Subgroups — C₂×C₅×#5515 #14480932

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#929	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₅×#67	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5515	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#896	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#889	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#539	—	3	1	no	maximal, Hall
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₅×#67	C₂²	1	2	yes	—
16	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
22	C₂×C₅×#217	C₂²	1	2	yes	—
23	C₅×#930	C₂²	1	8	yes	—
24	C₅×#929	C₂²	1	16	yes	complemented
25	C₄×C₅×#67	C₂²	1	16	yes	complemented
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#924	C₂²	1	8	yes	complemented
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
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×#896	C₂²	1	16	yes	complemented
40	C₅×#894	C₂²	1	16	yes	complemented
41	C₅×#889	C₂²	1	16	yes	complemented
42	C₂×#5515	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#539	—	3	16	no	—
44	C₂×C₅×#126	—	3	2	no	—
45	C₂×C₅×#125	—	3	2	no	—
46	C₂×C₅×#123	—	3	2	no	—
47	C₂×C₅×#123	—	3	2	no	—
48	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
49	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
50	C₂×C₅×#121	—	3	1	no	—
51	C₂×C₄×C₅×D₄	—	3	2	no	—
52	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
53	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂³×C₅×D₃	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	4	no	—
56	C₂²×C₃×C₄×C₅	—	4	2	no	—
57	C₂²×C₃×C₄×C₅	—	4	2	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
65	C₂×C₅×#67	—	2	8	no	—
66	C₂×C₅×#67	C₂³	1	8	yes	—
67	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
69	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂×C₅×D₁₂	—	4	2	no	—
71	C₂×C₅×D₁₂	C₂³	1	4	yes	—
72	C₂×C₄×C₅×D₃	—	4	4	no	—
73	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
74	C₂×C₅×Dic₆	—	4	2	no	—
75	C₂×C₅×Dic₆	C₂³	1	4	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
78	C₅×#217	C₂³	1	8	yes	—
79	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
80	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
81	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
82	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
83	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
84	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
85	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
86	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
87	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
88	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
89	C₄×C₅×Dic₃	C₂³	1	8	yes	—
90	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#930	C₂×C₅	1	1	yes	characteristic
92	C₂×#929	C₂×C₅	1	2	yes	complemented
93	C₂×C₄×#67	C₂×C₅	1	2	yes	complemented
94	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
95	#5515	C₂×C₅	1	16	yes	direct product factor
96	C₂×#898	C₂×C₅	1	2	yes	complemented
97	C₂×#896	C₂×C₅	1	2	yes	complemented
98	C₂×#894	C₂×C₅	1	2	yes	complemented
99	C₂×#889	C₂×C₅	1	2	yes	complemented
100	C₂²×C₅×Q₈	—	3	1	no	—
101	C₂²×C₅×D₄	—	3	2	no	—
102	C₂²×C₅×D₄	—	3	1	no	—
103	C₂³×C₄×C₅	—	3	2	no	—
104	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
105	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
106	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
107	C₅×#126	—	3	16	no	—
108	C₅×#125	—	3	16	no	—
109	C₅×#123	—	3	16	no	—
110	C₅×#123	—	3	16	no	—
111	C₅×C₂²⋊Q₈	—	3	8	no	—
112	C₅×C₂²⋊Q₈	—	3	16	no	—
113	C₅×#121	—	3	8	no	—
114	C₄×C₅×D₄	—	3	16	no	—
115	C₂×C₅×C₄⋊C₄	—	3	2	no	—
116	C₂×C₅×C₄⋊C₄	—	3	2	no	—
117	C₂×C₅×C₄⋊C₄	—	3	2	no	—
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₂×C₅×C₄⋊C₄	—	3	1	no	—
120	C₂×C₅×C₄⋊C₄	—	3	1	no	—
121	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
123	C₂×C₅×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
124	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
125	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
126	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
127	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
128	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
129	C₂×C₄²×C₅	—	3	2	no	—
130	C₂×#539	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	#41	1	4	yes	—
134	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
135	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
136	C₂²×C₅×D₃	—	2	4	no	—
137	C₂²×C₅×D₃	—	2	4	no	—
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
140	C₂×C₃×C₄×C₅	—	2	8	no	—
141	C₂×C₃×C₄×C₅	—	2	4	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	4	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	4	4	no	—
146	C₂×C₃×C₄×C₅	—	4	4	no	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
151	C₅×#67	—	2	16	no	—
152	C₂×C₅×Dic₃	—	2	4	no	—
153	C₂×C₅×Dic₃	—	2	4	no	—
154	C₂×C₅×Dic₃	—	2	4	no	—
155	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
156	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
157	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
158	C₅×D₁₂	—	4	4	no	—
159	C₄×C₅×D₃	—	4	8	no	—
160	C₅×Dic₆	—	4	4	no	—
161	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
162	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
164	C₂²×#67	C₂²×C₅	1	2	yes	—
165	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
167	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
169	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
171	C₂×#217	C₂²×C₅	1	2	yes	—
172	#930	C₂²×C₅	1	8	yes	—
173	#929	C₂²×C₅	1	16	yes	complemented
174	C₄×#67	C₂²×C₅	1	16	yes	complemented
175	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
177	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
181	#924	C₂²×C₅	1	8	yes	complemented
182	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
183	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
184	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
185	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
186	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
187	#898	C₂²×C₅	1	16	yes	complemented
188	#896	C₂²×C₅	1	16	yes	complemented
189	#894	C₂²×C₅	1	16	yes	complemented
190	#889	C₂²×C₅	1	16	yes	complemented
191	C₂⁴×C₅	—	3	2	no	—
192	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₅×Q₈	—	3	4	no	—
194	C₂×C₅×Q₈	—	12	2	no	—
195	C₂×C₅×D₄	—	3	8	no	—
196	C₂×C₅×D₄	—	3	4	no	—
197	C₂×C₅×D₄	—	6	8	no	—
198	C₂×C₅×D₄	—	12	2	no	—
199	C₂²×C₄×C₅	—	2	4	no	—
200	C₂²×C₄×C₅	—	3	2	no	—
201	C₂²×C₄×C₅	—	3	2	no	—
202	C₂²×C₄×C₅	—	3	2	no	—
203	C₂²×C₄×C₅	—	3	8	no	—
204	C₂²×C₄×C₅	—	4	2	no	—
205	C₂²×C₄×C₅	—	4	2	no	—
206	C₂²×C₄×C₅	—	12	4	no	—
207	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
208	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
209	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
213	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
214	C₅×C₄⋊C₄	—	3	8	no	—
215	C₅×C₄⋊C₄	—	3	4	no	—
216	C₅×C₄⋊C₄	—	3	8	no	—
217	C₅×C₄⋊C₄	—	3	8	no	—
218	C₅×C₄⋊C₄	—	3	4	no	—
219	C₅×C₄⋊C₄	—	3	8	no	—
220	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
221	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
222	C₅×C₂²⋊C₄	—	3	8	no	—
223	C₅×C₂²⋊C₄	—	3	8	no	—
224	C₅×C₂²⋊C₄	—	3	8	no	—
225	C₅×C₂²⋊C₄	—	3	8	no	—
226	C₅×C₂²⋊C₄	—	3	8	no	—
227	C₄²×C₅	—	3	8	no	—
228	#539	—	3	16	no	—
229	C₂×#126	—	3	2	no	—
230	C₂×#125	—	3	2	no	—
231	C₂×#123	—	3	2	no	—
232	C₂×#123	—	3	2	no	—
233	C₂×C₂²⋊Q₈	—	3	1	no	—
234	C₂×C₂²⋊Q₈	—	3	2	no	—
235	C₂×#121	—	3	1	no	—
236	C₂×C₄×D₄	—	3	2	no	—
237	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
238	C₂²×C₃×C₅	—	2	8	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
242	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
243	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
244	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
246	C₂×C₅×D₃	—	2	4	no	—
247	C₂×C₅×D₃	—	2	4	no	—
248	C₂×C₅×D₃	—	2	4	no	—
249	C₂×C₅×D₃	—	4	8	no	—
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	4	no	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₅×Dic₃	—	2	4	no	—
255	C₅×Dic₃	—	2	4	no	—
256	C₅×Dic₃	—	2	4	no	—
257	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
258	C₂³×D₃	C₂³×C₅	1	2	yes	—
259	C₂²×C₃×C₄	—	2	4	no	—
260	C₂²×C₃×C₄	—	4	2	no	—
261	C₂²×C₃×C₄	—	4	2	no	—
262	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
263	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
265	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
267	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
268	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
269	C₂×#67	—	2	8	no	—
270	C₂×#67	C₂³×C₅	1	8	yes	—
271	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
272	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
273	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
274	C₂×D₁₂	—	4	2	no	—
275	C₂×D₁₂	C₂³×C₅	1	4	yes	—
276	C₂×C₄×D₃	—	4	4	no	—
277	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
278	C₂×Dic₆	—	4	2	no	—
279	C₂×Dic₆	C₂³×C₅	1	4	yes	—
280	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
281	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
282	#217	C₂³×C₅	1	8	yes	—
283	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
284	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
285	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
286	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
287	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
288	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
289	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
290	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
291	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
292	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
293	C₄×Dic₃	C₂³×C₅	1	8	yes	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	3	4	no	—
297	C₂³×C₅	—	6	4	no	—
298	C₂³×C₅	—	6	4	no	—
299	C₂³×C₅	—	6	4	no	—
300	C₂³×C₅	#235	1	4	yes	—
301	C₂³×C₅	C₂³×D₃	1	2	yes	—
302	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
303	C₅×Q₈	—	12	4	no	—
304	C₅×D₄	—	6	16	no	—
305	C₅×D₄	—	12	4	no	—
306	C₂×C₄×C₅	—	2	8	no	—
307	C₂×C₄×C₅	—	2	4	no	—
308	C₂×C₄×C₅	—	2	4	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	3	4	no	—
312	C₂×C₄×C₅	—	3	4	no	—
313	C₂×C₄×C₅	—	3	4	no	—
314	C₂×C₄×C₅	—	4	4	no	—
315	C₂×C₄×C₅	—	4	4	no	—
316	C₂×C₄×C₅	—	6	4	no	—
317	C₂×C₄×C₅	—	6	4	no	—
318	C₂×C₄×C₅	—	6	4	no	—
319	C₂×C₄×C₅	—	12	8	no	—
320	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
321	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
322	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
323	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
324	C₂²×Q₈	—	3	1	no	—
325	C₂²×D₄	—	3	2	no	—
326	C₂²×D₄	—	3	1	no	—
327	C₂³×C₄	—	3	2	no	—
328	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
329	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
330	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
331	#126	—	3	16	no	—
332	#125	—	3	16	no	—
333	#123	—	3	16	no	—
334	#123	—	3	16	no	—
335	C₂²⋊Q₈	—	3	8	no	—
336	C₂²⋊Q₈	—	3	16	no	—
337	#121	—	3	8	no	—
338	C₄×D₄	—	3	16	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	2	no	—
342	C₂×C₄⋊C₄	—	3	2	no	—
343	C₂×C₄⋊C₄	—	3	1	no	—
344	C₂×C₄⋊C₄	—	3	2	no	—
345	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
348	C₂×C₂²⋊C₄	—	3	2	no	—
349	C₂×C₂²⋊C₄	—	3	2	no	—
350	C₂×C₂²⋊C₄	—	3	2	no	—
351	C₂×C₂²⋊C₄	—	3	2	no	—
352	C₂×C₂²⋊C₄	—	3	2	no	—
353	C₂×C₄²	—	3	2	no	—
354	C₂×C₃×C₅	—	2	4	no	—
355	C₂×C₃×C₅	#539	1	4	yes	complemented
356	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
357	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
359	C₅×D₃	—	4	4	no	—
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	2	2	no	—
362	C₂³×C₃	C₅×#41	1	4	yes	—
363	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
364	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
365	C₂²×D₃	—	2	4	no	—
366	C₂²×D₃	—	2	4	no	—
367	C₂²×D₃	—	2	4	no	—
368	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
369	C₂×C₃×C₄	—	2	8	no	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	4	4	no	—
375	C₂×C₃×C₄	—	4	4	no	—
376	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
377	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
378	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
379	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
380	#67	—	2	16	no	—
381	C₂×Dic₃	—	2	4	no	—
382	C₂×Dic₃	—	2	4	no	—
383	C₂×Dic₃	—	2	4	no	—
384	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
385	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
386	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
387	D₁₂	—	4	4	no	—
388	C₄×D₃	—	4	8	no	—
389	Dic₆	—	4	4	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	8	no	—
393	C₂²×C₅	—	6	4	no	—
394	C₂²×C₅	—	6	4	no	—
395	C₂²×C₅	—	6	4	no	—
396	C₂²×C₅	—	12	8	no	—
397	C₂²×C₅	C₂×#235	1	4	yes	—
398	C₂²×C₅	C₂×#235	1	2	yes	—
399	C₂²×C₅	#1004	1	2	yes	—
400	C₂²×C₅	#1007	1	2	yes	—
401	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
402	C₄×C₅	—	2	4	no	—
403	C₄×C₅	—	2	4	no	—
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	6	4	no	—
407	C₄×C₅	—	6	4	no	—
408	C₄×C₅	—	6	4	no	—
409	C₂⁴	—	3	2	no	—
410	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
411	C₂×Q₈	—	3	4	no	—
412	C₂×Q₈	—	12	2	no	—
413	C₂×D₄	—	3	8	no	—
414	C₂×D₄	—	3	4	no	—
415	C₂×D₄	—	6	8	no	—
416	C₂×D₄	—	12	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	3	2	no	—
419	C₂²×C₄	—	3	2	no	—
420	C₂²×C₄	—	3	2	no	—
421	C₂²×C₄	—	3	8	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	12	4	no	—
425	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
426	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
427	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
430	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
431	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
432	C₄⋊C₄	—	3	8	no	—
433	C₄⋊C₄	—	3	4	no	—
434	C₄⋊C₄	—	3	8	no	—
435	C₄⋊C₄	—	3	8	no	—
436	C₄⋊C₄	—	3	4	no	—
437	C₄⋊C₄	—	3	8	no	—
438	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
439	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
440	C₂²⋊C₄	—	3	8	no	—
441	C₂²⋊C₄	—	3	8	no	—
442	C₂²⋊C₄	—	3	8	no	—
443	C₂²⋊C₄	—	3	8	no	—
444	C₂²⋊C₄	—	3	8	no	—
445	C₄²	—	3	8	no	—
446	C₃×C₅	C₂×#539	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	8	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
451	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
452	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
454	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
455	C₂×D₃	—	2	4	no	—
456	C₂×D₃	—	2	4	no	—
457	C₂×D₃	—	2	4	no	—
458	C₂×D₃	—	4	8	no	—
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	2	4	no	—
462	C₃×C₄	—	2	2	no	—
463	Dic₃	—	2	4	no	—
464	Dic₃	—	2	4	no	—
465	Dic₃	—	2	4	no	—
466	C₂×C₅	—	2	4	no	—
467	C₂×C₅	—	12	4	no	—
468	C₂×C₅	#5515	1	4	yes	direct product factor
469	C₂×C₅	C₂²×#235	1	1	yes	characteristic
470	C₂×C₅	C₂×#1004	1	1	yes	characteristic
471	C₂×C₅	C₂×#1007	1	1	yes	characteristic
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	3	4	no	—
475	C₂³	—	6	4	no	—
476	C₂³	—	6	4	no	—
477	C₂³	—	6	4	no	—
478	C₂³	C₅×#235	1	4	yes	—
479	C₂³	C₂³×C₅×D₃	1	2	yes	—
480	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
481	Q₈	—	12	4	no	—
482	D₄	—	6	16	no	—
483	D₄	—	12	4	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	3	4	no	—
490	C₂×C₄	—	3	4	no	—
491	C₂×C₄	—	3	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	6	4	no	—
495	C₂×C₄	—	6	4	no	—
496	C₂×C₄	—	6	4	no	—
497	C₂×C₄	—	12	8	no	—
498	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
499	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
500	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
501	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
502	C₂×C₃	—	2	4	no	—
503	C₂×C₃	C₅×#539	1	4	yes	complemented
504	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
505	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
507	D₃	—	4	4	no	—
508	C₅	C₂×#5515	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	6	4	no	—
513	C₂²	—	6	4	no	—
514	C₂²	—	6	4	no	—
515	C₂²	—	12	8	no	—
516	C₂²	C₂×C₅×#235	1	4	yes	—
517	C₂²	C₂×C₅×#235	1	2	yes	—
518	C₂²	C₅×#1004	1	2	yes	—
519	C₂²	C₅×#1007	1	2	yes	—
520	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
521	C₄	—	2	4	no	—
522	C₄	—	2	4	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	6	4	no	—
526	C₄	—	6	4	no	—
527	C₄	—	6	4	no	—
528	C₃	C₂×C₅×#539	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	2	4	no	—
530	C₂	—	12	4	no	—
531	C₂	C₅×#5515	1	4	yes	direct product factor
532	C₂	C₂²×C₅×#235	1	1	yes	characteristic
533	C₂	C₂×C₅×#1004	1	1	yes	characteristic
534	C₂	C₂×C₅×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#930	C₂
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂×C₅×#929	C₂	semidirect
4. C₂×C₄×C₅×#67	C₂	semidirect
5. C₂×C₅×#924	C₂	semidirect
6. C₅×#5515	C₂	direct (N × H)
7. C₂×C₅×#898	C₂	semidirect
8. C₂×C₅×#896	C₂	semidirect
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#889	C₂	semidirect
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₅×#929	C₂²	semidirect
25. C₄×C₅×#67	C₂²	semidirect
32. C₅×#924	C₂²	semidirect
38. C₅×#898	C₂²	semidirect
39. C₅×#896	C₂²	semidirect
40. C₅×#894	C₂²	semidirect
41. C₅×#889	C₂²	semidirect
42. C₂×#5515	C₅	direct (N × H)
52. C₂²×C₅×C₄⋊C₄	D₃	semidirect
90. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
92. C₂×#929	C₂×C₅	semidirect
93. C₂×C₄×#67	C₂×C₅	semidirect
94. C₂×#924	C₂×C₅	semidirect
95. #5515	C₂×C₅	direct (N × H)
96. C₂×#898	C₂×C₅	semidirect
97. C₂×#896	C₂×C₅	semidirect
98. C₂×#894	C₂×C₅	semidirect
99. C₂×#889	C₂×C₅	semidirect
123. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
170. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
173. #929	C₂²×C₅	semidirect
174. C₄×#67	C₂²×C₅	semidirect
181. #924	C₂²×C₅	semidirect
187. #898	C₂²×C₅	semidirect
188. #896	C₂²×C₅	semidirect
189. #894	C₂²×C₅	semidirect
190. #889	C₂²×C₅	semidirect
237. C₂²×C₄⋊C₄	C₅×D₃	semidirect
347. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
355. C₂×C₃×C₅	#539	semidirect
446. C₃×C₅	C₂×#539	semidirect
468. C₂×C₅	#5515	direct (N × H)
503. C₂×C₃	C₅×#539	semidirect
508. C₅	C₂×#5515	direct (N × H)
528. C₃	C₂×C₅×#539	semidirect
531. C₂	C₅×#5515	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×C₃×C₅×C₄⋊C₄	2
C₂×C₅×#930	2
C₂×C₅×#929	2
C₂×C₄×C₅×#67	2
C₂×C₅×#924	2
C₅×#5515	2
C₂×C₅×#898	2
C₂×C₅×#896	2
C₂×C₅×#894	2
C₂×C₅×#889	2
C₂×C₅×#539	3
C₂×#5515	5

Subgroups — C2×C5×#5515 #14480932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5515 #14480932