Subgroups — C₂×C₅×#5695 #14483622

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5695	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#895	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#893	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#553	—	3	1	no	maximal, Hall
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
22	C₃×C₅×#125	C₂²	1	8	yes	complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
38	C₅×#898	C₂²	1	16	yes	complemented
39	C₅×#895	C₂²	1	16	yes	complemented
40	C₅×#895	C₂²	1	8	yes	complemented
41	C₅×#895	C₂²	1	8	yes	complemented
42	C₅×#894	C₂²	1	16	yes	complemented
43	C₅×#893	C₂²	1	16	yes	complemented
44	C₅×#892	C₂²	1	8	yes	complemented
45	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
46	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
47	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
48	C₂×#5695	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#553	—	3	16	no	—
50	C₂×C₅×#126	—	3	2	no	—
51	C₂×C₅×#125	D₃	1	1	yes	characteristic, complemented
52	C₂×C₅×#123	—	3	2	no	—
53	C₂×C₅×#121	—	3	2	no	—
54	C₂×C₅×#121	—	3	1	no	—
55	C₂×C₅×#121	—	3	1	no	—
56	C₂×C₄×C₅×D₄	—	3	2	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₂×C₅×#117	—	3	1	no	—
60	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
61	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₂³×C₅×D₃	C₂³	1	2	yes	—
63	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₅×D₁₂	—	2	4	no	—
73	C₂×C₅×D₁₂	—	2	8	no	—
74	C₂×C₅×D₁₂	—	2	4	no	—
75	C₂×C₅×D₁₂	—	4	4	no	—
76	C₂×C₅×D₁₂	C₂³	1	4	yes	—
77	C₂×C₅×D₁₂	C₂³	1	4	yes	—
78	C₂×C₅×D₁₂	C₂³	1	8	yes	—
79	C₂×C₅×D₁₂	C₂³	1	8	yes	—
80	C₂×C₄×C₅×D₃	—	2	4	no	—
81	C₂×C₄×C₅×D₃	—	2	4	no	—
82	C₂×C₄×C₅×D₃	—	4	4	no	—
83	C₂×C₄×C₅×D₃	—	4	4	no	—
84	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
85	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
86	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
87	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
91	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
92	C₃×C₄²×C₅	C₂³	1	4	yes	—
93	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
95	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
96	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
97	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
98	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
99	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
100	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
101	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
102	C₄×C₅×Dic₃	C₂³	1	8	yes	—
103	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
104	#5695	C₂×C₅	1	16	yes	direct product factor
105	C₂×#898	C₂×C₅	1	2	yes	complemented
106	C₂×#895	C₂×C₅	1	2	yes	complemented
107	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#894	C₂×C₅	1	2	yes	complemented
110	C₂×#893	C₂×C₅	1	2	yes	complemented
111	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂²×C₅×D₄	—	3	2	no	—
116	C₂²×C₅×D₄	—	3	1	no	—
117	C₂²×C₅×D₄	—	3	1	no	—
118	C₂²×C₅×D₄	—	3	2	no	—
119	C₂³×C₄×C₅	—	3	1	no	—
120	C₂³×C₄×C₅	—	3	1	no	—
121	C₂³×C₄×C₅	—	3	2	no	—
122	C₂³×C₄×C₅	—	3	2	no	—
123	C₅×#126	—	3	16	no	—
124	C₅×#125	C₂×D₃	1	8	yes	complemented
125	C₅×#123	—	3	16	no	—
126	C₅×#121	—	3	16	no	—
127	C₅×#121	—	3	8	no	—
128	C₅×#121	—	3	8	no	—
129	C₄×C₅×D₄	—	3	16	no	—
130	C₄×C₅×D₄	—	3	8	no	—
131	C₄×C₅×D₄	—	3	8	no	—
132	C₅×#117	—	3	8	no	—
133	C₂×C₅×C₄⋊C₄	—	3	2	no	—
134	C₂×C₅×C₄⋊C₄	—	3	1	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	3	8	no	—
137	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
138	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
140	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
141	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
142	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
143	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
144	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
146	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
147	C₂×C₄²×C₅	—	3	2	no	—
148	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
149	C₂×#553	—	3	1	no	Sylow
150	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
151	C₂²×C₅×D₃	—	2	2	no	—
152	C₂²×C₅×D₃	—	2	2	no	—
153	C₂²×C₅×D₃	—	2	2	no	—
154	C₂²×C₅×D₃	—	2	4	no	—
155	C₂²×C₅×D₃	—	2	2	no	—
156	C₂²×C₅×D₃	—	2	4	no	—
157	C₂²×C₅×D₃	—	2	4	no	—
158	C₂²×C₅×D₃	—	2	2	no	—
159	C₂²×C₅×D₃	#41	1	4	yes	—
160	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
161	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
162	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
163	C₂×C₃×C₄×C₅	—	2	4	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	4	no	—
167	C₂×C₃×C₄×C₅	#41	1	4	yes	—
168	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
169	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
170	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
171	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
172	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
173	C₂×C₅×Dic₃	—	2	2	no	—
174	C₂×C₅×Dic₃	—	2	2	no	—
175	C₂×C₅×Dic₃	—	2	4	no	—
176	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
177	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
178	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
179	C₅×D₁₂	—	2	8	no	—
180	C₅×D₁₂	—	2	16	no	—
181	C₅×D₁₂	—	2	8	no	—
182	C₅×D₁₂	—	4	8	no	—
183	C₄×C₅×D₃	—	2	8	no	—
184	C₄×C₅×D₃	—	2	8	no	—
185	C₄×C₅×D₃	—	4	8	no	—
186	C₄×C₅×D₃	—	4	8	no	—
187	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
188	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
189	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
190	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
191	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
192	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
193	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
194	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
195	C₃×#125	C₂²×C₅	1	8	yes	complemented
196	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
201	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
204	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
205	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
206	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
207	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
209	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
210	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
211	#898	C₂²×C₅	1	16	yes	complemented
212	#895	C₂²×C₅	1	16	yes	complemented
213	#895	C₂²×C₅	1	8	yes	complemented
214	#895	C₂²×C₅	1	8	yes	complemented
215	#894	C₂²×C₅	1	16	yes	complemented
216	#893	C₂²×C₅	1	16	yes	complemented
217	#892	C₂²×C₅	1	8	yes	complemented
218	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
219	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
220	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
221	C₂⁴×C₅	—	3	1	no	—
222	C₂⁴×C₅	—	3	1	no	—
223	C₂⁴×C₅	—	3	2	no	—
224	C₂×C₅×D₄	—	3	8	no	—
225	C₂×C₅×D₄	—	3	4	no	—
226	C₂×C₅×D₄	—	3	4	no	—
227	C₂×C₅×D₄	—	3	8	no	—
228	C₂×C₅×D₄	—	6	8	no	—
229	C₂×C₅×D₄	—	6	4	no	—
230	C₂×C₅×D₄	—	6	4	no	—
231	C₂×C₅×D₄	—	12	4	no	—
232	C₂²×C₄×C₅	—	3	1	no	—
233	C₂²×C₄×C₅	—	3	2	no	—
234	C₂²×C₄×C₅	—	3	1	no	—
235	C₂²×C₄×C₅	—	3	4	no	—
236	C₂²×C₄×C₅	—	3	4	no	—
237	C₂²×C₄×C₅	—	3	8	no	—
238	C₂²×C₄×C₅	—	3	8	no	—
239	C₂²×C₄×C₅	—	6	4	no	—
240	C₂²×C₄×C₅	—	6	4	no	—
241	C₂²×C₄×C₅	—	12	4	no	—
242	C₂²×C₄×C₅	—	12	4	no	—
243	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
244	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
247	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
248	C₅×C₄⋊C₄	—	3	4	no	—
249	C₅×C₄⋊C₄	—	3	8	no	—
250	C₅×C₄⋊C₄	—	3	4	no	—
251	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
252	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
253	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
254	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
255	C₅×C₂²⋊C₄	—	3	8	no	—
256	C₅×C₂²⋊C₄	—	3	4	no	—
257	C₅×C₂²⋊C₄	—	3	8	no	—
258	C₅×C₂²⋊C₄	—	3	8	no	—
259	C₅×C₂²⋊C₄	—	3	4	no	—
260	C₅×C₂²⋊C₄	—	3	8	no	—
261	C₄²×C₅	—	3	8	no	—
262	C₄²×C₅	C₂²×D₃	1	4	yes	—
263	#553	—	3	16	no	—
264	C₂×#126	—	3	2	no	—
265	C₂×#125	C₅×D₃	1	1	yes	characteristic, complemented
266	C₂×#123	—	3	2	no	—
267	C₂×#121	—	3	2	no	—
268	C₂×#121	—	3	1	no	—
269	C₂×#121	—	3	1	no	—
270	C₂×C₄×D₄	—	3	2	no	—
271	C₂×C₄×D₄	—	3	1	no	—
272	C₂×C₄×D₄	—	3	1	no	—
273	C₂×#117	—	3	1	no	—
274	C₂²×C₄⋊C₄	—	3	1	no	—
275	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
276	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
277	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
278	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
279	C₂×C₅×D₃	—	2	8	no	—
280	C₂×C₅×D₃	—	2	2	no	—
281	C₂×C₅×D₃	—	2	2	no	—
282	C₂×C₅×D₃	—	2	2	no	—
283	C₂×C₅×D₃	—	2	4	no	—
284	C₂×C₅×D₃	—	2	2	no	—
285	C₂×C₅×D₃	—	2	4	no	—
286	C₂×C₅×D₃	—	2	4	no	—
287	C₂×C₅×D₃	—	2	2	no	—
288	C₂×C₅×D₃	—	4	4	no	—
289	C₂×C₅×D₃	—	4	8	no	—
290	C₂×C₅×D₃	C₂×#41	1	4	yes	—
291	C₃×C₄×C₅	—	2	4	no	—
292	C₃×C₄×C₅	—	2	2	no	—
293	C₃×C₄×C₅	—	2	2	no	—
294	C₃×C₄×C₅	—	2	4	no	—
295	C₃×C₄×C₅	C₂×#41	1	4	yes	—
296	C₅×Dic₃	—	2	2	no	—
297	C₅×Dic₃	—	2	2	no	—
298	C₅×Dic₃	—	2	4	no	—
299	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
300	C₂³×D₃	C₂³×C₅	1	2	yes	—
301	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
302	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
303	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
304	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
306	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
308	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
309	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
310	C₂×D₁₂	—	2	4	no	—
311	C₂×D₁₂	—	2	8	no	—
312	C₂×D₁₂	—	2	4	no	—
313	C₂×D₁₂	—	4	4	no	—
314	C₂×D₁₂	C₂³×C₅	1	4	yes	—
315	C₂×D₁₂	C₂³×C₅	1	4	yes	—
316	C₂×D₁₂	C₂³×C₅	1	8	yes	—
317	C₂×D₁₂	C₂³×C₅	1	8	yes	—
318	C₂×C₄×D₃	—	2	4	no	—
319	C₂×C₄×D₃	—	2	4	no	—
320	C₂×C₄×D₃	—	4	4	no	—
321	C₂×C₄×D₃	—	4	4	no	—
322	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
323	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
324	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
325	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
326	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
327	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
328	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
329	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
330	C₃×C₄²	C₂³×C₅	1	4	yes	—
331	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
332	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
333	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
334	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
335	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
336	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
337	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
338	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
339	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
340	C₄×Dic₃	C₂³×C₅	1	8	yes	—
341	C₂³×C₅	—	3	4	no	—
342	C₂³×C₅	—	3	2	no	—
343	C₂³×C₅	—	3	2	no	—
344	C₂³×C₅	—	3	4	no	—
345	C₂³×C₅	—	6	2	no	—
346	C₂³×C₅	—	6	2	no	—
347	C₂³×C₅	—	6	2	no	—
348	C₂³×C₅	—	6	4	no	—
349	C₂³×C₅	—	6	2	no	—
350	C₂³×C₅	—	6	4	no	—
351	C₂³×C₅	—	6	4	no	—
352	C₂³×C₅	—	6	2	no	—
353	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
354	C₅×D₄	—	6	16	no	—
355	C₅×D₄	—	6	8	no	—
356	C₅×D₄	—	6	8	no	—
357	C₅×D₄	—	12	8	no	—
358	C₂×C₄×C₅	—	2	4	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	4	no	—
362	C₂×C₄×C₅	—	3	2	no	—
363	C₂×C₄×C₅	—	3	4	no	—
364	C₂×C₄×C₅	—	3	2	no	—
365	C₂×C₄×C₅	—	6	2	no	—
366	C₂×C₄×C₅	—	6	2	no	—
367	C₂×C₄×C₅	—	6	4	no	—
368	C₂×C₄×C₅	—	6	8	no	—
369	C₂×C₄×C₅	—	6	8	no	—
370	C₂×C₄×C₅	—	12	8	no	—
371	C₂×C₄×C₅	—	12	8	no	—
372	C₂×C₄×C₅	#239	1	4	yes	—
373	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
374	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
375	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
376	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
377	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
378	C₂²×D₄	—	3	2	no	—
379	C₂²×D₄	—	3	1	no	—
380	C₂²×D₄	—	3	1	no	—
381	C₂²×D₄	—	3	2	no	—
382	C₂³×C₄	—	3	1	no	—
383	C₂³×C₄	—	3	1	no	—
384	C₂³×C₄	—	3	2	no	—
385	C₂³×C₄	—	3	2	no	—
386	#126	—	3	16	no	—
387	#125	C₂×C₅×D₃	1	8	yes	complemented
388	#123	—	3	16	no	—
389	#121	—	3	16	no	—
390	#121	—	3	8	no	—
391	#121	—	3	8	no	—
392	C₄×D₄	—	3	16	no	—
393	C₄×D₄	—	3	8	no	—
394	C₄×D₄	—	3	8	no	—
395	#117	—	3	8	no	—
396	C₂×C₄⋊C₄	—	3	1	no	—
397	C₂×C₄⋊C₄	—	3	2	no	—
398	C₂×C₄⋊C₄	—	3	1	no	—
399	C₂×C₄⋊C₄	—	3	8	no	—
400	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
404	C₂×C₂²⋊C₄	—	3	2	no	—
405	C₂×C₂²⋊C₄	—	3	1	no	—
406	C₂×C₂²⋊C₄	—	3	2	no	—
407	C₂×C₂²⋊C₄	—	3	2	no	—
408	C₂×C₂²⋊C₄	—	3	1	no	—
409	C₂×C₂²⋊C₄	—	3	2	no	—
410	C₂×C₄²	—	3	2	no	—
411	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
412	C₂×C₃×C₅	#553	1	4	yes	complemented
413	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
414	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
415	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₅×D₃	—	2	4	no	—
417	C₅×D₃	—	4	2	no	—
418	C₅×D₃	—	4	4	no	—
419	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
420	C₂²×D₃	—	2	2	no	—
421	C₂²×D₃	—	2	2	no	—
422	C₂²×D₃	—	2	2	no	—
423	C₂²×D₃	—	2	4	no	—
424	C₂²×D₃	—	2	2	no	—
425	C₂²×D₃	—	2	4	no	—
426	C₂²×D₃	—	2	4	no	—
427	C₂²×D₃	—	2	2	no	—
428	C₂²×D₃	C₅×#41	1	4	yes	—
429	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
430	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
431	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
432	C₂×C₃×C₄	—	2	4	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	2	no	—
435	C₂×C₃×C₄	—	2	4	no	—
436	C₂×C₃×C₄	C₅×#41	1	4	yes	—
437	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
438	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
439	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
440	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
441	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
442	C₂×Dic₃	—	2	2	no	—
443	C₂×Dic₃	—	2	2	no	—
444	C₂×Dic₃	—	2	4	no	—
445	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
446	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
447	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
448	D₁₂	—	2	8	no	—
449	D₁₂	—	2	16	no	—
450	D₁₂	—	2	8	no	—
451	D₁₂	—	4	8	no	—
452	C₄×D₃	—	2	8	no	—
453	C₄×D₃	—	2	8	no	—
454	C₄×D₃	—	4	8	no	—
455	C₄×D₃	—	4	8	no	—
456	C₂²×C₅	—	3	4	no	—
457	C₂²×C₅	—	6	8	no	—
458	C₂²×C₅	—	6	2	no	—
459	C₂²×C₅	—	6	2	no	—
460	C₂²×C₅	—	6	2	no	—
461	C₂²×C₅	—	6	4	no	—
462	C₂²×C₅	—	6	2	no	—
463	C₂²×C₅	—	6	4	no	—
464	C₂²×C₅	—	6	4	no	—
465	C₂²×C₅	—	6	2	no	—
466	C₂²×C₅	—	12	4	no	—
467	C₂²×C₅	—	12	8	no	—
468	C₂²×C₅	C₂×#239	1	2	yes	—
469	C₂²×C₅	D₃×#41	1	2	yes	—
470	C₂²×C₅	#1009	1	2	yes	—
471	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
472	C₄×C₅	—	2	4	no	—
473	C₄×C₅	—	2	2	no	—
474	C₄×C₅	—	2	2	no	—
475	C₄×C₅	—	2	4	no	—
476	C₄×C₅	—	6	2	no	—
477	C₄×C₅	—	6	2	no	—
478	C₄×C₅	—	6	4	no	—
479	C₄×C₅	C₂×#239	1	4	yes	—
480	C₂⁴	—	3	1	no	—
481	C₂⁴	—	3	1	no	—
482	C₂⁴	—	3	2	no	—
483	C₂×D₄	—	3	8	no	—
484	C₂×D₄	—	3	4	no	—
485	C₂×D₄	—	3	4	no	—
486	C₂×D₄	—	3	8	no	—
487	C₂×D₄	—	6	8	no	—
488	C₂×D₄	—	6	4	no	—
489	C₂×D₄	—	6	4	no	—
490	C₂×D₄	—	12	4	no	—
491	C₂²×C₄	—	3	1	no	—
492	C₂²×C₄	—	3	2	no	—
493	C₂²×C₄	—	3	1	no	—
494	C₂²×C₄	—	3	4	no	—
495	C₂²×C₄	—	3	4	no	—
496	C₂²×C₄	—	3	8	no	—
497	C₂²×C₄	—	3	8	no	—
498	C₂²×C₄	—	6	4	no	—
499	C₂²×C₄	—	6	4	no	—
500	C₂²×C₄	—	12	4	no	—
501	C₂²×C₄	—	12	4	no	—
502	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
503	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
506	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
507	C₄⋊C₄	—	3	4	no	—
508	C₄⋊C₄	—	3	8	no	—
509	C₄⋊C₄	—	3	4	no	—
510	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
511	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
512	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
513	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
514	C₂²⋊C₄	—	3	8	no	—
515	C₂²⋊C₄	—	3	4	no	—
516	C₂²⋊C₄	—	3	8	no	—
517	C₂²⋊C₄	—	3	8	no	—
518	C₂²⋊C₄	—	3	4	no	—
519	C₂²⋊C₄	—	3	8	no	—
520	C₄²	—	3	8	no	—
521	C₄²	C₂²×C₅×D₃	1	4	yes	—
522	C₃×C₅	C₂×#553	1	1	yes	characteristic, complemented, Hall
523	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
524	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
525	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
526	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
527	C₂×D₃	—	2	8	no	—
528	C₂×D₃	—	2	2	no	—
529	C₂×D₃	—	2	2	no	—
530	C₂×D₃	—	2	2	no	—
531	C₂×D₃	—	2	4	no	—
532	C₂×D₃	—	2	2	no	—
533	C₂×D₃	—	2	4	no	—
534	C₂×D₃	—	2	4	no	—
535	C₂×D₃	—	2	2	no	—
536	C₂×D₃	—	4	4	no	—
537	C₂×D₃	—	4	8	no	—
538	C₂×D₃	C₂×C₅×#41	1	4	yes	—
539	C₃×C₄	—	2	4	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	2	no	—
542	C₃×C₄	—	2	4	no	—
543	C₃×C₄	C₂×C₅×#41	1	4	yes	—
544	Dic₃	—	2	2	no	—
545	Dic₃	—	2	2	no	—
546	Dic₃	—	2	4	no	—
547	C₂×C₅	—	6	4	no	—
548	C₂×C₅	—	12	2	no	—
549	C₂×C₅	—	12	4	no	—
550	C₂×C₅	#5695	1	4	yes	direct product factor
551	C₂×C₅	C₂²×#239	1	1	yes	characteristic
552	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
553	C₂×C₅	C₂×#1009	1	1	yes	characteristic
554	C₂³	—	3	4	no	—
555	C₂³	—	3	2	no	—
556	C₂³	—	3	2	no	—
557	C₂³	—	3	4	no	—
558	C₂³	—	6	2	no	—
559	C₂³	—	6	2	no	—
560	C₂³	—	6	2	no	—
561	C₂³	—	6	4	no	—
562	C₂³	—	6	2	no	—
563	C₂³	—	6	4	no	—
564	C₂³	—	6	4	no	—
565	C₂³	—	6	2	no	—
566	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
567	D₄	—	6	16	no	—
568	D₄	—	6	8	no	—
569	D₄	—	6	8	no	—
570	D₄	—	12	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	3	2	no	—
576	C₂×C₄	—	3	4	no	—
577	C₂×C₄	—	3	2	no	—
578	C₂×C₄	—	6	2	no	—
579	C₂×C₄	—	6	2	no	—
580	C₂×C₄	—	6	4	no	—
581	C₂×C₄	—	6	8	no	—
582	C₂×C₄	—	6	8	no	—
583	C₂×C₄	—	12	8	no	—
584	C₂×C₄	—	12	8	no	—
585	C₂×C₄	C₅×#239	1	4	yes	—
586	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
587	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
588	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
589	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
590	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
591	C₂×C₃	C₅×#553	1	4	yes	complemented
592	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
593	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
594	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
595	D₃	—	2	4	no	—
596	D₃	—	4	2	no	—
597	D₃	—	4	4	no	—
598	C₅	C₂×#5695	1	1	yes	characteristic, direct product factor, Sylow
599	C₂²	—	3	4	no	—
600	C₂²	—	6	8	no	—
601	C₂²	—	6	2	no	—
602	C₂²	—	6	2	no	—
603	C₂²	—	6	2	no	—
604	C₂²	—	6	4	no	—
605	C₂²	—	6	2	no	—
606	C₂²	—	6	4	no	—
607	C₂²	—	6	4	no	—
608	C₂²	—	6	2	no	—
609	C₂²	—	12	4	no	—
610	C₂²	—	12	8	no	—
611	C₂²	C₂×C₅×#239	1	2	yes	—
612	C₂²	C₅×D₃×#41	1	2	yes	—
613	C₂²	C₅×#1009	1	2	yes	—
614	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
615	C₄	—	2	4	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	4	no	—
619	C₄	—	6	2	no	—
620	C₄	—	6	2	no	—
621	C₄	—	6	4	no	—
622	C₄	C₂×C₅×#239	1	4	yes	—
623	C₃	C₂×C₅×#553	1	1	yes	characteristic, complemented, Sylow
624	C₂	—	6	4	no	—
625	C₂	—	12	2	no	—
626	C₂	—	12	4	no	—
627	C₂	C₅×#5695	1	4	yes	direct product factor
628	C₂	C₂²×C₅×#239	1	1	yes	characteristic
629	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
630	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#125	D₃
hypocenter	C₃	C₂×C₅×#553
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₅×#5695	C₂	direct (N × H)
3. C₂×C₅×#898	C₂	semidirect
4. C₂×C₅×#895	C₂	semidirect
5. C₂×C₅×#895	C₂	semidirect
6. C₂×C₅×#895	C₂	semidirect
7. C₂×C₅×#894	C₂	semidirect
8. C₂×C₅×#893	C₂	semidirect
9. C₂×C₅×#892	C₂	semidirect
10. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
11. C₂×C₄×C₅×D₁₂	C₂	semidirect
12. C₂×C₄×C₅×D₁₂	C₂	semidirect
22. C₃×C₅×#125	C₂²	semidirect
38. C₅×#898	C₂²	semidirect
39. C₅×#895	C₂²	semidirect
40. C₅×#895	C₂²	semidirect
41. C₅×#895	C₂²	semidirect
42. C₅×#894	C₂²	semidirect
43. C₅×#893	C₂²	semidirect
44. C₅×#892	C₂²	semidirect
45. C₅×D₃×C₄⋊C₄	C₂²	semidirect
46. C₄×C₅×D₁₂	C₂²	semidirect
47. C₄×C₅×D₁₂	C₂²	semidirect
48. C₂×#5695	C₅	direct (N × H)
51. C₂×C₅×#125	D₃	semidirect
103. C₂×C₃×#125	C₂×C₅	semidirect
104. #5695	C₂×C₅	direct (N × H)
105. C₂×#898	C₂×C₅	semidirect
106. C₂×#895	C₂×C₅	semidirect
107. C₂×#895	C₂×C₅	semidirect
108. C₂×#895	C₂×C₅	semidirect
109. C₂×#894	C₂×C₅	semidirect
110. C₂×#893	C₂×C₅	semidirect
111. C₂×#892	C₂×C₅	semidirect
112. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
113. C₂×C₄×D₁₂	C₂×C₅	semidirect
114. C₂×C₄×D₁₂	C₂×C₅	semidirect
124. C₅×#125	C₂×D₃	semidirect
195. C₃×#125	C₂²×C₅	semidirect
211. #898	C₂²×C₅	semidirect
212. #895	C₂²×C₅	semidirect
213. #895	C₂²×C₅	semidirect
214. #895	C₂²×C₅	semidirect
215. #894	C₂²×C₅	semidirect
216. #893	C₂²×C₅	semidirect
217. #892	C₂²×C₅	semidirect
218. D₃×C₄⋊C₄	C₂²×C₅	semidirect
219. C₄×D₁₂	C₂²×C₅	semidirect
220. C₄×D₁₂	C₂²×C₅	semidirect
265. C₂×#125	C₅×D₃	semidirect
387. #125	C₂×C₅×D₃	semidirect
412. C₂×C₃×C₅	#553	semidirect
522. C₃×C₅	C₂×#553	semidirect
550. C₂×C₅	#5695	direct (N × H)
591. C₂×C₃	C₅×#553	semidirect
598. C₅	C₂×#5695	direct (N × H)
623. C₃	C₂×C₅×#553	semidirect
627. C₂	C₅×#5695	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#125	2
C₅×#5695	2
C₂×C₅×#898	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#892	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#553	3
C₂×#5695	5

Subgroups — C2×C5×#5695 #14483622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5695 #14483622