Subgroups — C₂×#11745986 #14294765

Order 1920.

864 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6710	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic
4	#11745986	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64750	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂³×C₅×Dic₃	C₄	1	2	yes	—
8	C₂×#6710	—	2	2	no	—
9	C₂×#6710	—	2	1	no	—
10	C₂×#6710	C₄	1	4	yes	complemented
11	C₂×#6710	C₂²	1	2	yes	—
12	C₂²×C₃⋊#168	—	2	1	no	—
13	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
14	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₄	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₃×#681	—	2	2	no	—
20	C₂×C₃×#681	—	2	1	no	—
21	C₂×C₃×#681	C₄	1	4	yes	complemented
22	C₂×C₃×#681	C₂²	1	2	yes	—
23	C₂²×C₃×#168	—	2	1	no	—
24	C₂×#4554	—	5	1	no	maximal, Hall
25	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
26	C₂²×#681	—	3	1	no	—
27	C₂²×#681	D₃	1	1	yes	characteristic
28	#64750	—	3	4	no	—
29	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₂²×C₅×Dic₃	—	2	2	no	—
42	C₂²×C₅×Dic₃	—	4	4	no	—
43	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
44	#6710	—	2	4	no	—
45	#6710	—	2	2	no	—
46	#6710	C₂×C₄	1	4	yes	complemented
47	C₂×C₃⋊#168	—	2	4	no	—
48	C₂×C₃⋊#168	—	2	2	no	—
49	C₅×C₄⋊Dic₃	—	2	2	no	—
50	C₅×C₄⋊Dic₃	—	2	2	no	—
51	C₅×C₄⋊Dic₃	—	2	2	no	—
52	C₅×C₄⋊Dic₃	—	2	2	no	—
53	C₃×#681	—	2	4	no	—
54	C₃×#681	—	2	2	no	—
55	C₃×#681	C₂×C₄	1	4	yes	complemented
56	C₂×C₃×#168	—	2	4	no	—
57	C₂×C₃×#168	—	2	2	no	—
58	C₂²×C₃×M₁₆	—	5	1	no	—
59	C₂²×C₄⋊Dic₃	D₅	1	1	yes	characteristic
60	C₂²×#208	—	5	1	no	—
61	#4554	—	5	4	no	—
62	C₂³×C₄×C₅	—	3	2	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	—	3	2	no	—
65	C₂×C₅×C₄⋊C₄	—	3	2	no	—
66	C₂×C₅×C₄⋊C₄	—	6	1	no	—
67	C₂×C₅×C₄⋊C₄	—	6	1	no	—
68	C₂×C₅×C₄⋊C₄	—	6	1	no	—
69	C₂×C₅×C₄⋊C₄	—	6	1	no	—
70	C₂×#681	—	2	1	no	—
71	C₂×#681	—	2	2	no	—
72	C₂×#681	—	3	4	no	—
73	C₂×#681	—	3	2	no	—
74	C₂×#681	—	6	1	no	—
75	C₂×#681	—	6	2	no	—
76	C₂×#681	Dic₃	1	4	yes	complemented
77	C₂×#681	C₂×D₃	1	2	yes	—
78	C₂²×#168	—	2	1	no	—
79	C₂²×#168	—	6	1	no	—
80	C₂×#343	—	15	1	no	Sylow
81	C₂³×C₃×C₅	—	2	2	no	—
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	C₄²	1	2	yes	—
84	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
85	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
86	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
87	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
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	C₂²⋊C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₅×Dic₃	—	2	4	no	—
107	C₂×C₅×Dic₃	—	4	4	no	—
108	C₂×C₅×Dic₃	—	4	4	no	—
109	C₂×C₅×Dic₃	—	4	4	no	—
110	C₃⋊#168	—	2	4	no	—
111	C₃×#168	—	2	4	no	—
112	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
113	C₂³×Dic₃	Dic₅	1	2	yes	—
114	C₂×C₃×M₁₆	—	5	4	no	—
115	C₂×C₃×M₁₆	—	5	2	no	—
116	C₂×C₃×M₁₆	—	10	2	no	—
117	C₂×C₃×M₁₆	—	10	1	no	—
118	C₂²×C₃×C₈	—	10	1	no	—
119	C₂×C₄⋊Dic₃	—	2	1	no	—
120	C₂×C₄⋊Dic₃	—	2	1	no	—
121	C₂×C₄⋊Dic₃	—	2	1	no	—
122	C₂×C₄⋊Dic₃	—	2	1	no	—
123	C₂×C₄⋊Dic₃	Dic₅	1	2	yes	—
124	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	—
125	C₂×#208	—	5	4	no	—
126	C₂×#208	—	5	2	no	—
127	C₂×#208	—	10	2	no	—
128	C₂×#208	—	10	1	no	—
129	C₂²×C₃⋊C₈	—	10	1	no	—
130	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	—	6	2	no	—
133	C₂²×C₄×C₅	—	6	2	no	—
134	C₂²×C₄×C₅	—	12	4	no	—
135	C₂²×C₄×C₅	Dic₆	1	2	yes	—
136	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
138	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
139	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
141	C₂²×C₄×C₅	#67	1	1	yes	characteristic
142	C₂²×C₄×C₅	#67	1	1	yes	characteristic
143	C₂²×C₄×C₅	#67	1	2	yes	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₅×C₄⋊C₄	—	6	2	no	—
146	C₅×C₄⋊C₄	—	6	2	no	—
147	C₅×C₄⋊C₄	—	6	2	no	—
148	C₅×C₄⋊C₄	—	6	2	no	—
149	#681	—	2	4	no	—
150	#681	—	2	2	no	—
151	#681	—	3	4	no	—
152	#681	—	6	4	no	—
153	#681	—	6	2	no	—
154	#681	C₂×Dic₃	1	4	yes	complemented
155	C₂×#168	—	2	4	no	—
156	C₂×#168	—	2	2	no	—
157	C₂×#168	—	6	4	no	—
158	C₂×#168	—	6	2	no	—
159	C₂²×M₁₆	—	5	1	no	—
160	C₂²×M₁₆	—	15	1	no	—
161	C₂²×C₄⋊C₄	—	3	1	no	—
162	#343	—	15	4	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	—	2	4	no	—
165	C₂²×C₃×C₅	—	2	1	no	—
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	—	2	1	no	—
169	C₂²×C₃×C₅	#95	1	2	yes	—
170	C₂²×C₃×C₅	#95	1	2	yes	—
171	C₂²×C₃×C₅	#100	1	2	yes	—
172	C₂²×C₃×C₅	#101	1	2	yes	—
173	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₃×C₄×C₅	#95	1	2	yes	—
177	C₃×C₄×C₅	#95	1	2	yes	—
178	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₅×Dic₃	—	4	4	no	—
183	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
185	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
186	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
187	C₂²×C₃×C₄	D₂₀	1	2	yes	—
188	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
194	C₂²×Dic₃	—	2	2	no	—
195	C₂²×Dic₃	—	2	2	no	—
196	C₂²×Dic₃	—	4	4	no	—
197	C₂²×Dic₃	C₂×Dic₅	1	4	yes	—
198	C₃×M₁₆	—	5	4	no	—
199	C₃×M₁₆	—	10	4	no	—
200	C₃×M₁₆	—	10	2	no	—
201	C₂×C₃×C₈	—	10	4	no	—
202	C₂×C₃×C₈	—	10	2	no	—
203	C₄⋊Dic₃	—	2	2	no	—
204	C₄⋊Dic₃	—	2	2	no	—
205	C₄⋊Dic₃	—	2	2	no	—
206	C₄⋊Dic₃	—	2	2	no	—
207	#208	—	5	4	no	—
208	#208	—	10	4	no	—
209	#208	—	10	2	no	—
210	C₂×C₃⋊C₈	—	10	4	no	—
211	C₂×C₃⋊C₈	—	10	2	no	—
212	C₂³×C₅	—	2	2	no	—
213	C₂³×C₅	—	2	2	no	—
214	C₂³×C₅	C₄×Dic₃	1	2	yes	—
215	C₂³×C₅	Dic₃⋊C₄	1	2	yes	—
216	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
218	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	—	6	4	no	—
220	C₂×C₄×C₅	—	12	4	no	—
221	C₂×C₄×C₅	—	12	4	no	—
222	C₂×C₄×C₅	—	12	4	no	—
223	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
224	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
225	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
226	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
227	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
228	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
229	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
232	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
233	C₂×C₄×C₅	#217	1	2	yes	—
234	C₂×C₄×C₅	#217	1	2	yes	—
235	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
241	#168	—	2	4	no	—
242	#168	—	6	4	no	—
243	C₂³×C₄	—	3	2	no	—
244	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
245	C₂×M₁₆	—	5	4	no	—
246	C₂×M₁₆	—	5	2	no	—
247	C₂×M₁₆	—	10	1	no	—
248	C₂×M₁₆	—	10	2	no	—
249	C₂×M₁₆	—	15	4	no	—
250	C₂×M₁₆	—	15	2	no	—
251	C₂×M₁₆	—	30	2	no	—
252	C₂×M₁₆	—	30	1	no	—
253	C₂²×C₈	—	10	1	no	—
254	C₂²×C₈	—	30	1	no	—
255	C₂×C₄⋊C₄	—	3	2	no	—
256	C₂×C₄⋊C₄	—	3	2	no	—
257	C₂×C₄⋊C₄	—	6	1	no	—
258	C₂×C₄⋊C₄	—	6	1	no	—
259	C₂×C₄⋊C₄	—	6	1	no	—
260	C₂×C₄⋊C₄	—	6	1	no	—
261	C₂×C₃×C₅	—	2	2	no	—
262	C₂×C₃×C₅	—	2	1	no	—
263	C₂×C₃×C₅	—	2	1	no	—
264	C₂×C₃×C₅	#343	1	4	yes	complemented
265	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
266	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
267	C₂×C₃×C₅	C₂×#101	1	1	yes	characteristic
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	C₄×Dic₅	1	2	yes	—
271	C₂³×C₃	C₄⋊Dic₅	1	2	yes	—
272	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
273	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
274	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
276	C₂×C₃×C₄	#683	1	2	yes	—
277	C₂×C₃×C₄	#683	1	2	yes	—
278	C₂×C₃×C₄	#683	1	2	yes	—
279	C₂×C₃×C₄	#683	1	2	yes	—
280	C₂×C₃×C₄	C₄⋊Dic₅	1	2	yes	—
281	C₂×C₃×C₄	#685	1	2	yes	—
282	C₂×C₃×C₄	#685	1	2	yes	—
283	C₂×C₃×C₄	#685	1	2	yes	—
284	C₂×C₃×C₄	#685	1	2	yes	—
285	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
293	C₂×Dic₃	—	2	4	no	—
294	C₂×Dic₃	—	4	4	no	—
295	C₂×Dic₃	—	4	4	no	—
296	C₂×Dic₃	—	4	4	no	—
297	C₃×C₈	—	10	4	no	—
298	C₃⋊C₈	—	10	4	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	4	no	—
304	C₂²×C₅	—	2	4	no	—
305	C₂²×C₅	#823	1	2	yes	—
306	C₂²×C₅	#824	1	2	yes	—
307	C₂²×C₅	C₃⋊#95	1	2	yes	—
308	C₂²×C₅	C₃⋊#95	1	2	yes	—
309	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
310	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
311	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
312	C₄×C₅	—	12	4	no	—
313	C₄×C₅	C₃⋊#95	1	2	yes	—
314	C₄×C₅	C₃⋊#95	1	2	yes	—
315	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
316	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
317	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
318	C₄×C₅	C₂×#217	1	1	yes	characteristic
319	C₂⁴	D₃×Dic₅	1	1	yes	characteristic
320	C₂²×C₄	—	3	4	no	—
321	C₂²×C₄	—	6	2	no	—
322	C₂²×C₄	—	6	2	no	—
323	C₂²×C₄	—	12	4	no	—
324	C₂²×C₄	D₅×Dic₃	1	2	yes	—
325	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
326	C₂²×C₄	#1200	1	2	yes	—
327	C₂²×C₄	#1201	1	1	yes	characteristic
328	C₂²×C₄	#1201	1	1	yes	characteristic
329	C₂²×C₄	#1202	1	2	yes	—
330	C₂²×C₄	#1203	1	1	yes	characteristic
331	C₂²×C₄	#1203	1	1	yes	characteristic
332	C₂²×C₄	#1204	1	2	yes	—
333	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
334	M₁₆	—	5	4	no	—
335	M₁₆	—	10	4	no	—
336	M₁₆	—	10	2	no	—
337	M₁₆	—	15	4	no	—
338	M₁₆	—	30	4	no	—
339	M₁₆	—	30	2	no	—
340	C₂×C₈	—	10	4	no	—
341	C₂×C₈	—	10	2	no	—
342	C₂×C₈	—	30	4	no	—
343	C₂×C₈	—	30	2	no	—
344	C₄⋊C₄	—	6	2	no	—
345	C₄⋊C₄	—	6	2	no	—
346	C₄⋊C₄	—	6	2	no	—
347	C₄⋊C₄	—	6	2	no	—
348	C₃×C₅	C₂×#343	1	1	yes	characteristic, complemented, Hall
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	2	1	no	—
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	4	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	#3963	1	2	yes	—
356	C₂²×C₃	#3963	1	2	yes	—
357	C₂²×C₃	#3965	1	2	yes	—
358	C₂²×C₃	#3968	1	2	yes	—
359	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
360	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
361	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
362	C₃×C₄	#3963	1	2	yes	—
363	C₃×C₄	#3963	1	2	yes	—
364	C₃×C₄	C₂×#683	1	1	yes	characteristic
365	C₃×C₄	C₂×#683	1	1	yes	characteristic
366	C₃×C₄	C₂×#685	1	1	yes	characteristic
367	C₃×C₄	C₂×#685	1	1	yes	characteristic
368	Dic₃	—	4	4	no	—
369	C₂×C₅	—	2	2	no	—
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	#4554	1	4	yes	complemented
373	C₂×C₅	C₂×#823	1	1	yes	characteristic
374	C₂×C₅	C₂×#824	1	1	yes	characteristic
375	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	Dic₃×Dic₅	1	2	yes	—
379	C₂³	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
380	C₂³	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
381	C₂³	Dic₃⋊Dic₅	1	2	yes	—
382	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
383	C₂×C₄	—	6	4	no	—
384	C₂×C₄	—	12	4	no	—
385	C₂×C₄	—	12	4	no	—
386	C₂×C₄	—	12	4	no	—
387	C₂×C₄	Dic₃×Dic₅	1	2	yes	—
388	C₂×C₄	#6665	1	2	yes	—
389	C₂×C₄	#6665	1	2	yes	—
390	C₂×C₄	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
391	C₂×C₄	(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
392	C₂×C₄	#6667	1	2	yes	—
393	C₂×C₄	#6667	1	2	yes	—
394	C₂×C₄	#6668	1	2	yes	—
395	C₂×C₄	#6668	1	2	yes	—
396	C₂×C₄	#6669	1	2	yes	—
397	C₂×C₄	#6669	1	2	yes	—
398	C₂×C₄	Dic₃⋊Dic₅	1	2	yes	—
399	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
400	C₂×C₄	C₂×#1200	1	1	yes	characteristic
401	C₂×C₄	C₂×#1201	1	1	yes	characteristic
402	C₂×C₄	C₂×#1202	1	1	yes	characteristic
403	C₂×C₄	C₂×#1203	1	1	yes	characteristic
404	C₂×C₄	C₂×#1204	1	1	yes	characteristic
405	C₈	—	10	4	no	—
406	C₈	—	30	4	no	—
407	C₂×C₃	—	2	2	no	—
408	C₂×C₃	—	2	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	#64750	1	4	yes	complemented
411	C₂×C₃	C₂×#3963	1	1	yes	characteristic
412	C₂×C₃	C₂×#3965	1	1	yes	characteristic
413	C₂×C₃	C₂×#3968	1	1	yes	characteristic
414	C₅	C₂×#4554	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	4	no	—
421	C₂²	#90959	1	2	yes	—
422	C₂²	#90962	1	2	yes	—
423	C₂²	#90994	1	2	yes	—
424	C₂²	#90994	1	2	yes	—
425	C₂²	C₂×Dic₃×Dic₅	1	1	yes	characteristic
426	C₂²	C₂×(C₂×D₃)⋊Dic₅	1	1	yes	characteristic
427	C₂²	C₂×Dic₃⋊Dic₅	1	1	yes	characteristic
428	C₄	—	12	4	no	—
429	C₄	#90994	1	2	yes	—
430	C₄	#90994	1	2	yes	—
431	C₄	C₂×#6665	1	1	yes	characteristic
432	C₄	C₂×#6667	1	1	yes	characteristic
433	C₄	C₂×#6668	1	1	yes	characteristic
434	C₄	C₂×#6669	1	1	yes	characteristic
435	C₃	C₂×#64750	1	1	yes	characteristic, complemented, Sylow
436	C₂	—	2	2	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	#11745986	1	4	yes	direct product factor
440	C₂	C₂×#90959	1	1	yes	characteristic
441	C₂	C₂×#90962	1	1	yes	characteristic
442	C₂	C₂×#90994	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	(C₂×D₃)⋊Dic₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#343
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. #11745986	C₂	direct (N × H)
10. C₂×#6710	C₄	semidirect
21. C₂×C₃×#681	C₄	semidirect
46. #6710	C₂×C₄	semidirect
55. C₃×#681	C₂×C₄	semidirect
76. C₂×#681	Dic₃	semidirect
154. #681	C₂×Dic₃	semidirect
264. C₂×C₃×C₅	#343	semidirect
348. C₃×C₅	C₂×#343	semidirect
372. C₂×C₅	#4554	semidirect
410. C₂×C₃	#64750	semidirect
414. C₅	C₂×#4554	semidirect
435. C₃	C₂×#64750	semidirect
439. C₂	#11745986	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×#6710	2
C₂²×C₅×C₄⋊Dic₃	2
C₂²×C₃×#681	2
#11745986	2
C₂×#64750	3
C₂×#4554	5

Subgroups — C2×#11745986 #14294765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745986 #14294765