Subgroups — C₂×C₅×#5002 #14412313

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5002	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#810	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#809	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#416	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₅×#67	—	2	1	no	—
10	C₂×C₅×#235	—	2	4	no	—
11	C₂×C₅×#235	—	2	2	no	—
12	C₂×C₅×#235	C₄	1	8	yes	complemented
13	C₂×C₅×#235	C₂²	1	4	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	—	2	1	no	—
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	—	2	2	no	—
18	C₃×C₅×#117	C₂²	1	4	yes	complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
21	C₂×C₃×C₄²×C₅	—	2	1	no	—
22	C₂²×C₅×C₃⋊C₈	—	2	4	no	—
23	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	C₂²×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
25	C₅×#810	C₂²	1	8	yes	complemented
26	C₅×#809	C₂²	1	8	yes	complemented
27	C₂×#5002	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×#41	—	3	1	no	—
29	C₂³×C₅×C₈	—	3	1	no	—
30	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
31	C₅×#416	—	3	8	no	—
32	C₂×C₅×#103	—	3	2	no	—
33	C₂×C₅×#102	—	3	2	no	—
34	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
35	C₂³×C₅×D₃	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂×C₅×#67	—	2	8	no	—
44	C₂×C₅×#67	—	2	4	no	—
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₅×#235	—	2	16	no	—
47	C₅×#235	—	2	8	no	—
48	C₅×#235	C₂×C₄	1	16	yes	complemented
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₅×D₁₂	—	2	2	no	—
51	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
52	C₂×C₅×D₁₂	C₂³	1	2	yes	—
53	C₂×C₄×C₅×D₃	—	2	8	no	—
54	C₂×C₄×C₅×D₃	—	2	4	no	—
55	C₂×C₅×Dic₆	—	2	1	no	—
56	C₂×C₅×Dic₆	—	2	2	no	—
57	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
58	C₂×C₅×Dic₆	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₄²×C₅	—	2	4	no	—
63	C₂×C₅×C₃⋊C₈	—	2	4	no	—
64	C₂×C₅×C₃⋊C₈	—	2	8	no	—
65	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
66	C₂²×#235	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂³×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
69	#5002	C₂×C₅	1	8	yes	direct product factor
70	C₂×#810	C₂×C₅	1	2	yes	complemented
71	C₂×#809	C₂×C₅	1	2	yes	complemented
72	C₂×C₅×#41	—	3	8	no	—
73	C₂×C₅×#41	—	3	4	no	—
74	C₂×C₅×#41	—	6	4	no	—
75	C₂×C₅×#41	—	6	2	no	—
76	C₂²×C₅×Q₈	—	3	1	no	—
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂²×C₅×D₄	—	6	1	no	—
79	C₂³×C₄×C₅	—	6	1	no	—
80	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	3	2	no	—
82	C₂²×C₅×C₈	—	3	4	no	—
83	C₂²×C₅×C₈	—	6	4	no	—
84	C₅×#117	—	2	2	no	—
85	C₅×#117	C₂×D₃	1	4	yes	complemented
86	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₅×#103	—	3	8	no	—
90	C₅×#102	—	3	8	no	—
91	C₂×#416	—	3	1	no	Sylow
92	C₂³×C₃×C₅	—	2	4	no	—
93	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
94	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	4	no	—
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	4	4	no	—
99	C₂×C₃×C₄×C₅	—	2	4	no	—
100	C₂×C₃×C₄×C₅	—	4	4	no	—
101	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	8	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₅×#67	—	2	16	no	—
111	C₂×C₅×Dic₃	—	2	4	no	—
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₅×D₁₂	—	2	4	no	—
114	C₅×D₁₂	—	2	2	no	—
115	C₅×D₁₂	C₂²×C₄	1	4	yes	—
116	C₄×C₅×D₃	—	2	16	no	—
117	C₅×Dic₆	—	2	4	no	—
118	C₅×Dic₆	—	2	2	no	—
119	C₅×Dic₆	C₂²×C₄	1	4	yes	—
120	C₅×C₃⋊C₈	—	2	4	no	—
121	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
122	C₂²×#67	—	2	1	no	—
123	C₂×#235	—	2	4	no	—
124	C₂×#235	—	2	2	no	—
125	C₂×#235	C₄×C₅	1	8	yes	complemented
126	C₂×#235	C₂²×C₅	1	4	yes	—
127	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
128	C₂²×C₄×D₃	—	2	1	no	—
129	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
130	C₃×#117	—	2	2	no	—
131	C₃×#117	C₂²×C₅	1	4	yes	complemented
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₃×C₄²	—	2	1	no	—
135	C₂²×C₃⋊C₈	—	2	4	no	—
136	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
137	C₂²×C₃⋊C₈	C₂²×C₅	1	4	yes	complemented
138	#810	C₂²×C₅	1	8	yes	complemented
139	#809	C₂²×C₅	1	8	yes	complemented
140	C₂⁴×C₅	—	6	1	no	—
141	C₂⁴×C₅	#67	1	1	yes	characteristic
142	C₅×#41	—	3	16	no	—
143	C₅×#41	—	6	16	no	—
144	C₅×#41	—	6	8	no	—
145	C₂×C₅×Q₈	—	3	4	no	—
146	C₂×C₅×Q₈	—	3	2	no	—
147	C₂×C₅×Q₈	—	6	2	no	—
148	C₂×C₅×Q₈	—	6	1	no	—
149	C₂×C₅×D₄	—	3	4	no	—
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	6	8	no	—
152	C₂×C₅×D₄	—	6	4	no	—
153	C₂×C₅×D₄	—	6	2	no	—
154	C₂×C₅×D₄	—	6	1	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	6	1	no	—
157	C₂²×C₄×C₅	—	6	8	no	—
158	C₂²×C₄×C₅	—	6	4	no	—
159	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
160	C₂²×C₄×C₅	D₁₂	1	4	yes	—
161	C₂²×C₄×C₅	#67	1	2	yes	—
162	C₂²×C₄×C₅	#67	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
165	C₂×C₅×C₈	—	3	4	no	—
166	C₂×C₅×C₈	—	6	4	no	—
167	C₂×C₅×C₈	—	6	8	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
170	C₅×C₂²⋊C₄	—	2	4	no	—
171	C₄²×C₅	—	2	4	no	—
172	C₂²×#41	—	3	1	no	—
173	C₂³×C₈	—	3	1	no	—
174	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
175	#416	—	3	8	no	—
176	C₂×#103	—	3	2	no	—
177	C₂×#102	—	3	2	no	—
178	C₂²×C₃×C₅	—	2	4	no	—
179	C₂²×C₃×C₅	—	2	8	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂²×C₃×C₅	#135	1	4	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₅×D₃	—	2	4	no	—
185	C₂×C₅×D₃	—	4	4	no	—
186	C₂×C₅×D₃	—	4	8	no	—
187	C₃×C₄×C₅	—	4	4	no	—
188	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
189	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
190	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₅×Dic₃	—	2	4	no	—
193	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
194	C₂³×D₃	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
197	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
198	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
202	C₂×#67	—	2	8	no	—
203	C₂×#67	—	2	4	no	—
204	C₂²×Dic₃	—	2	1	no	—
205	#235	—	2	16	no	—
206	#235	—	2	8	no	—
207	#235	C₂×C₄×C₅	1	16	yes	complemented
208	C₂×D₁₂	—	2	2	no	—
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
211	C₂×D₁₂	C₂³×C₅	1	2	yes	—
212	C₂×C₄×D₃	—	2	8	no	—
213	C₂×C₄×D₃	—	2	4	no	—
214	C₂×Dic₆	—	2	2	no	—
215	C₂×Dic₆	—	2	1	no	—
216	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
217	C₂×Dic₆	C₂³×C₅	1	2	yes	—
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
220	C₃×C₂²⋊C₄	—	2	4	no	—
221	C₃×C₄²	—	2	4	no	—
222	C₂×C₃⋊C₈	—	2	4	no	—
223	C₂×C₃⋊C₈	—	2	8	no	—
224	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	6	4	no	—
227	C₂³×C₅	—	6	2	no	—
228	C₂³×C₅	—	12	4	no	—
229	C₂³×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
230	C₂³×C₅	C₂×#67	1	2	yes	—
231	C₂³×C₅	C₂×#67	1	1	yes	characteristic
232	C₅×Q₈	—	3	4	no	—
233	C₅×Q₈	—	6	4	no	—
234	C₅×Q₈	—	6	2	no	—
235	C₅×D₄	—	3	4	no	—
236	C₅×D₄	—	6	16	no	—
237	C₅×D₄	—	6	4	no	—
238	C₅×D₄	—	6	2	no	—
239	C₂×C₄×C₅	—	2	4	no	—
240	C₂×C₄×C₅	—	4	4	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	16	no	—
244	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
245	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	8	yes	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
247	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
248	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
249	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
250	C₂×C₄×C₅	C₂×#67	1	2	yes	—
251	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
253	C₅×C₈	—	6	4	no	—
254	C₂×#41	—	3	8	no	—
255	C₂×#41	—	3	4	no	—
256	C₂×#41	—	6	4	no	—
257	C₂×#41	—	6	2	no	—
258	C₂²×Q₈	—	3	1	no	—
259	C₂²×D₄	—	3	1	no	—
260	C₂²×D₄	—	6	1	no	—
261	C₂³×C₄	—	6	1	no	—
262	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂²×C₈	—	3	2	no	—
264	C₂²×C₈	—	3	4	no	—
265	C₂²×C₈	—	6	4	no	—
266	#117	—	2	2	no	—
267	#117	C₂×C₅×D₃	1	4	yes	complemented
268	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	#103	—	3	8	no	—
272	#102	—	3	8	no	—
273	C₂×C₃×C₅	—	2	4	no	—
274	C₂×C₃×C₅	#416	1	4	yes	complemented
275	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#135	1	2	yes	—
277	C₅×D₃	—	4	4	no	—
278	C₂³×C₃	—	2	4	no	—
279	C₂³×C₃	C₅×C₂²⋊C₄	1	4	yes	—
280	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
281	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂²×D₃	—	2	4	no	—
283	C₂²×D₃	—	2	2	no	—
284	C₂²×D₃	—	4	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	4	4	no	—
287	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
288	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	8	yes	—
289	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
290	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
291	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	#67	—	2	16	no	—
297	C₂×Dic₃	—	2	4	no	—
298	C₂×Dic₃	—	2	2	no	—
299	D₁₂	—	2	4	no	—
300	D₁₂	—	2	2	no	—
301	D₁₂	C₂²×C₄×C₅	1	4	yes	—
302	C₄×D₃	—	2	16	no	—
303	Dic₆	—	2	4	no	—
304	Dic₆	—	2	2	no	—
305	Dic₆	C₂²×C₄×C₅	1	4	yes	—
306	C₃⋊C₈	—	2	4	no	—
307	C₂²×C₅	—	2	8	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	6	4	no	—
310	C₂²×C₅	—	12	8	no	—
311	C₂²×C₅	—	12	4	no	—
312	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
313	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
314	C₂²×C₅	#950	1	4	yes	—
315	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
316	C₄×C₅	—	4	4	no	—
317	C₄×C₅	—	6	4	no	—
318	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
319	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
320	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
321	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
322	C₂⁴	—	6	1	no	—
323	C₂⁴	C₅×#67	1	1	yes	characteristic
324	#41	—	3	16	no	—
325	#41	—	6	16	no	—
326	#41	—	6	8	no	—
327	C₂×Q₈	—	3	4	no	—
328	C₂×Q₈	—	3	2	no	—
329	C₂×Q₈	—	6	2	no	—
330	C₂×Q₈	—	6	1	no	—
331	C₂×D₄	—	3	4	no	—
332	C₂×D₄	—	3	2	no	—
333	C₂×D₄	—	6	8	no	—
334	C₂×D₄	—	6	4	no	—
335	C₂×D₄	—	6	2	no	—
336	C₂×D₄	—	6	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	6	1	no	—
339	C₂²×C₄	—	6	8	no	—
340	C₂²×C₄	—	6	4	no	—
341	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
342	C₂²×C₄	C₅×D₁₂	1	4	yes	—
343	C₂²×C₄	C₅×#67	1	1	yes	characteristic
344	C₂²×C₄	C₅×#67	1	2	yes	—
345	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
347	C₂×C₈	—	3	4	no	—
348	C₂×C₈	—	6	4	no	—
349	C₂×C₈	—	6	8	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₃×C₅	C₂×#416	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	2	8	no	—
356	C₂²×C₃	—	2	4	no	—
357	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
358	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
359	C₂²×C₃	C₅×#135	1	4	yes	—
360	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
361	C₂×D₃	—	2	4	no	—
362	C₂×D₃	—	4	8	no	—
363	C₂×D₃	—	4	4	no	—
364	C₃×C₄	—	4	4	no	—
365	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
366	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
367	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
368	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
369	Dic₃	—	2	4	no	—
370	C₂×C₅	—	2	4	no	—
371	C₂×C₅	—	12	4	no	—
372	C₂×C₅	#5002	1	4	yes	direct product factor
373	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
374	C₂×C₅	C₂×#950	1	2	yes	—
375	C₂³	—	2	4	no	—
376	C₂³	—	6	4	no	—
377	C₂³	—	6	2	no	—
378	C₂³	—	12	4	no	—
379	C₂³	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
380	C₂³	C₂×C₅×#67	1	2	yes	—
381	C₂³	C₂×C₅×#67	1	1	yes	characteristic
382	Q₈	—	3	4	no	—
383	Q₈	—	6	4	no	—
384	Q₈	—	6	2	no	—
385	D₄	—	3	4	no	—
386	D₄	—	6	16	no	—
387	D₄	—	6	4	no	—
388	D₄	—	6	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	6	4	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	16	no	—
394	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
395	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	8	yes	—
396	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
397	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
398	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
399	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
400	C₂×C₄	C₂×C₅×#67	1	2	yes	—
401	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
402	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
403	C₈	—	6	4	no	—
404	C₂×C₃	—	2	4	no	—
405	C₂×C₃	C₅×#416	1	4	yes	complemented
406	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
407	C₂×C₃	C₂×C₅×#135	1	2	yes	—
408	D₃	—	4	4	no	—
409	C₅	C₂×#5002	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	8	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	6	4	no	—
413	C₂²	—	12	8	no	—
414	C₂²	—	12	4	no	—
415	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
416	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
417	C₂²	C₅×#950	1	4	yes	—
418	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
419	C₄	—	4	4	no	—
420	C₄	—	6	4	no	—
421	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
422	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
423	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
424	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
425	C₃	C₂×C₅×#416	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	2	4	no	—
427	C₂	—	12	4	no	—
428	C₂	C₅×#5002	1	4	yes	direct product factor
429	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
430	C₂	C₂×C₅×#950	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₂×C₅×#416
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂³×C₅×C₃⋊C₈	C₂	semidirect
4. C₅×#5002	C₂	direct (N × H)
5. C₂×C₅×#810	C₂	semidirect
6. C₂×C₅×#809	C₂	semidirect
12. C₂×C₅×#235	C₄	semidirect
18. C₃×C₅×#117	C₂²	semidirect
24. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
25. C₅×#810	C₂²	semidirect
26. C₅×#809	C₂²	semidirect
27. C₂×#5002	C₅	direct (N × H)
30. C₂×C₅×#117	D₃	semidirect
48. C₅×#235	C₂×C₄	semidirect
67. C₂×C₃×#117	C₂×C₅	semidirect
68. C₂³×C₃⋊C₈	C₂×C₅	semidirect
69. #5002	C₂×C₅	direct (N × H)
70. C₂×#810	C₂×C₅	semidirect
71. C₂×#809	C₂×C₅	semidirect
85. C₅×#117	C₂×D₃	semidirect
125. C₂×#235	C₄×C₅	semidirect
131. C₃×#117	C₂²×C₅	semidirect
137. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
138. #810	C₂²×C₅	semidirect
139. #809	C₂²×C₅	semidirect
174. C₂×#117	C₅×D₃	semidirect
207. #235	C₂×C₄×C₅	semidirect
267. #117	C₂×C₅×D₃	semidirect
274. C₂×C₃×C₅	#416	semidirect
354. C₃×C₅	C₂×#416	semidirect
372. C₂×C₅	#5002	direct (N × H)
405. C₂×C₃	C₅×#416	semidirect
409. C₅	C₂×#5002	direct (N × H)
425. C₃	C₂×C₅×#416	semidirect
428. C₂	C₅×#5002	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×C₅×#235	2
C₂×C₃×C₅×#117	2
C₂³×C₅×C₃⋊C₈	2
C₅×#5002	2
C₂×C₅×#810	2
C₂×C₅×#809	2
C₂×C₅×#416	3
C₂×#5002	5

Subgroups — C2×C5×#5002 #14412313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5002 #14412313