Subgroups — C₂×#11745981 #14294544

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×C₄⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₃×#168	C₂	1	1	yes	maximal, characteristic
4	#11745981	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64749	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₅	—	2	1	no	—
8	C₂³×C₅×Dic₃	—	2	1	no	—
9	C₂×C₄⋊Dic₁₅	—	2	1	no	—
10	C₂×C₄⋊Dic₁₅	—	2	2	no	—
11	C₂×C₄⋊Dic₁₅	C₄	1	4	yes	complemented
12	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
14	C₂×C₅×C₄⋊Dic₃	—	2	2	no	—
15	C₂×C₅×C₄⋊Dic₃	C₄	1	4	yes	complemented
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂²×C₃×#168	—	2	2	no	—
18	C₂²×C₃×#168	—	2	2	no	—
19	C₂²×C₃×#168	C₄	1	4	yes	complemented
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₂×#4551	—	5	1	no	maximal, Hall
22	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
23	C₂²×C₄⋊Dic₅	—	3	1	no	—
24	C₂³×#168	D₃	1	1	yes	characteristic
25	#64749	—	3	4	no	—
26	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₅	—	2	4	no	—
36	C₂²×Dic₁₅	—	2	2	no	—
37	C₂²×Dic₁₅	—	4	2	no	—
38	C₂²×Dic₁₅	—	4	2	no	—
39	C₂²×C₅×Dic₃	—	2	4	no	—
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₂²×C₅×Dic₃	—	4	2	no	—
42	C₂²×C₅×Dic₃	—	4	2	no	—
43	C₄⋊Dic₁₅	—	2	4	no	—
44	C₄⋊Dic₁₅	—	2	2	no	—
45	C₄⋊Dic₁₅	C₂×C₄	1	4	yes	complemented
46	C₅×C₄⋊Dic₃	—	2	4	no	—
47	C₅×C₄⋊Dic₃	—	2	2	no	—
48	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×#168	—	2	8	no	—
50	C₂×C₃×#168	—	2	2	no	—
51	C₂×C₃×#168	—	2	2	no	—
52	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
53	C₂³×C₃×C₈	—	5	1	no	—
54	C₂²×C₄⋊Dic₃	—	5	1	no	—
55	C₂²×C₄⋊Dic₃	D₅	1	1	yes	characteristic
56	#4551	—	5	4	no	—
57	C₂³×C₄×C₅	—	6	1	no	—
58	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
59	C₂³×Dic₅	—	6	1	no	—
60	C₂×C₅×C₄⋊C₄	—	3	4	no	—
61	C₂×C₅×C₄⋊C₄	—	3	2	no	—
62	C₂×C₅×C₄⋊C₄	—	6	1	no	—
63	C₂×C₅×C₄⋊C₄	—	6	2	no	—
64	C₂×C₄⋊Dic₅	—	3	4	no	—
65	C₂×C₄⋊Dic₅	—	3	2	no	—
66	C₂×C₄⋊Dic₅	—	6	1	no	—
67	C₂×C₄⋊Dic₅	—	6	2	no	—
68	C₂²×#168	—	2	2	no	—
69	C₂²×#168	—	2	2	no	—
70	C₂²×#168	Dic₃	1	4	yes	complemented
71	C₂²×#168	C₂×D₃	1	2	yes	—
72	C₂×#340	—	15	1	no	Sylow
73	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
74	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
75	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
76	C₂³×C₃×C₅	D₈	1	2	yes	—
77	C₂³×C₃×C₅	SD₁₆	1	2	yes	—
78	C₂³×C₃×C₅	SD₁₆	1	2	yes	—
79	C₂³×C₃×C₅	Q₁₆	1	2	yes	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
85	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
87	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂×Dic₁₅	—	2	4	no	—
95	C₂×Dic₁₅	—	4	8	no	—
96	C₂×Dic₁₅	—	4	2	no	—
97	C₂×Dic₁₅	—	4	2	no	—
98	C₂×C₅×Dic₃	—	2	4	no	—
99	C₂×C₅×Dic₃	—	4	8	no	—
100	C₂×C₅×Dic₃	—	4	2	no	—
101	C₂×C₅×Dic₃	—	4	2	no	—
102	C₃×#168	—	2	4	no	—
103	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
104	C₂³×Dic₃	—	2	1	no	—
105	C₂³×Dic₃	—	10	1	no	—
106	C₂²×C₃×C₈	—	5	4	no	—
107	C₂²×C₃×C₈	—	5	2	no	—
108	C₂²×C₃×C₈	—	10	2	no	—
109	C₂²×C₃×C₈	—	10	2	no	—
110	C₂×C₄⋊Dic₃	—	2	2	no	—
111	C₂×C₄⋊Dic₃	—	2	1	no	—
112	C₂×C₄⋊Dic₃	—	5	4	no	—
113	C₂×C₄⋊Dic₃	—	5	2	no	—
114	C₂×C₄⋊Dic₃	—	10	2	no	—
115	C₂×C₄⋊Dic₃	—	10	1	no	—
116	C₂×C₄⋊Dic₃	Dic₅	1	4	yes	complemented
117	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	—
118	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	6	4	no	—
120	C₂²×C₄×C₅	—	6	2	no	—
121	C₂²×C₄×C₅	—	12	2	no	—
122	C₂²×C₄×C₅	—	12	2	no	—
123	C₂²×C₄×C₅	Dic₆	1	2	yes	—
124	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
125	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
126	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
128	C₂²×C₄×C₅	#67	1	2	yes	—
129	C₂²×C₄×C₅	#67	1	2	yes	—
130	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₂²×Dic₅	—	6	4	no	—
132	C₂²×Dic₅	—	6	2	no	—
133	C₂²×Dic₅	—	12	2	no	—
134	C₂²×Dic₅	—	12	2	no	—
135	C₅×C₄⋊C₄	—	3	4	no	—
136	C₅×C₄⋊C₄	—	6	4	no	—
137	C₅×C₄⋊C₄	—	6	2	no	—
138	C₄⋊Dic₅	—	3	4	no	—
139	C₄⋊Dic₅	—	6	4	no	—
140	C₄⋊Dic₅	—	6	2	no	—
141	C₂×#168	—	2	8	no	—
142	C₂×#168	—	2	2	no	—
143	C₂×#168	—	2	2	no	—
144	C₂×#168	C₂×Dic₃	1	4	yes	complemented
145	C₂³×C₈	—	5	1	no	—
146	C₂²×C₄⋊C₄	—	3	1	no	—
147	C₂²×C₄⋊C₄	—	15	1	no	—
148	#340	—	15	4	no	—
149	C₂²×C₃×C₅	#95	1	4	yes	—
150	C₂²×C₃×C₅	#102	1	4	yes	—
151	C₂²×C₃×C₅	#102	1	4	yes	—
152	C₂²×C₃×C₅	#103	1	4	yes	—
153	C₂²×C₃×C₅	#103	1	4	yes	—
154	C₂²×C₃×C₅	#106	1	4	yes	—
155	C₂²×C₃×C₅	#107	1	4	yes	—
156	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
163	C₃×C₄×C₅	#95	1	4	yes	—
164	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
165	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
168	Dic₁₅	—	4	4	no	—
169	C₅×Dic₃	—	4	4	no	—
170	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
172	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
173	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
174	C₂²×C₃×C₄	D₂₀	1	2	yes	—
175	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
177	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₂²×Dic₃	—	2	4	no	—
180	C₂²×Dic₃	—	2	2	no	—
181	C₂²×Dic₃	—	4	2	no	—
182	C₂²×Dic₃	—	4	2	no	—
183	C₂²×Dic₃	—	10	4	no	—
184	C₂²×Dic₃	—	10	2	no	—
185	C₂²×Dic₃	—	20	2	no	—
186	C₂²×Dic₃	—	20	2	no	—
187	C₂×C₃×C₈	—	5	4	no	—
188	C₂×C₃×C₈	—	10	8	no	—
189	C₂×C₃×C₈	—	10	2	no	—
190	C₂×C₃×C₈	—	10	2	no	—
191	C₄⋊Dic₃	—	2	4	no	—
192	C₄⋊Dic₃	—	2	2	no	—
193	C₄⋊Dic₃	—	5	4	no	—
194	C₄⋊Dic₃	—	10	4	no	—
195	C₄⋊Dic₃	—	10	2	no	—
196	C₄⋊Dic₃	C₂×Dic₅	1	4	yes	complemented
197	C₂³×C₅	#204	1	2	yes	—
198	C₂³×C₅	#204	1	2	yes	—
199	C₂³×C₅	D₂₄	1	2	yes	—
200	C₂³×C₅	Dic₁₂	1	2	yes	—
201	C₂³×C₅	C₄⋊Dic₃	1	2	yes	—
202	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
203	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
204	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
205	C₂×C₄×C₅	—	6	4	no	—
206	C₂×C₄×C₅	—	12	8	no	—
207	C₂×C₄×C₅	—	12	2	no	—
208	C₂×C₄×C₅	—	12	2	no	—
209	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
210	C₂×C₄×C₅	Dic₃⋊C₄	1	4	yes	—
211	C₂×C₄×C₅	Dic₃⋊C₄	1	4	yes	—
212	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
213	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
214	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
215	C₂×C₄×C₅	#217	1	4	yes	—
216	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
222	C₂×Dic₅	—	6	4	no	—
223	C₂×Dic₅	—	12	8	no	—
224	C₂×Dic₅	—	12	2	no	—
225	C₂×Dic₅	—	12	2	no	—
226	#168	—	2	4	no	—
227	C₂³×C₄	—	6	1	no	—
228	C₂³×C₄	—	30	1	no	—
229	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
230	C₂²×C₈	—	5	4	no	—
231	C₂²×C₈	—	5	2	no	—
232	C₂²×C₈	—	10	2	no	—
233	C₂²×C₈	—	10	2	no	—
234	C₂×C₄⋊C₄	—	3	4	no	—
235	C₂×C₄⋊C₄	—	3	2	no	—
236	C₂×C₄⋊C₄	—	6	2	no	—
237	C₂×C₄⋊C₄	—	6	1	no	—
238	C₂×C₄⋊C₄	—	15	4	no	—
239	C₂×C₄⋊C₄	—	15	2	no	—
240	C₂×C₄⋊C₄	—	30	2	no	—
241	C₂×C₄⋊C₄	—	30	1	no	—
242	C₂×C₃×C₅	#340	1	8	yes	complemented
243	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×#106	1	1	yes	characteristic
249	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
250	C₂³×C₃	#683	1	2	yes	—
251	C₂³×C₃	#685	1	2	yes	—
252	C₂³×C₃	#686	1	2	yes	—
253	C₂³×C₃	#687	1	2	yes	—
254	C₂³×C₃	#688	1	2	yes	—
255	C₂³×C₃	#689	1	2	yes	—
256	C₂³×C₃	C₂²⋊Dic₅	1	2	yes	—
257	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
259	C₂×C₃×C₄	#683	1	2	yes	—
260	C₂×C₃×C₄	#683	1	4	yes	—
261	C₂×C₃×C₄	C₄⋊Dic₅	1	4	yes	—
262	C₂×C₃×C₄	#685	1	4	yes	—
263	C₂×C₃×C₄	#685	1	2	yes	—
264	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
271	C₂×Dic₃	—	2	4	no	—
272	C₂×Dic₃	—	4	8	no	—
273	C₂×Dic₃	—	4	2	no	—
274	C₂×Dic₃	—	4	2	no	—
275	C₂×Dic₃	—	10	4	no	—
276	C₂×Dic₃	—	20	8	no	—
277	C₂×Dic₃	—	20	2	no	—
278	C₂×Dic₃	—	20	2	no	—
279	C₃×C₈	—	10	4	no	—
280	C₂²×C₅	#816	1	4	yes	—
281	C₂²×C₅	#816	1	4	yes	—
282	C₂²×C₅	#817	1	4	yes	—
283	C₂²×C₅	#818	1	4	yes	—
284	C₂²×C₅	#821	1	4	yes	—
285	C₂²×C₅	#821	1	4	yes	—
286	C₂²×C₅	C₃⋊#95	1	4	yes	—
287	C₂²×C₅	C₂×#204	1	1	yes	characteristic
288	C₂²×C₅	C₂×#204	1	1	yes	characteristic
289	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
290	C₂²×C₅	C₂×Dic₁₂	1	1	yes	characteristic
291	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
292	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
293	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
294	C₄×C₅	—	12	4	no	—
295	C₄×C₅	C₃⋊#95	1	4	yes	—
296	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
297	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
298	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
299	C₄×C₅	C₂×#217	1	1	yes	characteristic
300	Dic₅	—	12	4	no	—
301	C₂⁴	#1203	1	1	yes	characteristic
302	C₂²×C₄	—	6	4	no	—
303	C₂²×C₄	—	6	2	no	—
304	C₂²×C₄	—	12	2	no	—
305	C₂²×C₄	—	12	2	no	—
306	C₂²×C₄	—	30	4	no	—
307	C₂²×C₄	—	30	2	no	—
308	C₂²×C₄	—	60	2	no	—
309	C₂²×C₄	—	60	2	no	—
310	C₂²×C₄	D₅×Dic₃	1	2	yes	—
311	C₂²×C₄	D₃×Dic₅	1	2	yes	—
312	C₂²×C₄	#1200	1	2	yes	—
313	C₂²×C₄	#1201	1	2	yes	—
314	C₂²×C₄	#1202	1	2	yes	—
315	C₂²×C₄	#1203	1	1	yes	characteristic
316	C₂²×C₄	#1204	1	2	yes	—
317	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
318	C₂×C₈	—	5	4	no	—
319	C₂×C₈	—	10	8	no	—
320	C₂×C₈	—	10	2	no	—
321	C₂×C₈	—	10	2	no	—
322	C₄⋊C₄	—	3	4	no	—
323	C₄⋊C₄	—	6	4	no	—
324	C₄⋊C₄	—	6	2	no	—
325	C₄⋊C₄	—	15	4	no	—
326	C₄⋊C₄	—	30	4	no	—
327	C₄⋊C₄	—	30	2	no	—
328	C₃×C₅	C₂×#340	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	#3939	1	4	yes	—
330	C₂²×C₃	#3940	1	4	yes	—
331	C₂²×C₃	#3941	1	4	yes	—
332	C₂²×C₃	#3942	1	4	yes	—
333	C₂²×C₃	#3963	1	4	yes	—
334	C₂²×C₃	#3964	1	4	yes	—
335	C₂²×C₃	#3967	1	4	yes	—
336	C₂²×C₃	C₂×#683	1	1	yes	characteristic
337	C₂²×C₃	C₂×#685	1	1	yes	characteristic
338	C₂²×C₃	C₂×#686	1	1	yes	characteristic
339	C₂²×C₃	C₂×#687	1	1	yes	characteristic
340	C₂²×C₃	C₂×#688	1	1	yes	characteristic
341	C₂²×C₃	C₂×#689	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
343	C₃×C₄	#3963	1	4	yes	—
344	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
345	C₃×C₄	C₂×#683	1	1	yes	characteristic
346	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
347	C₃×C₄	C₂×#685	1	1	yes	characteristic
348	Dic₃	—	4	4	no	—
349	Dic₃	—	20	4	no	—
350	C₂×C₅	#4551	1	8	yes	complemented
351	C₂×C₅	C₂×#816	1	1	yes	characteristic
352	C₂×C₅	C₂×#816	1	1	yes	characteristic
353	C₂×C₅	C₂×#817	1	1	yes	characteristic
354	C₂×C₅	C₂×#818	1	1	yes	characteristic
355	C₂×C₅	C₂×#821	1	1	yes	characteristic
356	C₂×C₅	C₂×#821	1	1	yes	characteristic
357	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
358	C₂³	#6654	1	2	yes	—
359	C₂³	#6659	1	2	yes	—
360	C₂³	#6660	1	2	yes	—
361	C₂³	#6663	1	2	yes	—
362	C₂³	(C₂×D₃)⋊Dic₅	1	2	yes	—
363	C₂³	#6667	1	2	yes	—
364	C₂³	#6668	1	2	yes	—
365	C₂³	C₂×#1203	1	1	yes	characteristic
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	—	12	8	no	—
368	C₂×C₄	—	12	2	no	—
369	C₂×C₄	—	12	2	no	—
370	C₂×C₄	—	30	4	no	—
371	C₂×C₄	—	60	8	no	—
372	C₂×C₄	—	60	2	no	—
373	C₂×C₄	—	60	2	no	—
374	C₂×C₄	Dic₃×Dic₅	1	4	yes	—
375	C₂×C₄	#6665	1	4	yes	—
376	C₂×C₄	(C₂×D₃)⋊Dic₅	1	2	yes	—
377	C₂×C₄	#6667	1	2	yes	—
378	C₂×C₄	#6668	1	2	yes	—
379	C₂×C₄	#6669	1	4	yes	—
380	C₂×C₄	Dic₃⋊Dic₅	1	4	yes	—
381	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
382	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
383	C₂×C₄	C₂×#1200	1	1	yes	characteristic
384	C₂×C₄	C₂×#1201	1	1	yes	characteristic
385	C₂×C₄	C₂×#1202	1	1	yes	characteristic
386	C₂×C₄	C₂×#1204	1	1	yes	characteristic
387	C₈	—	10	4	no	—
388	C₂×C₃	#64749	1	8	yes	complemented
389	C₂×C₃	C₂×#3939	1	1	yes	characteristic
390	C₂×C₃	C₂×#3940	1	1	yes	characteristic
391	C₂×C₃	C₂×#3941	1	1	yes	characteristic
392	C₂×C₃	C₂×#3942	1	1	yes	characteristic
393	C₂×C₃	C₂×#3963	1	1	yes	characteristic
394	C₂×C₃	C₂×#3964	1	1	yes	characteristic
395	C₂×C₃	C₂×#3967	1	1	yes	characteristic
396	C₅	C₂×#4551	1	1	yes	characteristic, complemented, Sylow
397	C₂²	#90967	1	4	yes	—
398	C₂²	#90969	1	4	yes	—
399	C₂²	#90973	1	4	yes	—
400	C₂²	#90975	1	4	yes	—
401	C₂²	#90985	1	4	yes	—
402	C₂²	#90988	1	4	yes	—
403	C₂²	#90994	1	4	yes	—
404	C₂²	C₂×#6654	1	1	yes	characteristic
405	C₂²	C₂×#6659	1	1	yes	characteristic
406	C₂²	C₂×#6660	1	1	yes	characteristic
407	C₂²	C₂×#6663	1	1	yes	characteristic
408	C₂²	C₂×(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
409	C₂²	C₂×#6667	1	1	yes	characteristic
410	C₂²	C₂×#6668	1	1	yes	characteristic
411	C₄	—	12	4	no	—
412	C₄	—	60	4	no	—
413	C₄	#90994	1	4	yes	—
414	C₄	C₂×Dic₃×Dic₅	1	1	yes	characteristic
415	C₄	C₂×#6665	1	1	yes	characteristic
416	C₄	C₂×#6669	1	1	yes	characteristic
417	C₄	C₂×Dic₃⋊Dic₅	1	1	yes	characteristic
418	C₃	C₂×#64749	1	1	yes	characteristic, complemented, Sylow
419	C₂	#11745981	1	8	yes	direct product factor
420	C₂	C₂×#90967	1	1	yes	characteristic
421	C₂	C₂×#90969	1	1	yes	characteristic
422	C₂	C₂×#90973	1	1	yes	characteristic
423	C₂	C₂×#90975	1	1	yes	characteristic
424	C₂	C₂×#90985	1	1	yes	characteristic
425	C₂	C₂×#90988	1	1	yes	characteristic
426	C₂	C₂×#90994	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	#1203
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle, prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#340
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. #11745981	C₂	direct (N × H)
11. C₂×C₄⋊Dic₁₅	C₄	semidirect
15. C₂×C₅×C₄⋊Dic₃	C₄	semidirect
19. C₂²×C₃×#168	C₄	semidirect
45. C₄⋊Dic₁₅	C₂×C₄	semidirect
48. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
52. C₂×C₃×#168	C₂×C₄	semidirect
70. C₂²×#168	Dic₃	semidirect
116. C₂×C₄⋊Dic₃	Dic₅	semidirect
144. C₂×#168	C₂×Dic₃	semidirect
196. C₄⋊Dic₃	C₂×Dic₅	semidirect
242. C₂×C₃×C₅	#340	semidirect
328. C₃×C₅	C₂×#340	semidirect
350. C₂×C₅	#4551	semidirect
388. C₂×C₃	#64749	semidirect
396. C₅	C₂×#4551	semidirect
418. C₃	C₂×#64749	semidirect
419. C₂	#11745981	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×C₄⋊Dic₁₅	2
C₂²×C₅×C₄⋊Dic₃	2
C₂³×C₃×#168	2
#11745981	2
C₂×#64749	3
C₂×#4551	5

Subgroups — C2×#11745981 #14294544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745981 #14294544