Subgroups — C₅×D₃×#466 #14427672

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5157	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5038	C₂	1	2	yes	maximal, complemented
8	C₅×#4883	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4775	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#466	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	—	2	2	no	—
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#121	C₂²	1	2	yes	complemented
19	C₅×#939	—	2	2	no	—
20	C₅×#938	C₂²	1	2	yes	complemented
21	C₂×C₅×#213	C₂²	1	2	yes	complemented
22	C₅×#930	C₂²	1	2	yes	complemented
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₅×D₃×D₈	—	2	4	no	—
25	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₃×C₈	—	2	4	no	—
27	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#895	C₂²	1	2	yes	complemented
32	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₅×#884	—	2	2	no	—
34	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
35	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₅×#832	C₂²	1	2	yes	complemented
38	C₅×#821	C₂²	1	2	yes	complemented
39	C₅×#818	C₂²	1	1	yes	characteristic, complemented
40	C₅×#809	C₂²	1	2	yes	complemented
41	C₅×#807	C₂²	1	2	yes	complemented
42	D₃×#466	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂²×C₅×D₈	—	3	1	no	—
44	C₂³×C₅×C₈	—	3	1	no	—
45	C₂×C₅×#121	—	3	2	no	—
46	C₅×#466	—	3	1	no	—
47	C₅×#466	—	3	2	no	—
48	C₅×#466	—	3	1	no	—
49	C₅×#466	—	3	1	no	—
50	C₅×#466	—	3	2	no	—
51	C₅×#466	D₃	1	1	yes	characteristic, direct product factor
52	C₂×C₅×#107	—	3	1	no	—
53	C₂×C₅×#102	—	3	2	no	—
54	C₂³×C₅×D₃	—	2	2	no	—
55	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×#67	—	2	2	no	—
60	C₂×C₅×#67	—	2	2	no	—
61	C₂×C₅×#67	—	2	2	no	—
62	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₅×D₃×D₄	—	2	4	no	—
64	C₅×D₃×D₄	—	2	4	no	—
65	C₅×D₃×D₄	—	4	8	no	—
66	C₂×C₅×D₁₂	—	2	2	no	—
67	C₂×C₅×D₁₂	C₂³	1	2	yes	—
68	C₂×C₄×C₅×D₃	—	2	2	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
73	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₃×C₅×D₈	—	2	2	no	—
76	C₂×C₃×C₅×C₈	—	2	2	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₅×#217	—	2	2	no	—
82	C₅×#213	—	2	4	no	—
83	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	—	2	2	no	—
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×D₂₄	—	2	2	no	—
91	C₅×D₃×C₈	—	2	2	no	—
92	C₅×D₃×C₈	—	2	2	no	—
93	C₅×D₃×C₈	—	2	2	no	—
94	C₅×D₃×C₈	D₄	1	4	yes	complemented
95	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
97	D₃×#121	C₂×C₅	1	2	yes	complemented
98	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
99	#5157	C₂×C₅	1	1	yes	characteristic, complemented
100	#5115	C₂×C₅	1	1	yes	characteristic, complemented
101	#5038	C₂×C₅	1	2	yes	complemented
102	#4883	C₂×C₅	1	1	yes	characteristic, complemented
103	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
104	#4775	C₂×C₅	1	2	yes	complemented
105	D₃×#102	C₂×C₅	1	2	yes	complemented
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	6	2	no	—
108	C₂³×C₄×C₅	—	3	1	no	—
109	C₂×C₅×D₈	—	3	2	no	—
110	C₂×C₅×D₈	—	3	1	no	—
111	C₂×C₅×D₈	—	6	4	no	—
112	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂²×C₅×C₈	—	3	1	no	—
114	C₂²×C₅×C₈	—	3	1	no	—
115	C₂²×C₅×C₈	—	3	1	no	—
116	C₂²×C₅×C₈	—	3	1	no	—
117	C₂²×C₅×C₈	—	3	1	no	—
118	C₂²×C₅×C₈	—	6	4	no	—
119	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
120	C₅×#121	—	3	2	no	—
121	C₅×#121	—	3	2	no	—
122	C₅×#121	—	3	2	no	—
123	C₅×#121	—	6	2	no	—
124	C₅×#121	—	6	2	no	—
125	C₅×#121	C₂×D₃	1	2	yes	complemented
126	C₂×C₅×C₄⋊C₄	—	3	2	no	—
127	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
128	C₅×#107	—	3	1	no	—
129	C₅×#107	—	3	2	no	—
130	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
131	C₅×#102	—	3	2	no	—
132	C₅×#102	—	3	2	no	—
133	C₅×#102	—	3	2	no	—
134	C₅×#102	C₂×D₃	1	2	yes	complemented
135	C₂×#466	—	3	1	no	Sylow
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	2	no	—
139	C₂²×C₅×D₃	—	2	2	no	—
140	C₂²×C₅×D₃	—	2	2	no	—
141	C₂²×C₅×D₃	—	4	4	no	—
142	C₂²×C₅×D₃	—	4	4	no	—
143	C₂²×C₅×D₃	—	4	4	no	—
144	C₂²×C₅×D₃	D₈	1	4	yes	complemented
145	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	—	2	2	no	—
149	C₃×C₅×D₄	—	4	4	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₅×#67	—	4	4	no	—
156	C₅×#67	—	4	4	no	—
157	C₅×#67	—	4	4	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	—	2	2	no	—
160	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
162	C₅×D₁₂	—	2	2	no	—
163	C₅×D₁₂	—	2	2	no	—
164	C₅×D₁₂	—	4	4	no	—
165	C₄×C₅×D₃	—	2	2	no	—
166	C₄×C₅×D₃	—	2	1	no	—
167	C₄×C₅×D₃	—	2	1	no	—
168	C₄×C₅×D₃	—	2	2	no	—
169	C₄×C₅×D₃	—	4	4	no	—
170	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
171	C₄×C₅×D₃	#41	1	2	yes	—
172	C₃×C₅×C₈	—	2	1	no	—
173	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
174	C₅×C₃⋊C₈	—	2	1	no	—
175	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
176	C₂×D₃×D₄	—	2	2	no	—
177	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
178	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₃×#121	C₂²×C₅	1	2	yes	complemented
182	#939	—	2	2	no	—
183	#938	C₂²×C₅	1	2	yes	complemented
184	C₂×#213	C₂²×C₅	1	2	yes	complemented
185	#930	C₂²×C₅	1	2	yes	complemented
186	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
187	D₃×D₈	—	2	4	no	—
188	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₂×D₃×C₈	—	2	4	no	—
190	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
192	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
194	#895	C₂²×C₅	1	2	yes	complemented
195	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
196	#884	—	2	2	no	—
197	D₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
199	C₃×#102	C₂²×C₅	1	2	yes	complemented
200	#832	C₂²×C₅	1	2	yes	complemented
201	#821	C₂²×C₅	1	2	yes	complemented
202	#818	C₂²×C₅	1	1	yes	characteristic, complemented
203	#809	C₂²×C₅	1	2	yes	complemented
204	#807	C₂²×C₅	1	2	yes	complemented
205	C₂⁴×C₅	—	3	1	no	—
206	C₂⁴×C₅	—	6	2	no	—
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	—	3	2	no	—
209	C₂×C₅×D₄	—	6	2	no	—
210	C₂×C₅×D₄	—	6	4	no	—
211	C₂×C₅×D₄	—	6	4	no	—
212	C₂×C₅×D₄	—	6	2	no	—
213	C₂×C₅×D₄	—	6	2	no	—
214	C₂×C₅×D₄	—	6	2	no	—
215	C₂×C₅×D₄	—	12	8	no	—
216	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
217	C₂²×C₄×C₅	—	3	1	no	—
218	C₂²×C₄×C₅	—	3	1	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	1	no	—
222	C₂²×C₄×C₅	—	6	2	no	—
223	C₂²×C₄×C₅	—	6	2	no	—
224	C₂²×C₄×C₅	—	6	2	no	—
225	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
226	C₅×D₈	—	2	2	no	—
227	C₅×D₈	—	6	4	no	—
228	C₅×D₈	—	6	2	no	—
229	C₂×C₅×C₈	—	2	2	no	—
230	C₂×C₅×C₈	—	3	1	no	—
231	C₂×C₅×C₈	—	3	4	no	—
232	C₂×C₅×C₈	—	3	1	no	—
233	C₂×C₅×C₈	—	6	2	no	—
234	C₂×C₅×C₈	—	6	2	no	—
235	C₂×C₅×C₈	—	6	2	no	—
236	C₂×C₅×C₈	—	6	2	no	—
237	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
239	C₅×C₄⋊C₄	—	3	2	no	—
240	C₅×C₄⋊C₄	—	6	2	no	—
241	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
242	C₅×C₂²⋊C₄	—	2	2	no	—
243	C₅×C₂²⋊C₄	—	6	2	no	—
244	C₅×C₂²⋊C₄	—	6	2	no	—
245	C₅×C₂²⋊C₄	—	6	2	no	—
246	C₂²×D₈	—	3	1	no	—
247	C₂³×C₈	—	3	1	no	—
248	C₂×#121	—	3	2	no	—
249	#466	—	3	1	no	—
250	#466	—	3	1	no	—
251	#466	—	3	2	no	—
252	#466	—	3	1	no	—
253	#466	—	3	2	no	—
254	#466	C₅×D₃	1	1	yes	characteristic, direct product factor
255	C₂×#107	—	3	1	no	—
256	C₂×#102	—	3	2	no	—
257	C₂²×C₃×C₅	—	2	1	no	—
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	—	4	2	no	—
260	C₂²×C₃×C₅	—	4	2	no	—
261	C₂²×C₃×C₅	—	4	2	no	—
262	C₂²×C₃×C₅	C₂×D₈	1	2	yes	complemented
263	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₅×D₃	—	2	1	no	—
265	C₂×C₅×D₃	—	2	1	no	—
266	C₂×C₅×D₃	—	2	8	no	—
267	C₂×C₅×D₃	—	4	2	no	—
268	C₂×C₅×D₃	—	4	2	no	—
269	C₂×C₅×D₃	—	4	2	no	—
270	C₂×C₅×D₃	—	8	8	no	—
271	C₂×C₅×D₃	#121	1	2	yes	—
272	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
273	C₂×C₅×D₃	C₂×D₈	1	2	yes	complemented
274	C₂×C₅×D₃	#135	1	2	yes	—
275	C₃×C₄×C₅	—	2	1	no	—
276	C₃×C₄×C₅	—	4	2	no	—
277	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
279	C₅×Dic₃	—	2	1	no	—
280	C₅×Dic₃	—	4	2	no	—
281	C₅×Dic₃	#121	1	2	yes	—
282	C₂³×D₃	—	2	2	no	—
283	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×D₄	—	2	2	no	—
285	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
286	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
287	C₂×#67	—	2	2	no	—
288	C₂×#67	—	2	2	no	—
289	C₂×#67	—	2	2	no	—
290	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
291	D₃×D₄	—	2	4	no	—
292	D₃×D₄	—	2	4	no	—
293	D₃×D₄	—	4	8	no	—
294	C₂×D₁₂	—	2	2	no	—
295	C₂×D₁₂	C₂³×C₅	1	2	yes	—
296	C₂×C₄×D₃	—	2	2	no	—
297	C₂×C₄×D₃	—	2	2	no	—
298	C₂×C₄×D₃	—	2	2	no	—
299	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
300	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
301	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
302	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
303	C₃×D₈	—	2	2	no	—
304	C₂×C₃×C₈	—	2	2	no	—
305	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
308	C₃×C₂²⋊C₄	—	2	2	no	—
309	#217	—	2	2	no	—
310	#213	—	2	4	no	—
311	(C₂×D₃)⋊C₄	—	2	2	no	—
312	(C₂×D₃)⋊C₄	—	2	2	no	—
313	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
314	Dic₃⋊C₄	—	2	2	no	—
315	C₂×C₃⋊C₈	—	2	2	no	—
316	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
317	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
318	D₂₄	—	2	2	no	—
319	D₃×C₈	—	2	2	no	—
320	D₃×C₈	—	2	2	no	—
321	D₃×C₈	—	2	2	no	—
322	D₃×C₈	C₅×D₄	1	4	yes	complemented
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	3	1	no	—
325	C₂³×C₅	—	3	4	no	—
326	C₂³×C₅	—	3	1	no	—
327	C₂³×C₅	—	6	2	no	—
328	C₂³×C₅	—	6	2	no	—
329	C₂³×C₅	—	6	2	no	—
330	C₂³×C₅	—	12	4	no	—
331	C₂³×C₅	—	12	4	no	—
332	C₂³×C₅	—	12	4	no	—
333	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
334	C₅×D₄	—	2	2	no	—
335	C₅×D₄	—	2	2	no	—
336	C₅×D₄	—	4	4	no	—
337	C₅×D₄	—	6	2	no	—
338	C₅×D₄	—	6	2	no	—
339	C₅×D₄	—	12	4	no	—
340	C₅×D₄	—	12	4	no	—
341	C₅×D₄	—	12	4	no	—
342	C₅×D₄	—	12	4	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	3	1	no	—
347	C₂×C₄×C₅	—	3	2	no	—
348	C₂×C₄×C₅	—	3	2	no	—
349	C₂×C₄×C₅	—	3	1	no	—
350	C₂×C₄×C₅	—	6	2	no	—
351	C₂×C₄×C₅	—	6	2	no	—
352	C₂×C₄×C₅	—	6	2	no	—
353	C₂×C₄×C₅	—	6	1	no	—
354	C₂×C₄×C₅	—	6	1	no	—
355	C₂×C₄×C₅	—	6	2	no	—
356	C₂×C₄×C₅	—	12	4	no	—
357	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
359	C₅×C₈	—	2	1	no	—
360	C₅×C₈	—	3	2	no	—
361	C₅×C₈	—	6	1	no	—
362	C₅×C₈	D₃×D₄	1	2	yes	complemented
363	C₂²×D₄	—	3	2	no	—
364	C₂²×D₄	—	6	2	no	—
365	C₂³×C₄	—	3	1	no	—
366	C₂×D₈	—	3	2	no	—
367	C₂×D₈	—	3	1	no	—
368	C₂×D₈	—	6	4	no	—
369	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
370	C₂²×C₈	—	3	1	no	—
371	C₂²×C₈	—	3	1	no	—
372	C₂²×C₈	—	3	1	no	—
373	C₂²×C₈	—	3	1	no	—
374	C₂²×C₈	—	3	1	no	—
375	C₂²×C₈	—	6	4	no	—
376	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
377	#121	—	3	2	no	—
378	#121	—	3	2	no	—
379	#121	—	3	2	no	—
380	#121	—	6	2	no	—
381	#121	—	6	2	no	—
382	#121	C₂×C₅×D₃	1	2	yes	complemented
383	C₂×C₄⋊C₄	—	3	2	no	—
384	C₂×C₂²⋊C₄	—	6	2	no	—
385	#107	—	3	1	no	—
386	#107	—	3	2	no	—
387	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
388	#102	—	3	2	no	—
389	#102	—	3	2	no	—
390	#102	—	3	2	no	—
391	#102	C₂×C₅×D₃	1	2	yes	complemented
392	C₂×C₃×C₅	—	2	2	no	—
393	C₂×C₃×C₅	—	8	2	no	—
394	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
395	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
396	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
397	C₅×D₃	—	2	2	no	—
398	C₅×D₃	—	8	2	no	—
399	C₅×D₃	#466	1	4	yes	direct product factor
400	C₂³×C₃	—	2	2	no	—
401	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
402	C₂²×D₃	—	2	2	no	—
403	C₂²×D₃	—	2	2	no	—
404	C₂²×D₃	—	2	2	no	—
405	C₂²×D₃	—	4	4	no	—
406	C₂²×D₃	—	4	4	no	—
407	C₂²×D₃	—	4	4	no	—
408	C₂²×D₃	C₅×D₈	1	4	yes	complemented
409	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
411	C₃×D₄	—	2	2	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	4	4	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
419	#67	—	4	4	no	—
420	#67	—	4	4	no	—
421	#67	—	4	4	no	—
422	C₂×Dic₃	—	2	2	no	—
423	C₂×Dic₃	—	2	2	no	—
424	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
426	D₁₂	—	2	2	no	—
427	D₁₂	—	2	2	no	—
428	D₁₂	—	4	4	no	—
429	C₄×D₃	—	2	2	no	—
430	C₄×D₃	—	2	1	no	—
431	C₄×D₃	—	2	1	no	—
432	C₄×D₃	—	2	2	no	—
433	C₄×D₃	—	4	4	no	—
434	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
435	C₄×D₃	C₅×#41	1	2	yes	—
436	C₃×C₈	—	2	1	no	—
437	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
438	C₃⋊C₈	—	2	1	no	—
439	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	3	2	no	—
443	C₂²×C₅	—	3	2	no	—
444	C₂²×C₅	—	3	2	no	—
445	C₂²×C₅	—	3	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	—	4	2	no	—
449	C₂²×C₅	—	6	8	no	—
450	C₂²×C₅	—	6	1	no	—
451	C₂²×C₅	—	6	1	no	—
452	C₂²×C₅	—	12	2	no	—
453	C₂²×C₅	—	12	2	no	—
454	C₂²×C₅	—	12	2	no	—
455	C₂²×C₅	—	24	8	no	—
456	C₂²×C₅	D₃×D₈	1	2	yes	complemented
457	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
458	C₄×C₅	—	2	1	no	—
459	C₄×C₅	—	3	2	no	—
460	C₄×C₅	—	4	2	no	—
461	C₄×C₅	—	6	1	no	—
462	C₄×C₅	—	12	2	no	—
463	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
464	C₄×C₅	D₃×#41	1	1	yes	characteristic
465	C₂⁴	—	3	1	no	—
466	C₂⁴	—	6	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	3	2	no	—
469	C₂×D₄	—	6	2	no	—
470	C₂×D₄	—	6	4	no	—
471	C₂×D₄	—	6	4	no	—
472	C₂×D₄	—	6	2	no	—
473	C₂×D₄	—	6	2	no	—
474	C₂×D₄	—	6	2	no	—
475	C₂×D₄	—	12	8	no	—
476	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	3	1	no	—
480	C₂²×C₄	—	3	1	no	—
481	C₂²×C₄	—	3	1	no	—
482	C₂²×C₄	—	6	2	no	—
483	C₂²×C₄	—	6	2	no	—
484	C₂²×C₄	—	6	2	no	—
485	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
486	D₈	—	2	2	no	—
487	D₈	—	6	4	no	—
488	D₈	—	6	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	3	1	no	—
491	C₂×C₈	—	3	4	no	—
492	C₂×C₈	—	3	1	no	—
493	C₂×C₈	—	6	2	no	—
494	C₂×C₈	—	6	2	no	—
495	C₂×C₈	—	6	2	no	—
496	C₂×C₈	—	6	2	no	—
497	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
498	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
499	C₄⋊C₄	—	3	2	no	—
500	C₄⋊C₄	—	6	2	no	—
501	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	6	2	no	—
504	C₂²⋊C₄	—	6	2	no	—
505	C₂²⋊C₄	—	6	2	no	—
506	C₃×C₅	C₂×#466	1	1	yes	characteristic, complemented, Hall
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	—	4	2	no	—
512	C₂²×C₃	C₂×C₅×D₈	1	2	yes	complemented
513	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
514	C₂×D₃	—	2	1	no	—
515	C₂×D₃	—	2	1	no	—
516	C₂×D₃	—	2	8	no	—
517	C₂×D₃	—	4	2	no	—
518	C₂×D₃	—	4	2	no	—
519	C₂×D₃	—	4	2	no	—
520	C₂×D₃	—	8	8	no	—
521	C₂×D₃	C₅×#121	1	2	yes	—
522	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
523	C₂×D₃	C₂×C₅×D₈	1	2	yes	complemented
524	C₂×D₃	C₅×#135	1	2	yes	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	4	2	no	—
527	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
528	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
529	Dic₃	—	2	1	no	—
530	Dic₃	—	4	2	no	—
531	Dic₃	C₅×#121	1	2	yes	—
532	C₂×C₅	—	2	2	no	—
533	C₂×C₅	—	3	4	no	—
534	C₂×C₅	—	6	2	no	—
535	C₂×C₅	—	8	2	no	—
536	C₂×C₅	—	24	2	no	—
537	C₂×C₅	D₃×#121	1	1	yes	characteristic
538	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
539	C₂×C₅	D₃×#135	1	1	yes	characteristic
540	C₂³	—	2	2	no	—
541	C₂³	—	3	1	no	—
542	C₂³	—	3	4	no	—
543	C₂³	—	3	1	no	—
544	C₂³	—	6	2	no	—
545	C₂³	—	6	2	no	—
546	C₂³	—	6	2	no	—
547	C₂³	—	12	4	no	—
548	C₂³	—	12	4	no	—
549	C₂³	—	12	4	no	—
550	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	4	no	—
554	D₄	—	6	2	no	—
555	D₄	—	6	2	no	—
556	D₄	—	12	4	no	—
557	D₄	—	12	4	no	—
558	D₄	—	12	4	no	—
559	D₄	—	12	4	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	3	1	no	—
564	C₂×C₄	—	3	2	no	—
565	C₂×C₄	—	3	2	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	6	2	no	—
568	C₂×C₄	—	6	2	no	—
569	C₂×C₄	—	6	2	no	—
570	C₂×C₄	—	6	1	no	—
571	C₂×C₄	—	6	1	no	—
572	C₂×C₄	—	6	2	no	—
573	C₂×C₄	—	12	4	no	—
574	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
576	C₈	—	2	1	no	—
577	C₈	—	3	2	no	—
578	C₈	—	6	1	no	—
579	C₈	C₅×D₃×D₄	1	2	yes	complemented
580	C₂×C₃	—	2	2	no	—
581	C₂×C₃	—	8	2	no	—
582	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
583	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
584	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
585	D₃	—	2	2	no	—
586	D₃	—	8	2	no	—
587	D₃	C₅×#466	1	4	yes	direct product factor
588	C₅	D₃×#466	1	1	yes	characteristic, direct product factor, Sylow
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	3	2	no	—
592	C₂²	—	3	2	no	—
593	C₂²	—	3	2	no	—
594	C₂²	—	3	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	6	8	no	—
599	C₂²	—	6	1	no	—
600	C₂²	—	6	1	no	—
601	C₂²	—	12	2	no	—
602	C₂²	—	12	2	no	—
603	C₂²	—	12	2	no	—
604	C₂²	—	24	8	no	—
605	C₂²	C₅×D₃×D₈	1	2	yes	complemented
606	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	3	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	6	1	no	—
611	C₄	—	12	2	no	—
612	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
613	C₄	C₅×D₃×#41	1	1	yes	characteristic
614	C₃	C₂×C₅×#466	1	1	yes	characteristic, complemented, Sylow
615	C₂	—	2	2	no	—
616	C₂	—	3	4	no	—
617	C₂	—	6	2	no	—
618	C₂	—	8	2	no	—
619	C₂	—	24	2	no	—
620	C₂	C₅×D₃×#121	1	1	yes	characteristic
621	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic
622	C₂	C₅×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#466	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#466	D₃
hypocenter	C₃	C₂×C₅×#466
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#466

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×D₈	C₂	semidirect
2. C₂²×C₅×D₃×C₈	C₂	semidirect
3. C₅×D₃×#121	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₅×#5157	C₂	semidirect
6. C₅×#5115	C₂	semidirect
7. C₅×#5038	C₂	semidirect
8. C₅×#4883	C₂	semidirect
9. C₅×D₃×#107	C₂	semidirect
10. C₅×#4775	C₂	semidirect
11. C₅×D₃×#102	C₂	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂²×C₃×C₅×C₈	C₂²	semidirect
18. C₃×C₅×#121	C₂²	semidirect
20. C₅×#938	C₂²	semidirect
21. C₂×C₅×#213	C₂²	semidirect
22. C₅×#930	C₂²	semidirect
23. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
25. C₂×C₅×D₂₄	C₂²	semidirect
29. C₂×C₅×D₃×C₈	C₂²	semidirect
30. C₂×C₅×D₃×C₈	C₂²	semidirect
31. C₅×#895	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₅×#832	C₂²	semidirect
38. C₅×#821	C₂²	semidirect
39. C₅×#818	C₂²	semidirect
40. C₅×#809	C₂²	semidirect
41. C₅×#807	C₂²	semidirect
42. D₃×#466	C₅	direct (N × H)
51. C₅×#466	D₃	direct (N × H)
94. C₅×D₃×C₈	D₄	semidirect
95. C₂×D₃×D₈	C₂×C₅	semidirect
96. C₂²×D₃×C₈	C₂×C₅	semidirect
97. D₃×#121	C₂×C₅	semidirect
98. C₃×#466	C₂×C₅	semidirect
99. #5157	C₂×C₅	semidirect
100. #5115	C₂×C₅	semidirect
101. #5038	C₂×C₅	semidirect
102. #4883	C₂×C₅	semidirect
103. D₃×#107	C₂×C₅	semidirect
104. #4775	C₂×C₅	semidirect
105. D₃×#102	C₂×C₅	semidirect
112. C₂×C₅×D₈	C₂×D₃	semidirect
119. C₂²×C₅×C₈	C₂×D₃	semidirect
125. C₅×#121	C₂×D₃	semidirect
130. C₅×#107	C₂×D₃	semidirect
134. C₅×#102	C₂×D₃	semidirect
144. C₂²×C₅×D₃	D₈	semidirect
173. C₃×C₅×C₈	C₂×D₄	semidirect
175. C₅×C₃⋊C₈	C₂×D₄	semidirect
179. C₂×C₃×D₈	C₂²×C₅	semidirect
180. C₂²×C₃×C₈	C₂²×C₅	semidirect
181. C₃×#121	C₂²×C₅	semidirect
183. #938	C₂²×C₅	semidirect
184. C₂×#213	C₂²×C₅	semidirect
185. #930	C₂²×C₅	semidirect
186. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
188. C₂×D₂₄	C₂²×C₅	semidirect
192. C₂×D₃×C₈	C₂²×C₅	semidirect
193. C₂×D₃×C₈	C₂²×C₅	semidirect
194. #895	C₂²×C₅	semidirect
198. C₃×#107	C₂²×C₅	semidirect
199. C₃×#102	C₂²×C₅	semidirect
200. #832	C₂²×C₅	semidirect
201. #821	C₂²×C₅	semidirect
202. #818	C₂²×C₅	semidirect
203. #809	C₂²×C₅	semidirect
204. #807	C₂²×C₅	semidirect
254. #466	C₅×D₃	direct (N × H)
262. C₂²×C₃×C₅	C₂×D₈	semidirect
273. C₂×C₅×D₃	C₂×D₈	semidirect
322. D₃×C₈	C₅×D₄	semidirect
362. C₅×C₈	D₃×D₄	semidirect
369. C₂×D₈	C₂×C₅×D₃	semidirect
376. C₂²×C₈	C₂×C₅×D₃	semidirect
382. #121	C₂×C₅×D₃	semidirect
387. #107	C₂×C₅×D₃	semidirect
391. #102	C₂×C₅×D₃	semidirect
399. C₅×D₃	#466	direct (N × H)
408. C₂²×D₃	C₅×D₈	semidirect
437. C₃×C₈	C₂×C₅×D₄	semidirect
439. C₃⋊C₈	C₂×C₅×D₄	semidirect
456. C₂²×C₅	D₃×D₈	semidirect
506. C₃×C₅	C₂×#466	semidirect
512. C₂²×C₃	C₂×C₅×D₈	semidirect
523. C₂×D₃	C₂×C₅×D₈	semidirect
579. C₈	C₅×D₃×D₄	semidirect
587. D₃	C₅×#466	direct (N × H)
588. C₅	D₃×#466	direct (N × H)
605. C₂²	C₅×D₃×D₈	semidirect
614. C₃	C₂×C₅×#466	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₂²×C₅×D₃×C₈	2
C₅×D₃×#121	2
C₃×C₅×#466	2
C₅×#5157	2
C₅×#5115	2
C₅×#5038	2
C₅×#4883	2
C₅×D₃×#107	2
C₅×#4775	2
C₅×D₃×#102	2
C₂×C₅×#466	3
D₃×#466	5

Subgroups — C5×D3×#466 #14427672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#466 #14427672