Subgroups — C₂×C₅×#5238 #14423412

Order 1920.

1624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5238	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#449	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	—	2	4	no	—
11	C₂×C₃×C₅×#41	—	2	4	no	—
12	C₂×C₃×C₅×#41	—	2	2	no	—
13	C₂×C₃×C₅×#41	C₂²	1	4	yes	complemented
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	—	2	1	no	—
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	—	2	1	no	—
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	—	2	1	no	—
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₅×#215	—	2	4	no	—
22	C₂×C₅×#215	C₂²	1	4	yes	complemented
23	C₂×C₅×#213	—	2	4	no	—
24	C₂×C₅×#213	C₂²	1	4	yes	complemented
25	C₅×#930	—	2	2	no	—
26	C₅×#930	C₂²	1	4	yes	complemented
27	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
28	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₅×#835	C₂²	1	4	yes	complemented
32	C₅×#832	C₂²	1	4	yes	complemented
33	C₅×#830	C₂²	1	4	yes	complemented
34	C₂×#5238	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₅×#41	D₃	1	1	yes	characteristic, complemented
36	C₂²×C₅×SD₁₆	—	3	1	no	—
37	C₂²×C₅×D₈	—	3	1	no	—
38	C₂×C₅×#121	—	3	1	no	—
39	C₅×#449	—	3	8	no	—
40	C₂×C₅×#103	—	3	1	no	—
41	C₂×C₅×#102	—	3	1	no	—
42	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
45	C₂³×C₅×D₃	—	2	1	no	—
46	C₃×C₅×#41	—	2	16	no	—
47	C₃×C₅×#41	—	2	8	no	—
48	C₃×C₅×#41	—	2	8	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	1	no	—
51	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
52	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₄	—	2	8	no	—
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	8	no	—
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	4	no	—
62	C₂²×C₃×C₄×C₅	—	2	2	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×#67	—	2	4	no	—
69	C₂×C₅×#67	—	4	4	no	—
70	C₂²×C₅×Dic₃	—	2	1	no	—
71	C₂×C₅×D₁₂	—	2	2	no	—
72	C₂×C₅×D₁₂	—	2	2	no	—
73	C₂×C₅×D₁₂	—	2	1	no	—
74	C₂×C₅×D₁₂	C₂³	1	2	yes	—
75	C₅×#215	—	2	8	no	—
76	C₅×#213	—	2	8	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
78	C₅×C₄⋊Dic₃	—	2	1	no	—
79	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
80	C₂×C₅×C₃⋊C₈	—	2	2	no	—
81	C₂×C₅×C₃⋊C₈	—	2	2	no	—
82	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂²×C₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
88	#5238	C₂×C₅	1	8	yes	direct product factor
89	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×C₅×#41	—	2	4	no	—
93	C₂×C₅×#41	—	2	4	no	—
94	C₂×C₅×#41	—	2	2	no	—
95	C₂×C₅×#41	C₂×D₃	1	4	yes	complemented
96	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
97	C₂²×C₅×D₄	—	2	1	no	—
98	C₂²×C₅×D₄	—	3	1	no	—
99	C₂²×C₅×D₄	—	6	1	no	—
100	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
101	C₂³×C₄×C₅	—	2	1	no	—
102	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
103	C₂×C₅×SD₁₆	—	3	4	no	—
104	C₂×C₅×SD₁₆	—	6	4	no	—
105	C₂×C₅×D₈	—	3	4	no	—
106	C₂×C₅×D₈	—	6	4	no	—
107	C₂²×C₅×C₈	—	3	1	no	—
108	C₂²×C₅×C₈	—	3	1	no	—
109	C₅×#121	—	3	4	no	—
110	C₅×#121	—	6	2	no	—
111	C₂×C₅×C₄⋊C₄	—	3	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
113	C₅×#103	—	3	4	no	—
114	C₅×#102	—	3	4	no	—
115	C₅×C₂²⋊C₈	—	3	4	no	—
116	C₂×#449	—	3	1	no	Sylow
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	4	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	—	4	2	no	—
123	C₂³×C₃×C₅	—	4	2	no	—
124	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
125	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₅×D₃	—	2	2	no	—
127	C₂²×C₅×D₃	—	4	2	no	—
128	C₂²×C₅×D₃	—	4	2	no	—
129	C₂²×C₅×D₃	—	4	2	no	—
130	C₃×C₅×Q₈	—	2	4	no	—
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
133	C₃×C₅×D₄	—	2	16	no	—
134	C₃×C₅×D₄	—	2	4	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	C₂×D₄	1	4	yes	complemented
137	C₂×C₃×C₄×C₅	—	2	16	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	4	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	4	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×#67	—	4	8	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	4	2	no	—
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	—	2	2	no	—
154	C₅×D₁₂	—	4	2	no	—
155	C₅×C₃⋊C₈	—	2	2	no	—
156	C₅×C₃⋊C₈	—	2	2	no	—
157	C₂×C₃×#41	—	2	4	no	—
158	C₂×C₃×#41	—	2	4	no	—
159	C₂×C₃×#41	—	2	2	no	—
160	C₂×C₃×#41	C₂²×C₅	1	4	yes	complemented
161	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
162	C₂²×C₃×D₄	—	2	1	no	—
163	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
164	C₂³×C₃×C₄	—	2	1	no	—
165	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂²×#67	—	2	1	no	—
167	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
168	C₂×#215	—	2	4	no	—
169	C₂×#215	C₂²×C₅	1	4	yes	complemented
170	C₂×#213	—	2	4	no	—
171	C₂×#213	C₂²×C₅	1	4	yes	complemented
172	#930	—	2	2	no	—
173	#930	C₂²×C₅	1	4	yes	complemented
174	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
175	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
177	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
178	#835	C₂²×C₅	1	4	yes	complemented
179	#832	C₂²×C₅	1	4	yes	complemented
180	#830	C₂²×C₅	1	4	yes	complemented
181	C₂⁴×C₅	—	2	1	no	—
182	C₂⁴×C₅	—	6	1	no	—
183	C₂⁴×C₅	#67	1	1	yes	characteristic
184	C₅×#41	—	2	16	no	—
185	C₅×#41	—	2	8	no	—
186	C₅×#41	—	2	8	no	—
187	C₂×C₅×Q₈	—	2	2	no	—
188	C₂×C₅×Q₈	—	2	1	no	—
189	C₂×C₅×Q₈	#67	1	4	yes	complemented
190	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
191	C₂×C₅×D₄	—	2	8	no	—
192	C₂×C₅×D₄	—	2	4	no	—
193	C₂×C₅×D₄	—	2	1	no	—
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	3	2	no	—
196	C₂×C₅×D₄	—	6	4	no	—
197	C₂×C₅×D₄	—	6	2	no	—
198	C₂×C₅×D₄	—	6	2	no	—
199	C₂×C₅×D₄	—	6	1	no	—
200	C₂×C₅×D₄	—	12	4	no	—
201	C₂×C₅×D₄	#67	1	4	yes	complemented
202	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
203	C₂²×C₄×C₅	—	2	8	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	4	no	—
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	—	2	2	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	#67	1	2	yes	—
210	C₂²×C₄×C₅	#67	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×SD₁₆	—	6	8	no	—
214	C₅×D₈	—	6	8	no	—
215	C₂×C₅×C₈	—	3	2	no	—
216	C₂×C₅×C₈	—	3	2	no	—
217	C₂×C₅×C₈	—	6	2	no	—
218	C₂×C₅×C₈	—	6	2	no	—
219	C₅×C₄⋊C₄	—	3	2	no	—
220	C₅×C₄⋊C₄	—	6	1	no	—
221	C₅×C₂²⋊C₄	—	6	4	no	—
222	C₂²×#41	C₅×D₃	1	1	yes	characteristic, complemented
223	C₂²×SD₁₆	—	3	1	no	—
224	C₂²×D₈	—	3	1	no	—
225	C₂×#121	—	3	1	no	—
226	#449	—	3	8	no	—
227	C₂×#103	—	3	1	no	—
228	C₂×#102	—	3	1	no	—
229	C₂×C₂²⋊C₈	—	3	1	no	—
230	C₂²×C₃×C₅	—	2	2	no	—
231	C₂²×C₃×C₅	—	2	4	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	—	4	2	no	—
235	C₂²×C₃×C₅	—	4	2	no	—
236	C₂²×C₃×C₅	—	4	4	no	—
237	C₂²×C₃×C₅	—	4	8	no	—
238	C₂²×C₃×C₅	#120	1	2	yes	—
239	C₂²×C₃×C₅	#135	1	2	yes	—
240	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
241	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₅×D₃	—	4	2	no	—
243	C₂×C₅×D₃	—	4	2	no	—
244	C₂×C₅×D₃	—	4	2	no	—
245	C₂×C₅×D₃	—	8	4	no	—
246	C₃×C₄×C₅	—	2	2	no	—
247	C₃×C₄×C₅	—	2	4	no	—
248	C₃×C₄×C₅	#120	1	2	yes	—
249	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₅×Dic₃	—	4	2	no	—
252	C₂⁴×C₃	—	2	1	no	—
253	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
254	C₂³×D₃	—	2	1	no	—
255	C₃×#41	—	2	16	no	—
256	C₃×#41	—	2	8	no	—
257	C₃×#41	—	2	8	no	—
258	C₂×C₃×Q₈	—	2	2	no	—
259	C₂×C₃×Q₈	—	2	1	no	—
260	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
261	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
262	C₂×C₃×D₄	—	2	8	no	—
263	C₂×C₃×D₄	—	2	4	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
267	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
268	C₂²×C₃×C₄	—	2	8	no	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	2	4	no	—
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
275	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×#67	—	2	4	no	—
278	C₂×#67	—	4	4	no	—
279	C₂²×Dic₃	—	2	1	no	—
280	C₂×D₁₂	—	2	2	no	—
281	C₂×D₁₂	—	2	2	no	—
282	C₂×D₁₂	—	2	1	no	—
283	C₂×D₁₂	C₂³×C₅	1	2	yes	—
284	#215	—	2	8	no	—
285	#213	—	2	8	no	—
286	(C₂×D₃)⋊C₄	—	2	4	no	—
287	C₄⋊Dic₃	—	2	1	no	—
288	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
289	C₂×C₃⋊C₈	—	2	2	no	—
290	C₂×C₃⋊C₈	—	2	2	no	—
291	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
292	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	4	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	4	2	no	—
299	C₂³×C₅	—	4	2	no	—
300	C₂³×C₅	—	6	2	no	—
301	C₂³×C₅	—	12	2	no	—
302	C₂³×C₅	—	12	2	no	—
303	C₂³×C₅	—	12	2	no	—
304	C₂³×C₅	C₂×#67	1	2	yes	—
305	C₂³×C₅	C₂×#67	1	1	yes	characteristic
306	C₅×Q₈	—	2	4	no	—
307	C₅×Q₈	—	2	2	no	—
308	C₅×Q₈	C₂×#67	1	4	yes	complemented
309	C₅×D₄	—	2	16	no	—
310	C₅×D₄	—	2	4	no	—
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	6	2	no	—
313	C₅×D₄	—	6	2	no	—
314	C₅×D₄	—	12	8	no	—
315	C₅×D₄	—	12	2	no	—
316	C₅×D₄	C₂×#67	1	4	yes	complemented
317	C₂×C₄×C₅	—	2	16	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	4	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	4	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	12	2	no	—
326	C₂×C₄×C₅	C₂×#67	1	2	yes	—
327	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#67	1	2	yes	—
329	C₂×C₄×C₅	C₂×#67	1	2	yes	—
330	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
331	C₅×C₈	—	6	2	no	—
332	C₅×C₈	—	6	2	no	—
333	C₂×#41	—	2	4	no	—
334	C₂×#41	—	2	4	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	C₂×C₅×D₃	1	4	yes	complemented
337	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	3	1	no	—
340	C₂²×D₄	—	6	1	no	—
341	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
344	C₂×SD₁₆	—	3	4	no	—
345	C₂×SD₁₆	—	6	4	no	—
346	C₂×D₈	—	3	4	no	—
347	C₂×D₈	—	6	4	no	—
348	C₂²×C₈	—	3	1	no	—
349	C₂²×C₈	—	3	1	no	—
350	#121	—	3	4	no	—
351	#121	—	6	2	no	—
352	C₂×C₄⋊C₄	—	3	1	no	—
353	C₂×C₂²⋊C₄	—	6	1	no	—
354	#103	—	3	4	no	—
355	#102	—	3	4	no	—
356	C₂²⋊C₈	—	3	4	no	—
357	C₂×C₃×C₅	—	4	2	no	—
358	C₂×C₃×C₅	—	4	4	no	—
359	C₂×C₃×C₅	#449	1	4	yes	complemented
360	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
361	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
362	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₅×D₃	—	8	2	no	—
364	C₂³×C₃	—	2	2	no	—
365	C₂³×C₃	—	2	4	no	—
366	C₂³×C₃	—	2	2	no	—
367	C₂³×C₃	—	2	2	no	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	4	2	no	—
370	C₂³×C₃	—	4	2	no	—
371	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
372	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×D₃	—	2	2	no	—
374	C₂²×D₃	—	4	2	no	—
375	C₂²×D₃	—	4	2	no	—
376	C₂²×D₃	—	4	2	no	—
377	C₃×Q₈	—	2	4	no	—
378	C₃×Q₈	—	2	2	no	—
379	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
380	C₃×D₄	—	2	16	no	—
381	C₃×D₄	—	2	4	no	—
382	C₃×D₄	—	2	2	no	—
383	C₃×D₄	C₂×C₅×D₄	1	4	yes	complemented
384	C₂×C₃×C₄	—	2	16	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	4	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	4	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
392	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
394	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
395	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
396	#67	—	4	8	no	—
397	C₂×Dic₃	—	2	2	no	—
398	C₂×Dic₃	—	4	2	no	—
399	D₁₂	—	2	2	no	—
400	D₁₂	—	2	2	no	—
401	D₁₂	—	4	2	no	—
402	C₃⋊C₈	—	2	2	no	—
403	C₃⋊C₈	—	2	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	4	no	—
408	C₂²×C₅	—	4	4	no	—
409	C₂²×C₅	—	4	8	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	2	no	—
412	C₂²×C₅	—	12	2	no	—
413	C₂²×C₅	—	12	2	no	—
414	C₂²×C₅	—	12	2	no	—
415	C₂²×C₅	—	24	4	no	—
416	C₂²×C₅	#949	1	2	yes	—
417	C₂²×C₅	#950	1	2	yes	—
418	C₂²×C₅	#953	1	2	yes	—
419	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	4	no	—
422	C₄×C₅	—	12	2	no	—
423	C₄×C₅	#953	1	2	yes	—
424	C₄×C₅	C₂²×#67	1	1	yes	characteristic
425	C₄×C₅	C₂²×#67	1	1	yes	characteristic
426	C₂⁴	—	2	1	no	—
427	C₂⁴	—	6	1	no	—
428	C₂⁴	C₅×#67	1	1	yes	characteristic
429	#41	—	2	16	no	—
430	#41	—	2	8	no	—
431	#41	—	2	8	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₅×#67	1	4	yes	complemented
435	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	3	2	no	—
441	C₂×D₄	—	6	4	no	—
442	C₂×D₄	—	6	2	no	—
443	C₂×D₄	—	6	2	no	—
444	C₂×D₄	—	6	1	no	—
445	C₂×D₄	—	12	4	no	—
446	C₂×D₄	C₅×#67	1	4	yes	complemented
447	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	6	1	no	—
454	C₂²×C₄	C₅×#67	1	1	yes	characteristic
455	C₂²×C₄	C₅×#67	1	2	yes	—
456	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
457	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
458	SD₁₆	—	6	8	no	—
459	D₈	—	6	8	no	—
460	C₂×C₈	—	3	2	no	—
461	C₂×C₈	—	3	2	no	—
462	C₂×C₈	—	6	2	no	—
463	C₂×C₈	—	6	2	no	—
464	C₄⋊C₄	—	3	2	no	—
465	C₄⋊C₄	—	6	1	no	—
466	C₂²⋊C₄	—	6	4	no	—
467	C₃×C₅	C₂×#449	1	1	yes	characteristic, complemented, Hall
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	4	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	4	4	no	—
473	C₂²×C₃	—	4	8	no	—
474	C₂²×C₃	—	4	2	no	—
475	C₂²×C₃	—	4	2	no	—
476	C₂²×C₃	C₅×#120	1	2	yes	—
477	C₂²×C₃	C₅×#135	1	2	yes	—
478	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
479	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
480	C₂×D₃	—	4	2	no	—
481	C₂×D₃	—	4	2	no	—
482	C₂×D₃	—	4	2	no	—
483	C₂×D₃	—	8	4	no	—
484	C₃×C₄	—	2	2	no	—
485	C₃×C₄	—	2	4	no	—
486	C₃×C₄	C₅×#120	1	2	yes	—
487	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
489	Dic₃	—	4	2	no	—
490	C₂×C₅	—	4	2	no	—
491	C₂×C₅	—	4	4	no	—
492	C₂×C₅	—	24	2	no	—
493	C₂×C₅	#5238	1	4	yes	direct product factor
494	C₂×C₅	C₂×#949	1	1	yes	characteristic
495	C₂×C₅	C₂×#950	1	1	yes	characteristic
496	C₂×C₅	C₂×#953	1	1	yes	characteristic
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	6	2	no	—
505	C₂³	—	12	2	no	—
506	C₂³	—	12	2	no	—
507	C₂³	—	12	2	no	—
508	C₂³	C₂×C₅×#67	1	2	yes	—
509	C₂³	C₂×C₅×#67	1	1	yes	characteristic
510	Q₈	—	2	4	no	—
511	Q₈	—	2	2	no	—
512	Q₈	C₂×C₅×#67	1	4	yes	complemented
513	D₄	—	2	16	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	2	no	—
516	D₄	—	6	2	no	—
517	D₄	—	6	2	no	—
518	D₄	—	12	8	no	—
519	D₄	—	12	2	no	—
520	D₄	C₂×C₅×#67	1	4	yes	complemented
521	C₂×C₄	—	2	16	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	6	2	no	—
529	C₂×C₄	—	12	2	no	—
530	C₂×C₄	C₂×C₅×#67	1	2	yes	—
531	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
532	C₂×C₄	C₂×C₅×#67	1	2	yes	—
533	C₂×C₄	C₂×C₅×#67	1	2	yes	—
534	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
535	C₈	—	6	2	no	—
536	C₈	—	6	2	no	—
537	C₂×C₃	—	4	2	no	—
538	C₂×C₃	—	4	4	no	—
539	C₂×C₃	C₅×#449	1	4	yes	complemented
540	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
541	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
542	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
543	D₃	—	8	2	no	—
544	C₅	C₂×#5238	1	1	yes	characteristic, direct product factor, Sylow
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	8	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	12	2	no	—
554	C₂²	—	12	2	no	—
555	C₂²	—	12	2	no	—
556	C₂²	—	24	4	no	—
557	C₂²	C₅×#949	1	2	yes	—
558	C₂²	C₅×#950	1	2	yes	—
559	C₂²	C₅×#953	1	2	yes	—
560	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
561	C₄	—	2	2	no	—
562	C₄	—	2	4	no	—
563	C₄	—	12	2	no	—
564	C₄	C₅×#953	1	2	yes	—
565	C₄	C₂²×C₅×#67	1	1	yes	characteristic
566	C₄	C₂²×C₅×#67	1	1	yes	characteristic
567	C₃	C₂×C₅×#449	1	1	yes	characteristic, complemented, Sylow
568	C₂	—	4	2	no	—
569	C₂	—	4	4	no	—
570	C₂	—	24	2	no	—
571	C₂	C₅×#5238	1	4	yes	direct product factor
572	C₂	C₂×C₅×#949	1	1	yes	characteristic
573	C₂	C₂×C₅×#950	1	1	yes	characteristic
574	C₂	C₂×C₅×#953	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₂×C₅×#449
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×#41	C₂	semidirect
2. C₂²×C₅×#215	C₂	semidirect
3. C₂²×C₅×#213	C₂	semidirect
4. C₂×C₅×#930	C₂	semidirect
5. C₅×#5238	C₂	direct (N × H)
6. C₂×C₅×#835	C₂	semidirect
7. C₂×C₅×#832	C₂	semidirect
8. C₂×C₅×#830	C₂	semidirect
13. C₂×C₃×C₅×#41	C₂²	semidirect
22. C₂×C₅×#215	C₂²	semidirect
24. C₂×C₅×#213	C₂²	semidirect
26. C₅×#930	C₂²	semidirect
31. C₅×#835	C₂²	semidirect
32. C₅×#832	C₂²	semidirect
33. C₅×#830	C₂²	semidirect
34. C₂×#5238	C₅	direct (N × H)
35. C₂²×C₅×#41	D₃	semidirect
51. C₂×C₃×C₅×Q₈	D₄	semidirect
57. C₂×C₃×C₅×D₄	D₄	semidirect
84. C₂²×C₃×#41	C₂×C₅	semidirect
85. C₂²×#215	C₂×C₅	semidirect
86. C₂²×#213	C₂×C₅	semidirect
87. C₂×#930	C₂×C₅	semidirect
88. #5238	C₂×C₅	direct (N × H)
89. C₂×#835	C₂×C₅	semidirect
90. C₂×#832	C₂×C₅	semidirect
91. C₂×#830	C₂×C₅	semidirect
95. C₂×C₅×#41	C₂×D₃	semidirect
132. C₃×C₅×Q₈	C₂×D₄	semidirect
136. C₃×C₅×D₄	C₂×D₄	semidirect
160. C₂×C₃×#41	C₂²×C₅	semidirect
169. C₂×#215	C₂²×C₅	semidirect
171. C₂×#213	C₂²×C₅	semidirect
173. #930	C₂²×C₅	semidirect
178. #835	C₂²×C₅	semidirect
179. #832	C₂²×C₅	semidirect
180. #830	C₂²×C₅	semidirect
189. C₂×C₅×Q₈	#67	semidirect
201. C₂×C₅×D₄	#67	semidirect
222. C₂²×#41	C₅×D₃	semidirect
260. C₂×C₃×Q₈	C₅×D₄	semidirect
266. C₂×C₃×D₄	C₅×D₄	semidirect
308. C₅×Q₈	C₂×#67	semidirect
316. C₅×D₄	C₂×#67	semidirect
336. C₂×#41	C₂×C₅×D₃	semidirect
359. C₂×C₃×C₅	#449	semidirect
379. C₃×Q₈	C₂×C₅×D₄	semidirect
383. C₃×D₄	C₂×C₅×D₄	semidirect
434. C₂×Q₈	C₅×#67	semidirect
446. C₂×D₄	C₅×#67	semidirect
467. C₃×C₅	C₂×#449	semidirect
493. C₂×C₅	#5238	direct (N × H)
512. Q₈	C₂×C₅×#67	semidirect
520. D₄	C₂×C₅×#67	semidirect
539. C₂×C₃	C₅×#449	semidirect
544. C₅	C₂×#5238	direct (N × H)
567. C₃	C₂×C₅×#449	semidirect
571. C₂	C₅×#5238	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×C₃×C₅×#41	2
C₂²×C₅×#215	2
C₂²×C₅×#213	2
C₂×C₅×#930	2
C₅×#5238	2
C₂×C₅×#835	2
C₂×C₅×#832	2
C₂×C₅×#830	2
C₂×C₅×#449	3
C₂×#5238	5

Subgroups — C2×C5×#5238 #14423412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5238 #14423412