Subgroups — C₂×C₅×#5217 #14423181

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#213	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5217	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#447	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	—	2	8	no	—
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	—	2	2	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	—	2	1	no	—
16	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×#213	—	2	8	no	—
18	C₂×C₅×#213	C₂²	1	8	yes	complemented
19	C₅×#930	—	2	2	no	—
20	C₅×#930	C₂²	1	4	yes	complemented
21	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
24	C₅×#832	C₂²	1	8	yes	complemented
25	C₅×#830	C₂²	1	4	yes	complemented
26	C₂×#5217	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂³×C₅×D₄	D₃	1	1	yes	characteristic, complemented
28	C₂²×C₅×D₈	—	3	2	no	—
29	C₂×C₅×#121	—	3	1	no	—
30	C₅×#447	—	3	8	no	—
31	C₂×C₅×#102	—	3	2	no	—
32	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
33	C₂⁴×C₃×C₅	—	2	8	no	—
34	C₂⁴×C₃×C₅	—	2	2	no	—
35	C₂⁴×C₃×C₅	—	2	4	no	—
36	C₂⁴×C₃×C₅	—	4	4	no	—
37	C₂⁴×C₃×C₅	—	4	4	no	—
38	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
39	C₂³×C₅×D₃	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	8	no	—
41	C₂×C₃×C₅×D₄	—	2	16	no	—
42	C₂×C₃×C₅×D₄	—	2	16	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	4	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
47	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	2	4	no	—
54	C₂×C₅×#67	—	4	4	no	—
55	C₂²×C₅×Dic₃	—	2	1	no	—
56	C₂×C₅×D₁₂	—	2	4	no	—
57	C₂×C₅×D₁₂	—	2	1	no	—
58	C₂×C₅×D₁₂	C₂³	1	2	yes	complemented
59	C₅×#213	—	2	16	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₅×C₄⋊Dic₃	C₂³	1	2	yes	complemented
63	C₂×C₅×C₃⋊C₈	—	2	4	no	—
64	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	complemented
65	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂²×#213	C₂×C₅	1	2	yes	complemented
67	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
68	#5217	C₂×C₅	1	8	yes	direct product factor
69	C₂×#832	C₂×C₅	1	2	yes	complemented
70	C₂×#830	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂⁵×C₅	—	2	1	no	—
72	C₂²×C₅×D₄	—	2	8	no	—
73	C₂²×C₅×D₄	—	2	2	no	—
74	C₂²×C₅×D₄	—	2	1	no	—
75	C₂²×C₅×D₄	—	3	1	no	—
76	C₂²×C₅×D₄	—	6	1	no	—
77	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
78	C₂²×C₅×D₄	C₂×D₃	1	4	yes	complemented
79	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
80	C₂×C₅×D₈	—	3	8	no	—
81	C₂×C₅×D₈	—	6	8	no	—
82	C₂²×C₅×C₈	—	3	2	no	—
83	C₅×#121	—	3	4	no	—
84	C₅×#121	—	6	2	no	—
85	C₂×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
87	C₅×#102	—	3	8	no	—
88	C₅×C₂²⋊C₈	—	3	4	no	—
89	C₂×#447	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	2	no	—
92	C₂³×C₃×C₅	—	2	16	no	—
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	4	8	no	—
96	C₂³×C₃×C₅	—	4	32	no	—
97	C₂³×C₃×C₅	—	4	4	no	—
98	C₂³×C₃×C₅	—	4	8	no	—
99	C₂³×C₃×C₅	—	4	4	no	—
100	C₂³×C₃×C₅	D₈	1	4	yes	complemented
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	4	2	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂²×C₅×D₃	—	4	2	no	—
107	C₃×C₅×D₄	—	2	16	no	—
108	C₃×C₅×D₄	—	2	8	no	—
109	C₃×C₅×D₄	—	2	4	no	—
110	C₃×C₅×D₄	C₂×D₄	1	8	yes	complemented
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×#67	—	4	8	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	4	2	no	—
121	C₅×D₁₂	—	2	4	no	—
122	C₅×D₁₂	—	4	2	no	—
123	C₅×C₃⋊C₈	—	2	4	no	—
124	C₂⁵×C₃	—	2	1	no	—
125	C₂²×C₃×D₄	—	2	8	no	—
126	C₂²×C₃×D₄	—	2	1	no	—
127	C₂²×C₃×D₄	—	2	2	no	—
128	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
129	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
130	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
131	C₂²×#67	—	2	1	no	—
132	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
133	C₂×#213	—	2	8	no	—
134	C₂×#213	C₂²×C₅	1	8	yes	complemented
135	#930	—	2	2	no	—
136	#930	C₂²×C₅	1	4	yes	complemented
137	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
138	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
140	#832	C₂²×C₅	1	8	yes	complemented
141	#830	C₂²×C₅	1	4	yes	complemented
142	C₂⁴×C₅	—	2	8	no	—
143	C₂⁴×C₅	—	2	4	no	—
144	C₂⁴×C₅	—	2	2	no	—
145	C₂⁴×C₅	—	4	4	no	—
146	C₂⁴×C₅	—	4	4	no	—
147	C₂⁴×C₅	—	6	1	no	—
148	C₂⁴×C₅	#67	1	1	yes	characteristic
149	C₂×C₅×D₄	—	2	8	no	—
150	C₂×C₅×D₄	—	2	16	no	—
151	C₂×C₅×D₄	—	2	16	no	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	4	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	—	3	2	no	—
156	C₂×C₅×D₄	—	6	4	no	—
157	C₂×C₅×D₄	—	6	4	no	—
158	C₂×C₅×D₄	—	6	1	no	—
159	C₂×C₅×D₄	—	12	4	no	—
160	C₂×C₅×D₄	#67	1	8	yes	complemented
161	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
162	C₂²×C₄×C₅	—	2	4	no	—
163	C₂²×C₄×C₅	—	6	1	no	—
164	C₂²×C₄×C₅	#67	1	2	yes	—
165	C₂²×C₄×C₅	#67	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₅×D₈	—	6	16	no	—
169	C₂×C₅×C₈	—	3	4	no	—
170	C₂×C₅×C₈	—	6	4	no	—
171	C₅×C₄⋊C₄	—	3	2	no	—
172	C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×C₂²⋊C₄	—	6	4	no	—
174	C₂³×D₄	C₅×D₃	1	1	yes	characteristic, complemented
175	C₂²×D₈	—	3	2	no	—
176	C₂×#121	—	3	1	no	—
177	#447	—	3	8	no	—
178	C₂×#102	—	3	2	no	—
179	C₂×C₂²⋊C₈	—	3	1	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	8	no	—
183	C₂²×C₃×C₅	—	2	8	no	—
184	C₂²×C₃×C₅	—	4	32	no	—
185	C₂²×C₃×C₅	—	4	4	no	—
186	C₂²×C₃×C₅	—	4	4	no	—
187	C₂²×C₃×C₅	—	4	16	no	—
188	C₂²×C₃×C₅	#120	1	2	yes	—
189	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
190	C₂²×C₃×C₅	C₂×D₈	1	4	yes	complemented
191	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₅×D₃	—	4	2	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	8	4	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	#120	1	2	yes	—
199	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₅×Dic₃	—	4	2	no	—
201	C₂⁴×C₃	—	2	8	no	—
202	C₂⁴×C₃	—	2	2	no	—
203	C₂⁴×C₃	—	2	4	no	—
204	C₂⁴×C₃	—	4	4	no	—
205	C₂⁴×C₃	—	4	4	no	—
206	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
207	C₂³×D₃	—	2	1	no	—
208	C₂×C₃×D₄	—	2	8	no	—
209	C₂×C₃×D₄	—	2	16	no	—
210	C₂×C₃×D₄	—	2	16	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	—	2	4	no	—
213	C₂×C₃×D₄	—	2	4	no	—
214	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
215	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
216	C₂²×C₃×C₄	—	2	4	no	—
217	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
219	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂×#67	—	2	4	no	—
222	C₂×#67	—	4	4	no	—
223	C₂²×Dic₃	—	2	1	no	—
224	C₂×D₁₂	—	2	4	no	—
225	C₂×D₁₂	—	2	1	no	—
226	C₂×D₁₂	C₂³×C₅	1	2	yes	complemented
227	#213	—	2	16	no	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	C₄⋊Dic₃	—	2	1	no	—
230	C₄⋊Dic₃	C₂³×C₅	1	2	yes	complemented
231	C₂×C₃⋊C₈	—	2	4	no	—
232	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
233	C₂³×C₅	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	16	no	—
236	C₂³×C₅	—	2	8	no	—
237	C₂³×C₅	—	2	4	no	—
238	C₂³×C₅	—	4	32	no	—
239	C₂³×C₅	—	4	8	no	—
240	C₂³×C₅	—	4	4	no	—
241	C₂³×C₅	—	4	8	no	—
242	C₂³×C₅	—	4	4	no	—
243	C₂³×C₅	—	6	2	no	—
244	C₂³×C₅	—	12	2	no	—
245	C₂³×C₅	—	12	2	no	—
246	C₂³×C₅	—	12	2	no	—
247	C₂³×C₅	#213	1	4	yes	complemented
248	C₂³×C₅	C₂×#67	1	2	yes	—
249	C₂³×C₅	C₂×#67	1	1	yes	characteristic
250	C₅×D₄	—	2	16	no	—
251	C₅×D₄	—	2	8	no	—
252	C₅×D₄	—	2	4	no	—
253	C₅×D₄	—	6	4	no	—
254	C₅×D₄	—	12	8	no	—
255	C₅×D₄	—	12	2	no	—
256	C₅×D₄	C₂×#67	1	8	yes	complemented
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	—	2	4	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	12	2	no	—
262	C₂×C₄×C₅	C₂×#67	1	2	yes	—
263	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×#67	1	4	yes	—
265	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
266	C₅×C₈	—	6	4	no	—
267	C₂⁵	—	2	1	no	—
268	C₂²×D₄	—	2	8	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	3	1	no	—
272	C₂²×D₄	—	6	1	no	—
273	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
274	C₂²×D₄	C₂×C₅×D₃	1	4	yes	complemented
275	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×D₈	—	3	8	no	—
277	C₂×D₈	—	6	8	no	—
278	C₂²×C₈	—	3	2	no	—
279	#121	—	3	4	no	—
280	#121	—	6	2	no	—
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₂²⋊C₄	—	6	1	no	—
283	#102	—	3	8	no	—
284	C₂²⋊C₈	—	3	4	no	—
285	C₂×C₃×C₅	—	2	4	no	—
286	C₂×C₃×C₅	—	4	8	no	—
287	C₂×C₃×C₅	#447	1	4	yes	complemented
288	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
290	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₅×D₃	—	8	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	16	no	—
295	C₂³×C₃	—	2	8	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	4	32	no	—
298	C₂³×C₃	—	4	8	no	—
299	C₂³×C₃	—	4	4	no	—
300	C₂³×C₃	—	4	8	no	—
301	C₂³×C₃	—	4	4	no	—
302	C₂³×C₃	C₅×D₈	1	4	yes	complemented
303	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
304	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂²×D₃	—	2	2	no	—
306	C₂²×D₃	—	4	2	no	—
307	C₂²×D₃	—	4	2	no	—
308	C₂²×D₃	—	4	2	no	—
309	C₃×D₄	—	2	16	no	—
310	C₃×D₄	—	2	8	no	—
311	C₃×D₄	—	2	4	no	—
312	C₃×D₄	C₂×C₅×D₄	1	8	yes	complemented
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
319	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
320	#67	—	4	8	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	4	2	no	—
323	D₁₂	—	2	4	no	—
324	D₁₂	—	4	2	no	—
325	C₃⋊C₈	—	2	4	no	—
326	C₂²×C₅	—	2	8	no	—
327	C₂²×C₅	—	2	2	no	—
328	C₂²×C₅	—	2	2	no	—
329	C₂²×C₅	—	2	8	no	—
330	C₂²×C₅	—	4	32	no	—
331	C₂²×C₅	—	4	16	no	—
332	C₂²×C₅	—	4	4	no	—
333	C₂²×C₅	—	4	4	no	—
334	C₂²×C₅	—	12	2	no	—
335	C₂²×C₅	—	12	2	no	—
336	C₂²×C₅	—	12	2	no	—
337	C₂²×C₅	—	24	4	no	—
338	C₂²×C₅	C₂×#213	1	2	yes	—
339	C₂²×C₅	C₂×#213	1	4	yes	complemented
340	C₂²×C₅	#932	1	2	yes	—
341	C₂²×C₅	#953	1	2	yes	—
342	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	12	2	no	—
345	C₄×C₅	#953	1	2	yes	—
346	C₄×C₅	C₂²×#67	1	2	yes	—
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	4	4	no	—
351	C₂⁴	—	4	4	no	—
352	C₂⁴	—	6	1	no	—
353	C₂⁴	C₅×#67	1	1	yes	characteristic
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	16	no	—
356	C₂×D₄	—	2	16	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	3	2	no	—
361	C₂×D₄	—	6	4	no	—
362	C₂×D₄	—	6	4	no	—
363	C₂×D₄	—	6	1	no	—
364	C₂×D₄	—	12	4	no	—
365	C₂×D₄	C₅×#67	1	8	yes	complemented
366	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	6	1	no	—
369	C₂²×C₄	C₅×#67	1	1	yes	characteristic
370	C₂²×C₄	C₅×#67	1	2	yes	—
371	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
372	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	D₈	—	6	16	no	—
374	C₂×C₈	—	3	4	no	—
375	C₂×C₈	—	6	4	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	—	6	1	no	—
378	C₂²⋊C₄	—	6	4	no	—
379	C₃×C₅	C₂×#447	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	8	no	—
384	C₂²×C₃	—	4	32	no	—
385	C₂²×C₃	—	4	16	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	4	4	no	—
388	C₂²×C₃	C₅×#120	1	2	yes	—
389	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
390	C₂²×C₃	C₂×C₅×D₈	1	4	yes	complemented
391	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
392	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₂×D₃	—	4	2	no	—
394	C₂×D₃	—	4	2	no	—
395	C₂×D₃	—	4	2	no	—
396	C₂×D₃	—	8	4	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	C₅×#120	1	2	yes	—
399	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
400	Dic₃	—	4	2	no	—
401	C₂×C₅	—	2	4	no	—
402	C₂×C₅	—	4	8	no	—
403	C₂×C₅	—	24	2	no	—
404	C₂×C₅	#5217	1	4	yes	direct product factor
405	C₂×C₅	C₂²×#213	1	1	yes	characteristic
406	C₂×C₅	C₂×#932	1	1	yes	characteristic
407	C₂×C₅	C₂×#953	1	1	yes	characteristic
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	16	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	32	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	6	2	no	—
419	C₂³	—	12	2	no	—
420	C₂³	—	12	2	no	—
421	C₂³	—	12	2	no	—
422	C₂³	C₅×#213	1	4	yes	complemented
423	C₂³	C₂×C₅×#67	1	2	yes	—
424	C₂³	C₂×C₅×#67	1	1	yes	characteristic
425	D₄	—	2	16	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	6	4	no	—
429	D₄	—	12	8	no	—
430	D₄	—	12	2	no	—
431	D₄	C₂×C₅×#67	1	8	yes	complemented
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	12	2	no	—
437	C₂×C₄	C₂×C₅×#67	1	2	yes	—
438	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
439	C₂×C₄	C₂×C₅×#67	1	4	yes	—
440	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
441	C₈	—	6	4	no	—
442	C₂×C₃	—	2	4	no	—
443	C₂×C₃	—	4	8	no	—
444	C₂×C₃	C₅×#447	1	4	yes	complemented
445	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
446	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
447	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
448	D₃	—	8	2	no	—
449	C₅	C₂×#5217	1	1	yes	characteristic, direct product factor, Sylow
450	C₂²	—	2	8	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	4	32	no	—
455	C₂²	—	4	16	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	12	2	no	—
459	C₂²	—	12	2	no	—
460	C₂²	—	12	2	no	—
461	C₂²	—	24	4	no	—
462	C₂²	C₂×C₅×#213	1	2	yes	—
463	C₂²	C₂×C₅×#213	1	4	yes	complemented
464	C₂²	C₅×#932	1	2	yes	—
465	C₂²	C₅×#953	1	2	yes	—
466	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	12	2	no	—
469	C₄	C₅×#953	1	2	yes	—
470	C₄	C₂²×C₅×#67	1	2	yes	—
471	C₃	C₂×C₅×#447	1	1	yes	characteristic, complemented, Sylow
472	C₂	—	2	4	no	—
473	C₂	—	4	8	no	—
474	C₂	—	24	2	no	—
475	C₂	C₅×#5217	1	4	yes	direct product factor
476	C₂	C₂²×C₅×#213	1	1	yes	characteristic
477	C₂	C₂×C₅×#932	1	1	yes	characteristic
478	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	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂³×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#447
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂²×C₅×#213	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₅×#5217	C₂	direct (N × H)
5. C₂×C₅×#832	C₂	semidirect
6. C₂×C₅×#830	C₂	semidirect
13. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₅×D₁₂	C₂²	semidirect
18. C₂×C₅×#213	C₂²	semidirect
20. C₅×#930	C₂²	semidirect
22. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
23. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
24. C₅×#832	C₂²	semidirect
25. C₅×#830	C₂²	semidirect
26. C₂×#5217	C₅	direct (N × H)
27. C₂³×C₅×D₄	D₃	semidirect
46. C₂×C₃×C₅×D₄	D₄	semidirect
58. C₂×C₅×D₁₂	C₂³	semidirect
62. C₅×C₄⋊Dic₃	C₂³	semidirect
64. C₂×C₅×C₃⋊C₈	C₂³	semidirect
65. C₂³×C₃×D₄	C₂×C₅	semidirect
66. C₂²×#213	C₂×C₅	semidirect
67. C₂×#930	C₂×C₅	semidirect
68. #5217	C₂×C₅	direct (N × H)
69. C₂×#832	C₂×C₅	semidirect
70. C₂×#830	C₂×C₅	semidirect
78. C₂²×C₅×D₄	C₂×D₃	semidirect
100. C₂³×C₃×C₅	D₈	semidirect
110. C₃×C₅×D₄	C₂×D₄	semidirect
129. C₂²×C₃×D₄	C₂²×C₅	semidirect
132. C₂²×D₁₂	C₂²×C₅	semidirect
134. C₂×#213	C₂²×C₅	semidirect
136. #930	C₂²×C₅	semidirect
138. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
139. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
140. #832	C₂²×C₅	semidirect
141. #830	C₂²×C₅	semidirect
160. C₂×C₅×D₄	#67	semidirect
174. C₂³×D₄	C₅×D₃	semidirect
190. C₂²×C₃×C₅	C₂×D₈	semidirect
214. C₂×C₃×D₄	C₅×D₄	semidirect
226. C₂×D₁₂	C₂³×C₅	semidirect
230. C₄⋊Dic₃	C₂³×C₅	semidirect
232. C₂×C₃⋊C₈	C₂³×C₅	semidirect
247. C₂³×C₅	#213	semidirect
256. C₅×D₄	C₂×#67	semidirect
274. C₂²×D₄	C₂×C₅×D₃	semidirect
287. C₂×C₃×C₅	#447	semidirect
302. C₂³×C₃	C₅×D₈	semidirect
312. C₃×D₄	C₂×C₅×D₄	semidirect
339. C₂²×C₅	C₂×#213	semidirect
365. C₂×D₄	C₅×#67	semidirect
379. C₃×C₅	C₂×#447	semidirect
390. C₂²×C₃	C₂×C₅×D₈	semidirect
404. C₂×C₅	#5217	direct (N × H)
422. C₂³	C₅×#213	semidirect
431. D₄	C₂×C₅×#67	semidirect
444. C₂×C₃	C₅×#447	semidirect
449. C₅	C₂×#5217	direct (N × H)
463. C₂²	C₂×C₅×#213	semidirect
471. C₃	C₂×C₅×#447	semidirect
475. C₂	C₅×#5217	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂²×C₅×#213	2
C₂×C₅×#930	2
C₅×#5217	2
C₂×C₅×#832	2
C₂×C₅×#830	2
C₂×C₅×#447	3
C₂×#5217	5

Subgroups — C2×C5×#5217 #14423181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5217 #14423181