Subgroups — C₂×C₃×#65128 #14413051

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65128	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65128	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×#685	C₄	1	1	yes	characteristic
15	C₂×C₃×#685	C₄	1	1	yes	characteristic
16	C₂×C₃×#683	C₄	1	1	yes	characteristic
17	C₂×C₃×#683	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
21	C₂×C₃×#676	—	2	4	no	—
22	C₂×C₃×#676	C₂²	1	4	yes	—
23	C₂×C₃×C₈×D₅	—	2	4	no	—
24	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
25	C₃×#4018	C₄	1	4	yes	—
26	C₃×#4018	C₂²	1	4	yes	—
27	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
28	C₃×#3946	C₂²	1	4	yes	complemented
29	C₃×#3946	C₂²	1	4	yes	complemented
30	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
31	C₂×C₃×#424	—	5	1	no	maximal, Hall
32	C₂²×#676	C₂×C₃	1	1	yes	characteristic
33	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
34	C₂×#4018	C₂×C₃	1	1	yes	characteristic
35	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
39	#65128	C₂×C₃	1	8	yes	direct product factor
40	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
49	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	—	2	2	no	—
52	C₂×C₃×C₅×C₈	—	2	2	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
56	C₃×C₄²×C₅	C₂³	1	2	yes	—
57	C₃×#685	C₂×C₄	1	4	yes	—
58	C₃×#685	C₂×C₄	1	4	yes	—
59	C₃×#683	C₂×C₄	1	4	yes	—
60	C₃×#683	C₂×C₄	1	4	yes	—
61	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
62	C₃×C₄×Dic₅	C₂³	1	2	yes	—
63	C₂×C₃×#168	—	2	2	no	—
64	C₂×C₃×#168	—	2	2	no	—
65	C₂×C₃×#168	C₂³	1	2	yes	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₃×#676	—	2	8	no	—
68	C₃×C₈×D₅	—	2	8	no	—
69	C₂²×C₃×M₁₆	—	5	1	no	—
70	C₂³×C₃×C₈	—	5	1	no	—
71	C₂×C₃×#117	—	5	1	no	—
72	C₃×#424	—	5	8	no	—
73	C₂×C₃×C₄⋊C₈	—	5	1	no	—
74	C₂×C₃×C₄⋊C₈	—	5	1	no	—
75	C₂×C₃×C₄⋊C₈	—	5	1	no	—
76	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
77	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₂×#685	C₃×C₄	1	1	yes	characteristic
82	C₂×#685	C₃×C₄	1	1	yes	characteristic
83	C₂×#683	C₃×C₄	1	1	yes	characteristic
84	C₂×#683	C₃×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
86	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
87	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
88	C₂×#676	—	2	4	no	—
89	C₂×#676	C₂²×C₃	1	4	yes	—
90	C₂×C₈×D₅	—	2	4	no	—
91	C₂×C₈×D₅	C₂²×C₃	1	4	yes	—
92	#4018	C₃×C₄	1	4	yes	—
93	#4018	C₂²×C₃	1	4	yes	—
94	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
95	#3946	C₂²×C₃	1	4	yes	complemented
96	#3946	C₂²×C₃	1	4	yes	complemented
97	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
98	C₂×#424	—	5	1	no	Sylow
99	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃×D₅	—	2	2	no	—
101	C₂²×C₃×D₅	—	2	2	no	—
102	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
103	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₂×C₃×Dic₅	—	2	2	no	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
118	C₃×C₄×D₅	C₄⋊C₄	1	8	yes	—
119	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
120	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	—	2	2	no	—
123	C₃×#168	—	2	2	no	—
124	C₃×#168	—	2	2	no	—
125	C₂³×C₃×C₄	—	5	1	no	—
126	C₂×C₃×M₁₆	—	5	4	no	—
127	C₂×C₃×M₁₆	—	10	4	no	—
128	C₂²×C₃×C₈	—	5	1	no	—
129	C₂²×C₃×C₈	—	5	1	no	—
130	C₂²×C₃×C₈	—	5	4	no	—
131	C₂²×C₃×C₈	—	10	4	no	—
132	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
133	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
134	C₃×#117	—	5	4	no	—
135	C₃×#117	—	5	4	no	—
136	C₂×C₃×C₄⋊C₄	—	5	1	no	—
137	C₂×C₃×C₄⋊C₄	—	5	1	no	—
138	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
139	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
140	C₂×C₃×C₄²	—	5	1	no	—
141	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
142	C₃×C₄⋊C₈	—	5	4	no	—
143	C₃×C₄⋊C₈	—	5	4	no	—
144	C₃×C₄⋊C₈	—	5	4	no	—
145	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
146	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
154	C₂×C₄×D₅	C₃×D₄	1	4	yes	—
155	C₂×C₄×D₅	C₃×Q₈	1	4	yes	—
156	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	2	2	no	—
159	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
160	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
161	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
162	C₄²×C₅	C₂³×C₃	1	2	yes	—
163	#685	C₂×C₃×C₄	1	4	yes	—
164	#685	C₂×C₃×C₄	1	4	yes	—
165	#683	C₂×C₃×C₄	1	4	yes	—
166	#683	C₂×C₃×C₄	1	4	yes	—
167	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
168	C₄×Dic₅	C₂³×C₃	1	2	yes	—
169	C₂×#168	—	2	2	no	—
170	C₂×#168	—	2	2	no	—
171	C₂×#168	C₂³×C₃	1	2	yes	—
172	C₂×#168	C₂³×C₃	1	2	yes	—
173	#676	—	2	8	no	—
174	C₈×D₅	—	2	8	no	—
175	C₂²×M₁₆	—	5	1	no	—
176	C₂³×C₈	—	5	1	no	—
177	C₂×#117	—	5	1	no	—
178	#424	—	5	8	no	—
179	C₂×C₄⋊C₈	—	5	1	no	—
180	C₂×C₄⋊C₈	—	5	1	no	—
181	C₂×C₄⋊C₈	—	5	1	no	—
182	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
183	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
184	C₂²×C₃×C₅	#131	1	2	yes	—
185	C₂²×C₃×C₅	#131	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	2	no	—
188	C₂×C₃×D₅	—	2	2	no	—
189	C₂×C₃×D₅	—	2	8	no	—
190	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	—	2	2	no	—
198	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
199	C₂⁴×C₃	—	5	1	no	—
200	C₂²×C₃×C₄	—	5	1	no	—
201	C₂²×C₃×C₄	—	5	2	no	—
202	C₂²×C₃×C₄	—	5	4	no	—
203	C₂²×C₃×C₄	—	5	4	no	—
204	C₂²×C₃×C₄	—	5	2	no	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
210	C₃×M₁₆	—	10	8	no	—
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	—	10	8	no	—
216	C₂×C₃×C₈	—	10	2	no	—
217	C₂×C₃×C₈	—	10	2	no	—
218	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
219	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
220	C₃×C₄⋊C₄	—	5	4	no	—
221	C₃×C₄⋊C₄	—	5	4	no	—
222	C₃×C₂²⋊C₄	—	5	4	no	—
223	C₃×C₂²⋊C₄	—	5	4	no	—
224	C₃×C₄²	—	5	2	no	—
225	C₃×C₄²	—	5	2	no	—
226	C₃×C₄²	C₄×D₅	1	2	yes	—
227	C₃×C₄²	C₂²×D₅	1	2	yes	—
228	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
229	C₂²×D₅	—	2	2	no	—
230	C₂²×D₅	—	2	2	no	—
231	C₂²×D₅	C₃×C₄⋊C₄	1	4	yes	—
232	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
239	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
240	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
241	C₂×Dic₅	—	2	2	no	—
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	C₃×C₄⋊C₄	1	4	yes	—
244	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
245	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
247	C₄×D₅	C₃×C₄⋊C₄	1	8	yes	—
248	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
249	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	2	no	—
252	#168	—	2	2	no	—
253	#168	—	2	2	no	—
254	C₂³×C₄	—	5	1	no	—
255	C₂×M₁₆	—	5	4	no	—
256	C₂×M₁₆	—	10	4	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₂²×C₈	—	5	1	no	—
259	C₂²×C₈	—	5	4	no	—
260	C₂²×C₈	—	10	4	no	—
261	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
262	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
263	#117	—	5	4	no	—
264	#117	—	5	4	no	—
265	C₂×C₄⋊C₄	—	5	1	no	—
266	C₂×C₄⋊C₄	—	5	1	no	—
267	C₂×C₂²⋊C₄	—	5	1	no	—
268	C₂×C₂²⋊C₄	—	5	1	no	—
269	C₂×C₄²	—	5	1	no	—
270	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
271	C₄⋊C₈	—	5	4	no	—
272	C₄⋊C₈	—	5	4	no	—
273	C₄⋊C₈	—	5	4	no	—
274	C₄⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
275	C₂×C₃×C₅	#424	1	4	yes	complemented
276	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
278	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
279	C₃×D₅	—	2	4	no	—
280	C₂³×C₃	—	5	2	no	—
281	C₂³×C₃	—	5	4	no	—
282	C₂³×C₃	—	10	2	no	—
283	C₂³×C₃	—	10	2	no	—
284	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	5	4	no	—
289	C₂×C₃×C₄	—	5	4	no	—
290	C₂×C₃×C₄	—	5	4	no	—
291	C₂×C₃×C₄	—	5	8	no	—
292	C₂×C₃×C₄	—	5	2	no	—
293	C₂×C₃×C₄	—	5	2	no	—
294	C₂×C₃×C₄	—	10	2	no	—
295	C₂×C₃×C₄	—	10	2	no	—
296	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
297	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
298	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
299	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
300	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
301	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	—	10	2	no	—
305	C₃×C₈	—	10	2	no	—
306	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
307	C₂²×C₅	C₃×#131	1	2	yes	—
308	C₂²×C₅	C₃×#131	1	2	yes	—
309	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
310	C₂×D₅	—	2	2	no	—
311	C₂×D₅	—	2	2	no	—
312	C₂×D₅	—	2	8	no	—
313	C₂×D₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
317	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
318	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
319	Dic₅	—	2	2	no	—
320	Dic₅	—	2	2	no	—
321	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
322	C₂⁴	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	2	no	—
325	C₂²×C₄	—	5	4	no	—
326	C₂²×C₄	—	5	4	no	—
327	C₂²×C₄	—	5	2	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
331	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
333	M₁₆	—	10	8	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	5	2	no	—
337	C₂×C₈	—	5	2	no	—
338	C₂×C₈	—	10	8	no	—
339	C₂×C₈	—	10	2	no	—
340	C₂×C₈	—	10	2	no	—
341	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
342	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
343	C₄⋊C₄	—	5	4	no	—
344	C₄⋊C₄	—	5	4	no	—
345	C₂²⋊C₄	—	5	4	no	—
346	C₂²⋊C₄	—	5	4	no	—
347	C₄²	—	5	2	no	—
348	C₄²	—	5	2	no	—
349	C₄²	C₃×C₄×D₅	1	2	yes	—
350	C₄²	C₂²×C₃×D₅	1	2	yes	—
351	C₃×C₅	C₂×#424	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	5	4	no	—
353	C₂²×C₃	—	10	2	no	—
354	C₂²×C₃	—	10	2	no	—
355	C₂²×C₃	—	10	8	no	—
356	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
357	C₂²×C₃	#4047	1	2	yes	—
358	C₂²×C₃	#4053	1	2	yes	—
359	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	5	4	no	—
363	C₃×C₄	—	10	2	no	—
364	C₃×C₄	—	10	2	no	—
365	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
366	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
367	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
368	C₂×C₅	C₃×#424	1	4	yes	complemented
369	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
370	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
371	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
372	D₅	—	2	4	no	—
373	C₂³	—	5	2	no	—
374	C₂³	—	5	4	no	—
375	C₂³	—	10	2	no	—
376	C₂³	—	10	2	no	—
377	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	4	no	—
382	C₂×C₄	—	5	4	no	—
383	C₂×C₄	—	5	4	no	—
384	C₂×C₄	—	5	8	no	—
385	C₂×C₄	—	5	2	no	—
386	C₂×C₄	—	5	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	10	2	no	—
389	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
390	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
391	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
392	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
393	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
394	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	10	2	no	—
398	C₈	—	10	2	no	—
399	C₂×C₃	—	10	4	no	—
400	C₂×C₃	#65128	1	4	yes	direct product factor
401	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
402	C₂×C₃	C₂×#4047	1	1	yes	characteristic
403	C₂×C₃	C₂×#4053	1	1	yes	characteristic
404	C₅	C₂×C₃×#424	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	5	4	no	—
406	C₂²	—	10	8	no	—
407	C₂²	—	10	2	no	—
408	C₂²	—	10	2	no	—
409	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
410	C₂²	C₃×#4047	1	2	yes	—
411	C₂²	C₃×#4053	1	2	yes	—
412	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	5	4	no	—
416	C₄	—	10	2	no	—
417	C₄	—	10	2	no	—
418	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
419	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
420	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
421	C₃	C₂×#65128	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	10	4	no	—
423	C₂	C₃×#65128	1	4	yes	direct product factor
424	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
425	C₂	C₂×C₃×#4047	1	1	yes	characteristic
426	C₂	C₂×C₃×#4053	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₂×C₃×#424
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₂×C₃×#3946	C₂	semidirect
6. C₂×C₃×#3946	C₂	semidirect
7. C₂×C₃×C₄⋊#168	C₂	semidirect
8. C₃×#65128	C₂	direct (N × H)
9. C₂×#65128	C₃	direct (N × H)
27. C₃×C₅×C₄⋊C₈	C₂²	semidirect
28. C₃×#3946	C₂²	semidirect
29. C₃×#3946	C₂²	semidirect
30. C₃×C₄⋊#168	C₂²	semidirect
35. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
36. C₂×#3946	C₂×C₃	semidirect
37. C₂×#3946	C₂×C₃	semidirect
38. C₂×C₄⋊#168	C₂×C₃	semidirect
39. #65128	C₂×C₃	direct (N × H)
76. C₂×C₃×C₄⋊C₈	D₅	semidirect
94. C₅×C₄⋊C₈	C₂²×C₃	semidirect
95. #3946	C₂²×C₃	semidirect
96. #3946	C₂²×C₃	semidirect
97. C₄⋊#168	C₂²×C₃	semidirect
145. C₃×C₄⋊C₈	C₂×D₅	semidirect
182. C₂×C₄⋊C₈	C₃×D₅	semidirect
274. C₄⋊C₈	C₂×C₃×D₅	semidirect
275. C₂×C₃×C₅	#424	semidirect
351. C₃×C₅	C₂×#424	semidirect
368. C₂×C₅	C₃×#424	semidirect
400. C₂×C₃	#65128	direct (N × H)
404. C₅	C₂×C₃×#424	semidirect
421. C₃	C₂×#65128	direct (N × H)
423. C₂	C₃×#65128	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×#676	2
C₂²×C₃×C₈×D₅	2
C₂×C₃×#4018	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3946	2
C₂×C₃×C₄⋊#168	2
C₃×#65128	2
C₂×#65128	3
C₂×C₃×#424	5

Subgroups — C2×C3×#65128 #14413051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65128 #14413051