Subgroups — C₂×#11748319 #14413859

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
2	C₂×#91114	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
4	C₂×#90982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90952	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748319	C₂	1	8	yes	maximal, direct product factor
8	C₂×Dic₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65009	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
17	C₃×#4072	C₄	1	4	yes	—
18	C₃×#4072	C₂²	1	4	yes	—
19	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
21	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	#91114	C₂²	1	4	yes	—
24	C₅×#830	C₂²	1	4	yes	—
25	#90982	C₂²	1	4	yes	complemented
26	#90982	C₂²	1	4	yes	complemented
27	#90952	C₂²	1	4	yes	complemented
28	Dic₅×C₃⋊C₈	C₂²	1	4	yes	complemented
29	C₂×#5000	—	5	1	no	maximal, Hall
30	C₂×#4072	D₃	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
32	C₂×C₂²⋊#168	—	3	1	no	—
33	C₂×#3947	—	3	1	no	—
34	C₂×#3946	—	3	1	no	—
35	C₂×#3946	—	3	1	no	—
36	C₂×C₈×Dic₅	—	3	1	no	—
37	#65009	—	3	8	no	—
38	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	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	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃⋊#168	—	2	2	no	—
50	C₂×C₃⋊#168	—	2	2	no	—
51	C₂×C₃⋊#168	C₂³	1	2	yes	—
52	C₂×C₃⋊#168	C₂³	1	2	yes	—
53	C₂×C₅×C₃⋊C₈	—	2	2	no	—
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
56	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
57	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
58	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
59	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
60	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
61	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
62	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
63	C₃×C₄×Dic₅	C₂³	1	2	yes	—
64	C₃×C₄×Dic₅	C₂³	1	2	yes	—
65	C₂×C₃×#117	—	5	1	no	—
66	C₂×#830	—	5	1	no	—
67	C₂×#830	D₅	1	1	yes	characteristic
68	#5000	—	5	8	no	—
69	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
70	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
71	C₂×#803	—	5	1	no	—
72	C₂×C₄×C₃⋊C₈	—	5	1	no	—
73	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₅×C₈	—	3	1	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂×C₂²⋊Dic₅	Dic₃	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₅	Dic₃	1	1	yes	characteristic
78	#4072	Dic₃	1	4	yes	—
79	#4072	C₂×D₃	1	4	yes	—
80	C₂×C₄⋊Dic₅	Dic₃	1	1	yes	characteristic
81	C₂×C₄⋊Dic₅	Dic₃	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
84	C₂²×#168	—	3	1	no	—
85	C₂²×#168	—	3	1	no	—
86	C₅×C₂²⋊C₈	—	3	4	no	—
87	C₂²⋊#168	—	3	4	no	—
88	#3947	—	3	4	no	—
89	#3946	—	3	4	no	—
90	#3946	—	3	4	no	—
91	C₈×Dic₅	—	3	4	no	—
92	C₂×#433	—	15	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
97	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
115	C₃⋊#168	—	2	2	no	—
116	C₃⋊#168	—	2	2	no	—
117	C₅×C₃⋊C₈	—	2	2	no	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
120	C₃×#117	—	5	4	no	—
121	C₃×#117	—	5	4	no	—
122	C₂×C₃×C₄⋊C₄	—	5	1	no	—
123	C₂×C₃×C₄⋊C₄	—	5	1	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
125	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₂×C₃×C₄²	—	5	1	no	—
128	C₂²×C₃⋊C₈	—	5	1	no	—
129	C₂²×C₃⋊C₈	—	5	1	no	—
130	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
131	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
132	#830	—	5	4	no	—
133	#830	C₂×D₅	1	4	yes	—
134	C₄⋊(C₃⋊C₈)	—	5	4	no	—
135	C₄⋊(C₃⋊C₈)	—	5	4	no	—
136	#803	—	5	4	no	—
137	C₄×C₃⋊C₈	—	5	4	no	—
138	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
143	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
146	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
147	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
148	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
149	C₂×C₅×C₈	—	3	2	no	—
150	C₂×C₅×C₈	—	3	2	no	—
151	C₂×C₅×C₈	—	6	2	no	—
152	C₂×C₅×C₈	—	6	2	no	—
153	C₂²⋊Dic₅	C₂×Dic₃	1	4	yes	—
154	C₂²⋊Dic₅	C₂×Dic₃	1	4	yes	—
155	C₄⋊Dic₅	C₂×Dic₃	1	4	yes	—
156	C₄⋊Dic₅	C₂×Dic₃	1	4	yes	—
157	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
158	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
159	C₄×Dic₅	C₂²×D₃	1	2	yes	—
160	C₄×Dic₅	C₂²×D₃	1	2	yes	—
161	C₂×#168	—	3	2	no	—
162	C₂×#168	—	3	2	no	—
163	C₂×#168	—	6	2	no	—
164	C₂×#168	—	6	2	no	—
165	C₂×#117	—	5	1	no	—
166	#433	—	15	8	no	—
167	C₂×C₄⋊C₈	—	15	1	no	—
168	C₂×C₄⋊C₈	—	15	1	no	—
169	C₂×C₂²⋊C₈	—	3	1	no	—
170	C₂×C₂²⋊C₈	—	15	1	no	—
171	C₂×#97	—	15	1	no	—
172	C₂×C₄×C₈	—	15	1	no	—
173	C₂²×C₃×C₅	—	2	2	no	—
174	C₂²×C₃×C₅	—	2	2	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	4	4	no	—
177	C₂²×C₃×C₅	#117	1	2	yes	—
178	C₂²×C₃×C₅	#131	1	2	yes	—
179	C₂²×C₃×C₅	#131	1	2	yes	—
180	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₃×C₄×C₅	—	2	2	no	—
182	C₃×C₄×C₅	#117	1	2	yes	—
183	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
185	C₃×Dic₅	—	2	2	no	—
186	C₃×Dic₅	—	2	2	no	—
187	C₃×Dic₅	—	2	2	no	—
188	C₃×Dic₅	—	2	2	no	—
189	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	—	5	1	no	—
193	C₂²×C₃×C₄	—	5	1	no	—
194	C₂²×C₃×C₄	—	5	1	no	—
195	C₂²×C₃×C₄	—	5	1	no	—
196	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
198	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
199	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	5	4	no	—
201	C₃×C₄⋊C₄	—	5	4	no	—
202	C₃×C₂²⋊C₄	—	5	4	no	—
203	C₃×C₂²⋊C₄	—	5	4	no	—
204	C₃×C₄²	—	5	2	no	—
205	C₃×C₄²	—	5	2	no	—
206	C₃×C₄²	—	5	2	no	—
207	C₃×C₄²	—	5	2	no	—
208	C₂×C₃⋊C₈	—	2	2	no	—
209	C₂×C₃⋊C₈	—	2	2	no	—
210	C₂×C₃⋊C₈	—	5	2	no	—
211	C₂×C₃⋊C₈	—	5	2	no	—
212	C₂×C₃⋊C₈	—	10	2	no	—
213	C₂×C₃⋊C₈	—	10	2	no	—
214	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
215	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
220	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	4	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	#235	1	2	yes	—
226	C₂×C₄×C₅	#235	1	2	yes	—
227	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
228	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
230	C₂×Dic₅	—	2	2	no	—
231	C₂×Dic₅	—	2	2	no	—
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	2	2	no	—
234	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
235	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
236	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
237	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
238	C₅×C₈	—	6	2	no	—
239	C₅×C₈	—	6	2	no	—
240	#168	—	6	2	no	—
241	#168	—	6	2	no	—
242	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
243	C₂²×C₈	—	3	1	no	—
244	C₂²×C₈	—	3	1	no	—
245	C₂²×C₈	—	15	1	no	—
246	C₂²×C₈	—	15	1	no	—
247	#117	—	5	4	no	—
248	#117	—	5	4	no	—
249	C₂×C₄⋊C₄	—	5	1	no	—
250	C₂×C₄⋊C₄	—	5	1	no	—
251	C₂×C₂²⋊C₄	—	5	1	no	—
252	C₂×C₂²⋊C₄	—	5	1	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	5	1	no	—
255	C₄⋊C₈	—	15	4	no	—
256	C₄⋊C₈	—	15	4	no	—
257	C₂²⋊C₈	—	3	4	no	—
258	C₂²⋊C₈	—	15	4	no	—
259	#97	—	15	4	no	—
260	C₄×C₈	—	15	4	no	—
261	C₂×C₃×C₅	—	4	2	no	—
262	C₂×C₃×C₅	#433	1	4	yes	complemented
263	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	—	2	2	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
270	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	5	2	no	—
276	C₂×C₃×C₄	—	5	2	no	—
277	C₂×C₃×C₄	—	5	2	no	—
278	C₂×C₃×C₄	—	5	2	no	—
279	C₂×C₃×C₄	—	10	2	no	—
280	C₂×C₃×C₄	—	10	2	no	—
281	C₂×C₃×C₄	—	10	2	no	—
282	C₂×C₃×C₄	—	10	2	no	—
283	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
284	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	#711	1	2	yes	—
286	C₂×C₃×C₄	#711	1	2	yes	—
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	C₃⋊C₈	—	2	2	no	—
289	C₃⋊C₈	—	2	2	no	—
290	C₃⋊C₈	—	10	2	no	—
291	C₃⋊C₈	—	10	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	4	4	no	—
296	C₂²×C₅	#926	1	2	yes	—
297	C₂²×C₅	#948	1	2	yes	—
298	C₂²×C₅	#948	1	2	yes	—
299	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	#926	1	2	yes	—
302	C₄×C₅	C₂×#235	1	1	yes	characteristic
303	C₄×C₅	C₂×#235	1	1	yes	characteristic
304	Dic₅	—	2	2	no	—
305	Dic₅	—	2	2	no	—
306	Dic₅	—	2	2	no	—
307	Dic₅	—	2	2	no	—
308	C₂⁴	D₅×Dic₃	1	1	yes	characteristic
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
316	C₂²×C₄	D₅×Dic₃	1	2	yes	—
317	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
318	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
319	C₂×C₈	—	3	2	no	—
320	C₂×C₈	—	3	2	no	—
321	C₂×C₈	—	6	2	no	—
322	C₂×C₈	—	6	2	no	—
323	C₂×C₈	—	15	2	no	—
324	C₂×C₈	—	15	2	no	—
325	C₂×C₈	—	30	2	no	—
326	C₂×C₈	—	30	2	no	—
327	C₄⋊C₄	—	5	4	no	—
328	C₄⋊C₄	—	5	4	no	—
329	C₂²⋊C₄	—	5	4	no	—
330	C₂²⋊C₄	—	5	4	no	—
331	C₄²	—	5	2	no	—
332	C₄²	—	5	2	no	—
333	C₄²	—	5	2	no	—
334	C₄²	—	5	2	no	—
335	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	4	4	no	—
340	C₂²×C₃	#4023	1	2	yes	—
341	C₂²×C₃	#4047	1	2	yes	—
342	C₂²×C₃	#4053	1	2	yes	—
343	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	10	2	no	—
346	C₃×C₄	—	10	2	no	—
347	C₃×C₄	—	10	2	no	—
348	C₃×C₄	—	10	2	no	—
349	C₃×C₄	#4023	1	2	yes	—
350	C₃×C₄	C₂×#711	1	1	yes	characteristic
351	C₃×C₄	C₂×#711	1	1	yes	characteristic
352	C₂×C₅	—	4	2	no	—
353	C₂×C₅	#5000	1	4	yes	complemented
354	C₂×C₅	C₂×#926	1	1	yes	characteristic
355	C₂×C₅	C₂×#948	1	1	yes	characteristic
356	C₂×C₅	C₂×#948	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×D₅×Dic₃	1	2	yes	—
361	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	5	2	no	—
369	C₂×C₄	—	5	2	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	10	2	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
375	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
376	C₂×C₄	#6782	1	2	yes	—
377	C₂×C₄	#6782	1	2	yes	—
378	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
379	C₈	—	6	2	no	—
380	C₈	—	6	2	no	—
381	C₈	—	30	2	no	—
382	C₈	—	30	2	no	—
383	C₂×C₃	—	4	2	no	—
384	C₂×C₃	#65009	1	4	yes	complemented
385	C₂×C₃	C₂×#4023	1	1	yes	characteristic
386	C₂×C₃	C₂×#4047	1	1	yes	characteristic
387	C₂×C₃	C₂×#4053	1	1	yes	characteristic
388	C₅	C₂×#5000	1	1	yes	characteristic, complemented, Sylow
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	#91283	1	2	yes	—
394	C₂²	#91284	1	2	yes	—
395	C₂²	#91528	1	2	yes	—
396	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	10	2	no	—
399	C₄	—	10	2	no	—
400	C₄	—	10	2	no	—
401	C₄	—	10	2	no	—
402	C₄	#91528	1	2	yes	—
403	C₄	C₂×#6782	1	1	yes	characteristic
404	C₄	C₂×#6782	1	1	yes	characteristic
405	C₃	C₂×#65009	1	1	yes	characteristic, complemented, Sylow
406	C₂	—	4	2	no	—
407	C₂	#11748319	1	4	yes	direct product factor
408	C₂	C₂×#91283	1	1	yes	characteristic
409	C₂	C₂×#91284	1	1	yes	characteristic
410	C₂	C₂×#91528	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#433
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. C₂×#90982	C₂	semidirect
5. C₂×#90982	C₂	semidirect
6. C₂×#90952	C₂	semidirect
7. #11748319	C₂	direct (N × H)
8. C₂×Dic₅×C₃⋊C₈	C₂	semidirect
25. #90982	C₂²	semidirect
26. #90982	C₂²	semidirect
27. #90952	C₂²	semidirect
28. Dic₅×C₃⋊C₈	C₂²	semidirect
262. C₂×C₃×C₅	#433	semidirect
335. C₃×C₅	C₂×#433	semidirect
353. C₂×C₅	#5000	semidirect
384. C₂×C₃	#65009	semidirect
388. C₅	C₂×#5000	semidirect
405. C₃	C₂×#65009	semidirect
407. C₂	#11748319	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#4072	2
C₂×#91114	2
C₂×C₅×#830	2
C₂×#90982	2
C₂×#90952	2
#11748319	2
C₂×Dic₅×C₃⋊C₈	2
C₂×#65009	3
C₂×#5000	5

Subgroups — C2×#11748319 #14413859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748319 #14413859