Subgroups — C₂×C₃×#65126 #14412998

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 388 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	2	yes	maximal
2	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3946	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65126	C₂	1	8	yes	maximal, direct product factor
7	C₂×#65126	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	2	yes	—
17	C₂×C₃×#676	—	2	8	no	—
18	C₂×C₃×#676	C₂²	1	8	yes	—
19	C₃×C₄²×D₅	C₄	1	4	yes	—
20	C₃×C₄²×D₅	C₂²	1	4	yes	—
21	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
22	C₃×#3946	C₂²	1	8	yes	complemented
23	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
24	C₂×C₃×#423	—	5	1	no	maximal, Hall
25	C₂²×#676	C₂×C₃	1	2	yes	—
26	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3946	C₂×C₃	1	2	yes	complemented
29	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
30	#65126	C₂×C₃	1	8	yes	direct product factor
31	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	—	2	4	no	—
39	C₂×C₃×C₄×D₅	—	2	4	no	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
44	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
45	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	4	no	—
47	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
48	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
49	C₃×C₄²×C₅	C₂³	1	2	yes	—
50	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
51	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
52	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
53	C₃×C₄×Dic₅	C₂³	1	2	yes	—
54	C₂×C₃×#168	—	2	4	no	—
55	C₂×C₃×#168	C₂³	1	4	yes	—
56	C₃×#676	—	2	16	no	—
57	C₂²×C₃×M₁₆	—	5	2	no	—
58	C₂²×C₃×C₄²	—	5	1	no	—
59	C₃×#423	—	5	8	no	—
60	C₂×C₃×C₄⋊C₈	—	5	2	no	—
61	C₂×C₃×C₄⋊C₈	—	5	1	no	—
62	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
63	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
71	C₂²×#168	C₂²×C₃	1	2	yes	—
72	C₂×#676	—	2	8	no	—
73	C₂×#676	C₂²×C₃	1	8	yes	—
74	C₄²×D₅	C₃×C₄	1	4	yes	—
75	C₄²×D₅	C₂²×C₃	1	4	yes	—
76	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
77	#3946	C₂²×C₃	1	8	yes	complemented
78	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
79	C₂×#423	—	5	1	no	Sylow
80	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₃×D₅	—	2	2	no	—
82	C₂²×C₃×D₅	—	2	2	no	—
83	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
84	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₂×C₃×Dic₅	—	2	2	no	—
94	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
95	C₂×C₃×Dic₅	M₁₆	1	4	yes	complemented
96	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
99	C₃×C₄×D₅	—	2	8	no	—
100	C₃×C₄×D₅	—	2	8	no	—
101	C₃×C₄×D₅	C₄⋊C₄	1	8	yes	—
102	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
103	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
104	C₃×C₅×C₈	—	2	4	no	—
105	C₃×#168	—	2	4	no	—
106	C₂³×C₃×C₄	—	5	1	no	—
107	C₂³×C₃×C₄	—	5	1	no	—
108	C₂³×C₃×C₄	—	5	1	no	—
109	C₂×C₃×M₁₆	—	5	8	no	—
110	C₂×C₃×M₁₆	—	10	8	no	—
111	C₂²×C₃×C₈	—	5	2	no	—
112	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
113	C₂×C₃×C₄²	—	5	1	no	—
114	C₂×C₃×C₄²	—	5	1	no	—
115	C₂×C₃×C₄²	—	5	1	no	—
116	C₂×C₃×C₄²	—	5	4	no	—
117	C₂×C₃×C₄²	—	5	4	no	—
118	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
119	C₃×C₄⋊C₈	—	5	8	no	—
120	C₃×C₄⋊C₈	—	5	4	no	—
121	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
122	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅	—	2	4	no	—
130	C₂×C₄×D₅	—	2	4	no	—
131	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
132	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
133	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
134	C₂×C₄×D₅	C₃×D₄	1	4	yes	—
135	C₂×C₄×D₅	C₃×Q₈	1	4	yes	—
136	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
137	C₂×C₅×C₈	—	2	4	no	—
138	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
139	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
140	C₄²×C₅	C₂³×C₃	1	2	yes	—
141	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
142	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
143	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
144	C₄×Dic₅	C₂³×C₃	1	2	yes	—
145	C₂×#168	—	2	4	no	—
146	C₂×#168	C₂³×C₃	1	4	yes	—
147	#676	—	2	16	no	—
148	C₂²×M₁₆	—	5	2	no	—
149	C₂²×C₄²	—	5	1	no	—
150	#423	—	5	8	no	—
151	C₂×C₄⋊C₈	—	5	2	no	—
152	C₂×C₄⋊C₈	—	5	1	no	—
153	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
154	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
155	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
156	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
157	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₃×D₅	—	2	2	no	—
159	C₂×C₃×D₅	—	2	2	no	—
160	C₂×C₃×D₅	—	2	8	no	—
161	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
164	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
165	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
167	C₃×Dic₅	—	2	2	no	—
168	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
169	C₃×Dic₅	C₂×M₁₆	1	4	yes	complemented
170	C₂⁴×C₃	—	5	1	no	—
171	C₂²×C₃×C₄	—	5	1	no	—
172	C₂²×C₃×C₄	—	5	1	no	—
173	C₂²×C₃×C₄	—	5	2	no	—
174	C₂²×C₃×C₄	—	5	4	no	—
175	C₂²×C₃×C₄	—	5	4	no	—
176	C₂²×C₃×C₄	—	5	2	no	—
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	4	no	—
179	C₂²×C₃×C₄	—	5	4	no	—
180	C₂²×C₃×C₄	—	10	4	no	—
181	C₂²×C₃×C₄	—	10	4	no	—
182	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
185	C₃×M₁₆	—	10	16	no	—
186	C₂×C₃×C₈	—	2	4	no	—
187	C₂×C₃×C₈	—	5	4	no	—
188	C₂×C₃×C₈	—	10	4	no	—
189	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
190	C₃×C₄²	—	5	4	no	—
191	C₃×C₄²	—	5	4	no	—
192	C₃×C₄²	—	5	2	no	—
193	C₃×C₄²	—	5	2	no	—
194	C₃×C₄²	C₄×D₅	1	2	yes	—
195	C₃×C₄²	C₂²×D₅	1	2	yes	—
196	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
197	C₂²×D₅	—	2	2	no	—
198	C₂²×D₅	—	2	2	no	—
199	C₂²×D₅	C₃×C₄⋊C₄	1	4	yes	—
200	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
203	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
204	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
206	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
207	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
208	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
209	C₂×Dic₅	—	2	2	no	—
210	C₂×Dic₅	C₃×C₄⋊C₄	1	4	yes	—
211	C₂×Dic₅	C₃×M₁₆	1	4	yes	complemented
212	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
213	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
214	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
215	C₄×D₅	—	2	8	no	—
216	C₄×D₅	—	2	8	no	—
217	C₄×D₅	C₃×C₄⋊C₄	1	8	yes	—
218	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
219	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
220	C₅×C₈	—	2	4	no	—
221	#168	—	2	4	no	—
222	C₂³×C₄	—	5	1	no	—
223	C₂³×C₄	—	5	1	no	—
224	C₂³×C₄	—	5	1	no	—
225	C₂×M₁₆	—	5	8	no	—
226	C₂×M₁₆	—	10	8	no	—
227	C₂²×C₈	—	5	2	no	—
228	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
229	C₂×C₄²	—	5	1	no	—
230	C₂×C₄²	—	5	1	no	—
231	C₂×C₄²	—	5	1	no	—
232	C₂×C₄²	—	5	4	no	—
233	C₂×C₄²	—	5	4	no	—
234	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
235	C₄⋊C₈	—	5	8	no	—
236	C₄⋊C₈	—	5	4	no	—
237	C₄⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
238	C₂×C₃×C₅	#423	1	4	yes	complemented
239	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
242	C₃×D₅	—	2	4	no	—
243	C₂³×C₃	—	5	2	no	—
244	C₂³×C₃	—	5	4	no	—
245	C₂³×C₃	—	10	2	no	—
246	C₂³×C₃	—	10	2	no	—
247	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	5	2	no	—
250	C₂×C₃×C₄	—	5	2	no	—
251	C₂×C₃×C₄	—	5	4	no	—
252	C₂×C₃×C₄	—	5	4	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	—	5	4	no	—
255	C₂×C₃×C₄	—	5	8	no	—
256	C₂×C₃×C₄	—	5	2	no	—
257	C₂×C₃×C₄	—	10	8	no	—
258	C₂×C₃×C₄	—	10	2	no	—
259	C₂×C₃×C₄	—	10	8	no	—
260	C₂×C₃×C₄	#676	1	4	yes	complemented
261	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
262	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
264	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
265	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
266	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
267	C₃×C₈	—	2	4	no	—
268	C₃×C₈	—	10	4	no	—
269	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
270	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
271	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
272	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
273	C₂×D₅	—	2	2	no	—
274	C₂×D₅	—	2	2	no	—
275	C₂×D₅	—	2	8	no	—
276	C₂×D₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
279	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
280	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
281	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
282	Dic₅	—	2	2	no	—
283	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
284	Dic₅	C₂×C₃×M₁₆	1	4	yes	complemented
285	C₂⁴	—	5	1	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	—	5	2	no	—
289	C₂²×C₄	—	5	4	no	—
290	C₂²×C₄	—	5	4	no	—
291	C₂²×C₄	—	5	2	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	4	no	—
294	C₂²×C₄	—	5	4	no	—
295	C₂²×C₄	—	10	4	no	—
296	C₂²×C₄	—	10	4	no	—
297	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
298	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
300	M₁₆	—	10	16	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	5	4	no	—
303	C₂×C₈	—	10	4	no	—
304	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
305	C₄²	—	5	4	no	—
306	C₄²	—	5	4	no	—
307	C₄²	—	5	2	no	—
308	C₄²	—	5	2	no	—
309	C₄²	C₃×C₄×D₅	1	2	yes	—
310	C₄²	C₂²×C₃×D₅	1	2	yes	—
311	C₃×C₅	C₂×#423	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	5	4	no	—
313	C₂²×C₃	—	10	2	no	—
314	C₂²×C₃	—	10	2	no	—
315	C₂²×C₃	—	10	8	no	—
316	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
317	C₂²×C₃	C₂×#676	1	2	yes	—
318	C₂²×C₃	D₅×M₁₆	1	2	yes	—
319	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	5	4	no	—
322	C₃×C₄	—	5	4	no	—
323	C₃×C₄	—	10	2	no	—
324	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
325	C₃×C₄	C₂×#676	1	4	yes	complemented
326	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
327	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
328	C₂×C₅	C₃×#423	1	4	yes	complemented
329	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
330	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
331	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
332	D₅	—	2	4	no	—
333	C₂³	—	5	2	no	—
334	C₂³	—	5	4	no	—
335	C₂³	—	10	2	no	—
336	C₂³	—	10	2	no	—
337	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	5	2	no	—
340	C₂×C₄	—	5	2	no	—
341	C₂×C₄	—	5	4	no	—
342	C₂×C₄	—	5	4	no	—
343	C₂×C₄	—	5	4	no	—
344	C₂×C₄	—	5	4	no	—
345	C₂×C₄	—	5	8	no	—
346	C₂×C₄	—	5	2	no	—
347	C₂×C₄	—	10	8	no	—
348	C₂×C₄	—	10	2	no	—
349	C₂×C₄	—	10	8	no	—
350	C₂×C₄	C₃×#676	1	4	yes	complemented
351	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
352	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
354	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
355	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
356	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	10	4	no	—
359	C₂×C₃	—	10	4	no	—
360	C₂×C₃	#65126	1	4	yes	direct product factor
361	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₃	C₂²×#676	1	1	yes	characteristic
363	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
364	C₅	C₂×C₃×#423	1	1	yes	characteristic, complemented, Sylow
365	C₂²	—	5	4	no	—
366	C₂²	—	10	8	no	—
367	C₂²	—	10	2	no	—
368	C₂²	—	10	2	no	—
369	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
370	C₂²	C₂×C₃×#676	1	2	yes	—
371	C₂²	C₃×D₅×M₁₆	1	2	yes	—
372	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	5	4	no	—
375	C₄	—	5	4	no	—
376	C₄	—	10	2	no	—
377	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
378	C₄	C₂×C₃×#676	1	4	yes	complemented
379	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
380	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
381	C₃	C₂×#65126	1	1	yes	characteristic, direct product factor, Sylow
382	C₂	—	10	4	no	—
383	C₂	C₃×#65126	1	4	yes	direct product factor
384	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
385	C₂	C₂²×C₃×#676	1	1	yes	characteristic
386	C₂	C₂×C₃×D₅×M₁₆	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×#423
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
3. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₂×C₃×#3946	C₂	semidirect
5. C₂×C₃×C₄⋊#168	C₂	semidirect
6. C₃×#65126	C₂	direct (N × H)
7. C₂×#65126	C₃	direct (N × H)
21. C₃×C₅×C₄⋊C₈	C₂²	semidirect
22. C₃×#3946	C₂²	semidirect
23. C₃×C₄⋊#168	C₂²	semidirect
27. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
28. C₂×#3946	C₂×C₃	semidirect
29. C₂×C₄⋊#168	C₂×C₃	semidirect
30. #65126	C₂×C₃	direct (N × H)
62. C₂×C₃×C₄⋊C₈	D₅	semidirect
76. C₅×C₄⋊C₈	C₂²×C₃	semidirect
77. #3946	C₂²×C₃	semidirect
78. C₄⋊#168	C₂²×C₃	semidirect
86. C₂×C₃×C₄×C₅	M₁₆	semidirect
95. C₂×C₃×Dic₅	M₁₆	semidirect
121. C₃×C₄⋊C₈	C₂×D₅	semidirect
153. C₂×C₄⋊C₈	C₃×D₅	semidirect
164. C₃×C₄×C₅	C₂×M₁₆	semidirect
169. C₃×Dic₅	C₂×M₁₆	semidirect
202. C₂×C₄×C₅	C₃×M₁₆	semidirect
211. C₂×Dic₅	C₃×M₁₆	semidirect
237. C₄⋊C₈	C₂×C₃×D₅	semidirect
238. C₂×C₃×C₅	#423	semidirect
260. C₂×C₃×C₄	#676	semidirect
279. C₄×C₅	C₂×C₃×M₁₆	semidirect
284. Dic₅	C₂×C₃×M₁₆	semidirect
311. C₃×C₅	C₂×#423	semidirect
325. C₃×C₄	C₂×#676	semidirect
328. C₂×C₅	C₃×#423	semidirect
350. C₂×C₄	C₃×#676	semidirect
360. C₂×C₃	#65126	direct (N × H)
364. C₅	C₂×C₃×#423	semidirect
378. C₄	C₂×C₃×#676	semidirect
381. C₃	C₂×#65126	direct (N × H)
383. C₂	C₃×#65126	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
C₂×C₃×C₄²×D₅	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3946	2
C₂×C₃×C₄⋊#168	2
C₃×#65126	2
C₂×#65126	3
C₂×C₃×#423	5

Subgroups — C2×C3×#65126 #14412998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65126 #14412998