Subgroups — C₂×C₃×#65009 #14413821

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×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3947	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×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65009	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65009	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	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×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
14	C₂×C₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
15	C₃×#4072	C₄	1	4	yes	—
16	C₃×#4072	C₂²	1	4	yes	—
17	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
24	C₃×C₂²⋊#168	C₂²	1	4	yes	—
25	C₃×#3947	C₂²	1	4	yes	complemented
26	C₃×#3946	C₂²	1	4	yes	complemented
27	C₃×#3946	C₂²	1	4	yes	complemented
28	C₃×C₈×Dic₅	C₂²	1	4	yes	complemented
29	C₂×C₃×#433	—	5	1	no	maximal, Hall
30	C₂×#4072	C₂×C₃	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
32	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic
33	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
37	#65009	C₂×C₃	1	8	yes	direct product factor
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×C₅×C₈	—	2	2	no	—
50	C₂×C₃×C₅×C₈	—	2	2	no	—
51	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
54	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
56	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
57	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
58	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
59	C₃×C₄×Dic₅	C₂³	1	2	yes	—
60	C₃×C₄×Dic₅	C₂³	1	2	yes	—
61	C₂×C₃×#168	—	2	2	no	—
62	C₂×C₃×#168	—	2	2	no	—
63	C₂×C₃×#168	C₂³	1	2	yes	—
64	C₂×C₃×#168	C₂³	1	2	yes	—
65	C₂×C₃×#117	—	5	1	no	—
66	C₃×#433	—	5	8	no	—
67	C₂×C₃×C₄⋊C₈	—	5	1	no	—
68	C₂×C₃×C₄⋊C₈	—	5	1	no	—
69	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
70	C₂×C₃×C₂²⋊C₈	D₅	1	1	yes	characteristic
71	C₂×C₃×#97	—	5	1	no	—
72	C₂×C₃×C₄×C₈	—	5	1	no	—
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₅	C₃×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₅	C₃×C₄	1	1	yes	characteristic
78	#4072	C₃×C₄	1	4	yes	—
79	#4072	C₂²×C₃	1	4	yes	—
80	C₂×C₄⋊Dic₅	C₃×C₄	1	1	yes	characteristic
81	C₂×C₄⋊Dic₅	C₃×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
85	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
86	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
87	C₂²⋊#168	C₂²×C₃	1	4	yes	—
88	#3947	C₂²×C₃	1	4	yes	complemented
89	#3946	C₂²×C₃	1	4	yes	complemented
90	#3946	C₂²×C₃	1	4	yes	complemented
91	C₈×Dic₅	C₂²×C₃	1	4	yes	complemented
92	C₂×#433	—	5	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×C₅×C₈	—	2	2	no	—
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃×#168	—	2	2	no	—
118	C₃×#168	—	2	2	no	—
119	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	—	5	1	no	—
121	C₂²×C₃×C₈	—	5	1	no	—
122	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
123	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
124	C₃×#117	—	5	4	no	—
125	C₃×#117	—	5	4	no	—
126	C₂×C₃×C₄⋊C₄	—	5	1	no	—
127	C₂×C₃×C₄⋊C₄	—	5	1	no	—
128	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
129	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
130	C₂×C₃×C₄²	—	5	1	no	—
131	C₂×C₃×C₄²	—	5	1	no	—
132	C₃×C₄⋊C₈	—	5	4	no	—
133	C₃×C₄⋊C₈	—	5	4	no	—
134	C₃×C₂²⋊C₈	—	5	4	no	—
135	C₃×C₂²⋊C₈	C₂×D₅	1	4	yes	—
136	C₃×#97	—	5	4	no	—
137	C₃×C₄×C₈	—	5	4	no	—
138	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
143	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
144	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
145	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
152	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
153	C₂²⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
154	C₂²⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
155	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
156	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
157	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
158	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
159	C₄×Dic₅	C₂³×C₃	1	2	yes	—
160	C₄×Dic₅	C₂³×C₃	1	2	yes	—
161	C₂×#168	—	2	2	no	—
162	C₂×#168	—	2	2	no	—
163	C₂×#168	C₂³×C₃	1	2	yes	—
164	C₂×#168	C₂³×C₃	1	2	yes	—
165	C₂×#117	—	5	1	no	—
166	#433	—	5	8	no	—
167	C₂×C₄⋊C₈	—	5	1	no	—
168	C₂×C₄⋊C₈	—	5	1	no	—
169	C₂×C₂²⋊C₈	—	5	1	no	—
170	C₂×C₂²⋊C₈	C₃×D₅	1	1	yes	characteristic
171	C₂×#97	—	5	1	no	—
172	C₂×C₄×C₈	—	5	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	C₂×C₃×C₈	—	2	2	no	—
201	C₂×C₃×C₈	—	2	2	no	—
202	C₂×C₃×C₈	—	5	2	no	—
203	C₂×C₃×C₈	—	5	2	no	—
204	C₂×C₃×C₈	—	10	2	no	—
205	C₂×C₃×C₈	—	10	2	no	—
206	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
207	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
208	C₃×C₄⋊C₄	—	5	4	no	—
209	C₃×C₄⋊C₄	—	5	4	no	—
210	C₃×C₂²⋊C₄	—	5	4	no	—
211	C₃×C₂²⋊C₄	—	5	4	no	—
212	C₃×C₄²	—	5	2	no	—
213	C₃×C₄²	—	5	2	no	—
214	C₃×C₄²	—	5	2	no	—
215	C₃×C₄²	—	5	2	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
220	C₂³×C₅	C₂²×C₃×C₄	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	C₂²×C₃×C₄	1	2	yes	—
226	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₃×#41	1	2	yes	—
228	C₂×C₄×C₅	C₃×#41	1	2	yes	—
229	C₂×C₄×C₅	C₂⁴×C₃	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×C₃×C₄	1	2	yes	—
235	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
236	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
237	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	2	no	—
240	#168	—	2	2	no	—
241	#168	—	2	2	no	—
242	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
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	—	5	4	no	—
256	C₄⋊C₈	—	5	4	no	—
257	C₂²⋊C₈	—	5	4	no	—
258	C₂²⋊C₈	C₂×C₃×D₅	1	4	yes	—
259	#97	—	5	4	no	—
260	C₄×C₈	—	5	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	C₃×#117	1	2	yes	—
297	C₂²×C₅	C₃×#131	1	2	yes	—
298	C₂²×C₅	C₃×#131	1	2	yes	—
299	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	C₃×#117	1	2	yes	—
302	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
303	C₄×C₅	C₂×C₃×#41	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	C₃×C₄×D₅	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	C₃×C₄×D₅	1	1	yes	characteristic
316	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
317	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
318	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	5	2	no	—
322	C₂×C₈	—	5	2	no	—
323	C₂×C₈	—	10	2	no	—
324	C₂×C₈	—	10	2	no	—
325	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
326	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
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	C₃×#433	1	4	yes	complemented
354	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
355	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
356	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
361	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	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×C₃×C₄×D₅	1	2	yes	—
375	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
376	C₂×C₄	C₃×#711	1	2	yes	—
377	C₂×C₄	C₃×#711	1	2	yes	—
378	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	10	2	no	—
382	C₈	—	10	2	no	—
383	C₂×C₃	—	4	2	no	—
384	C₂×C₃	#65009	1	4	yes	direct product factor
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×C₃×#433	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	C₃×#4023	1	2	yes	—
394	C₂²	C₃×#4047	1	2	yes	—
395	C₂²	C₃×#4053	1	2	yes	—
396	C₂²	C₂²×C₃×C₄×D₅	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	C₃×#4023	1	2	yes	—
403	C₄	C₂×C₃×#711	1	1	yes	characteristic
404	C₄	C₂×C₃×#711	1	1	yes	characteristic
405	C₃	C₂×#65009	1	1	yes	characteristic, direct product factor, Sylow
406	C₂	—	4	2	no	—
407	C₂	C₃×#65009	1	4	yes	direct product factor
408	C₂	C₂×C₃×#4023	1	1	yes	characteristic
409	C₂	C₂×C₃×#4047	1	1	yes	characteristic
410	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×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₂²⋊C₈	D₅
hypocenter	C₅	C₂×C₃×#433
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×#3947	C₂	semidirect
5. C₂×C₃×#3946	C₂	semidirect
6. C₂×C₃×#3946	C₂	semidirect
7. C₂×C₃×C₈×Dic₅	C₂	semidirect
8. C₃×#65009	C₂	direct (N × H)
9. C₂×#65009	C₃	direct (N × H)
25. C₃×#3947	C₂²	semidirect
26. C₃×#3946	C₂²	semidirect
27. C₃×#3946	C₂²	semidirect
28. C₃×C₈×Dic₅	C₂²	semidirect
33. C₂×#3947	C₂×C₃	semidirect
34. C₂×#3946	C₂×C₃	semidirect
35. C₂×#3946	C₂×C₃	semidirect
36. C₂×C₈×Dic₅	C₂×C₃	semidirect
37. #65009	C₂×C₃	direct (N × H)
88. #3947	C₂²×C₃	semidirect
89. #3946	C₂²×C₃	semidirect
90. #3946	C₂²×C₃	semidirect
91. C₈×Dic₅	C₂²×C₃	semidirect
262. C₂×C₃×C₅	#433	semidirect
335. C₃×C₅	C₂×#433	semidirect
353. C₂×C₅	C₃×#433	semidirect
384. C₂×C₃	#65009	direct (N × H)
388. C₅	C₂×C₃×#433	semidirect
405. C₃	C₂×#65009	direct (N × H)
407. C₂	C₃×#65009	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×C₃×C₅×C₂²⋊C₈	2
C₂×C₃×C₂²⋊#168	2
C₂×C₃×#3947	2
C₂×C₃×#3946	2
C₂×C₃×C₈×Dic₅	2
C₃×#65009	2
C₂×#65009	3
C₂×C₃×#433	5

Subgroups — C2×C3×#65009 #14413821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65009 #14413821