Subgroups — C₃×#10615524 #14411804

Order 1920.

1548 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65418	C₂	1	3	yes	maximal, complemented
5	C₃×#65415	C₂	1	3	yes	maximal, complemented
6	C₃×#65399	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#3952	C₂	1	3	yes	maximal, complemented
8	#10615524	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₃×D₅×#41	—	2	4	no	—
11	C₃×D₅×#41	—	2	4	no	—
12	C₂×C₃×#713	C₄	1	1	yes	characteristic
13	C₂×C₃×Q₈×D₅	C₄	1	1	yes	characteristic
14	C₂×C₃×#711	C₄	1	3	yes	—
15	C₂×C₃×D₄×D₅	C₄	1	3	yes	—
16	C₂×C₃×#709	C₂²	1	3	yes	—
17	C₂²×C₃×C₄×D₅	C₂²	1	3	yes	—
18	C₃×C₅×#131	—	2	4	no	—
19	C₂×C₃×C₅×M₁₆	C₂²	1	3	yes	complemented
20	C₂²×C₃×C₅×C₈	C₂²	1	3	yes	complemented
21	C₃×#4094	—	2	4	no	—
22	C₂×C₃×#681	C₂²	1	3	yes	complemented
23	C₂²×C₃×#168	C₂²	1	3	yes	complemented
24	C₃×#3952	C₂²	1	1	yes	characteristic
25	C₃×#3952	C₂²	1	3	yes	—
26	C₃×#3952	C₂²	1	3	yes	complemented
27	C₃×#3952	C₂²	1	3	yes	complemented
28	C₃×#3952	C₂²	1	6	yes	complemented
29	C₃×#2880	—	5	1	no	maximal, Hall
30	C₂×D₅×#41	C₂×C₃	1	1	yes	characteristic
31	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
33	#65418	C₂×C₃	1	3	yes	complemented
34	#65415	C₂×C₃	1	3	yes	complemented
35	#65399	C₂×C₃	1	3	yes	complemented
36	C₂×#3952	C₂×C₃	1	3	yes	complemented
37	C₂³×C₃×D₅	C₂×C₄	1	3	yes	—
38	C₃×C₅×#41	D₄	1	4	yes	—
39	C₃×C₅×#41	D₄	1	4	yes	—
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₅×D₄	C₂×C₄	1	3	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
43	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	6	yes	—
44	C₂²×C₃×Dic₅	C₂×C₄	1	3	yes	—
45	C₃×#713	—	2	4	no	—
46	C₃×Q₈×D₅	—	2	4	no	—
47	C₃×#711	—	2	12	no	—
48	C₃×D₄×D₅	—	2	12	no	—
49	C₃×#709	—	2	6	no	—
50	C₃×#709	—	2	6	no	—
51	C₂×C₃×D₂₀	C₂×C₄	1	3	yes	—
52	C₂×C₃×C₄×D₅	—	2	6	no	—
53	C₂×C₃×C₄×D₅	—	2	6	no	—
54	C₂×C₃×C₄×D₅	C₂×C₄	1	3	yes	—
55	C₂×C₃×C₄×D₅	C₂×C₄	1	3	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂³	1	3	yes	—
58	C₂×C₃×Dic₁₀	C₂×C₄	1	3	yes	—
59	C₃×C₅×M₁₆	—	2	6	no	—
60	C₂×C₃×C₅×C₈	—	2	6	no	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	3	yes	—
63	C₃×#681	—	2	6	no	—
64	C₂×C₃×#168	—	2	6	no	—
65	C₂×C₃×#168	C₂³	1	1	yes	characteristic
66	C₂×C₃×#168	C₂³	1	3	yes	—
67	C₂²×C₃×#41	—	5	1	no	—
68	C₂×C₃×#131	—	5	1	no	—
69	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
70	C₃×#408	—	5	3	no	—
71	C₃×#408	—	5	3	no	—
72	C₃×#407	—	5	3	no	—
73	C₂×C₃×C₂²⋊C₈	—	5	3	no	—
74	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
75	D₅×#41	—	2	4	no	—
76	D₅×#41	—	2	4	no	—
77	C₂×#713	C₃×C₄	1	1	yes	characteristic
78	C₂×Q₈×D₅	C₃×C₄	1	1	yes	characteristic
79	C₂×#711	C₃×C₄	1	3	yes	—
80	C₂×D₄×D₅	C₃×C₄	1	3	yes	—
81	C₂×#709	C₂²×C₃	1	3	yes	—
82	C₂²×C₄×D₅	C₂²×C₃	1	3	yes	—
83	C₅×#131	—	2	4	no	—
84	C₂×C₅×M₁₆	C₂²×C₃	1	3	yes	complemented
85	C₂²×C₅×C₈	C₂²×C₃	1	3	yes	complemented
86	#4094	—	2	4	no	—
87	C₂×#681	C₂²×C₃	1	3	yes	complemented
88	C₂²×#168	C₂²×C₃	1	3	yes	complemented
89	#3952	C₂²×C₃	1	1	yes	characteristic
90	#3952	C₂²×C₃	1	3	yes	—
91	#3952	C₂²×C₃	1	3	yes	complemented
92	#3952	C₂²×C₃	1	3	yes	complemented
93	#3952	C₂²×C₃	1	6	yes	complemented
94	#2880	—	5	1	no	Sylow
95	C₂³×C₃×C₅	C₂²×C₄	1	3	yes	—
96	C₂²×C₃×D₅	—	2	6	no	—
97	C₂²×C₃×D₅	—	2	6	no	—
98	C₂²×C₃×D₅	—	4	3	no	—
99	C₂²×C₃×D₅	C₂²×C₄	1	3	yes	—
100	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
101	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
102	C₃×C₅×D₄	C₂²⋊C₄	1	12	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	6	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₃×C₂²⋊D₅	—	2	12	no	—
108	C₂×C₃×Dic₅	—	2	6	no	—
109	C₂×C₃×Dic₅	C₂²×C₄	1	3	yes	—
110	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
111	C₃×D₂₀	—	2	6	no	—
112	C₃×C₄×D₅	—	2	6	no	—
113	C₃×C₄×D₅	—	2	6	no	—
114	C₃×C₄×D₅	—	2	1	no	—
115	C₃×C₄×D₅	—	2	1	no	—
116	C₃×C₄×D₅	—	2	3	no	—
117	C₃×C₄×D₅	—	2	3	no	—
118	C₃×Dic₁₀	—	2	6	no	—
119	C₃×C₅×C₈	—	2	1	no	—
120	C₃×C₅×C₈	—	2	3	no	—
121	C₃×#168	—	2	1	no	—
122	C₃×#168	—	2	3	no	—
123	C₂×C₃×#41	—	5	1	no	—
124	C₂×C₃×#41	—	5	3	no	—
125	C₂×C₃×#41	—	5	3	no	—
126	C₂×C₃×#41	—	10	4	no	—
127	C₂×C₃×#41	—	10	4	no	—
128	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
129	C₂²×C₃×Q₈	—	5	1	no	—
130	C₂²×C₃×D₄	—	5	3	no	—
131	C₂³×C₃×C₄	—	5	3	no	—
132	C₃×#131	—	2	4	no	—
133	C₃×#131	—	10	4	no	—
134	C₂×C₃×M₁₆	—	5	3	no	—
135	C₂×C₃×M₁₆	C₂×D₅	1	3	yes	complemented
136	C₂²×C₃×C₈	—	5	3	no	—
137	C₂²×C₃×C₈	C₂×D₅	1	3	yes	complemented
138	C₃×C₂²⋊C₈	—	5	1	no	—
139	C₃×C₂²⋊C₈	—	5	3	no	—
140	C₃×C₂²⋊C₈	—	5	3	no	—
141	C₃×C₂²⋊C₈	—	5	3	no	—
142	C₃×C₂²⋊C₈	—	5	6	no	—
143	C₂³×D₅	C₂×C₃×C₄	1	3	yes	—
144	C₅×#41	C₃×D₄	1	4	yes	—
145	C₅×#41	C₃×D₄	1	4	yes	—
146	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×C₅×D₄	C₂×C₃×C₄	1	3	yes	—
148	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
149	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	6	yes	—
150	C₂²×Dic₅	C₂×C₃×C₄	1	3	yes	—
151	#713	—	2	4	no	—
152	Q₈×D₅	—	2	4	no	—
153	#711	—	2	12	no	—
154	D₄×D₅	—	2	12	no	—
155	#709	—	2	6	no	—
156	#709	—	2	6	no	—
157	C₂×D₂₀	C₂×C₃×C₄	1	3	yes	—
158	C₂×C₄×D₅	—	2	6	no	—
159	C₂×C₄×D₅	—	2	6	no	—
160	C₂×C₄×D₅	C₂×C₃×C₄	1	3	yes	—
161	C₂×C₄×D₅	C₂×C₃×C₄	1	3	yes	—
162	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂³×C₃	1	3	yes	—
164	C₂×Dic₁₀	C₂×C₃×C₄	1	3	yes	—
165	C₅×M₁₆	—	2	6	no	—
166	C₂×C₅×C₈	—	2	6	no	—
167	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂³×C₃	1	3	yes	—
169	#681	—	2	6	no	—
170	C₂×#168	—	2	6	no	—
171	C₂×#168	C₂³×C₃	1	1	yes	characteristic
172	C₂×#168	C₂³×C₃	1	3	yes	—
173	C₂²×#41	—	5	1	no	—
174	C₂×#131	—	5	1	no	—
175	C₂×#131	C₃×D₅	1	1	yes	characteristic, complemented
176	#408	—	5	3	no	—
177	#408	—	5	3	no	—
178	#407	—	5	3	no	—
179	C₂×C₂²⋊C₈	—	5	3	no	—
180	C₂²×C₃×C₅	—	2	3	no	—
181	C₂²×C₃×C₅	—	2	3	no	—
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	6	yes	—
183	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₃×D₅	—	2	1	no	—
185	C₂×C₃×D₅	—	2	1	no	—
186	C₂×C₃×D₅	—	2	3	no	—
187	C₂×C₃×D₅	—	2	3	no	—
188	C₂×C₃×D₅	—	2	3	no	—
189	C₂×C₃×D₅	—	4	12	no	—
190	C₂×C₃×D₅	#131	1	2	yes	complemented
191	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	6	yes	—
192	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₃×Dic₅	—	2	3	no	—
195	C₃×Dic₅	—	2	1	no	—
196	C₂⁴×C₃	—	5	3	no	—
197	C₃×#41	—	10	4	no	—
198	C₃×#41	—	10	12	no	—
199	C₃×#41	—	10	6	no	—
200	C₃×#41	—	10	6	no	—
201	C₃×#41	D₂₀	1	4	yes	—
202	C₃×#41	C₂²⋊D₅	1	4	yes	—
203	C₂×C₃×Q₈	—	5	3	no	—
204	C₂×C₃×Q₈	—	10	4	no	—
205	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
206	C₂×C₃×D₄	—	5	6	no	—
207	C₂×C₃×D₄	—	5	3	no	—
208	C₂×C₃×D₄	—	10	12	no	—
209	C₂×C₃×D₄	C₄×D₅	1	3	yes	—
210	C₂²×C₃×C₄	—	5	3	no	—
211	C₂²×C₃×C₄	—	5	3	no	—
212	C₂²×C₃×C₄	—	5	3	no	—
213	C₂²×C₃×C₄	—	5	1	no	—
214	C₂²×C₃×C₄	—	5	3	no	—
215	C₂²×C₃×C₄	—	10	6	no	—
216	C₂²×C₃×C₄	—	10	6	no	—
217	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
218	C₃×M₁₆	—	2	6	no	—
219	C₃×M₁₆	—	10	6	no	—
220	C₂×C₃×C₈	—	2	6	no	—
221	C₂×C₃×C₈	—	5	1	no	—
222	C₂×C₃×C₈	—	5	3	no	—
223	C₂×C₃×C₈	—	10	6	no	—
224	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
225	C₂×C₃×C₈	C₂²×D₅	1	3	yes	—
226	C₂³×C₅	C₂²×C₃×C₄	1	3	yes	—
227	C₂²×D₅	—	2	6	no	—
228	C₂²×D₅	—	2	6	no	—
229	C₂²×D₅	—	4	3	no	—
230	C₂²×D₅	C₂²×C₃×C₄	1	3	yes	—
231	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₅×Q₈	C₃×C₂²⋊C₄	1	4	yes	—
233	C₅×D₄	C₃×C₂²⋊C₄	1	12	yes	—
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	3	yes	—
235	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
236	C₂×C₄×C₅	C₂×C₃×D₄	1	6	yes	—
237	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
238	C₂²⋊D₅	—	2	12	no	—
239	C₂×Dic₅	—	2	6	no	—
240	C₂×Dic₅	C₂²×C₃×C₄	1	3	yes	—
241	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	D₂₀	—	2	6	no	—
243	C₄×D₅	—	2	6	no	—
244	C₄×D₅	—	2	6	no	—
245	C₄×D₅	—	2	1	no	—
246	C₄×D₅	—	2	1	no	—
247	C₄×D₅	—	2	3	no	—
248	C₄×D₅	—	2	3	no	—
249	Dic₁₀	—	2	6	no	—
250	C₅×C₈	—	2	1	no	—
251	C₅×C₈	—	2	3	no	—
252	#168	—	2	1	no	—
253	#168	—	2	3	no	—
254	C₂×#41	—	5	1	no	—
255	C₂×#41	—	5	3	no	—
256	C₂×#41	—	5	3	no	—
257	C₂×#41	—	10	4	no	—
258	C₂×#41	—	10	4	no	—
259	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
260	C₂²×Q₈	—	5	1	no	—
261	C₂²×D₄	—	5	3	no	—
262	C₂³×C₄	—	5	3	no	—
263	#131	—	2	4	no	—
264	#131	—	10	4	no	—
265	C₂×M₁₆	—	5	3	no	—
266	C₂×M₁₆	C₂×C₃×D₅	1	3	yes	complemented
267	C₂²×C₈	—	5	3	no	—
268	C₂²×C₈	C₂×C₃×D₅	1	3	yes	complemented
269	C₂²⋊C₈	—	5	1	no	—
270	C₂²⋊C₈	—	5	3	no	—
271	C₂²⋊C₈	—	5	3	no	—
272	C₂²⋊C₈	—	5	3	no	—
273	C₂²⋊C₈	—	5	6	no	—
274	C₂×C₃×C₅	—	2	6	no	—
275	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₂×C₃×C₅	#568	1	1	yes	characteristic
278	C₃×D₅	—	2	2	no	—
279	C₃×D₅	—	4	3	no	—
280	C₂³×C₃	—	5	1	no	—
281	C₂³×C₃	—	5	3	no	—
282	C₂³×C₃	—	10	6	no	—
283	C₂³×C₃	—	10	6	no	—
284	C₂³×C₃	—	20	3	no	—
285	C₂³×C₃	C₂×C₄×D₅	1	3	yes	—
286	C₃×Q₈	—	10	6	no	—
287	C₃×Q₈	#685	1	4	yes	—
288	C₃×D₄	—	10	12	no	—
289	C₃×D₄	—	10	6	no	—
290	C₃×D₄	#685	1	12	yes	—
291	C₂×C₃×C₄	—	5	1	no	—
292	C₂×C₃×C₄	—	5	3	no	—
293	C₂×C₃×C₄	—	10	6	no	—
294	C₂×C₃×C₄	—	10	1	no	—
295	C₂×C₃×C₄	—	10	3	no	—
296	C₂×C₃×C₄	—	10	1	no	—
297	C₂×C₃×C₄	—	10	3	no	—
298	C₂×C₃×C₄	—	10	6	no	—
299	C₂×C₃×C₄	—	10	6	no	—
300	C₂×C₃×C₄	C₂×C₄×D₅	1	3	yes	—
301	C₂×C₃×C₄	C₂×D₂₀	1	6	yes	—
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	6	yes	—
303	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	3	no	—
306	C₃×C₈	—	10	1	no	—
307	C₃×C₈	—	10	3	no	—
308	C₂²×C₅	—	2	3	no	—
309	C₂²×C₅	—	2	3	no	—
310	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
311	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
312	C₂×D₅	—	2	1	no	—
313	C₂×D₅	—	2	1	no	—
314	C₂×D₅	—	2	3	no	—
315	C₂×D₅	—	2	3	no	—
316	C₂×D₅	—	2	3	no	—
317	C₂×D₅	—	4	12	no	—
318	C₂×D₅	C₃×#131	1	2	yes	complemented
319	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	6	yes	—
320	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
321	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
322	Dic₅	—	2	3	no	—
323	Dic₅	—	2	1	no	—
324	C₂⁴	—	5	3	no	—
325	#41	—	10	4	no	—
326	#41	—	10	12	no	—
327	#41	—	10	6	no	—
328	#41	—	10	6	no	—
329	#41	C₃×D₂₀	1	4	yes	—
330	#41	C₃×C₂²⋊D₅	1	4	yes	—
331	C₂×Q₈	—	5	3	no	—
332	C₂×Q₈	—	10	4	no	—
333	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
334	C₂×D₄	—	5	6	no	—
335	C₂×D₄	—	5	3	no	—
336	C₂×D₄	—	10	12	no	—
337	C₂×D₄	C₃×C₄×D₅	1	3	yes	—
338	C₂²×C₄	—	5	3	no	—
339	C₂²×C₄	—	5	3	no	—
340	C₂²×C₄	—	5	3	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	3	no	—
343	C₂²×C₄	—	10	6	no	—
344	C₂²×C₄	—	10	6	no	—
345	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
346	M₁₆	—	2	6	no	—
347	M₁₆	—	10	6	no	—
348	C₂×C₈	—	2	6	no	—
349	C₂×C₈	—	5	1	no	—
350	C₂×C₈	—	5	3	no	—
351	C₂×C₈	—	10	6	no	—
352	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
353	C₂×C₈	C₂²×C₃×D₅	1	3	yes	—
354	C₃×C₅	#2880	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	2	3	no	—
356	C₂²×C₃	—	2	3	no	—
357	C₂²×C₃	—	5	2	no	—
358	C₂²×C₃	—	10	1	no	—
359	C₂²×C₃	—	10	1	no	—
360	C₂²×C₃	—	10	3	no	—
361	C₂²×C₃	—	10	3	no	—
362	C₂²×C₃	—	10	3	no	—
363	C₂²×C₃	—	20	12	no	—
364	C₂²×C₃	C₂×#685	1	6	yes	—
365	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
366	C₃×C₄	—	10	1	no	—
367	C₃×C₄	—	10	3	no	—
368	C₃×C₄	C₂×#685	1	6	yes	—
369	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
370	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
371	C₂×C₅	—	2	6	no	—
372	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
374	C₂×C₅	C₃×#568	1	1	yes	characteristic
375	D₅	—	2	2	no	—
376	D₅	—	4	3	no	—
377	C₂³	—	5	1	no	—
378	C₂³	—	5	3	no	—
379	C₂³	—	10	6	no	—
380	C₂³	—	10	6	no	—
381	C₂³	—	20	3	no	—
382	C₂³	C₂×C₃×C₄×D₅	1	3	yes	—
383	Q₈	—	10	6	no	—
384	Q₈	C₃×#685	1	4	yes	—
385	D₄	—	10	12	no	—
386	D₄	—	10	6	no	—
387	D₄	C₃×#685	1	12	yes	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	3	no	—
390	C₂×C₄	—	10	6	no	—
391	C₂×C₄	—	10	1	no	—
392	C₂×C₄	—	10	3	no	—
393	C₂×C₄	—	10	1	no	—
394	C₂×C₄	—	10	3	no	—
395	C₂×C₄	—	10	6	no	—
396	C₂×C₄	—	10	6	no	—
397	C₂×C₄	C₂×C₃×C₄×D₅	1	3	yes	—
398	C₂×C₄	C₂×C₃×D₂₀	1	6	yes	—
399	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	6	yes	—
400	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
401	C₈	—	2	1	no	—
402	C₈	—	2	3	no	—
403	C₈	—	10	1	no	—
404	C₈	—	10	3	no	—
405	C₂×C₃	—	2	6	no	—
406	C₂×C₃	—	10	2	no	—
407	C₂×C₃	—	20	3	no	—
408	C₂×C₃	D₅×#131	1	1	yes	characteristic
409	C₂×C₃	#66084	1	1	yes	characteristic
410	C₂×C₃	C₂²×#685	1	1	yes	characteristic
411	C₅	C₃×#2880	1	1	yes	characteristic, complemented, Sylow
412	C₂²	—	2	3	no	—
413	C₂²	—	2	3	no	—
414	C₂²	—	5	2	no	—
415	C₂²	—	10	1	no	—
416	C₂²	—	10	1	no	—
417	C₂²	—	10	3	no	—
418	C₂²	—	10	3	no	—
419	C₂²	—	10	3	no	—
420	C₂²	—	20	12	no	—
421	C₂²	C₂×C₃×#685	1	6	yes	—
422	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
423	C₄	—	10	1	no	—
424	C₄	—	10	3	no	—
425	C₄	C₂×C₃×#685	1	6	yes	—
426	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
427	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
428	C₃	#10615524	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	2	6	no	—
430	C₂	—	10	2	no	—
431	C₂	—	20	3	no	—
432	C₂	C₃×D₅×#131	1	1	yes	characteristic
433	C₂	C₃×#66084	1	1	yes	characteristic
434	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×D₅×#41	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₅
hypocenter	C₅	C₃×#2880
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₂×C₃×#4094	C₂	semidirect
4. C₃×#65418	C₂	semidirect
5. C₃×#65415	C₂	semidirect
6. C₃×#65399	C₂	semidirect
7. C₂×C₃×#3952	C₂	semidirect
8. #10615524	C₃	direct (N × H)
19. C₂×C₃×C₅×M₁₆	C₂²	semidirect
20. C₂²×C₃×C₅×C₈	C₂²	semidirect
22. C₂×C₃×#681	C₂²	semidirect
23. C₂²×C₃×#168	C₂²	semidirect
26. C₃×#3952	C₂²	semidirect
27. C₃×#3952	C₂²	semidirect
28. C₃×#3952	C₂²	semidirect
31. C₂×C₅×#131	C₂×C₃	semidirect
32. C₂×#4094	C₂×C₃	semidirect
33. #65418	C₂×C₃	semidirect
34. #65415	C₂×C₃	semidirect
35. #65399	C₂×C₃	semidirect
36. C₂×#3952	C₂×C₃	semidirect
69. C₂×C₃×#131	D₅	semidirect
84. C₂×C₅×M₁₆	C₂²×C₃	semidirect
85. C₂²×C₅×C₈	C₂²×C₃	semidirect
87. C₂×#681	C₂²×C₃	semidirect
88. C₂²×#168	C₂²×C₃	semidirect
91. #3952	C₂²×C₃	semidirect
92. #3952	C₂²×C₃	semidirect
93. #3952	C₂²×C₃	semidirect
135. C₂×C₃×M₁₆	C₂×D₅	semidirect
137. C₂²×C₃×C₈	C₂×D₅	semidirect
175. C₂×#131	C₃×D₅	semidirect
190. C₂×C₃×D₅	#131	semidirect
266. C₂×M₁₆	C₂×C₃×D₅	semidirect
268. C₂²×C₈	C₂×C₃×D₅	semidirect
318. C₂×D₅	C₃×#131	semidirect
354. C₃×C₅	#2880	semidirect
411. C₅	C₃×#2880	semidirect
428. C₃	#10615524	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×D₅×#41	2
C₂×C₃×C₅×#131	2
C₂×C₃×#4094	2
C₃×#65418	2
C₃×#65415	2
C₃×#65399	2
C₂×C₃×#3952	2
#10615524	3
C₃×#2880	5

Subgroups — C3×#10615524 #14411804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615524 #14411804