	C₂×C₂²⋊Dic₅	C₂²×C₃	1	3	yes	—
88	Q₈×Dic₅	C₂²×C₃	1	8	yes	complemented
89	#4086	C₂²×C₃	1	24	yes	complemented
90	#4084	C₂²×C₃	1	24	yes	complemented
91	#4076	C₂²×C₃	1	24	yes	complemented
92	C₄×C₂²⋊D₅	C₂²×C₃	1	24	yes	complemented
93	C₂×#685	C₂²×C₃	1	3	yes	—
94	C₂×C₄⋊Dic₅	C₂²×C₃	1	3	yes	—
95	C₂×#683	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₄×Dic₅	C₂²×C₃	1	3	yes	—
97	C₂×#550	—	5	1	no	Sylow
98	C₂³×C₃×C₅	—	2	6	no	—
99	C₂³×C₃×C₅	—	2	6	no	—
100	C₂³×C₃×C₅	—	2	6	no	—
101	C₂³×C₃×C₅	C₂⁴	1	6	yes	—
102	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
103	C₂²×C₃×D₅	—	2	6	no	—
104	C₂²×C₃×D₅	—	2	6	no	—
105	C₂²×C₃×D₅	—	2	6	no	—
106	C₂²×C₃×D₅	C₂⁴	1	6	yes	—
107	C₃×C₅×Q₈	C₂×D₄	1	16	yes	complemented
108	C₃×C₅×D₄	—	2	24	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	24	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	12	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
114	C₃×C₂²⋊D₅	—	2	24	no	—
115	C₃×C₂²⋊D₅	—	4	24	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	2	6	no	—
118	C₂×C₃×Dic₅	#41	1	4	yes	complemented
119	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
120	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
121	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
122	C₃×D₂₀	—	2	24	no	—
123	C₃×C₄×D₅	—	2	24	no	—
124	C₂×C₃×#41	—	2	8	no	—
125	C₂×C₃×#41	—	5	8	no	—
126	C₂×C₃×#41	—	10	8	no	—
127	C₂×C₃×#41	C₂×D₅	1	8	yes	complemented
128	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
129	C₂²×C₃×D₄	—	5	3	no	—
130	C₂²×C₃×D₄	—	5	6	no	—
131	C₂²×C₃×D₄	—	5	3	no	—
132	C₂²×C₃×D₄	C₂×D₅	1	3	yes	—
133	C₂³×C₃×C₄	—	5	3	no	—
134	C₂³×C₃×C₄	C₂×D₅	1	3	yes	—
135	C₃×#127	—	5	24	no	—
136	C₃×#121	—	5	24	no	—
137	C₃×#121	—	5	24	no	—
138	C₃×C₄×Q₈	—	5	8	no	—
139	C₃×C₄×D₄	—	5	24	no	—
140	C₂×C₃×C₄⋊C₄	—	5	1	no	—
141	C₂×C₃×C₄⋊C₄	—	5	3	no	—
142	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
143	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
144	C₂×C₃×C₄²	—	5	3	no	—
145	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
146	C₂³×D₅	C₂³×C₃	1	3	yes	—
147	C₅×#41	—	2	32	no	—
148	C₂×C₅×Q₈	C₃×D₄	1	8	yes	complemented
149	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
150	C₂×C₅×D₄	—	2	12	no	—
151	C₂×C₅×D₄	C₂³×C₃	1	12	yes	—
152	C₂²×C₄×C₅	—	2	12	no	—
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂³×C₃	1	12	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
156	C₂×C₂²⋊D₅	—	2	12	no	—
157	C₂×C₂²⋊D₅	—	4	12	no	—
158	C₂×C₂²⋊D₅	C₂³×C₃	1	12	yes	—
159	C₂×C₂²⋊D₅	C₂³×C₃	1	24	yes	—
160	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
161	C₂²×Dic₅	C₂³×C₃	1	3	yes	—
162	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
163	#713	—	2	32	no	—
164	C₂×D₂₀	—	2	12	no	—
165	C₂×D₂₀	C₂³×C₃	1	12	yes	—
166	C₂×C₄×D₅	—	2	12	no	—
167	C₂×C₄×D₅	C₂³×C₃	1	12	yes	—
168	C₂²⋊Dic₅	C₂³×C₃	1	12	yes	—
169	#685	C₂³×C₃	1	12	yes	—
170	C₄⋊Dic₅	C₂³×C₃	1	12	yes	—
171	#683	C₂³×C₃	1	4	yes	—
172	C₄×Dic₅	C₂³×C₃	1	12	yes	—
173	C₂²×#41	—	5	1	no	—
174	C₂²×#41	C₃×D₅	1	1	yes	characteristic, complemented
175	#550	—	5	16	no	—
176	C₂×#127	—	5	3	no	—
177	C₂×#121	—	5	3	no	—
178	C₂×#121	—	5	3	no	—
179	C₂×C₄×Q₈	—	5	1	no	—
180	C₂×C₄×D₄	—	5	3	no	—
181	C₂²×C₃×C₅	—	2	6	no	—
182	C₂²×C₃×C₅	—	2	6	no	—
183	C₂²×C₃×C₅	—	2	6	no	—
184	C₂²×C₃×C₅	—	4	12	no	—
185	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
186	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
187	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
188	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
189	C₂×C₃×D₅	—	2	6	no	—
190	C₂×C₃×D₅	—	2	6	no	—
191	C₂×C₃×D₅	—	2	6	no	—
192	C₂×C₃×D₅	—	4	12	no	—
193	C₃×C₄×C₅	—	2	2	no	—
194	C₃×C₄×C₅	C₂²×D₄	1	12	yes	—
195	C₃×Dic₅	—	2	2	no	—
196	C₃×Dic₅	—	2	6	no	—
197	C₃×Dic₅	C₂×#41	1	4	yes	complemented
198	C₂⁴×C₃	—	5	3	no	—
199	C₂⁴×C₃	C₂²×D₅	1	3	yes	—
200	C₃×#41	—	2	32	no	—
201	C₃×#41	—	10	32	no	—
202	C₂×C₃×Q₈	C₂²⋊D₅	1	8	yes	complemented
203	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
204	C₂×C₃×D₄	—	2	12	no	—
205	C₂×C₃×D₄	—	5	12	no	—
206	C₂×C₃×D₄	—	5	24	no	—
207	C₂×C₃×D₄	—	5	12	no	—
208	C₂×C₃×D₄	—	10	12	no	—
209	C₂×C₃×D₄	—	10	12	no	—
210	C₂×C₃×D₄	—	20	12	no	—
211	C₂×C₃×D₄	C₂²×D₅	1	12	yes	—
212	C₂²×C₃×C₄	—	2	12	no	—
213	C₂²×C₃×C₄	—	5	1	no	—
214	C₂²×C₃×C₄	—	5	3	no	—
215	C₂²×C₃×C₄	—	5	1	no	—
216	C₂²×C₃×C₄	—	5	12	no	—
217	C₂²×C₃×C₄	—	10	12	no	—
218	C₂²×C₃×C₄	C₂²×D₅	1	12	yes	—
219	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
221	C₃×C₄⋊C₄	—	5	4	no	—
222	C₃×C₄⋊C₄	—	5	12	no	—
223	C₃×C₂²⋊C₄	—	5	12	no	—
224	C₃×C₂²⋊C₄	—	5	12	no	—
225	C₃×C₄²	—	5	12	no	—
226	C₂³×C₅	—	2	6	no	—
227	C₂³×C₅	—	2	6	no	—
228	C₂³×C₅	—	2	6	no	—
229	C₂³×C₅	C₂⁴×C₃	1	6	yes	—
230	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
231	C₂²×D₅	—	2	6	no	—
232	C₂²×D₅	—	2	6	no	—
233	C₂²×D₅	—	2	6	no	—
234	C₂²×D₅	C₂⁴×C₃	1	6	yes	—
235	C₅×Q₈	C₂×C₃×D₄	1	16	yes	complemented
236	C₅×D₄	—	2	24	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	24	no	—
239	C₂×C₄×C₅	C₂×C₃×D₄	1	12	yes	—
240	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
241	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
242	C₂²⋊D₅	—	2	24	no	—
243	C₂²⋊D₅	—	4	24	no	—
244	C₂×Dic₅	—	2	2	no	—
245	C₂×Dic₅	—	2	6	no	—
246	C₂×Dic₅	C₃×#41	1	4	yes	complemented
247	C₂×Dic₅	C₂⁴×C₃	1	6	yes	—
248	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
249	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
250	D₂₀	—	2	24	no	—
251	C₄×D₅	—	2	24	no	—
252	C₂×#41	—	2	8	no	—
253	C₂×#41	—	5	8	no	—
254	C₂×#41	—	10	8	no	—
255	C₂×#41	C₂×C₃×D₅	1	8	yes	complemented
256	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
257	C₂²×D₄	—	5	3	no	—
258	C₂²×D₄	—	5	6	no	—
259	C₂²×D₄	—	5	3	no	—
260	C₂²×D₄	C₂×C₃×D₅	1	3	yes	—
261	C₂³×C₄	—	5	3	no	—
262	C₂³×C₄	C₂×C₃×D₅	1	3	yes	—
263	#127	—	5	24	no	—
264	#121	—	5	24	no	—
265	#121	—	5	24	no	—
266	C₄×Q₈	—	5	8	no	—
267	C₄×D₄	—	5	24	no	—
268	C₂×C₄⋊C₄	—	5	1	no	—
269	C₂×C₄⋊C₄	—	5	3	no	—
270	C₂×C₂²⋊C₄	—	5	3	no	—
271	C₂×C₂²⋊C₄	—	5	3	no	—
272	C₂×C₄²	—	5	3	no	—
273	C₂×C₃×C₅	—	4	6	no	—
274	C₂×C₃×C₅	#550	1	4	yes	complemented
275	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
278	C₃×D₅	—	4	6	no	—
279	C₂³×C₃	—	2	6	no	—
280	C₂³×C₃	—	2	6	no	—
281	C₂³×C₃	—	2	6	no	—
282	C₂³×C₃	—	5	6	no	—
283	C₂³×C₃	—	10	6	no	—
284	C₂³×C₃	—	10	6	no	—
285	C₂³×C₃	—	10	6	no	—
286	C₂³×C₃	C₂³×D₅	1	6	yes	—
287	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
288	C₃×Q₈	C₂×C₂²⋊D₅	1	16	yes	complemented
289	C₃×D₄	—	2	24	no	—
290	C₃×D₄	—	10	24	no	—
291	C₃×D₄	—	10	24	no	—
292	C₃×D₄	—	20	24	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	24	no	—
295	C₂×C₃×C₄	—	5	4	no	—
296	C₂×C₃×C₄	—	5	2	no	—
297	C₂×C₃×C₄	—	5	6	no	—
298	C₂×C₃×C₄	—	5	2	no	—
299	C₂×C₃×C₄	—	10	6	no	—
300	C₂×C₃×C₄	—	10	2	no	—
301	C₂×C₃×C₄	—	10	24	no	—
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	12	yes	—
303	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
304	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
305	C₂²×C₅	—	2	6	no	—
306	C₂²×C₅	—	2	6	no	—
307	C₂²×C₅	—	2	6	no	—
308	C₂²×C₅	—	4	12	no	—
309	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
310	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
311	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
313	C₂×D₅	—	2	6	no	—
314	C₂×D₅	—	2	6	no	—
315	C₂×D₅	—	2	6	no	—
316	C₂×D₅	—	4	12	no	—
317	C₄×C₅	—	2	2	no	—
318	C₄×C₅	C₂²×C₃×D₄	1	12	yes	—
319	Dic₅	—	2	2	no	—
320	Dic₅	—	2	6	no	—
321	Dic₅	C₂×C₃×#41	1	4	yes	complemented
322	C₂⁴	—	5	3	no	—
323	C₂⁴	C₂²×C₃×D₅	1	3	yes	—
324	#41	—	2	32	no	—
325	#41	—	10	32	no	—
326	C₂×Q₈	C₃×C₂²⋊D₅	1	8	yes	complemented
327	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
328	C₂×D₄	—	2	12	no	—
329	C₂×D₄	—	5	12	no	—
330	C₂×D₄	—	5	24	no	—
331	C₂×D₄	—	5	12	no	—
332	C₂×D₄	—	10	12	no	—
333	C₂×D₄	—	10	12	no	—
334	C₂×D₄	—	20	12	no	—
335	C₂×D₄	C₂²×C₃×D₅	1	12	yes	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	3	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	—	5	12	no	—
341	C₂²×C₄	—	10	12	no	—
342	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₃×D₅	1	12	yes	—
344	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
345	C₄⋊C₄	—	5	4	no	—
346	C₄⋊C₄	—	5	12	no	—
347	C₂²⋊C₄	—	5	12	no	—
348	C₂²⋊C₄	—	5	12	no	—
349	C₄²	—	5	12	no	—
350	C₃×C₅	C₂×#550	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	—	2	6	no	—
352	C₂²×C₃	—	2	6	no	—
353	C₂²×C₃	—	2	6	no	—
354	C₂²×C₃	—	4	12	no	—
355	C₂²×C₃	—	10	6	no	—
356	C₂²×C₃	—	10	6	no	—
357	C₂²×C₃	—	10	6	no	—
358	C₂²×C₃	—	20	12	no	—
359	C₂²×C₃	D₅×#41	1	2	yes	—
360	C₂²×C₃	#4149	1	2	yes	—
361	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
362	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	5	4	no	—
365	C₃×C₄	—	10	6	no	—
366	C₃×C₄	—	10	2	no	—
367	C₃×C₄	C₂²×C₂²⋊D₅	1	12	yes	—
368	C₂×C₅	—	4	6	no	—
369	C₂×C₅	C₃×#550	1	4	yes	complemented
370	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
371	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
372	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
373	D₅	—	4	6	no	—
374	C₂³	—	2	6	no	—
375	C₂³	—	2	6	no	—
376	C₂³	—	2	6	no	—
377	C₂³	—	5	6	no	—
378	C₂³	—	10	6	no	—
379	C₂³	—	10	6	no	—
380	C₂³	—	10	6	no	—
381	C₂³	C₂³×C₃×D₅	1	6	yes	—
382	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
383	Q₈	C₂×C₃×C₂²⋊D₅	1	16	yes	complemented
384	D₄	—	2	24	no	—
385	D₄	—	10	24	no	—
386	D₄	—	10	24	no	—
387	D₄	—	20	24	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	24	no	—
390	C₂×C₄	—	5	4	no	—
391	C₂×C₄	—	5	2	no	—
392	C₂×C₄	—	5	6	no	—
393	C₂×C₄	—	5	2	no	—
394	C₂×C₄	—	10	6	no	—
395	C₂×C₄	—	10	2	no	—
396	C₂×C₄	—	10	24	no	—
397	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	12	yes	—
398	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
399	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
400	C₂×C₃	—	4	6	no	—
401	C₂×C₃	—	20	6	no	—
402	C₂×C₃	#66168	1	4	yes	direct product factor
403	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
404	C₂×C₃	C₂×#4149	1	1	yes	characteristic
405	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
406	C₅	C₂×C₃×#550	1	1	yes	characteristic, complemented, Sylow
407	C₂²	—	2	6	no	—
408	C₂²	—	2	6	no	—
409	C₂²	—	2	6	no	—
410	C₂²	—	4	12	no	—
411	C₂²	—	10	6	no	—
412	C₂²	—	10	6	no	—
413	C₂²	—	10	6	no	—
414	C₂²	—	20	12	no	—
415	C₂²	C₃×D₅×#41	1	2	yes	—
416	C₂²	C₃×#4149	1	2	yes	—
417	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
418	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	5	4	no	—
421	C₄	—	10	6	no	—
422	C₄	—	10	2	no	—
423	C₄	C₂²×C₃×C₂²⋊D₅	1	12	yes	—
424	C₃	C₂×#66168	1	1	yes	characteristic, direct product factor, Sylow
425	C₂	—	4	6	no	—
426	C₂	—	20	6	no	—
427	C₂	C₃×#66168	1	4	yes	direct product factor
428	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
429	C₂	C₂×C₃×#4149	1	1	yes	characteristic
430	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	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₃×#41	D₅
hypocenter	C₅	C₂×C₃×#550
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₃×#713	C₂	semidirect
3. C₃×#66168	C₂	direct (N × H)
4. C₂×C₃×Q₈×Dic₅	C₂	semidirect
5. C₂×C₃×#4086	C₂	semidirect
6. C₂×C₃×#4084	C₂	semidirect
7. C₂×C₃×#4076	C₂	semidirect
8. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
9. C₂×#66168	C₃	direct (N × H)
11. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₂×C₃×#713	C₂²	semidirect
22. C₃×Q₈×Dic₅	C₂²	semidirect
23. C₃×#4086	C₂²	semidirect
24. C₃×#4084	C₂²	semidirect
25. C₃×#4076	C₂²	semidirect
26. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
32. C₂²×C₅×#41	C₂×C₃	semidirect
33. C₂²×#713	C₂×C₃	semidirect
34. #66168	C₂×C₃	direct (N × H)
35. C₂×Q₈×Dic₅	C₂×C₃	semidirect
36. C₂×#4086	C₂×C₃	semidirect
37. C₂×#4084	C₂×C₃	semidirect
38. C₂×#4076	C₂×C₃	semidirect
39. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
43. C₂×C₃×C₅×Q₈	D₄	semidirect
69. C₂²×C₃×#41	D₅	semidirect
77. C₂×C₅×#41	C₂²×C₃	semidirect
84. C₂×#713	C₂²×C₃	semidirect
88. Q₈×Dic₅	C₂²×C₃	semidirect
89. #4086	C₂²×C₃	semidirect
90. #4084	C₂²×C₃	semidirect
91. #4076	C₂²×C₃	semidirect
92. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
107. C₃×C₅×Q₈	C₂×D₄	semidirect
118. C₂×C₃×Dic₅	#41	semidirect
127. C₂×C₃×#41	C₂×D₅	semidirect
148. C₂×C₅×Q₈	C₃×D₄	semidirect
174. C₂²×#41	C₃×D₅	semidirect
197. C₃×Dic₅	C₂×#41	semidirect
202. C₂×C₃×Q₈	C₂²⋊D₅	semidirect
235. C₅×Q₈	C₂×C₃×D₄	semidirect
246. C₂×Dic₅	C₃×#41	semidirect
255. C₂×#41	C₂×C₃×D₅	semidirect
274. C₂×C₃×C₅	#550	semidirect
288. C₃×Q₈	C₂×C₂²⋊D₅	semidirect
321. Dic₅	C₂×C₃×#41	semidirect
326. C₂×Q₈	C₃×C₂²⋊D₅	semidirect
350. C₃×C₅	C₂×#550	semidirect
369. C₂×C₅	C₃×#550	semidirect
383. Q₈	C₂×C₃×C₂²⋊D₅	semidirect
402. C₂×C₃	#66168	direct (N × H)
406. C₅	C₂×C₃×#550	semidirect
424. C₃	C₂×#66168	direct (N × H)
427. C₂	C₃×#66168	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×C₅×#41	2
C₂²×C₃×#713	2
C₃×#66168	2
C₂×C₃×Q₈×Dic₅	2
C₂×C₃×#4086	2
C₂×C₃×#4084	2
C₂×C₃×#4076	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₂×#66168	3
C₂×C₃×#550	5

Subgroups — C2×C3×#66168 #14482970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66168 #14482970