Subgroups — C₅×D₃×#534 #14480287

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5804	C₂	1	2	yes	maximal, complemented
4	C₅×#5653	C₂	1	4	yes	maximal, complemented
5	C₅×D₃×#123	C₂	1	4	yes	maximal, complemented
6	C₅×#5605	C₂	1	4	yes	maximal, complemented
7	C₅×D₃×#121	C₂	1	4	yes	maximal, complemented
8	C₅×#5589	C₂	1	4	yes	maximal, complemented
9	C₅×D₃×#120	C₂	1	4	yes	maximal, complemented
10	C₅×#5493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#534	—	3	1	no	maximal, Hall
13	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₅×D₃	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
16	C₂²×C₅×#67	C₂²	1	2	yes	complemented
17	C₂²×C₅×#67	C₂²	1	2	yes	complemented
18	C₂×C₅×D₃×D₄	—	2	16	no	—
19	C₂×C₅×D₃×D₄	C₂²	1	4	yes	—
20	C₂×C₅×D₃×D₄	C₂²	1	4	yes	complemented
21	C₂×C₅×D₃×D₄	C₂²	1	4	yes	complemented
22	C₂×C₅×D₃×D₄	C₂²	1	4	yes	complemented
23	C₂×C₅×D₃×D₄	C₂²	1	4	yes	complemented
24	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
25	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
26	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
27	C₃×C₅×#123	C₂²	1	4	yes	complemented
28	C₃×C₅×#121	C₂²	1	4	yes	complemented
29	C₃×C₅×#120	C₂²	1	4	yes	complemented
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₅×#953	C₂²	1	4	yes	complemented
32	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
33	C₅×#939	C₂²	1	8	yes	complemented
34	C₅×#938	C₂²	1	4	yes	complemented
35	C₅×#937	C₂²	1	8	yes	complemented
36	C₅×#937	C₂²	1	4	yes	complemented
37	C₅×#935	C₂²	1	4	yes	complemented
38	C₅×#930	C₂²	1	4	yes	complemented
39	C₅×#929	C₂²	1	4	yes	complemented
40	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
41	C₅×#895	C₂²	1	4	yes	complemented
42	C₅×#894	C₂²	1	8	yes	complemented
43	C₅×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
44	C₅×#886	C₂²	1	4	yes	complemented
45	C₅×#884	C₂²	1	8	yes	complemented
46	C₅×#883	C₂²	1	8	yes	complemented
47	C₅×#882	C₂²	1	8	yes	complemented
48	C₅×#882	C₂²	1	4	yes	complemented
49	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
50	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
51	C₅×D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
52	D₃×#534	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₂³×C₅×D₄	—	3	2	no	—
54	C₅×#534	—	3	2	no	—
55	C₅×#534	—	3	4	no	—
56	C₅×#534	—	3	4	no	—
57	C₅×#534	—	3	4	no	—
58	C₅×#534	—	3	1	no	—
59	C₅×#534	D₃	1	1	yes	characteristic, direct product factor
60	C₂×C₅×#123	—	3	4	no	—
61	C₂×C₅×#121	—	3	4	no	—
62	C₂×C₅×#120	—	3	4	no	—
63	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂⁴×C₃×C₅	C₂³	1	2	yes	complemented
66	C₂³×C₅×D₃	—	2	8	no	—
67	C₂³×C₅×D₃	—	4	4	no	—
68	C₂³×C₅×D₃	—	4	8	no	—
69	C₂³×C₅×D₃	D₄	1	8	yes	complemented
70	C₂³×C₅×D₃	C₂³	1	4	yes	—
71	C₂³×C₅×D₃	C₂³	1	2	yes	—
72	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂³×C₅×D₃	C₂³	1	2	yes	—
74	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₂³×C₅×D₃	C₂³	1	2	yes	complemented
76	C₂³×C₅×D₃	C₂³	1	4	yes	complemented
77	C₂×C₃×C₅×D₄	—	2	8	no	—
78	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
80	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
81	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
82	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
83	C₂×C₅×#67	—	2	8	no	—
84	C₂×C₅×#67	—	2	8	no	—
85	C₂×C₅×#67	C₂³	1	4	yes	—
86	C₂×C₅×#67	C₂³	1	4	yes	—
87	C₂×C₅×#67	C₂³	1	4	yes	complemented
88	C₂×C₅×#67	C₂³	1	4	yes	complemented
89	C₂×C₅×#67	C₂³	1	8	yes	complemented
90	C₂²×C₅×Dic₃	C₂³	1	2	yes	complemented
91	C₂²×C₅×Dic₃	C₂³	1	2	yes	complemented
92	C₅×D₃×D₄	—	2	16	no	—
93	C₅×D₃×D₄	—	2	16	no	—
94	C₅×D₃×D₄	—	2	16	no	—
95	C₅×D₃×D₄	—	2	16	no	—
96	C₅×D₃×D₄	—	4	8	no	—
97	C₂×C₅×D₁₂	—	2	8	no	—
98	C₂×C₅×D₁₂	C₂³	1	4	yes	—
99	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
100	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
101	C₂×C₄×C₅×D₃	—	2	8	no	—
102	C₂×C₄×C₅×D₃	—	4	4	no	—
103	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
104	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
105	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
106	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
107	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
108	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₅×#217	C₂³	1	4	yes	complemented
111	C₅×#217	C₂³	1	8	yes	complemented
112	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
113	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
114	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
115	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
116	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
117	C₂²×D₃×D₄	C₂×C₅	1	2	yes	complemented
118	C₃×#534	C₂×C₅	1	1	yes	characteristic, complemented
119	#5804	C₂×C₅	1	2	yes	complemented
120	#5653	C₂×C₅	1	4	yes	complemented
121	D₃×#123	C₂×C₅	1	4	yes	complemented
122	#5605	C₂×C₅	1	4	yes	complemented
123	D₃×#121	C₂×C₅	1	4	yes	complemented
124	#5589	C₂×C₅	1	4	yes	complemented
125	D₃×#120	C₂×C₅	1	4	yes	complemented
126	#5493	C₂×C₅	1	1	yes	characteristic, complemented
127	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
128	C₂⁵×C₅	—	3	1	no	—
129	C₂⁵×C₅	—	3	2	no	—
130	C₂²×C₅×D₄	—	3	2	no	—
131	C₂²×C₅×D₄	—	3	2	no	—
132	C₂²×C₅×D₄	—	3	4	no	—
133	C₂²×C₅×D₄	—	3	4	no	—
134	C₂²×C₅×D₄	—	3	4	no	—
135	C₂²×C₅×D₄	—	3	4	no	—
136	C₂²×C₅×D₄	—	3	4	no	—
137	C₂²×C₅×D₄	—	3	2	no	—
138	C₂²×C₅×D₄	—	6	16	no	—
139	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
140	C₂³×C₄×C₅	—	3	2	no	—
141	C₂³×C₄×C₅	—	3	2	no	—
142	C₅×#123	—	3	4	no	—
143	C₅×#123	—	3	4	no	—
144	C₅×#123	—	3	8	no	—
145	C₅×#123	—	3	8	no	—
146	C₅×#123	—	3	4	no	—
147	C₅×#123	C₂×D₃	1	4	yes	complemented
148	C₅×#121	—	3	4	no	—
149	C₅×#121	—	3	8	no	—
150	C₅×#121	—	3	4	no	—
151	C₅×#121	—	3	4	no	—
152	C₅×#121	—	3	8	no	—
153	C₅×#121	C₂×D₃	1	4	yes	complemented
154	C₅×#120	—	3	4	no	—
155	C₅×#120	—	3	4	no	—
156	C₅×#120	—	3	8	no	—
157	C₅×#120	—	3	8	no	—
158	C₅×#120	—	3	4	no	—
159	C₅×#120	C₂×D₃	1	4	yes	complemented
160	C₂×C₅×C₄⋊C₄	—	3	4	no	—
161	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
162	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
163	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
164	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
166	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
167	C₂×#534	—	3	1	no	Sylow
168	C₂³×C₃×C₅	—	2	4	no	—
169	C₂³×C₃×C₅	—	4	2	no	—
170	C₂³×C₃×C₅	—	4	4	no	—
171	C₂³×C₃×C₅	C₂×D₄	1	4	yes	complemented
172	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
173	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
174	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
175	C₂²×C₅×D₃	—	2	4	no	—
176	C₂²×C₅×D₃	—	2	8	no	—
177	C₂²×C₅×D₃	—	2	4	no	—
178	C₂²×C₅×D₃	—	2	8	no	—
179	C₂²×C₅×D₃	—	2	8	no	—
180	C₂²×C₅×D₃	—	2	16	no	—
181	C₂²×C₅×D₃	—	4	16	no	—
182	C₂²×C₅×D₃	—	4	4	no	—
183	C₂²×C₅×D₃	—	4	2	no	—
184	C₂²×C₅×D₃	—	4	8	no	—
185	C₂²×C₅×D₃	—	4	4	no	—
186	C₂²×C₅×D₃	—	4	32	no	—
187	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
188	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
189	C₂²×C₅×D₃	C₂×D₄	1	8	yes	complemented
190	C₂²×C₅×D₃	C₂×D₄	1	4	yes	complemented
191	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
192	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
193	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
195	C₃×C₅×D₄	—	2	8	no	—
196	C₃×C₅×D₄	—	2	8	no	—
197	C₃×C₅×D₄	—	4	4	no	—
198	C₂×C₃×C₄×C₅	—	2	4	no	—
199	C₂×C₃×C₄×C₅	—	4	2	no	—
200	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
201	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
202	C₅×#67	—	2	8	no	—
203	C₅×#67	—	2	8	no	—
204	C₅×#67	—	2	8	no	—
205	C₅×#67	—	2	8	no	—
206	C₅×#67	—	4	8	no	—
207	C₂×C₅×Dic₃	—	2	4	no	—
208	C₂×C₅×Dic₃	—	4	2	no	—
209	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
210	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
211	C₅×D₁₂	—	2	8	no	—
212	C₅×D₁₂	—	2	8	no	—
213	C₅×D₁₂	—	4	4	no	—
214	C₄×C₅×D₃	—	2	8	no	—
215	C₄×C₅×D₃	—	2	8	no	—
216	C₄×C₅×D₃	—	2	8	no	—
217	C₄×C₅×D₃	—	4	4	no	—
218	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
219	C₂⁴×D₃	C₂²×C₅	1	2	yes	complemented
220	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
221	C₂²×#67	C₂²×C₅	1	2	yes	complemented
222	C₂²×#67	C₂²×C₅	1	2	yes	complemented
223	C₂×D₃×D₄	—	2	16	no	—
224	C₂×D₃×D₄	C₂²×C₅	1	4	yes	—
225	C₂×D₃×D₄	C₂²×C₅	1	4	yes	complemented
226	C₂×D₃×D₄	C₂²×C₅	1	4	yes	complemented
227	C₂×D₃×D₄	C₂²×C₅	1	4	yes	complemented
228	C₂×D₃×D₄	C₂²×C₅	1	4	yes	complemented
229	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
230	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
231	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
232	C₃×#123	C₂²×C₅	1	4	yes	complemented
233	C₃×#121	C₂²×C₅	1	4	yes	complemented
234	C₃×#120	C₂²×C₅	1	4	yes	complemented
235	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
236	#953	C₂²×C₅	1	4	yes	complemented
237	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
238	#939	C₂²×C₅	1	8	yes	complemented
239	#938	C₂²×C₅	1	4	yes	complemented
240	#937	C₂²×C₅	1	8	yes	complemented
241	#937	C₂²×C₅	1	4	yes	complemented
242	#935	C₂²×C₅	1	4	yes	complemented
243	#930	C₂²×C₅	1	4	yes	complemented
244	#929	C₂²×C₅	1	4	yes	complemented
245	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
246	#895	C₂²×C₅	1	4	yes	complemented
247	#894	C₂²×C₅	1	8	yes	complemented
248	D₃×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
249	#886	C₂²×C₅	1	4	yes	complemented
250	#884	C₂²×C₅	1	8	yes	complemented
251	#883	C₂²×C₅	1	8	yes	complemented
252	#882	C₂²×C₅	1	8	yes	complemented
253	#882	C₂²×C₅	1	4	yes	complemented
254	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
255	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
256	D₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
257	C₂⁴×C₅	—	3	2	no	—
258	C₂⁴×C₅	—	3	1	no	—
259	C₂⁴×C₅	—	3	8	no	—
260	C₂⁴×C₅	—	3	1	no	—
261	C₂⁴×C₅	—	3	2	no	—
262	C₂⁴×C₅	—	3	4	no	—
263	C₂⁴×C₅	—	3	4	no	—
264	C₂⁴×C₅	—	3	2	no	—
265	C₂⁴×C₅	—	6	8	no	—
266	C₂⁴×C₅	—	12	4	no	—
267	C₂⁴×C₅	—	12	8	no	—
268	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
269	C₂⁴×C₅	C₂²×D₃	1	2	yes	complemented
270	C₂×C₅×D₄	—	2	8	no	—
271	C₂×C₅×D₄	—	3	4	no	—
272	C₂×C₅×D₄	—	3	4	no	—
273	C₂×C₅×D₄	—	3	4	no	—
274	C₂×C₅×D₄	—	3	4	no	—
275	C₂×C₅×D₄	—	3	8	no	—
276	C₂×C₅×D₄	—	3	4	no	—
277	C₂×C₅×D₄	—	3	4	no	—
278	C₂×C₅×D₄	—	3	4	no	—
279	C₂×C₅×D₄	—	6	8	no	—
280	C₂×C₅×D₄	—	6	16	no	—
281	C₂×C₅×D₄	—	6	16	no	—
282	C₂×C₅×D₄	—	6	16	no	—
283	C₂×C₅×D₄	—	6	16	no	—
284	C₂×C₅×D₄	—	6	8	no	—
285	C₂×C₅×D₄	—	6	8	no	—
286	C₂×C₅×D₄	—	12	8	no	—
287	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
288	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
289	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
290	C₂²×C₄×C₅	—	3	2	no	—
291	C₂²×C₄×C₅	—	3	2	no	—
292	C₂²×C₄×C₅	—	3	4	no	—
293	C₂²×C₄×C₅	—	3	4	no	—
294	C₂²×C₄×C₅	—	3	4	no	—
295	C₂²×C₄×C₅	—	3	4	no	—
296	C₂²×C₄×C₅	—	6	8	no	—
297	C₂²×C₄×C₅	—	12	4	no	—
298	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	complemented
299	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	complemented
300	C₅×C₄⋊C₄	—	3	8	no	—
301	C₅×C₄⋊C₄	—	3	4	no	—
302	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
303	C₅×C₂²⋊C₄	—	3	4	no	—
304	C₅×C₂²⋊C₄	—	3	8	no	—
305	C₅×C₂²⋊C₄	—	3	8	no	—
306	C₅×C₂²⋊C₄	—	3	8	no	—
307	C₅×C₂²⋊C₄	—	3	8	no	—
308	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
309	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
310	C₂³×D₄	—	3	2	no	—
311	#534	—	3	2	no	—
312	#534	—	3	4	no	—
313	#534	—	3	4	no	—
314	#534	—	3	4	no	—
315	#534	—	3	1	no	—
316	#534	C₅×D₃	1	1	yes	characteristic, direct product factor
317	C₂×#123	—	3	4	no	—
318	C₂×#121	—	3	4	no	—
319	C₂×#120	—	3	4	no	—
320	C₂²×C₂²⋊C₄	—	3	1	no	—
321	C₂²×C₃×C₅	—	2	2	no	—
322	C₂²×C₃×C₅	—	2	4	no	—
323	C₂²×C₃×C₅	—	2	4	no	—
324	C₂²×C₃×C₅	—	2	8	no	—
325	C₂²×C₃×C₅	—	4	4	no	—
326	C₂²×C₃×C₅	—	4	8	no	—
327	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
328	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
329	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
330	C₂×C₅×D₃	—	2	2	no	—
331	C₂×C₅×D₃	—	2	4	no	—
332	C₂×C₅×D₃	—	2	16	no	—
333	C₂×C₅×D₃	—	2	8	no	—
334	C₂×C₅×D₃	—	2	4	no	—
335	C₂×C₅×D₃	—	2	8	no	—
336	C₂×C₅×D₃	—	4	4	no	—
337	C₂×C₅×D₃	—	4	8	no	—
338	C₂×C₅×D₃	—	4	16	no	—
339	C₂×C₅×D₃	—	4	8	no	—
340	C₂×C₅×D₃	—	4	16	no	—
341	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
342	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
343	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
344	C₂×C₅×D₃	H(5,𝔽₂)	1	4	yes	—
345	C₃×C₄×C₅	—	2	4	no	—
346	C₃×C₄×C₅	—	2	4	no	—
347	C₅×Dic₃	—	2	4	no	—
348	C₅×Dic₃	—	2	4	no	—
349	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
350	C₂⁴×C₃	C₂³×C₅	1	2	yes	complemented
351	C₂³×D₃	—	2	8	no	—
352	C₂³×D₃	—	4	4	no	—
353	C₂³×D₃	—	4	8	no	—
354	C₂³×D₃	C₅×D₄	1	8	yes	complemented
355	C₂³×D₃	C₂³×C₅	1	4	yes	—
356	C₂³×D₃	C₂³×C₅	1	2	yes	—
357	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
358	C₂³×D₃	C₂³×C₅	1	2	yes	—
359	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
360	C₂³×D₃	C₂³×C₅	1	2	yes	complemented
361	C₂³×D₃	C₂³×C₅	1	4	yes	complemented
362	C₂×C₃×D₄	—	2	8	no	—
363	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
364	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
365	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
366	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	complemented
367	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	complemented
368	C₂×#67	—	2	8	no	—
369	C₂×#67	—	2	8	no	—
370	C₂×#67	C₂³×C₅	1	4	yes	—
371	C₂×#67	C₂³×C₅	1	4	yes	—
372	C₂×#67	C₂³×C₅	1	4	yes	complemented
373	C₂×#67	C₂³×C₅	1	4	yes	complemented
374	C₂×#67	C₂³×C₅	1	8	yes	complemented
375	C₂²×Dic₃	C₂³×C₅	1	2	yes	complemented
376	C₂²×Dic₃	C₂³×C₅	1	2	yes	complemented
377	D₃×D₄	—	2	16	no	—
378	D₃×D₄	—	2	16	no	—
379	D₃×D₄	—	2	16	no	—
380	D₃×D₄	—	2	16	no	—
381	D₃×D₄	—	4	8	no	—
382	C₂×D₁₂	—	2	8	no	—
383	C₂×D₁₂	C₂³×C₅	1	4	yes	—
384	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
385	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
386	C₂×C₄×D₃	—	2	8	no	—
387	C₂×C₄×D₃	—	4	4	no	—
388	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
389	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
390	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
391	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
392	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
393	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
394	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
395	#217	C₂³×C₅	1	4	yes	complemented
396	#217	C₂³×C₅	1	8	yes	complemented
397	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
398	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
399	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
400	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
401	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	3	1	no	—
404	C₂³×C₅	—	3	8	no	—
405	C₂³×C₅	—	3	4	no	—
406	C₂³×C₅	—	3	2	no	—
407	C₂³×C₅	—	3	1	no	—
408	C₂³×C₅	—	3	4	no	—
409	C₂³×C₅	—	3	8	no	—
410	C₂³×C₅	—	3	4	no	—
411	C₂³×C₅	—	4	2	no	—
412	C₂³×C₅	—	4	4	no	—
413	C₂³×C₅	—	6	4	no	—
414	C₂³×C₅	—	6	8	no	—
415	C₂³×C₅	—	6	8	no	—
416	C₂³×C₅	—	6	8	no	—
417	C₂³×C₅	—	6	16	no	—
418	C₂³×C₅	—	6	4	no	—
419	C₂³×C₅	—	12	2	no	—
420	C₂³×C₅	—	12	4	no	—
421	C₂³×C₅	—	12	4	no	—
422	C₂³×C₅	—	12	8	no	—
423	C₂³×C₅	—	12	16	no	—
424	C₂³×C₅	—	12	32	no	—
425	C₂³×C₅	D₃×D₄	1	4	yes	complemented
426	C₂³×C₅	C₂³×D₃	1	4	yes	—
427	C₂³×C₅	C₂³×D₃	1	2	yes	—
428	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
429	C₅×D₄	—	2	8	no	—
430	C₅×D₄	—	2	8	no	—
431	C₅×D₄	—	4	4	no	—
432	C₅×D₄	—	6	8	no	—
433	C₅×D₄	—	6	8	no	—
434	C₅×D₄	—	6	8	no	—
435	C₅×D₄	—	6	8	no	—
436	C₅×D₄	—	6	8	no	—
437	C₅×D₄	—	6	8	no	—
438	C₅×D₄	—	12	4	no	—
439	C₅×D₄	—	12	8	no	—
440	C₂×C₄×C₅	—	2	4	no	—
441	C₂×C₄×C₅	—	3	4	no	—
442	C₂×C₄×C₅	—	3	4	no	—
443	C₂×C₄×C₅	—	4	2	no	—
444	C₂×C₄×C₅	—	6	8	no	—
445	C₂×C₄×C₅	—	6	8	no	—
446	C₂×C₄×C₅	—	6	8	no	—
447	C₂×C₄×C₅	—	6	4	no	—
448	C₂×C₄×C₅	—	12	4	no	—
449	C₂×C₄×C₅	—	12	2	no	—
450	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
451	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
452	C₂⁵	—	3	1	no	—
453	C₂⁵	—	3	2	no	—
454	C₂²×D₄	—	3	2	no	—
455	C₂²×D₄	—	3	2	no	—
456	C₂²×D₄	—	3	4	no	—
457	C₂²×D₄	—	3	4	no	—
458	C₂²×D₄	—	3	4	no	—
459	C₂²×D₄	—	3	4	no	—
460	C₂²×D₄	—	3	4	no	—
461	C₂²×D₄	—	3	2	no	—
462	C₂²×D₄	—	6	16	no	—
463	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
464	C₂³×C₄	—	3	2	no	—
465	C₂³×C₄	—	3	2	no	—
466	#123	—	3	4	no	—
467	#123	—	3	4	no	—
468	#123	—	3	8	no	—
469	#123	—	3	8	no	—
470	#123	—	3	4	no	—
471	#123	C₂×C₅×D₃	1	4	yes	complemented
472	#121	—	3	4	no	—
473	#121	—	3	8	no	—
474	#121	—	3	4	no	—
475	#121	—	3	4	no	—
476	#121	—	3	8	no	—
477	#121	C₂×C₅×D₃	1	4	yes	complemented
478	#120	—	3	4	no	—
479	#120	—	3	4	no	—
480	#120	—	3	8	no	—
481	#120	—	3	8	no	—
482	#120	—	3	4	no	—
483	#120	C₂×C₅×D₃	1	4	yes	complemented
484	C₂×C₄⋊C₄	—	3	4	no	—
485	C₂×C₂²⋊C₄	—	3	1	no	—
486	C₂×C₂²⋊C₄	—	3	2	no	—
487	C₂×C₂²⋊C₄	—	3	4	no	—
488	C₂×C₂²⋊C₄	—	3	4	no	—
489	C₂×C₂²⋊C₄	—	3	8	no	—
490	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
491	C₂×C₃×C₅	—	2	4	no	—
492	C₂×C₃×C₅	—	2	2	no	—
493	C₂×C₃×C₅	—	4	4	no	—
494	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
495	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
496	C₅×D₃	—	2	4	no	—
497	C₅×D₃	—	2	2	no	—
498	C₅×D₃	—	4	4	no	—
499	C₅×D₃	#534	1	4	yes	direct product factor
500	C₂³×C₃	—	2	4	no	—
501	C₂³×C₃	—	4	2	no	—
502	C₂³×C₃	—	4	4	no	—
503	C₂³×C₃	C₂×C₅×D₄	1	4	yes	complemented
504	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
505	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
506	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
507	C₂²×D₃	—	2	4	no	—
508	C₂²×D₃	—	2	8	no	—
509	C₂²×D₃	—	2	4	no	—
510	C₂²×D₃	—	2	8	no	—
511	C₂²×D₃	—	2	8	no	—
512	C₂²×D₃	—	2	16	no	—
513	C₂²×D₃	—	4	16	no	—
514	C₂²×D₃	—	4	4	no	—
515	C₂²×D₃	—	4	2	no	—
516	C₂²×D₃	—	4	8	no	—
517	C₂²×D₃	—	4	4	no	—
518	C₂²×D₃	—	4	32	no	—
519	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
520	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
521	C₂²×D₃	C₂×C₅×D₄	1	8	yes	complemented
522	C₂²×D₃	C₂×C₅×D₄	1	4	yes	complemented
523	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
524	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
525	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
526	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
527	C₃×D₄	—	2	8	no	—
528	C₃×D₄	—	2	8	no	—
529	C₃×D₄	—	4	4	no	—
530	C₂×C₃×C₄	—	2	4	no	—
531	C₂×C₃×C₄	—	4	2	no	—
532	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
533	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
534	#67	—	2	8	no	—
535	#67	—	2	8	no	—
536	#67	—	2	8	no	—
537	#67	—	2	8	no	—
538	#67	—	4	8	no	—
539	C₂×Dic₃	—	2	4	no	—
540	C₂×Dic₃	—	4	2	no	—
541	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
542	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
543	D₁₂	—	2	8	no	—
544	D₁₂	—	2	8	no	—
545	D₁₂	—	4	4	no	—
546	C₄×D₃	—	2	8	no	—
547	C₄×D₃	—	2	8	no	—
548	C₄×D₃	—	2	8	no	—
549	C₄×D₃	—	4	4	no	—
550	C₂²×C₅	—	2	2	no	—
551	C₂²×C₅	—	2	4	no	—
552	C₂²×C₅	—	2	4	no	—
553	C₂²×C₅	—	2	8	no	—
554	C₂²×C₅	—	3	2	no	—
555	C₂²×C₅	—	3	4	no	—
556	C₂²×C₅	—	3	4	no	—
557	C₂²×C₅	—	3	2	no	—
558	C₂²×C₅	—	4	4	no	—
559	C₂²×C₅	—	4	8	no	—
560	C₂²×C₅	—	6	8	no	—
561	C₂²×C₅	—	6	16	no	—
562	C₂²×C₅	—	6	2	no	—
563	C₂²×C₅	—	6	4	no	—
564	C₂²×C₅	—	6	4	no	—
565	C₂²×C₅	—	6	8	no	—
566	C₂²×C₅	—	12	8	no	—
567	C₂²×C₅	—	12	4	no	—
568	C₂²×C₅	—	12	8	no	—
569	C₂²×C₅	—	12	16	no	—
570	C₂²×C₅	—	12	16	no	—
571	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
572	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
573	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
574	C₄×C₅	—	2	4	no	—
575	C₄×C₅	—	2	4	no	—
576	C₄×C₅	—	6	4	no	—
577	C₄×C₅	—	6	4	no	—
578	C₂⁴	—	3	2	no	—
579	C₂⁴	—	3	1	no	—
580	C₂⁴	—	3	8	no	—
581	C₂⁴	—	3	1	no	—
582	C₂⁴	—	3	2	no	—
583	C₂⁴	—	3	4	no	—
584	C₂⁴	—	3	4	no	—
585	C₂⁴	—	3	2	no	—
586	C₂⁴	—	6	8	no	—
587	C₂⁴	—	12	4	no	—
588	C₂⁴	—	12	8	no	—
589	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
590	C₂⁴	C₂²×C₅×D₃	1	2	yes	complemented
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	3	4	no	—
593	C₂×D₄	—	3	4	no	—
594	C₂×D₄	—	3	4	no	—
595	C₂×D₄	—	3	4	no	—
596	C₂×D₄	—	3	8	no	—
597	C₂×D₄	—	3	4	no	—
598	C₂×D₄	—	3	4	no	—
599	C₂×D₄	—	3	4	no	—
600	C₂×D₄	—	6	8	no	—
601	C₂×D₄	—	6	16	no	—
602	C₂×D₄	—	6	16	no	—
603	C₂×D₄	—	6	16	no	—
604	C₂×D₄	—	6	16	no	—
605	C₂×D₄	—	6	8	no	—
606	C₂×D₄	—	6	8	no	—
607	C₂×D₄	—	12	8	no	—
608	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
609	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
610	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
611	C₂²×C₄	—	3	2	no	—
612	C₂²×C₄	—	3	2	no	—
613	C₂²×C₄	—	3	4	no	—
614	C₂²×C₄	—	3	4	no	—
615	C₂²×C₄	—	3	4	no	—
616	C₂²×C₄	—	3	4	no	—
617	C₂²×C₄	—	6	8	no	—
618	C₂²×C₄	—	12	4	no	—
619	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	complemented
620	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	complemented
621	C₄⋊C₄	—	3	8	no	—
622	C₄⋊C₄	—	3	4	no	—
623	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
624	C₂²⋊C₄	—	3	4	no	—
625	C₂²⋊C₄	—	3	8	no	—
626	C₂²⋊C₄	—	3	8	no	—
627	C₂²⋊C₄	—	3	8	no	—
628	C₂²⋊C₄	—	3	8	no	—
629	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
630	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
631	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
632	C₂²×C₃	—	2	2	no	—
633	C₂²×C₃	—	2	4	no	—
634	C₂²×C₃	—	2	4	no	—
635	C₂²×C₃	—	2	8	no	—
636	C₂²×C₃	—	4	4	no	—
637	C₂²×C₃	—	4	8	no	—
638	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
639	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
640	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
641	C₂×D₃	—	2	2	no	—
642	C₂×D₃	—	2	4	no	—
643	C₂×D₃	—	2	16	no	—
644	C₂×D₃	—	2	8	no	—
645	C₂×D₃	—	2	4	no	—
646	C₂×D₃	—	2	8	no	—
647	C₂×D₃	—	4	4	no	—
648	C₂×D₃	—	4	8	no	—
649	C₂×D₃	—	4	16	no	—
650	C₂×D₃	—	4	8	no	—
651	C₂×D₃	—	4	16	no	—
652	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
653	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
654	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
655	C₂×D₃	C₅×H(5,𝔽₂)	1	4	yes	—
656	C₃×C₄	—	2	4	no	—
657	C₃×C₄	—	2	4	no	—
658	Dic₃	—	2	4	no	—
659	Dic₃	—	2	4	no	—
660	C₂×C₅	—	2	4	no	—
661	C₂×C₅	—	2	2	no	—
662	C₂×C₅	—	3	4	no	—
663	C₂×C₅	—	4	4	no	—
664	C₂×C₅	—	6	4	no	—
665	C₂×C₅	—	6	2	no	—
666	C₂×C₅	—	12	4	no	—
667	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
668	C₂×C₅	D₃×H(5,𝔽₂)	1	2	yes	—
669	C₂³	—	2	4	no	—
670	C₂³	—	3	1	no	—
671	C₂³	—	3	8	no	—
672	C₂³	—	3	4	no	—
673	C₂³	—	3	2	no	—
674	C₂³	—	3	1	no	—
675	C₂³	—	3	4	no	—
676	C₂³	—	3	8	no	—
677	C₂³	—	3	4	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	6	4	no	—
681	C₂³	—	6	8	no	—
682	C₂³	—	6	8	no	—
683	C₂³	—	6	8	no	—
684	C₂³	—	6	16	no	—
685	C₂³	—	6	4	no	—
686	C₂³	—	12	2	no	—
687	C₂³	—	12	4	no	—
688	C₂³	—	12	4	no	—
689	C₂³	—	12	8	no	—
690	C₂³	—	12	16	no	—
691	C₂³	—	12	32	no	—
692	C₂³	C₅×D₃×D₄	1	4	yes	complemented
693	C₂³	C₂³×C₅×D₃	1	4	yes	—
694	C₂³	C₂³×C₅×D₃	1	2	yes	—
695	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
696	D₄	—	2	8	no	—
697	D₄	—	2	8	no	—
698	D₄	—	4	4	no	—
699	D₄	—	6	8	no	—
700	D₄	—	6	8	no	—
701	D₄	—	6	8	no	—
702	D₄	—	6	8	no	—
703	D₄	—	6	8	no	—
704	D₄	—	6	8	no	—
705	D₄	—	12	4	no	—
706	D₄	—	12	8	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	3	4	no	—
709	C₂×C₄	—	3	4	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	6	8	no	—
712	C₂×C₄	—	6	8	no	—
713	C₂×C₄	—	6	8	no	—
714	C₂×C₄	—	6	4	no	—
715	C₂×C₄	—	12	4	no	—
716	C₂×C₄	—	12	2	no	—
717	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
718	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
719	C₂×C₃	—	2	4	no	—
720	C₂×C₃	—	2	2	no	—
721	C₂×C₃	—	4	4	no	—
722	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
723	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
724	D₃	—	2	4	no	—
725	D₃	—	2	2	no	—
726	D₃	—	4	4	no	—
727	D₃	C₅×#534	1	4	yes	direct product factor
728	C₅	D₃×#534	1	1	yes	characteristic, direct product factor, Sylow
729	C₂²	—	2	2	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	3	2	no	—
734	C₂²	—	3	4	no	—
735	C₂²	—	3	4	no	—
736	C₂²	—	3	2	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	8	no	—
739	C₂²	—	6	16	no	—
740	C₂²	—	6	8	no	—
741	C₂²	—	6	2	no	—
742	C₂²	—	6	4	no	—
743	C₂²	—	6	4	no	—
744	C₂²	—	6	8	no	—
745	C₂²	—	12	8	no	—
746	C₂²	—	12	4	no	—
747	C₂²	—	12	8	no	—
748	C₂²	—	12	16	no	—
749	C₂²	—	12	16	no	—
750	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
751	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
752	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	6	4	no	—
756	C₄	—	6	4	no	—
757	C₃	C₂×C₅×#534	1	1	yes	characteristic, complemented, Sylow
758	C₂	—	2	4	no	—
759	C₂	—	2	2	no	—
760	C₂	—	3	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	6	4	no	—
763	C₂	—	6	2	no	—
764	C₂	—	12	4	no	—
765	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
766	C₂	C₅×D₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#534	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#534	D₃
hypocenter	C₃	C₂×C₅×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#534

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×D₄	C₂	semidirect
2. C₃×C₅×#534	C₂	semidirect
3. C₅×#5804	C₂	semidirect
4. C₅×#5653	C₂	semidirect
5. C₅×D₃×#123	C₂	semidirect
6. C₅×#5605	C₂	semidirect
7. C₅×D₃×#121	C₂	semidirect
8. C₅×#5589	C₂	semidirect
9. C₅×D₃×#120	C₂	semidirect
10. C₅×#5493	C₂	semidirect
11. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂⁴×C₅×D₃	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₅×#67	C₂²	semidirect
17. C₂²×C₅×#67	C₂²	semidirect
20. C₂×C₅×D₃×D₄	C₂²	semidirect
21. C₂×C₅×D₃×D₄	C₂²	semidirect
22. C₂×C₅×D₃×D₄	C₂²	semidirect
23. C₂×C₅×D₃×D₄	C₂²	semidirect
24. C₂²×C₅×D₁₂	C₂²	semidirect
25. C₂²×C₄×C₅×D₃	C₂²	semidirect
26. C₂²×C₄×C₅×D₃	C₂²	semidirect
27. C₃×C₅×#123	C₂²	semidirect
28. C₃×C₅×#121	C₂²	semidirect
29. C₃×C₅×#120	C₂²	semidirect
30. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₅×#953	C₂²	semidirect
32. C₂×C₅×#217	C₂²	semidirect
33. C₅×#939	C₂²	semidirect
34. C₅×#938	C₂²	semidirect
35. C₅×#937	C₂²	semidirect
36. C₅×#937	C₂²	semidirect
37. C₅×#935	C₂²	semidirect
38. C₅×#930	C₂²	semidirect
39. C₅×#929	C₂²	semidirect
40. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₅×#895	C₂²	semidirect
42. C₅×#894	C₂²	semidirect
43. C₅×D₃×C₄⋊C₄	C₂²	semidirect
44. C₅×#886	C₂²	semidirect
45. C₅×#884	C₂²	semidirect
46. C₅×#883	C₂²	semidirect
47. C₅×#882	C₂²	semidirect
48. C₅×#882	C₂²	semidirect
49. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
50. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
51. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
52. D₃×#534	C₅	direct (N × H)
59. C₅×#534	D₃	direct (N × H)
65. C₂⁴×C₃×C₅	C₂³	semidirect
69. C₂³×C₅×D₃	D₄	semidirect
75. C₂³×C₅×D₃	C₂³	semidirect
76. C₂³×C₅×D₃	C₂³	semidirect
79. C₂×C₃×C₅×D₄	C₂³	semidirect
80. C₂×C₃×C₅×D₄	C₂³	semidirect
81. C₂²×C₃×C₄×C₅	C₂³	semidirect
82. C₂²×C₃×C₄×C₅	C₂³	semidirect
87. C₂×C₅×#67	C₂³	semidirect
88. C₂×C₅×#67	C₂³	semidirect
89. C₂×C₅×#67	C₂³	semidirect
90. C₂²×C₅×Dic₃	C₂³	semidirect
91. C₂²×C₅×Dic₃	C₂³	semidirect
99. C₂×C₅×D₁₂	C₂³	semidirect
100. C₂×C₅×D₁₂	C₂³	semidirect
105. C₂×C₄×C₅×D₃	C₂³	semidirect
106. C₂×C₄×C₅×D₃	C₂³	semidirect
107. C₃×C₅×C₄⋊C₄	C₂³	semidirect
108. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
110. C₅×#217	C₂³	semidirect
111. C₅×#217	C₂³	semidirect
112. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
113. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
114. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
115. C₅×C₄⋊Dic₃	C₂³	semidirect
116. C₅×Dic₃⋊C₄	C₂³	semidirect
117. C₂²×D₃×D₄	C₂×C₅	semidirect
118. C₃×#534	C₂×C₅	semidirect
119. #5804	C₂×C₅	semidirect
120. #5653	C₂×C₅	semidirect
121. D₃×#123	C₂×C₅	semidirect
122. #5605	C₂×C₅	semidirect
123. D₃×#121	C₂×C₅	semidirect
124. #5589	C₂×C₅	semidirect
125. D₃×#120	C₂×C₅	semidirect
126. #5493	C₂×C₅	semidirect
127. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
139. C₂²×C₅×D₄	C₂×D₃	semidirect
147. C₅×#123	C₂×D₃	semidirect
153. C₅×#121	C₂×D₃	semidirect
159. C₅×#120	C₂×D₃	semidirect
166. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
171. C₂³×C₃×C₅	C₂×D₄	semidirect
189. C₂²×C₅×D₃	C₂×D₄	semidirect
190. C₂²×C₅×D₃	C₂×D₄	semidirect
219. C₂⁴×D₃	C₂²×C₅	semidirect
220. C₂²×C₃×D₄	C₂²×C₅	semidirect
221. C₂²×#67	C₂²×C₅	semidirect
222. C₂²×#67	C₂²×C₅	semidirect
225. C₂×D₃×D₄	C₂²×C₅	semidirect
226. C₂×D₃×D₄	C₂²×C₅	semidirect
227. C₂×D₃×D₄	C₂²×C₅	semidirect
228. C₂×D₃×D₄	C₂²×C₅	semidirect
229. C₂²×D₁₂	C₂²×C₅	semidirect
230. C₂²×C₄×D₃	C₂²×C₅	semidirect
231. C₂²×C₄×D₃	C₂²×C₅	semidirect
232. C₃×#123	C₂²×C₅	semidirect
233. C₃×#121	C₂²×C₅	semidirect
234. C₃×#120	C₂²×C₅	semidirect
235. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
236. #953	C₂²×C₅	semidirect
237. C₂×#217	C₂²×C₅	semidirect
238. #939	C₂²×C₅	semidirect
239. #938	C₂²×C₅	semidirect
240. #937	C₂²×C₅	semidirect
241. #937	C₂²×C₅	semidirect
242. #935	C₂²×C₅	semidirect
243. #930	C₂²×C₅	semidirect
244. #929	C₂²×C₅	semidirect
245. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
246. #895	C₂²×C₅	semidirect
247. #894	C₂²×C₅	semidirect
248. D₃×C₄⋊C₄	C₂²×C₅	semidirect
249. #886	C₂²×C₅	semidirect
250. #884	C₂²×C₅	semidirect
251. #883	C₂²×C₅	semidirect
252. #882	C₂²×C₅	semidirect
253. #882	C₂²×C₅	semidirect
254. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
255. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
256. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
269. C₂⁴×C₅	C₂²×D₃	semidirect
288. C₂×C₅×D₄	C₂²×D₃	semidirect
289. C₂×C₅×D₄	C₂²×D₃	semidirect
298. C₂²×C₄×C₅	C₂²×D₃	semidirect
299. C₂²×C₄×C₅	C₂²×D₃	semidirect
302. C₅×C₄⋊C₄	C₂²×D₃	semidirect
308. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
309. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
316. #534	C₅×D₃	direct (N × H)
350. C₂⁴×C₃	C₂³×C₅	semidirect
354. C₂³×D₃	C₅×D₄	semidirect
360. C₂³×D₃	C₂³×C₅	semidirect
361. C₂³×D₃	C₂³×C₅	semidirect
364. C₂×C₃×D₄	C₂³×C₅	semidirect
365. C₂×C₃×D₄	C₂³×C₅	semidirect
366. C₂²×C₃×C₄	C₂³×C₅	semidirect
367. C₂²×C₃×C₄	C₂³×C₅	semidirect
372. C₂×#67	C₂³×C₅	semidirect
373. C₂×#67	C₂³×C₅	semidirect
374. C₂×#67	C₂³×C₅	semidirect
375. C₂²×Dic₃	C₂³×C₅	semidirect
376. C₂²×Dic₃	C₂³×C₅	semidirect
384. C₂×D₁₂	C₂³×C₅	semidirect
385. C₂×D₁₂	C₂³×C₅	semidirect
390. C₂×C₄×D₃	C₂³×C₅	semidirect
391. C₂×C₄×D₃	C₂³×C₅	semidirect
392. C₃×C₄⋊C₄	C₂³×C₅	semidirect
393. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
394. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
395. #217	C₂³×C₅	semidirect
396. #217	C₂³×C₅	semidirect
397. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
398. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
399. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
400. C₄⋊Dic₃	C₂³×C₅	semidirect
401. Dic₃⋊C₄	C₂³×C₅	semidirect
425. C₂³×C₅	D₃×D₄	semidirect
463. C₂²×D₄	C₂×C₅×D₃	semidirect
471. #123	C₂×C₅×D₃	semidirect
477. #121	C₂×C₅×D₃	semidirect
483. #120	C₂×C₅×D₃	semidirect
490. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
499. C₅×D₃	#534	direct (N × H)
503. C₂³×C₃	C₂×C₅×D₄	semidirect
521. C₂²×D₃	C₂×C₅×D₄	semidirect
522. C₂²×D₃	C₂×C₅×D₄	semidirect
590. C₂⁴	C₂²×C₅×D₃	semidirect
609. C₂×D₄	C₂²×C₅×D₃	semidirect
610. C₂×D₄	C₂²×C₅×D₃	semidirect
619. C₂²×C₄	C₂²×C₅×D₃	semidirect
620. C₂²×C₄	C₂²×C₅×D₃	semidirect
623. C₄⋊C₄	C₂²×C₅×D₃	semidirect
629. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
630. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
631. C₃×C₅	C₂×#534	semidirect
692. C₂³	C₅×D₃×D₄	semidirect
727. D₃	C₅×#534	direct (N × H)
728. C₅	D₃×#534	direct (N × H)
757. C₃	C₂×C₅×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₃×D₄	2
C₃×C₅×#534	2
C₅×#5804	2
C₅×#5653	2
C₅×D₃×#123	2
C₅×#5605	2
C₅×D₃×#121	2
C₅×#5589	2
C₅×D₃×#120	2
C₅×#5493	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#534	3
D₃×#534	5

Subgroups — C5×D3×#534 #14480287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#534 #14480287