Subgroups — C₂×C₅×#5674 #14480377

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×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5674	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#884	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#882	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#874	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×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	C₂²	1	2	yes	—
16	C₂²×C₅×#67	C₂²	1	4	yes	complemented
17	C₂×C₅×#239	—	2	8	no	—
18	C₂×C₅×#239	C₂²	1	8	yes	complemented
19	C₂×C₅×D₃×D₄	—	2	8	no	—
20	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
21	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
23	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₅×D₁₂	C₂²	1	4	yes	complemented
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
27	C₃×C₅×#124	C₂²	1	8	yes	complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
30	C₅×#947	C₂²	1	8	yes	complemented
31	C₅×#940	C₂²	1	8	yes	complemented
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₅×#884	C₂²	1	32	yes	complemented
37	C₅×#882	C₂²	1	32	yes	complemented
38	C₅×#874	C₂²	1	8	yes	complemented
39	C₅×#872	C₂²	1	8	yes	complemented
40	C₂×#5674	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	—	3	1	no	—
46	C₂×C₅×#124	—	3	1	no	—
47	C₂×C₅×#124	D₃	1	1	yes	characteristic, complemented
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	C₂³×C₅×D₃	—	2	8	no	—
53	C₂³×C₅×D₃	—	4	8	no	—
54	C₂³×C₅×D₃	C₂³	1	2	yes	—
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×Q₈	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
60	C₂×C₃×C₅×D₄	—	2	4	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₅×#67	—	2	8	no	—
66	C₂×C₅×#67	—	4	8	no	—
67	C₂×C₅×#67	C₂³	1	8	yes	—
68	C₂×C₅×#67	C₂³	1	16	yes	complemented
69	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₅×#239	—	2	32	no	—
72	C₅×D₃×D₄	—	2	32	no	—
73	C₂×C₅×D₁₂	—	2	8	no	—
74	C₂×C₅×D₁₂	—	2	4	no	—
75	C₂×C₅×D₁₂	—	2	4	no	—
76	C₂×C₅×D₁₂	—	4	8	no	—
77	C₂×C₅×D₁₂	C₂³	1	4	yes	—
78	C₂×C₅×D₁₂	C₂³	1	8	yes	—
79	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
80	C₂×C₅×D₁₂	C₂³	1	16	yes	complemented
81	C₂×C₄×C₅×D₃	—	2	8	no	—
82	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
83	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
84	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
85	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
86	C₃×C₄²×C₅	C₂³	1	4	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×#239	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#947	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
96	#5674	C₂×C₅	1	16	yes	direct product factor
97	C₂×#884	C₂×C₅	1	4	yes	complemented
98	C₂×#882	C₂×C₅	1	4	yes	complemented
99	C₂×#874	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	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂²×C₅×D₄	—	3	2	no	—
106	C₂²×C₅×D₄	—	3	4	no	—
107	C₂²×C₅×D₄	—	3	8	no	—
108	C₂²×C₅×D₄	—	3	2	no	—
109	C₂²×C₅×D₄	—	3	1	no	—
110	C₂²×C₅×D₄	—	3	1	no	—
111	C₂²×C₅×D₄	—	3	4	no	—
112	C₂²×C₅×D₄	—	6	8	no	—
113	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
114	C₂³×C₄×C₅	—	3	1	no	—
115	C₂³×C₄×C₅	—	3	2	no	—
116	C₅×#127	—	3	8	no	—
117	C₅×#127	—	3	8	no	—
118	C₅×#124	—	3	8	no	—
119	C₅×#124	C₂×D₃	1	8	yes	complemented
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	2	no	—
125	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
126	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
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	8	no	—
132	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
133	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
134	C₂²×C₅×D₃	—	2	4	no	—
135	C₂²×C₅×D₃	—	2	4	no	—
136	C₂²×C₅×D₃	—	2	4	no	—
137	C₂²×C₅×D₃	—	2	8	no	—
138	C₂²×C₅×D₃	—	2	8	no	—
139	C₂²×C₅×D₃	—	2	16	no	—
140	C₂²×C₅×D₃	—	4	16	no	—
141	C₂²×C₅×D₃	—	4	32	no	—
142	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
143	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
144	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
145	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
146	C₃×C₅×Q₈	—	2	8	no	—
147	C₃×C₅×D₄	—	2	8	no	—
148	C₂×C₃×C₄×C₅	—	2	4	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	4	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
154	C₅×#67	—	2	16	no	—
155	C₅×#67	—	4	16	no	—
156	C₂×C₅×Dic₃	—	2	4	no	—
157	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
158	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
159	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
160	C₅×D₁₂	—	2	16	no	—
161	C₅×D₁₂	—	2	8	no	—
162	C₅×D₁₂	—	2	8	no	—
163	C₅×D₁₂	—	4	16	no	—
164	C₄×C₅×D₃	—	2	16	no	—
165	C₄×C₅×D₃	C₂×D₄	1	16	yes	complemented
166	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
167	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
169	C₂²×#67	C₂²×C₅	1	2	yes	—
170	C₂²×#67	C₂²×C₅	1	4	yes	complemented
171	C₂×#239	—	2	8	no	—
172	C₂×#239	C₂²×C₅	1	8	yes	complemented
173	C₂×D₃×D₄	—	2	8	no	—
174	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
175	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
176	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
177	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₂²×D₁₂	C₂²×C₅	1	4	yes	complemented
179	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
180	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
181	C₃×#124	C₂²×C₅	1	8	yes	complemented
182	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
183	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
184	#947	C₂²×C₅	1	8	yes	complemented
185	#940	C₂²×C₅	1	8	yes	complemented
186	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
187	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
188	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
189	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
190	#884	C₂²×C₅	1	32	yes	complemented
191	#882	C₂²×C₅	1	32	yes	complemented
192	#874	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	2	no	—
197	C₂⁴×C₅	—	3	8	no	—
198	C₂⁴×C₅	—	6	8	no	—
199	C₂⁴×C₅	—	12	8	no	—
200	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
201	C₅×#41	—	6	32	no	—
202	C₂×C₅×Q₈	—	2	4	no	—
203	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
204	C₂×C₅×D₄	—	2	4	no	—
205	C₂×C₅×D₄	—	3	8	no	—
206	C₂×C₅×D₄	—	3	16	no	—
207	C₂×C₅×D₄	—	3	8	no	—
208	C₂×C₅×D₄	—	3	4	no	—
209	C₂×C₅×D₄	—	3	4	no	—
210	C₂×C₅×D₄	—	3	16	no	—
211	C₂×C₅×D₄	—	6	8	no	—
212	C₂×C₅×D₄	—	6	32	no	—
213	C₂×C₅×D₄	—	6	8	no	—
214	C₂×C₅×D₄	—	6	4	no	—
215	C₂×C₅×D₄	—	6	4	no	—
216	C₂×C₅×D₄	—	12	8	no	—
217	C₂×C₅×D₄	—	12	8	no	—
218	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
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	2	no	—
223	C₂²×C₄×C₅	—	3	8	no	—
224	C₂²×C₄×C₅	—	6	8	no	—
225	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
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	8	no	—
230	C₅×C₂²⋊C₄	—	3	16	no	—
231	C₅×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
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	—	3	1	no	—
239	C₂×#124	—	3	1	no	—
240	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
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	8	no	—
246	C₂²×C₃×C₅	—	4	8	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
248	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
249	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	8	no	—
251	C₂×C₅×D₃	—	2	4	no	—
252	C₂×C₅×D₃	—	2	4	no	—
253	C₂×C₅×D₃	—	2	4	no	—
254	C₂×C₅×D₃	—	2	8	no	—
255	C₂×C₅×D₃	—	2	8	no	—
256	C₂×C₅×D₃	—	4	32	no	—
257	C₂×C₅×D₃	—	4	8	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	—	2	4	no	—
262	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
263	C₅×Dic₃	—	2	4	no	—
264	C₅×Dic₃	C₂²×D₄	1	4	yes	—
265	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
266	C₂³×D₃	—	2	8	no	—
267	C₂³×D₃	—	4	8	no	—
268	C₂³×D₃	C₂³×C₅	1	2	yes	—
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×Q₈	—	2	4	no	—
273	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
276	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
277	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
278	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂×#67	—	2	8	no	—
280	C₂×#67	—	4	8	no	—
281	C₂×#67	C₂³×C₅	1	8	yes	—
282	C₂×#67	C₂³×C₅	1	16	yes	complemented
283	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
284	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
285	#239	—	2	32	no	—
286	D₃×D₄	—	2	32	no	—
287	C₂×D₁₂	—	2	8	no	—
288	C₂×D₁₂	—	2	4	no	—
289	C₂×D₁₂	—	2	4	no	—
290	C₂×D₁₂	—	4	8	no	—
291	C₂×D₁₂	C₂³×C₅	1	4	yes	—
292	C₂×D₁₂	C₂³×C₅	1	8	yes	—
293	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
294	C₂×D₁₂	C₂³×C₅	1	16	yes	complemented
295	C₂×C₄×D₃	—	2	8	no	—
296	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
297	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
298	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
299	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	complemented
300	C₃×C₄²	C₂³×C₅	1	4	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	8	no	—
307	C₂³×C₅	—	3	4	no	—
308	C₂³×C₅	—	3	2	no	—
309	C₂³×C₅	—	3	4	no	—
310	C₂³×C₅	—	3	4	no	—
311	C₂³×C₅	—	6	16	no	—
312	C₂³×C₅	—	6	4	no	—
313	C₂³×C₅	—	6	4	no	—
314	C₂³×C₅	—	6	4	no	—
315	C₂³×C₅	—	6	8	no	—
316	C₂³×C₅	—	6	8	no	—
317	C₂³×C₅	—	12	16	no	—
318	C₂³×C₅	—	12	32	no	—
319	C₂³×C₅	C₂³×D₃	1	4	yes	—
320	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
321	C₅×Q₈	—	2	8	no	—
322	C₅×D₄	—	2	8	no	—
323	C₅×D₄	—	6	16	no	—
324	C₅×D₄	—	6	16	no	—
325	C₅×D₄	—	6	8	no	—
326	C₅×D₄	—	6	8	no	—
327	C₅×D₄	—	12	16	no	—
328	C₅×D₄	—	12	16	no	—
329	C₂×C₄×C₅	—	2	4	no	—
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	3	4	no	—
332	C₂×C₄×C₅	—	3	2	no	—
333	C₂×C₄×C₅	—	3	16	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	D₃×D₄	1	4	yes	—
338	C₂×C₄×C₅	C₂³×D₃	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	C₂×C₅×D₃	1	1	yes	characteristic, complemented
345	C₂²×D₄	—	3	2	no	—
346	C₂²×D₄	—	3	4	no	—
347	C₂²×D₄	—	3	8	no	—
348	C₂²×D₄	—	3	2	no	—
349	C₂²×D₄	—	3	1	no	—
350	C₂²×D₄	—	3	1	no	—
351	C₂²×D₄	—	3	4	no	—
352	C₂²×D₄	—	6	8	no	—
353	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
354	C₂³×C₄	—	3	1	no	—
355	C₂³×C₄	—	3	2	no	—
356	#127	—	3	8	no	—
357	#127	—	3	8	no	—
358	#124	—	3	8	no	—
359	#124	C₂×C₅×D₃	1	8	yes	complemented
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	2	no	—
365	C₂×C₂²⋊C₄	—	3	4	no	—
366	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
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	#535	1	4	yes	complemented
371	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
372	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
373	C₅×D₃	—	2	4	no	—
374	C₅×D₃	—	4	4	no	—
375	C₅×D₃	—	4	4	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	8	no	—
378	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
379	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
380	C₂²×D₃	—	2	4	no	—
381	C₂²×D₃	—	2	4	no	—
382	C₂²×D₃	—	2	4	no	—
383	C₂²×D₃	—	2	8	no	—
384	C₂²×D₃	—	2	8	no	—
385	C₂²×D₃	—	2	16	no	—
386	C₂²×D₃	—	4	16	no	—
387	C₂²×D₃	—	4	32	no	—
388	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
389	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
390	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
391	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
392	C₃×Q₈	—	2	8	no	—
393	C₃×D₄	—	2	8	no	—
394	C₂×C₃×C₄	—	2	4	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	4	yes	—
399	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
400	#67	—	2	16	no	—
401	#67	—	4	16	no	—
402	C₂×Dic₃	—	2	4	no	—
403	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
404	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
405	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
406	D₁₂	—	2	16	no	—
407	D₁₂	—	2	8	no	—
408	D₁₂	—	2	8	no	—
409	D₁₂	—	4	16	no	—
410	C₄×D₃	—	2	16	no	—
411	C₄×D₃	C₂×C₅×D₄	1	16	yes	complemented
412	C₂²×C₅	—	2	4	no	—
413	C₂²×C₅	—	2	8	no	—
414	C₂²×C₅	—	3	4	no	—
415	C₂²×C₅	—	4	8	no	—
416	C₂²×C₅	—	6	8	no	—
417	C₂²×C₅	—	6	4	no	—
418	C₂²×C₅	—	6	4	no	—
419	C₂²×C₅	—	6	4	no	—
420	C₂²×C₅	—	6	8	no	—
421	C₂²×C₅	—	6	8	no	—
422	C₂²×C₅	—	12	32	no	—
423	C₂²×C₅	—	12	8	no	—
424	C₂²×C₅	—	12	8	no	—
425	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
426	C₂²×C₅	#1009	1	4	yes	—
427	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
428	C₄×C₅	—	2	4	no	—
429	C₄×C₅	—	2	4	no	—
430	C₄×C₅	—	3	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	2	no	—
436	C₂⁴	—	3	8	no	—
437	C₂⁴	—	6	8	no	—
438	C₂⁴	—	12	8	no	—
439	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
440	#41	—	6	32	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	3	8	no	—
445	C₂×D₄	—	3	16	no	—
446	C₂×D₄	—	3	8	no	—
447	C₂×D₄	—	3	4	no	—
448	C₂×D₄	—	3	4	no	—
449	C₂×D₄	—	3	16	no	—
450	C₂×D₄	—	6	8	no	—
451	C₂×D₄	—	6	32	no	—
452	C₂×D₄	—	6	8	no	—
453	C₂×D₄	—	6	4	no	—
454	C₂×D₄	—	6	4	no	—
455	C₂×D₄	—	12	8	no	—
456	C₂×D₄	—	12	8	no	—
457	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
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	8	no	—
463	C₂²×C₄	—	6	8	no	—
464	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
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	8	no	—
469	C₂²⋊C₄	—	3	16	no	—
470	C₂²⋊C₄	C₂²×C₅×D₃	1	16	yes	complemented
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	8	no	—
476	C₂²×C₃	—	4	8	no	—
477	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
478	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
479	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
480	C₂×D₃	—	2	8	no	—
481	C₂×D₃	—	2	4	no	—
482	C₂×D₃	—	2	4	no	—
483	C₂×D₃	—	2	4	no	—
484	C₂×D₃	—	2	8	no	—
485	C₂×D₃	—	2	8	no	—
486	C₂×D₃	—	4	32	no	—
487	C₂×D₃	—	4	8	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	—	2	4	no	—
492	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
493	Dic₃	—	2	4	no	—
494	Dic₃	C₂²×C₅×D₄	1	4	yes	—
495	C₂×C₅	—	4	4	no	—
496	C₂×C₅	—	6	4	no	—
497	C₂×C₅	—	12	4	no	—
498	C₂×C₅	—	12	4	no	—
499	C₂×C₅	#5674	1	4	yes	direct product factor
500	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
501	C₂×C₅	C₂×#1009	1	2	yes	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	3	4	no	—
505	C₂³	—	3	2	no	—
506	C₂³	—	3	4	no	—
507	C₂³	—	3	4	no	—
508	C₂³	—	6	16	no	—
509	C₂³	—	6	4	no	—
510	C₂³	—	6	4	no	—
511	C₂³	—	6	4	no	—
512	C₂³	—	6	8	no	—
513	C₂³	—	6	8	no	—
514	C₂³	—	12	16	no	—
515	C₂³	—	12	32	no	—
516	C₂³	C₂³×C₅×D₃	1	4	yes	—
517	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
518	Q₈	—	2	8	no	—
519	D₄	—	2	8	no	—
520	D₄	—	6	16	no	—
521	D₄	—	6	16	no	—
522	D₄	—	6	8	no	—
523	D₄	—	6	8	no	—
524	D₄	—	12	16	no	—
525	D₄	—	12	16	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	3	4	no	—
529	C₂×C₄	—	3	2	no	—
530	C₂×C₄	—	3	16	no	—
531	C₂×C₄	—	3	4	no	—
532	C₂×C₄	—	6	16	no	—
533	C₂×C₄	—	6	4	no	—
534	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
535	C₂×C₄	C₂³×C₅×D₃	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	C₅×#535	1	4	yes	complemented
540	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
541	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
542	D₃	—	2	4	no	—
543	D₃	—	4	4	no	—
544	D₃	—	4	4	no	—
545	C₅	C₂×#5674	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	2	4	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	3	4	no	—
549	C₂²	—	4	8	no	—
550	C₂²	—	6	8	no	—
551	C₂²	—	6	4	no	—
552	C₂²	—	6	4	no	—
553	C₂²	—	6	4	no	—
554	C₂²	—	6	8	no	—
555	C₂²	—	6	8	no	—
556	C₂²	—	12	32	no	—
557	C₂²	—	12	8	no	—
558	C₂²	—	12	8	no	—
559	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
560	C₂²	C₅×#1009	1	4	yes	—
561	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
562	C₄	—	2	4	no	—
563	C₄	—	2	4	no	—
564	C₄	—	3	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	—	6	4	no	—
570	C₂	—	12	4	no	—
571	C₂	—	12	4	no	—
572	C₂	C₅×#5674	1	4	yes	direct product factor
573	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
574	C₂	C₂×C₅×#1009	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×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#239	C₂	semidirect
2. C₂²×C₅×D₃×D₄	C₂	semidirect
3. C₂×C₃×C₅×#124	C₂	semidirect
4. C₂×C₅×#947	C₂	semidirect
5. C₂×C₅×#940	C₂	semidirect
6. C₅×#5674	C₂	direct (N × H)
7. C₂×C₅×#884	C₂	semidirect
8. C₂×C₅×#882	C₂	semidirect
9. C₂×C₅×#874	C₂	semidirect
10. C₂×C₅×#872	C₂	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
16. C₂²×C₅×#67	C₂²	semidirect
18. C₂×C₅×#239	C₂²	semidirect
20. C₂×C₅×D₃×D₄	C₂²	semidirect
23. C₂²×C₅×D₁₂	C₂²	semidirect
24. C₂²×C₅×D₁₂	C₂²	semidirect
26. C₂²×C₄×C₅×D₃	C₂²	semidirect
27. C₃×C₅×#124	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₄²×C₅	C₂²	semidirect
30. C₅×#947	C₂²	semidirect
31. C₅×#940	C₂²	semidirect
33. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
35. C₂×C₄×C₅×Dic₃	C₂²	semidirect
36. C₅×#884	C₂²	semidirect
37. C₅×#882	C₂²	semidirect
38. C₅×#874	C₂²	semidirect
39. C₅×#872	C₂²	semidirect
40. C₂×#5674	C₅	direct (N × H)
47. C₂×C₅×#124	D₃	semidirect
59. C₂×C₃×C₅×Q₈	C₂³	semidirect
68. C₂×C₅×#67	C₂³	semidirect
79. C₂×C₅×D₁₂	C₂³	semidirect
80. C₂×C₅×D₁₂	C₂³	semidirect
82. C₂×C₄×C₅×D₃	D₄	semidirect
84. C₂×C₄×C₅×D₃	C₂³	semidirect
85. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
86. C₃×C₄²×C₅	C₂³	semidirect
88. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
89. C₅×Dic₃⋊C₄	C₂³	semidirect
90. C₄×C₅×Dic₃	C₂³	semidirect
91. C₂²×#239	C₂×C₅	semidirect
92. C₂²×D₃×D₄	C₂×C₅	semidirect
93. C₂×C₃×#124	C₂×C₅	semidirect
94. C₂×#947	C₂×C₅	semidirect
95. C₂×#940	C₂×C₅	semidirect
96. #5674	C₂×C₅	direct (N × H)
97. C₂×#884	C₂×C₅	semidirect
98. C₂×#882	C₂×C₅	semidirect
99. C₂×#874	C₂×C₅	semidirect
100. C₂×#872	C₂×C₅	semidirect
104. C₂²×C₅×Q₈	C₂×D₃	semidirect
119. C₅×#124	C₂×D₃	semidirect
126. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
128. C₂×C₄²×C₅	C₂×D₃	semidirect
165. C₄×C₅×D₃	C₂×D₄	semidirect
167. C₂²×C₃×Q₈	C₂²×C₅	semidirect
170. C₂²×#67	C₂²×C₅	semidirect
172. C₂×#239	C₂²×C₅	semidirect
174. C₂×D₃×D₄	C₂²×C₅	semidirect
177. C₂²×D₁₂	C₂²×C₅	semidirect
178. C₂²×D₁₂	C₂²×C₅	semidirect
180. C₂²×C₄×D₃	C₂²×C₅	semidirect
181. C₃×#124	C₂²×C₅	semidirect
182. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
183. C₂×C₃×C₄²	C₂²×C₅	semidirect
184. #947	C₂²×C₅	semidirect
185. #940	C₂²×C₅	semidirect
187. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
188. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
189. C₂×C₄×Dic₃	C₂²×C₅	semidirect
190. #884	C₂²×C₅	semidirect
191. #882	C₂²×C₅	semidirect
192. #874	C₂²×C₅	semidirect
193. #872	C₂²×C₅	semidirect
203. C₂×C₅×Q₈	C₂²×D₃	semidirect
231. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
233. C₄²×C₅	C₂²×D₃	semidirect
240. C₂×#124	C₅×D₃	semidirect
273. C₂×C₃×Q₈	C₂³×C₅	semidirect
282. C₂×#67	C₂³×C₅	semidirect
293. C₂×D₁₂	C₂³×C₅	semidirect
294. C₂×D₁₂	C₂³×C₅	semidirect
296. C₂×C₄×D₃	C₅×D₄	semidirect
298. C₂×C₄×D₃	C₂³×C₅	semidirect
299. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
300. C₃×C₄²	C₂³×C₅	semidirect
302. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
303. Dic₃⋊C₄	C₂³×C₅	semidirect
304. C₄×Dic₃	C₂³×C₅	semidirect
344. C₂²×Q₈	C₂×C₅×D₃	semidirect
359. #124	C₂×C₅×D₃	semidirect
366. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
368. C₂×C₄²	C₂×C₅×D₃	semidirect
370. C₂×C₃×C₅	#535	semidirect
411. C₄×D₃	C₂×C₅×D₄	semidirect
442. C₂×Q₈	C₂²×C₅×D₃	semidirect
470. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
472. C₄²	C₂²×C₅×D₃	semidirect
473. C₃×C₅	C₂×#535	semidirect
499. C₂×C₅	#5674	direct (N × H)
539. C₂×C₃	C₅×#535	semidirect
545. C₅	C₂×#5674	direct (N × H)
567. C₃	C₂×C₅×#535	semidirect
572. C₂	C₅×#5674	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×#239	2
C₂²×C₅×D₃×D₄	2
C₂×C₃×C₅×#124	2
C₂×C₅×#947	2
C₂×C₅×#940	2
C₅×#5674	2
C₂×C₅×#884	2
C₂×C₅×#882	2
C₂×C₅×#874	2
C₂×C₅×#872	2
C₂×C₅×#535	3
C₂×#5674	5

Subgroups — C2×C5×#5674 #14480377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5674 #14480377