Subgroups — C₂×C₅×#5715 #14480362

Order 1920.

3792 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×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#939	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#937	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5715	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#535	—	3	1	no	maximal, Hall
12	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂²×C₅×#67	C₂²	1	2	yes	—
18	C₂²×C₅×#67	C₂²	1	4	yes	complemented
19	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
20	C₂×C₅×#237	—	2	8	no	—
21	C₂×C₅×#237	C₂²	1	8	yes	complemented
22	C₂×C₅×D₃×D₄	—	2	8	no	—
23	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
24	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#127	C₂²	1	8	yes	complemented
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#217	C₂²	1	4	yes	complemented
30	C₅×#940	C₂²	1	8	yes	complemented
31	C₅×#939	C₂²	1	32	yes	complemented
32	C₅×#937	C₂²	1	32	yes	complemented
33	C₅×#936	C₂²	1	8	yes	complemented
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₅×#875	C₂²	1	8	yes	complemented
39	C₅×#872	C₂²	1	8	yes	complemented
40	C₂×#5715	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂²×C₅×#41	—	3	1	no	—
42	C₂³×C₅×D₄	—	3	1	no	—
43	C₅×#535	—	3	16	no	—
44	C₂×C₅×#127	—	3	1	no	—
45	C₂×C₅×#127	D₃	1	1	yes	characteristic, complemented
46	C₂×C₅×#124	—	3	1	no	—
47	C₂×C₅×#124	—	3	1	no	—
48	C₂×C₅×#121	—	3	4	no	—
49	C₂×C₅×#120	—	3	4	no	—
50	C₂×C₅×#117	—	3	1	no	—
51	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
52	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
53	C₂³×C₅×D₃	—	2	8	no	—
54	C₂³×C₅×D₃	—	4	8	no	—
55	C₂³×C₅×D₃	C₂³	1	2	yes	—
56	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
57	C₂³×C₅×D₃	C₂³	1	8	yes	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	4	8	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
62	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
63	C₂×C₃×C₅×D₄	C₂³	1	16	yes	complemented
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₅×#67	—	2	8	no	—
67	C₂×C₅×#67	—	2	8	no	—
68	C₂×C₅×#67	—	4	8	no	—
69	C₂×C₅×#67	C₂³	1	8	yes	—
70	C₂×C₅×#67	C₂³	1	8	yes	—
71	C₂×C₅×#67	C₂³	1	16	yes	complemented
72	C₂²×C₅×Dic₃	—	2	8	no	—
73	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
75	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
76	C₂²×C₅×Dic₃	C₂³	1	8	yes	complemented
77	C₅×#237	—	2	32	no	—
78	C₅×D₃×D₄	—	2	32	no	—
79	C₂×C₅×D₁₂	—	2	4	no	—
80	C₂×C₅×D₁₂	C₂³	1	4	yes	—
81	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
82	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
83	C₂×C₅×Dic₆	—	2	4	no	—
84	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
85	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
86	C₅×#217	C₂³	1	16	yes	complemented
87	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
88	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
89	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
90	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
91	C₂²×#237	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#939	C₂×C₅	1	4	yes	complemented
96	C₂×#937	C₂×C₅	1	4	yes	complemented
97	C₂×#936	C₂×C₅	1	1	yes	characteristic, complemented
98	#5715	C₂×C₅	1	16	yes	direct product factor
99	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁵×C₅	—	3	2	no	—
102	C₂×C₅×#41	—	3	8	no	—
103	C₂×C₅×#41	—	6	8	no	—
104	C₂²×C₅×Q₈	—	3	1	no	—
105	C₂²×C₅×D₄	—	3	2	no	—
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	3	4	no	—
108	C₂²×C₅×D₄	—	3	8	no	—
109	C₂²×C₅×D₄	—	3	1	no	—
110	C₂²×C₅×D₄	—	6	8	no	—
111	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
113	C₂²×C₅×D₄	C₂×D₃	1	4	yes	complemented
114	C₂³×C₄×C₅	—	3	1	no	—
115	C₂³×C₄×C₅	—	3	2	no	—
116	C₅×#127	—	3	8	no	—
117	C₅×#127	C₂×D₃	1	8	yes	complemented
118	C₅×#124	—	3	8	no	—
119	C₅×#124	—	3	8	no	—
120	C₅×#121	—	3	32	no	—
121	C₅×#120	—	3	32	no	—
122	C₅×#117	—	3	8	no	—
123	C₂×C₅×C₄⋊C₄	—	3	2	no	—
124	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
125	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
126	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
127	C₂×C₄²×C₅	—	3	1	no	—
128	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
129	C₂×#535	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	4	no	—
131	C₂³×C₃×C₅	—	2	4	no	—
132	C₂³×C₃×C₅	—	2	8	no	—
133	C₂³×C₃×C₅	—	2	8	no	—
134	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
135	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
136	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
137	C₂²×C₅×D₃	—	2	4	no	—
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	—	2	8	no	—
140	C₂²×C₅×D₃	—	2	16	no	—
141	C₂²×C₅×D₃	—	4	16	no	—
142	C₂²×C₅×D₃	—	4	32	no	—
143	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
144	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
145	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
146	C₃×C₅×D₄	—	2	8	no	—
147	C₃×C₅×D₄	—	2	8	no	—
148	C₃×C₅×D₄	—	4	16	no	—
149	C₂×C₃×C₄×C₅	—	2	4	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
153	C₅×#67	—	2	16	no	—
154	C₅×#67	—	2	16	no	—
155	C₅×#67	—	4	16	no	—
156	C₂×C₅×Dic₃	—	2	4	no	—
157	C₂×C₅×Dic₃	—	2	4	no	—
158	C₂×C₅×Dic₃	—	2	16	no	—
159	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
160	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
161	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
162	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
163	C₅×D₁₂	—	2	8	no	—
164	C₄×C₅×D₃	C₂×D₄	1	16	yes	complemented
165	C₅×Dic₆	—	2	8	no	—
166	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
167	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
170	C₂²×#67	C₂²×C₅	1	2	yes	—
171	C₂²×#67	C₂²×C₅	1	2	yes	—
172	C₂²×#67	C₂²×C₅	1	4	yes	complemented
173	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
174	C₂×#237	—	2	8	no	—
175	C₂×#237	C₂²×C₅	1	8	yes	complemented
176	C₂×D₃×D₄	—	2	8	no	—
177	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
178	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
180	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₃×#127	C₂²×C₅	1	8	yes	complemented
182	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂×#217	C₂²×C₅	1	4	yes	complemented
184	#940	C₂²×C₅	1	8	yes	complemented
185	#939	C₂²×C₅	1	32	yes	complemented
186	#937	C₂²×C₅	1	32	yes	complemented
187	#936	C₂²×C₅	1	8	yes	complemented
188	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
189	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
190	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
191	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
192	#875	C₂²×C₅	1	8	yes	complemented
193	#872	C₂²×C₅	1	8	yes	complemented
194	C₂⁴×C₅	—	3	1	no	—
195	C₂⁴×C₅	—	3	2	no	—
196	C₂⁴×C₅	—	3	8	no	—
197	C₂⁴×C₅	—	6	8	no	—
198	C₂⁴×C₅	—	12	8	no	—
199	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
200	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
201	C₅×#41	—	6	32	no	—
202	C₂×C₅×Q₈	—	3	4	no	—
203	C₂×C₅×Q₈	—	6	4	no	—
204	C₂×C₅×D₄	—	2	4	no	—
205	C₂×C₅×D₄	—	2	4	no	—
206	C₂×C₅×D₄	—	3	8	no	—
207	C₂×C₅×D₄	—	3	8	no	—
208	C₂×C₅×D₄	—	3	16	no	—
209	C₂×C₅×D₄	—	3	4	no	—
210	C₂×C₅×D₄	—	4	8	no	—
211	C₂×C₅×D₄	—	6	32	no	—
212	C₂×C₅×D₄	—	6	8	no	—
213	C₂×C₅×D₄	—	6	8	no	—
214	C₂×C₅×D₄	—	6	4	no	—
215	C₂×C₅×D₄	—	12	8	no	—
216	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
217	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
218	C₂×C₅×D₄	C₂²×D₃	1	16	yes	complemented
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	8	no	—
221	C₂²×C₄×C₅	—	3	4	no	—
222	C₂²×C₄×C₅	—	3	8	no	—
223	C₂²×C₄×C₅	—	3	2	no	—
224	C₂²×C₄×C₅	—	3	2	no	—
225	C₂²×C₄×C₅	—	6	8	no	—
226	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
227	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
228	C₅×C₄⋊C₄	—	3	8	no	—
229	C₅×C₂²⋊C₄	—	3	16	no	—
230	C₅×C₂²⋊C₄	—	3	8	no	—
231	C₅×C₂²⋊C₄	—	3	16	no	—
232	C₄²×C₅	—	3	4	no	—
233	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
234	C₂²×#41	—	3	1	no	—
235	C₂³×D₄	—	3	1	no	—
236	#535	—	3	16	no	—
237	C₂×#127	—	3	1	no	—
238	C₂×#127	C₅×D₃	1	1	yes	characteristic, complemented
239	C₂×#124	—	3	1	no	—
240	C₂×#124	—	3	1	no	—
241	C₂×#121	—	3	4	no	—
242	C₂×#120	—	3	4	no	—
243	C₂×#117	—	3	1	no	—
244	C₂²×C₃×C₅	—	2	4	no	—
245	C₂²×C₃×C₅	—	2	4	no	—
246	C₂²×C₃×C₅	—	2	8	no	—
247	C₂²×C₃×C₅	—	2	8	no	—
248	C₂²×C₃×C₅	—	4	8	no	—
249	C₂²×C₃×C₅	—	4	8	no	—
250	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
251	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
252	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
253	C₂×C₅×D₃	—	2	8	no	—
254	C₂×C₅×D₃	—	2	4	no	—
255	C₂×C₅×D₃	—	2	4	no	—
256	C₂×C₅×D₃	—	2	8	no	—
257	C₂×C₅×D₃	—	4	32	no	—
258	C₂×C₅×D₃	—	4	8	no	—
259	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
260	C₃×C₄×C₅	—	2	4	no	—
261	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
262	C₅×Dic₃	—	2	4	no	—
263	C₅×Dic₃	—	2	4	no	—
264	C₅×Dic₃	C₂²×D₄	1	4	yes	—
265	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
266	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
267	C₂³×D₃	—	2	8	no	—
268	C₂³×D₃	—	4	8	no	—
269	C₂³×D₃	C₂³×C₅	1	2	yes	—
270	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
271	C₂³×D₃	C₂³×C₅	1	8	yes	—
272	C₂×C₃×D₄	—	2	4	no	—
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	4	8	no	—
275	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
276	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
277	C₂×C₃×D₄	C₂³×C₅	1	16	yes	complemented
278	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
279	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂×#67	—	2	8	no	—
281	C₂×#67	—	2	8	no	—
282	C₂×#67	—	4	8	no	—
283	C₂×#67	C₂³×C₅	1	8	yes	—
284	C₂×#67	C₂³×C₅	1	8	yes	—
285	C₂×#67	C₂³×C₅	1	16	yes	complemented
286	C₂²×Dic₃	—	2	8	no	—
287	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
288	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
289	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
290	C₂²×Dic₃	C₂³×C₅	1	8	yes	complemented
291	#237	—	2	32	no	—
292	D₃×D₄	—	2	32	no	—
293	C₂×D₁₂	—	2	4	no	—
294	C₂×D₁₂	C₂³×C₅	1	4	yes	—
295	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
296	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
297	C₂×Dic₆	—	2	4	no	—
298	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
299	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
300	#217	C₂³×C₅	1	16	yes	complemented
301	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
302	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
303	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
304	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
305	C₂³×C₅	—	2	4	no	—
306	C₂³×C₅	—	2	4	no	—
307	C₂³×C₅	—	2	8	no	—
308	C₂³×C₅	—	2	8	no	—
309	C₂³×C₅	—	3	4	no	—
310	C₂³×C₅	—	3	2	no	—
311	C₂³×C₅	—	3	4	no	—
312	C₂³×C₅	—	6	16	no	—
313	C₂³×C₅	—	6	4	no	—
314	C₂³×C₅	—	6	4	no	—
315	C₂³×C₅	—	6	8	no	—
316	C₂³×C₅	—	12	16	no	—
317	C₂³×C₅	—	12	32	no	—
318	C₂³×C₅	C₂³×D₃	1	4	yes	—
319	C₂³×C₅	C₂³×D₃	1	4	yes	—
320	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
321	C₅×Q₈	—	6	8	no	—
322	C₅×D₄	—	2	8	no	—
323	C₅×D₄	—	2	8	no	—
324	C₅×D₄	—	4	16	no	—
325	C₅×D₄	—	6	16	no	—
326	C₅×D₄	—	6	16	no	—
327	C₅×D₄	—	6	8	no	—
328	C₅×D₄	—	12	16	no	—
329	C₂×C₄×C₅	—	2	4	no	—
330	C₂×C₄×C₅	—	3	4	no	—
331	C₂×C₄×C₅	—	3	2	no	—
332	C₂×C₄×C₅	—	3	16	no	—
333	C₂×C₄×C₅	—	3	4	no	—
334	C₂×C₄×C₅	—	3	4	no	—
335	C₂×C₄×C₅	—	6	16	no	—
336	C₂×C₄×C₅	—	6	4	no	—
337	C₂×C₄×C₅	—	6	4	no	—
338	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
339	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
340	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
341	C₂⁵	—	3	2	no	—
342	C₂×#41	—	3	8	no	—
343	C₂×#41	—	6	8	no	—
344	C₂²×Q₈	—	3	1	no	—
345	C₂²×D₄	—	3	2	no	—
346	C₂²×D₄	—	3	2	no	—
347	C₂²×D₄	—	3	4	no	—
348	C₂²×D₄	—	3	8	no	—
349	C₂²×D₄	—	3	1	no	—
350	C₂²×D₄	—	6	8	no	—
351	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
352	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
353	C₂²×D₄	C₂×C₅×D₃	1	4	yes	complemented
354	C₂³×C₄	—	3	1	no	—
355	C₂³×C₄	—	3	2	no	—
356	#127	—	3	8	no	—
357	#127	C₂×C₅×D₃	1	8	yes	complemented
358	#124	—	3	8	no	—
359	#124	—	3	8	no	—
360	#121	—	3	32	no	—
361	#120	—	3	32	no	—
362	#117	—	3	8	no	—
363	C₂×C₄⋊C₄	—	3	2	no	—
364	C₂×C₂²⋊C₄	—	3	4	no	—
365	C₂×C₂²⋊C₄	—	3	2	no	—
366	C₂×C₂²⋊C₄	—	3	4	no	—
367	C₂×C₄²	—	3	1	no	—
368	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
369	C₂×C₃×C₅	—	4	4	no	—
370	C₂×C₃×C₅	—	4	4	no	—
371	C₂×C₃×C₅	#535	1	4	yes	complemented
372	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
374	C₅×D₃	—	2	4	no	—
375	C₅×D₃	—	4	4	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	4	no	—
378	C₂³×C₃	—	2	8	no	—
379	C₂³×C₃	—	2	8	no	—
380	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
381	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
382	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
383	C₂²×D₃	—	2	4	no	—
384	C₂²×D₃	—	2	4	no	—
385	C₂²×D₃	—	2	8	no	—
386	C₂²×D₃	—	2	16	no	—
387	C₂²×D₃	—	4	16	no	—
388	C₂²×D₃	—	4	32	no	—
389	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
390	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
391	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
392	C₃×D₄	—	2	8	no	—
393	C₃×D₄	—	2	8	no	—
394	C₃×D₄	—	4	16	no	—
395	C₂×C₃×C₄	—	2	4	no	—
396	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
397	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
398	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
399	#67	—	2	16	no	—
400	#67	—	2	16	no	—
401	#67	—	4	16	no	—
402	C₂×Dic₃	—	2	4	no	—
403	C₂×Dic₃	—	2	4	no	—
404	C₂×Dic₃	—	2	16	no	—
405	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
406	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
407	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
408	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
409	D₁₂	—	2	8	no	—
410	C₄×D₃	C₂×C₅×D₄	1	16	yes	complemented
411	Dic₆	—	2	8	no	—
412	C₂²×C₅	—	2	4	no	—
413	C₂²×C₅	—	2	4	no	—
414	C₂²×C₅	—	2	8	no	—
415	C₂²×C₅	—	2	8	no	—
416	C₂²×C₅	—	3	4	no	—
417	C₂²×C₅	—	4	8	no	—
418	C₂²×C₅	—	4	8	no	—
419	C₂²×C₅	—	6	4	no	—
420	C₂²×C₅	—	6	8	no	—
421	C₂²×C₅	—	6	4	no	—
422	C₂²×C₅	—	6	8	no	—
423	C₂²×C₅	—	12	32	no	—
424	C₂²×C₅	—	12	8	no	—
425	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
426	C₂²×C₅	#1004	1	4	yes	—
427	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
428	C₄×C₅	—	2	4	no	—
429	C₄×C₅	—	3	4	no	—
430	C₄×C₅	—	6	4	no	—
431	C₄×C₅	—	6	4	no	—
432	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
433	C₂⁴	—	3	1	no	—
434	C₂⁴	—	3	2	no	—
435	C₂⁴	—	3	8	no	—
436	C₂⁴	—	6	8	no	—
437	C₂⁴	—	12	8	no	—
438	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
439	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
440	#41	—	6	32	no	—
441	C₂×Q₈	—	3	4	no	—
442	C₂×Q₈	—	6	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	3	8	no	—
446	C₂×D₄	—	3	8	no	—
447	C₂×D₄	—	3	16	no	—
448	C₂×D₄	—	3	4	no	—
449	C₂×D₄	—	4	8	no	—
450	C₂×D₄	—	6	32	no	—
451	C₂×D₄	—	6	8	no	—
452	C₂×D₄	—	6	8	no	—
453	C₂×D₄	—	6	4	no	—
454	C₂×D₄	—	12	8	no	—
455	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
456	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
457	C₂×D₄	C₂²×C₅×D₃	1	16	yes	complemented
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	8	no	—
460	C₂²×C₄	—	3	4	no	—
461	C₂²×C₄	—	3	2	no	—
462	C₂²×C₄	—	3	2	no	—
463	C₂²×C₄	—	3	8	no	—
464	C₂²×C₄	—	6	8	no	—
465	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
466	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
467	C₄⋊C₄	—	3	8	no	—
468	C₂²⋊C₄	—	3	16	no	—
469	C₂²⋊C₄	—	3	8	no	—
470	C₂²⋊C₄	—	3	16	no	—
471	C₄²	—	3	4	no	—
472	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
473	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
474	C₂²×C₃	—	2	4	no	—
475	C₂²×C₃	—	2	4	no	—
476	C₂²×C₃	—	2	8	no	—
477	C₂²×C₃	—	2	8	no	—
478	C₂²×C₃	—	4	8	no	—
479	C₂²×C₃	—	4	8	no	—
480	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
481	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
482	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
483	C₂×D₃	—	2	8	no	—
484	C₂×D₃	—	2	4	no	—
485	C₂×D₃	—	2	4	no	—
486	C₂×D₃	—	2	8	no	—
487	C₂×D₃	—	4	32	no	—
488	C₂×D₃	—	4	8	no	—
489	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
490	C₃×C₄	—	2	4	no	—
491	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
492	Dic₃	—	2	4	no	—
493	Dic₃	—	2	4	no	—
494	Dic₃	C₂²×C₅×D₄	1	4	yes	—
495	C₂×C₅	—	4	4	no	—
496	C₂×C₅	—	4	4	no	—
497	C₂×C₅	—	6	4	no	—
498	C₂×C₅	—	12	4	no	—
499	C₂×C₅	#5715	1	4	yes	direct product factor
500	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
501	C₂×C₅	C₂×#1004	1	2	yes	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	3	4	no	—
507	C₂³	—	3	2	no	—
508	C₂³	—	3	4	no	—
509	C₂³	—	6	16	no	—
510	C₂³	—	6	4	no	—
511	C₂³	—	6	4	no	—
512	C₂³	—	6	8	no	—
513	C₂³	—	12	16	no	—
514	C₂³	—	12	32	no	—
515	C₂³	C₂³×C₅×D₃	1	4	yes	—
516	C₂³	C₂³×C₅×D₃	1	4	yes	—
517	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
518	Q₈	—	6	8	no	—
519	D₄	—	2	8	no	—
520	D₄	—	2	8	no	—
521	D₄	—	4	16	no	—
522	D₄	—	6	16	no	—
523	D₄	—	6	16	no	—
524	D₄	—	6	8	no	—
525	D₄	—	12	16	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	3	4	no	—
528	C₂×C₄	—	3	2	no	—
529	C₂×C₄	—	3	16	no	—
530	C₂×C₄	—	3	4	no	—
531	C₂×C₄	—	3	4	no	—
532	C₂×C₄	—	6	16	no	—
533	C₂×C₄	—	6	4	no	—
534	C₂×C₄	—	6	4	no	—
535	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
536	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
537	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
538	C₂×C₃	—	4	4	no	—
539	C₂×C₃	—	4	4	no	—
540	C₂×C₃	C₅×#535	1	4	yes	complemented
541	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
542	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
543	D₃	—	2	4	no	—
544	D₃	—	4	4	no	—
545	C₅	C₂×#5715	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	3	4	no	—
551	C₂²	—	4	8	no	—
552	C₂²	—	4	8	no	—
553	C₂²	—	6	4	no	—
554	C₂²	—	6	8	no	—
555	C₂²	—	6	4	no	—
556	C₂²	—	6	8	no	—
557	C₂²	—	12	32	no	—
558	C₂²	—	12	8	no	—
559	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
560	C₂²	C₅×#1004	1	4	yes	—
561	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
562	C₄	—	2	4	no	—
563	C₄	—	3	4	no	—
564	C₄	—	6	4	no	—
565	C₄	—	6	4	no	—
566	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
567	C₃	C₂×C₅×#535	1	1	yes	characteristic, complemented, Sylow
568	C₂	—	4	4	no	—
569	C₂	—	4	4	no	—
570	C₂	—	6	4	no	—
571	C₂	—	12	4	no	—
572	C₂	C₅×#5715	1	4	yes	direct product factor
573	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
574	C₂	C₂×C₅×#1004	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#127	D₃
hypocenter	C₃	C₂×C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#237	C₂	semidirect
2. C₂²×C₅×D₃×D₄	C₂	semidirect
3. C₂×C₃×C₅×#127	C₂	semidirect
4. C₂×C₅×#940	C₂	semidirect
5. C₂×C₅×#939	C₂	semidirect
6. C₂×C₅×#937	C₂	semidirect
7. C₂×C₅×#936	C₂	semidirect
8. C₅×#5715	C₂	direct (N × H)
9. C₂×C₅×#875	C₂	semidirect
10. C₂×C₅×#872	C₂	semidirect
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₂²×C₅×#67	C₂²	semidirect
19. C₂³×C₅×Dic₃	C₂²	semidirect
21. C₂×C₅×#237	C₂²	semidirect
23. C₂×C₅×D₃×D₄	C₂²	semidirect
26. C₂²×C₅×Dic₆	C₂²	semidirect
27. C₃×C₅×#127	C₂²	semidirect
28. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₂×C₅×#217	C₂²	semidirect
30. C₅×#940	C₂²	semidirect
31. C₅×#939	C₂²	semidirect
32. C₅×#937	C₂²	semidirect
33. C₅×#936	C₂²	semidirect
35. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₂×C₄×C₅×Dic₃	C₂²	semidirect
38. C₅×#875	C₂²	semidirect
39. C₅×#872	C₂²	semidirect
40. C₂×#5715	C₅	direct (N × H)
45. C₂×C₅×#127	D₃	semidirect
62. C₂×C₃×C₅×D₄	C₂³	semidirect
63. C₂×C₃×C₅×D₄	C₂³	semidirect
71. C₂×C₅×#67	C₂³	semidirect
76. C₂²×C₅×Dic₃	C₂³	semidirect
81. C₂×C₄×C₅×D₃	D₄	semidirect
84. C₂×C₅×Dic₆	C₂³	semidirect
85. C₃×C₄²×C₅	C₂³	semidirect
86. C₅×#217	C₂³	semidirect
88. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
89. C₅×Dic₃⋊C₄	C₂³	semidirect
90. C₄×C₅×Dic₃	C₂³	semidirect
91. C₂²×#237	C₂×C₅	semidirect
92. C₂²×D₃×D₄	C₂×C₅	semidirect
93. C₂×C₃×#127	C₂×C₅	semidirect
94. C₂×#940	C₂×C₅	semidirect
95. C₂×#939	C₂×C₅	semidirect
96. C₂×#937	C₂×C₅	semidirect
97. C₂×#936	C₂×C₅	semidirect
98. #5715	C₂×C₅	direct (N × H)
99. C₂×#875	C₂×C₅	semidirect
100. C₂×#872	C₂×C₅	semidirect
112. C₂²×C₅×D₄	C₂×D₃	semidirect
113. C₂²×C₅×D₄	C₂×D₃	semidirect
117. C₅×#127	C₂×D₃	semidirect
128. C₂×C₄²×C₅	C₂×D₃	semidirect
164. C₄×C₅×D₃	C₂×D₄	semidirect
168. C₂²×C₃×D₄	C₂²×C₅	semidirect
169. C₂²×C₃×D₄	C₂²×C₅	semidirect
172. C₂²×#67	C₂²×C₅	semidirect
173. C₂³×Dic₃	C₂²×C₅	semidirect
175. C₂×#237	C₂²×C₅	semidirect
177. C₂×D₃×D₄	C₂²×C₅	semidirect
180. C₂²×Dic₆	C₂²×C₅	semidirect
181. C₃×#127	C₂²×C₅	semidirect
182. C₂×C₃×C₄²	C₂²×C₅	semidirect
183. C₂×#217	C₂²×C₅	semidirect
184. #940	C₂²×C₅	semidirect
185. #939	C₂²×C₅	semidirect
186. #937	C₂²×C₅	semidirect
187. #936	C₂²×C₅	semidirect
189. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
190. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
191. C₂×C₄×Dic₃	C₂²×C₅	semidirect
192. #875	C₂²×C₅	semidirect
193. #872	C₂²×C₅	semidirect
217. C₂×C₅×D₄	C₂²×D₃	semidirect
218. C₂×C₅×D₄	C₂²×D₃	semidirect
233. C₄²×C₅	C₂²×D₃	semidirect
238. C₂×#127	C₅×D₃	semidirect
276. C₂×C₃×D₄	C₂³×C₅	semidirect
277. C₂×C₃×D₄	C₂³×C₅	semidirect
285. C₂×#67	C₂³×C₅	semidirect
290. C₂²×Dic₃	C₂³×C₅	semidirect
295. C₂×C₄×D₃	C₅×D₄	semidirect
298. C₂×Dic₆	C₂³×C₅	semidirect
299. C₃×C₄²	C₂³×C₅	semidirect
300. #217	C₂³×C₅	semidirect
302. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
303. Dic₃⋊C₄	C₂³×C₅	semidirect
304. C₄×Dic₃	C₂³×C₅	semidirect
352. C₂²×D₄	C₂×C₅×D₃	semidirect
353. C₂²×D₄	C₂×C₅×D₃	semidirect
357. #127	C₂×C₅×D₃	semidirect
368. C₂×C₄²	C₂×C₅×D₃	semidirect
371. C₂×C₃×C₅	#535	semidirect
410. C₄×D₃	C₂×C₅×D₄	semidirect
456. C₂×D₄	C₂²×C₅×D₃	semidirect
457. C₂×D₄	C₂²×C₅×D₃	semidirect
472. C₄²	C₂²×C₅×D₃	semidirect
473. C₃×C₅	C₂×#535	semidirect
499. C₂×C₅	#5715	direct (N × H)
540. C₂×C₃	C₅×#535	semidirect
545. C₅	C₂×#5715	direct (N × H)
567. C₃	C₂×C₅×#535	semidirect
572. C₂	C₅×#5715	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×#237	2
C₂²×C₅×D₃×D₄	2
C₂×C₃×C₅×#127	2
C₂×C₅×#940	2
C₂×C₅×#939	2
C₂×C₅×#937	2
C₂×C₅×#936	2
C₅×#5715	2
C₂×C₅×#875	2
C₂×C₅×#872	2
C₂×C₅×#535	3
C₂×#5715	5

Subgroups — C2×C5×#5715 #14480362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5715 #14480362