Subgroups — C₂×C₅×#5589 #14480296

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	C₂³×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5589	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#883	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#534	—	3	1	no	maximal, Hall
14	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic, complemented
15	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
19	C₂²×C₅×#67	—	2	8	no	—
20	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	2	yes	—
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₅×#67	C₂²	1	2	yes	complemented
24	C₂²×C₅×#67	C₂²	1	2	yes	complemented
25	C₂²×C₅×#67	C₂²	1	8	yes	complemented
26	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×D₃×D₄	—	2	8	no	—
28	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
29	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
32	C₃×C₅×#120	C₂²	1	8	yes	complemented
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₅×#953	C₂²	1	8	yes	complemented
36	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#217	C₂²	1	2	yes	complemented
38	C₂×C₅×#217	C₂²	1	2	yes	complemented
39	C₅×#938	C₂²	1	16	yes	complemented
40	C₅×#937	C₂²	1	16	yes	complemented
41	C₅×#935	C₂²	1	8	yes	complemented
42	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
43	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
46	C₅×#886	C₂²	1	8	yes	complemented
47	C₅×#884	C₂²	1	16	yes	complemented
48	C₅×#883	C₂²	1	16	yes	complemented
49	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₂×#5589	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂³×C₅×D₄	—	3	1	no	—
52	C₂³×C₅×D₄	—	3	1	no	—
53	C₅×#534	—	3	16	no	—
54	C₂×C₅×#123	—	3	1	no	—
55	C₂×C₅×#123	—	3	2	no	—
56	C₂×C₅×#123	—	3	1	no	—
57	C₂×C₅×#121	—	3	2	no	—
58	C₂×C₅×#121	—	3	2	no	—
59	C₂×C₅×#120	—	3	1	no	—
60	C₂×C₅×#120	—	3	2	no	—
61	C₂×C₅×#120	D₃	1	1	yes	characteristic, complemented
62	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
63	C₂⁴×C₃×C₅	—	2	4	no	—
64	C₂⁴×C₃×C₅	—	4	4	no	—
65	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
66	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
67	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
68	C₂⁴×C₃×C₅	C₂³	1	4	yes	complemented
69	C₂³×C₅×D₃	—	2	4	no	—
70	C₂³×C₅×D₃	—	4	4	no	—
71	C₂³×C₅×D₃	—	4	4	no	—
72	C₂³×C₅×D₃	D₄	1	8	yes	complemented
73	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
76	C₂³×C₅×D₃	C₂³	1	4	yes	—
77	C₂³×C₅×D₃	C₂³	1	4	yes	complemented
78	C₂×C₃×C₅×D₄	—	2	4	no	—
79	C₂×C₃×C₅×D₄	—	4	4	no	—
80	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
81	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
84	C₂×C₅×#67	—	2	4	no	—
85	C₂×C₅×#67	—	2	4	no	—
86	C₂×C₅×#67	—	2	8	no	—
87	C₂×C₅×#67	—	2	8	no	—
88	C₂×C₅×#67	—	2	32	no	—
89	C₂×C₅×#67	—	4	4	no	—
90	C₂×C₅×#67	C₂³	1	8	yes	—
91	C₂×C₅×#67	C₂³	1	4	yes	—
92	C₂×C₅×#67	C₂³	1	8	yes	complemented
93	C₂×C₅×#67	C₂³	1	4	yes	complemented
94	C₂×C₅×#67	C₂³	1	8	yes	complemented
95	C₂²×C₅×Dic₃	—	2	4	no	—
96	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
97	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
98	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
100	C₅×D₃×D₄	—	2	32	no	—
101	C₂×C₅×D₁₂	—	2	4	no	—
102	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
103	C₂×C₄×C₅×D₃	—	2	4	no	—
104	C₂×C₄×C₅×D₃	—	4	4	no	—
105	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
106	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
107	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
108	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
109	C₅×#217	C₂³	1	4	yes	complemented
110	C₅×#217	C₂³	1	8	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×C₄⋊Dic₃	C₂³	1	8	yes	complemented
115	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
116	C₂³×#67	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#953	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#938	C₂×C₅	1	2	yes	complemented
121	C₂×#937	C₂×C₅	1	2	yes	complemented
122	C₂×#935	C₂×C₅	1	1	yes	characteristic, complemented
123	#5589	C₂×C₅	1	16	yes	direct product factor
124	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂×#884	C₂×C₅	1	2	yes	complemented
126	C₂×#883	C₂×C₅	1	2	yes	complemented
127	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
128	C₂⁵×C₅	—	3	1	no	—
129	C₂⁵×C₅	—	3	1	no	—
130	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic, complemented
131	C₂²×C₅×D₄	—	3	2	no	—
132	C₂²×C₅×D₄	—	3	1	no	—
133	C₂²×C₅×D₄	—	3	1	no	—
134	C₂²×C₅×D₄	—	3	2	no	—
135	C₂²×C₅×D₄	—	3	8	no	—
136	C₂²×C₅×D₄	—	3	2	no	—
137	C₂²×C₅×D₄	—	3	8	no	—
138	C₂²×C₅×D₄	—	3	1	no	—
139	C₂²×C₅×D₄	—	6	8	no	—
140	C₂²×C₅×D₄	—	6	8	no	—
141	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
142	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
143	C₂³×C₄×C₅	—	3	1	no	—
144	C₂³×C₄×C₅	—	3	1	no	—
145	C₂³×C₄×C₅	—	3	2	no	—
146	C₅×#123	—	3	8	no	—
147	C₅×#123	—	3	16	no	—
148	C₅×#123	—	3	8	no	—
149	C₅×#121	—	3	16	no	—
150	C₅×#121	—	3	16	no	—
151	C₅×#120	—	3	8	no	—
152	C₅×#120	—	3	16	no	—
153	C₅×#120	C₂×D₃	1	8	yes	complemented
154	C₂×C₅×C₄⋊C₄	—	3	2	no	—
155	C₂×C₅×C₄⋊C₄	—	3	2	no	—
156	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
157	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
158	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
159	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
160	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
161	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
162	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
163	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
164	C₂×#534	—	3	1	no	Sylow
165	C₂³×C₃×C₅	—	2	4	no	—
166	C₂³×C₃×C₅	—	2	4	no	—
167	C₂³×C₃×C₅	—	2	8	no	—
168	C₂³×C₃×C₅	—	2	2	no	—
169	C₂³×C₃×C₅	—	2	4	no	—
170	C₂³×C₃×C₅	—	2	4	no	—
171	C₂³×C₃×C₅	—	2	4	no	—
172	C₂³×C₃×C₅	—	4	8	no	—
173	C₂³×C₃×C₅	—	4	16	no	—
174	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
175	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
176	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
177	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
178	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₅×D₃	—	2	4	no	—
180	C₂²×C₅×D₃	—	2	4	no	—
181	C₂²×C₅×D₃	—	2	2	no	—
182	C₂²×C₅×D₃	—	2	4	no	—
183	C₂²×C₅×D₃	—	2	8	no	—
184	C₂²×C₅×D₃	—	4	16	no	—
185	C₂²×C₅×D₃	—	4	8	no	—
186	C₂²×C₅×D₃	—	4	8	no	—
187	C₂²×C₅×D₃	—	4	16	no	—
188	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
189	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
190	C₂²×C₅×D₃	C₂×D₄	1	16	yes	complemented
191	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
192	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
193	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
194	C₃×C₅×D₄	—	2	8	no	—
195	C₃×C₅×D₄	—	4	8	no	—
196	C₂×C₃×C₄×C₅	—	2	2	no	—
197	C₂×C₃×C₄×C₅	—	2	4	no	—
198	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
199	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
200	C₅×#67	—	2	8	no	—
201	C₅×#67	—	2	8	no	—
202	C₅×#67	—	2	16	no	—
203	C₅×#67	—	2	16	no	—
204	C₅×#67	—	4	8	no	—
205	C₂×C₅×Dic₃	—	2	2	no	—
206	C₂×C₅×Dic₃	—	2	4	no	—
207	C₂×C₅×Dic₃	—	2	8	no	—
208	C₂×C₅×Dic₃	—	2	4	no	—
209	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
210	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
211	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
212	C₅×D₁₂	—	2	8	no	—
213	C₄×C₅×D₃	—	2	8	no	—
214	C₄×C₅×D₃	—	4	8	no	—
215	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
217	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
218	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
219	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
220	C₂²×#67	—	2	8	no	—
221	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
222	C₂²×#67	C₂²×C₅	1	2	yes	—
223	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
224	C₂²×#67	C₂²×C₅	1	2	yes	complemented
225	C₂²×#67	C₂²×C₅	1	2	yes	complemented
226	C₂²×#67	C₂²×C₅	1	8	yes	complemented
227	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₂×D₃×D₄	—	2	8	no	—
229	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
230	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
231	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
232	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
233	C₃×#120	C₂²×C₅	1	8	yes	complemented
234	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
236	#953	C₂²×C₅	1	8	yes	complemented
237	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₂×#217	C₂²×C₅	1	2	yes	complemented
239	C₂×#217	C₂²×C₅	1	2	yes	complemented
240	#938	C₂²×C₅	1	16	yes	complemented
241	#937	C₂²×C₅	1	16	yes	complemented
242	#935	C₂²×C₅	1	8	yes	complemented
243	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
244	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
245	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
246	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
247	#886	C₂²×C₅	1	8	yes	complemented
248	#884	C₂²×C₅	1	16	yes	complemented
249	#883	C₂²×C₅	1	16	yes	complemented
250	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
251	C₂⁴×C₅	—	2	4	no	—
252	C₂⁴×C₅	—	3	1	no	—
253	C₂⁴×C₅	—	3	1	no	—
254	C₂⁴×C₅	—	3	8	no	—
255	C₂⁴×C₅	—	3	4	no	—
256	C₂⁴×C₅	—	3	1	no	—
257	C₂⁴×C₅	—	3	4	no	—
258	C₂⁴×C₅	—	4	4	no	—
259	C₂⁴×C₅	—	6	4	no	—
260	C₂⁴×C₅	—	12	4	no	—
261	C₂⁴×C₅	—	12	4	no	—
262	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
263	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
264	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
265	C₂⁴×C₅	C₂²×D₃	1	4	yes	complemented
266	C₂×C₅×D₄	—	2	4	no	—
267	C₂×C₅×D₄	—	3	8	no	—
268	C₂×C₅×D₄	—	3	4	no	—
269	C₂×C₅×D₄	—	3	4	no	—
270	C₂×C₅×D₄	—	3	8	no	—
271	C₂×C₅×D₄	—	3	8	no	—
272	C₂×C₅×D₄	—	3	4	no	—
273	C₂×C₅×D₄	—	4	4	no	—
274	C₂×C₅×D₄	—	6	4	no	—
275	C₂×C₅×D₄	—	6	32	no	—
276	C₂×C₅×D₄	—	6	4	no	—
277	C₂×C₅×D₄	—	6	8	no	—
278	C₂×C₅×D₄	—	6	8	no	—
279	C₂×C₅×D₄	—	6	32	no	—
280	C₂×C₅×D₄	—	6	4	no	—
281	C₂×C₅×D₄	—	12	4	no	—
282	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
283	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
284	C₂²×C₄×C₅	—	3	4	no	—
285	C₂²×C₄×C₅	—	3	2	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	2	no	—
288	C₂²×C₄×C₅	—	3	4	no	—
289	C₂²×C₄×C₅	—	3	8	no	—
290	C₂²×C₄×C₅	—	6	4	no	—
291	C₂²×C₄×C₅	—	6	4	no	—
292	C₂²×C₄×C₅	—	12	4	no	—
293	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
294	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
295	C₅×C₄⋊C₄	—	3	8	no	—
296	C₅×C₄⋊C₄	—	3	8	no	—
297	C₅×C₂²⋊C₄	—	3	4	no	—
298	C₅×C₂²⋊C₄	—	3	8	no	—
299	C₅×C₂²⋊C₄	—	3	8	no	—
300	C₅×C₂²⋊C₄	—	3	8	no	—
301	C₅×C₂²⋊C₄	—	3	8	no	—
302	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
303	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
304	C₂³×D₄	—	3	1	no	—
305	C₂³×D₄	—	3	1	no	—
306	#534	—	3	16	no	—
307	C₂×#123	—	3	1	no	—
308	C₂×#123	—	3	2	no	—
309	C₂×#123	—	3	1	no	—
310	C₂×#121	—	3	2	no	—
311	C₂×#121	—	3	2	no	—
312	C₂×#120	—	3	1	no	—
313	C₂×#120	—	3	2	no	—
314	C₂×#120	C₅×D₃	1	1	yes	characteristic, complemented
315	C₂²×C₂²⋊C₄	—	3	1	no	—
316	C₂²×C₃×C₅	—	2	8	no	—
317	C₂²×C₃×C₅	—	2	4	no	—
318	C₂²×C₃×C₅	—	2	4	no	—
319	C₂²×C₃×C₅	—	2	2	no	—
320	C₂²×C₃×C₅	—	2	4	no	—
321	C₂²×C₃×C₅	—	2	4	no	—
322	C₂²×C₃×C₅	—	2	4	no	—
323	C₂²×C₃×C₅	—	4	16	no	—
324	C₂²×C₃×C₅	—	4	4	no	—
325	C₂²×C₃×C₅	—	4	8	no	—
326	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
327	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
328	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
329	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
330	C₂×C₅×D₃	—	2	8	no	—
331	C₂×C₅×D₃	—	2	8	no	—
332	C₂×C₅×D₃	—	2	4	no	—
333	C₂×C₅×D₃	—	2	4	no	—
334	C₂×C₅×D₃	—	2	2	no	—
335	C₂×C₅×D₃	—	2	4	no	—
336	C₂×C₅×D₃	—	4	16	no	—
337	C₂×C₅×D₃	—	4	16	no	—
338	C₂×C₅×D₃	—	4	4	no	—
339	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
340	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
341	C₃×C₄×C₅	—	2	2	no	—
342	C₃×C₄×C₅	—	2	4	no	—
343	C₅×Dic₃	—	2	2	no	—
344	C₅×Dic₃	—	2	4	no	—
345	C₅×Dic₃	—	2	4	no	—
346	C₂⁴×C₃	—	2	4	no	—
347	C₂⁴×C₃	—	4	4	no	—
348	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
349	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
350	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
351	C₂⁴×C₃	C₂³×C₅	1	4	yes	complemented
352	C₂³×D₃	—	2	4	no	—
353	C₂³×D₃	—	4	4	no	—
354	C₂³×D₃	—	4	4	no	—
355	C₂³×D₃	C₅×D₄	1	8	yes	complemented
356	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
357	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
358	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
359	C₂³×D₃	C₂³×C₅	1	4	yes	—
360	C₂³×D₃	C₂³×C₅	1	4	yes	complemented
361	C₂×C₃×D₄	—	2	4	no	—
362	C₂×C₃×D₄	—	4	4	no	—
363	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
364	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
365	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
367	C₂×#67	—	2	4	no	—
368	C₂×#67	—	2	4	no	—
369	C₂×#67	—	2	8	no	—
370	C₂×#67	—	2	8	no	—
371	C₂×#67	—	2	32	no	—
372	C₂×#67	—	4	4	no	—
373	C₂×#67	C₂³×C₅	1	8	yes	—
374	C₂×#67	C₂³×C₅	1	4	yes	—
375	C₂×#67	C₂³×C₅	1	8	yes	complemented
376	C₂×#67	C₂³×C₅	1	4	yes	complemented
377	C₂×#67	C₂³×C₅	1	8	yes	complemented
378	C₂²×Dic₃	—	2	4	no	—
379	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
380	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
381	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
382	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
383	D₃×D₄	—	2	32	no	—
384	C₂×D₁₂	—	2	4	no	—
385	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
386	C₂×C₄×D₃	—	2	4	no	—
387	C₂×C₄×D₃	—	4	4	no	—
388	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
389	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
390	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
391	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
392	#217	C₂³×C₅	1	4	yes	complemented
393	#217	C₂³×C₅	1	8	yes	complemented
394	#217	C₂³×C₅	1	8	yes	complemented
395	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
396	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
397	C₄⋊Dic₃	C₂³×C₅	1	8	yes	complemented
398	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
399	C₂³×C₅	—	2	4	no	—
400	C₂³×C₅	—	2	2	no	—
401	C₂³×C₅	—	2	4	no	—
402	C₂³×C₅	—	2	8	no	—
403	C₂³×C₅	—	2	4	no	—
404	C₂³×C₅	—	2	4	no	—
405	C₂³×C₅	—	2	4	no	—
406	C₂³×C₅	—	3	4	no	—
407	C₂³×C₅	—	3	4	no	—
408	C₂³×C₅	—	3	2	no	—
409	C₂³×C₅	—	3	2	no	—
410	C₂³×C₅	—	3	16	no	—
411	C₂³×C₅	—	3	2	no	—
412	C₂³×C₅	—	4	8	no	—
413	C₂³×C₅	—	4	16	no	—
414	C₂³×C₅	—	6	8	no	—
415	C₂³×C₅	—	6	4	no	—
416	C₂³×C₅	—	6	4	no	—
417	C₂³×C₅	—	6	2	no	—
418	C₂³×C₅	—	6	4	no	—
419	C₂³×C₅	—	12	8	no	—
420	C₂³×C₅	—	12	16	no	—
421	C₂³×C₅	—	12	8	no	—
422	C₂³×C₅	—	12	16	no	—
423	C₂³×C₅	D₃×D₄	1	4	yes	—
424	C₂³×C₅	C₂³×D₃	1	2	yes	—
425	C₂³×C₅	C₂³×D₃	1	4	yes	—
426	C₂³×C₅	C₂³×D₃	1	2	yes	—
427	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
428	C₅×D₄	—	2	8	no	—
429	C₅×D₄	—	4	8	no	—
430	C₅×D₄	—	6	8	no	—
431	C₅×D₄	—	6	8	no	—
432	C₅×D₄	—	6	16	no	—
433	C₅×D₄	—	6	16	no	—
434	C₅×D₄	—	6	8	no	—
435	C₅×D₄	—	12	8	no	—
436	C₂×C₄×C₅	—	2	2	no	—
437	C₂×C₄×C₅	—	2	4	no	—
438	C₂×C₄×C₅	—	3	4	no	—
439	C₂×C₄×C₅	—	3	2	no	—
440	C₂×C₄×C₅	—	3	4	no	—
441	C₂×C₄×C₅	—	6	8	no	—
442	C₂×C₄×C₅	—	6	8	no	—
443	C₂×C₄×C₅	—	6	2	no	—
444	C₂×C₄×C₅	—	6	4	no	—
445	C₂×C₄×C₅	—	6	4	no	—
446	C₂×C₄×C₅	—	12	8	no	—
447	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
448	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
449	C₂⁵	—	3	1	no	—
450	C₂⁵	—	3	1	no	—
451	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic, complemented
452	C₂²×D₄	—	3	2	no	—
453	C₂²×D₄	—	3	1	no	—
454	C₂²×D₄	—	3	1	no	—
455	C₂²×D₄	—	3	2	no	—
456	C₂²×D₄	—	3	8	no	—
457	C₂²×D₄	—	3	2	no	—
458	C₂²×D₄	—	3	8	no	—
459	C₂²×D₄	—	3	1	no	—
460	C₂²×D₄	—	6	8	no	—
461	C₂²×D₄	—	6	8	no	—
462	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
463	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
464	C₂³×C₄	—	3	1	no	—
465	C₂³×C₄	—	3	1	no	—
466	C₂³×C₄	—	3	2	no	—
467	#123	—	3	8	no	—
468	#123	—	3	16	no	—
469	#123	—	3	8	no	—
470	#121	—	3	16	no	—
471	#121	—	3	16	no	—
472	#120	—	3	8	no	—
473	#120	—	3	16	no	—
474	#120	C₂×C₅×D₃	1	8	yes	complemented
475	C₂×C₄⋊C₄	—	3	2	no	—
476	C₂×C₄⋊C₄	—	3	2	no	—
477	C₂×C₂²⋊C₄	—	3	1	no	—
478	C₂×C₂²⋊C₄	—	3	2	no	—
479	C₂×C₂²⋊C₄	—	3	2	no	—
480	C₂×C₂²⋊C₄	—	3	2	no	—
481	C₂×C₂²⋊C₄	—	3	2	no	—
482	C₂×C₂²⋊C₄	—	3	8	no	—
483	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
484	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
485	C₂×C₃×C₅	—	2	4	no	—
486	C₂×C₃×C₅	—	4	2	no	—
487	C₂×C₃×C₅	—	4	4	no	—
488	C₂×C₃×C₅	#534	1	4	yes	complemented
489	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
490	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
491	C₅×D₃	—	2	4	no	—
492	C₅×D₃	—	2	4	no	—
493	C₅×D₃	—	4	2	no	—
494	C₂³×C₃	—	2	4	no	—
495	C₂³×C₃	—	2	4	no	—
496	C₂³×C₃	—	2	8	no	—
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	4	no	—
499	C₂³×C₃	—	2	4	no	—
500	C₂³×C₃	—	2	4	no	—
501	C₂³×C₃	—	4	8	no	—
502	C₂³×C₃	—	4	16	no	—
503	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
504	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
505	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
506	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
507	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
508	C₂²×D₃	—	2	4	no	—
509	C₂²×D₃	—	2	4	no	—
510	C₂²×D₃	—	2	2	no	—
511	C₂²×D₃	—	2	4	no	—
512	C₂²×D₃	—	2	8	no	—
513	C₂²×D₃	—	4	16	no	—
514	C₂²×D₃	—	4	8	no	—
515	C₂²×D₃	—	4	8	no	—
516	C₂²×D₃	—	4	16	no	—
517	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
518	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
519	C₂²×D₃	C₂×C₅×D₄	1	16	yes	complemented
520	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
521	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
522	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
523	C₃×D₄	—	2	8	no	—
524	C₃×D₄	—	4	8	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	2	4	no	—
527	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
528	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
529	#67	—	2	8	no	—
530	#67	—	2	8	no	—
531	#67	—	2	16	no	—
532	#67	—	2	16	no	—
533	#67	—	4	8	no	—
534	C₂×Dic₃	—	2	2	no	—
535	C₂×Dic₃	—	2	4	no	—
536	C₂×Dic₃	—	2	8	no	—
537	C₂×Dic₃	—	2	4	no	—
538	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
539	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
540	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
541	D₁₂	—	2	8	no	—
542	C₄×D₃	—	2	8	no	—
543	C₄×D₃	—	4	8	no	—
544	C₂²×C₅	—	2	4	no	—
545	C₂²×C₅	—	2	8	no	—
546	C₂²×C₅	—	2	2	no	—
547	C₂²×C₅	—	2	4	no	—
548	C₂²×C₅	—	2	4	no	—
549	C₂²×C₅	—	2	4	no	—
550	C₂²×C₅	—	2	4	no	—
551	C₂²×C₅	—	3	4	no	—
552	C₂²×C₅	—	3	4	no	—
553	C₂²×C₅	—	4	16	no	—
554	C₂²×C₅	—	4	8	no	—
555	C₂²×C₅	—	4	4	no	—
556	C₂²×C₅	—	6	4	no	—
557	C₂²×C₅	—	6	4	no	—
558	C₂²×C₅	—	6	8	no	—
559	C₂²×C₅	—	6	8	no	—
560	C₂²×C₅	—	6	2	no	—
561	C₂²×C₅	—	6	4	no	—
562	C₂²×C₅	—	12	16	no	—
563	C₂²×C₅	—	12	16	no	—
564	C₂²×C₅	—	12	4	no	—
565	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
566	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
567	C₂²×C₅	#1004	1	4	yes	—
568	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
569	C₄×C₅	—	2	2	no	—
570	C₄×C₅	—	2	4	no	—
571	C₄×C₅	—	6	2	no	—
572	C₄×C₅	—	6	4	no	—
573	C₄×C₅	—	6	4	no	—
574	C₂⁴	—	2	4	no	—
575	C₂⁴	—	3	1	no	—
576	C₂⁴	—	3	1	no	—
577	C₂⁴	—	3	8	no	—
578	C₂⁴	—	3	4	no	—
579	C₂⁴	—	3	1	no	—
580	C₂⁴	—	3	4	no	—
581	C₂⁴	—	4	4	no	—
582	C₂⁴	—	6	4	no	—
583	C₂⁴	—	12	4	no	—
584	C₂⁴	—	12	4	no	—
585	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
587	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
588	C₂⁴	C₂²×C₅×D₃	1	4	yes	complemented
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	3	8	no	—
591	C₂×D₄	—	3	4	no	—
592	C₂×D₄	—	3	4	no	—
593	C₂×D₄	—	3	8	no	—
594	C₂×D₄	—	3	8	no	—
595	C₂×D₄	—	3	4	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	6	4	no	—
598	C₂×D₄	—	6	32	no	—
599	C₂×D₄	—	6	4	no	—
600	C₂×D₄	—	6	8	no	—
601	C₂×D₄	—	6	8	no	—
602	C₂×D₄	—	6	32	no	—
603	C₂×D₄	—	6	4	no	—
604	C₂×D₄	—	12	4	no	—
605	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
606	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
607	C₂²×C₄	—	3	2	no	—
608	C₂²×C₄	—	3	1	no	—
609	C₂²×C₄	—	3	2	no	—
610	C₂²×C₄	—	3	4	no	—
611	C₂²×C₄	—	3	4	no	—
612	C₂²×C₄	—	3	8	no	—
613	C₂²×C₄	—	6	4	no	—
614	C₂²×C₄	—	6	4	no	—
615	C₂²×C₄	—	12	4	no	—
616	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
617	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
618	C₄⋊C₄	—	3	8	no	—
619	C₄⋊C₄	—	3	8	no	—
620	C₂²⋊C₄	—	3	4	no	—
621	C₂²⋊C₄	—	3	8	no	—
622	C₂²⋊C₄	—	3	8	no	—
623	C₂²⋊C₄	—	3	8	no	—
624	C₂²⋊C₄	—	3	8	no	—
625	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
626	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
627	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
628	C₂²×C₃	—	2	8	no	—
629	C₂²×C₃	—	2	4	no	—
630	C₂²×C₃	—	2	4	no	—
631	C₂²×C₃	—	2	2	no	—
632	C₂²×C₃	—	2	4	no	—
633	C₂²×C₃	—	2	4	no	—
634	C₂²×C₃	—	2	4	no	—
635	C₂²×C₃	—	4	16	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	C₅×H(5,𝔽₂)	1	4	yes	—
641	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
642	C₂×D₃	—	2	8	no	—
643	C₂×D₃	—	2	8	no	—
644	C₂×D₃	—	2	4	no	—
645	C₂×D₃	—	2	4	no	—
646	C₂×D₃	—	2	2	no	—
647	C₂×D₃	—	2	4	no	—
648	C₂×D₃	—	4	16	no	—
649	C₂×D₃	—	4	16	no	—
650	C₂×D₃	—	4	4	no	—
651	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
652	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
653	C₃×C₄	—	2	2	no	—
654	C₃×C₄	—	2	4	no	—
655	Dic₃	—	2	2	no	—
656	Dic₃	—	2	4	no	—
657	Dic₃	—	2	4	no	—
658	C₂×C₅	—	2	4	no	—
659	C₂×C₅	—	4	4	no	—
660	C₂×C₅	—	4	2	no	—
661	C₂×C₅	—	6	4	no	—
662	C₂×C₅	—	6	4	no	—
663	C₂×C₅	—	12	2	no	—
664	C₂×C₅	#5589	1	4	yes	direct product factor
665	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
666	C₂×C₅	C₂×#1004	1	2	yes	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	3	4	no	—
675	C₂³	—	3	4	no	—
676	C₂³	—	3	2	no	—
677	C₂³	—	3	2	no	—
678	C₂³	—	3	16	no	—
679	C₂³	—	3	2	no	—
680	C₂³	—	4	8	no	—
681	C₂³	—	4	16	no	—
682	C₂³	—	6	8	no	—
683	C₂³	—	6	4	no	—
684	C₂³	—	6	4	no	—
685	C₂³	—	6	2	no	—
686	C₂³	—	6	4	no	—
687	C₂³	—	12	8	no	—
688	C₂³	—	12	16	no	—
689	C₂³	—	12	8	no	—
690	C₂³	—	12	16	no	—
691	C₂³	C₅×D₃×D₄	1	4	yes	—
692	C₂³	C₂³×C₅×D₃	1	2	yes	—
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	—	4	8	no	—
698	D₄	—	6	8	no	—
699	D₄	—	6	8	no	—
700	D₄	—	6	16	no	—
701	D₄	—	6	16	no	—
702	D₄	—	6	8	no	—
703	D₄	—	12	8	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	3	4	no	—
707	C₂×C₄	—	3	2	no	—
708	C₂×C₄	—	3	4	no	—
709	C₂×C₄	—	6	8	no	—
710	C₂×C₄	—	6	8	no	—
711	C₂×C₄	—	6	2	no	—
712	C₂×C₄	—	6	4	no	—
713	C₂×C₄	—	6	4	no	—
714	C₂×C₄	—	12	8	no	—
715	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
716	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
717	C₂×C₃	—	2	4	no	—
718	C₂×C₃	—	4	2	no	—
719	C₂×C₃	—	4	4	no	—
720	C₂×C₃	C₅×#534	1	4	yes	complemented
721	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
722	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
723	D₃	—	2	4	no	—
724	D₃	—	2	4	no	—
725	D₃	—	4	2	no	—
726	C₅	C₂×#5589	1	1	yes	characteristic, direct product factor, Sylow
727	C₂²	—	2	4	no	—
728	C₂²	—	2	8	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	3	4	no	—
735	C₂²	—	3	4	no	—
736	C₂²	—	4	16	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	6	4	no	—
740	C₂²	—	6	4	no	—
741	C₂²	—	6	8	no	—
742	C₂²	—	6	8	no	—
743	C₂²	—	6	2	no	—
744	C₂²	—	6	4	no	—
745	C₂²	—	12	16	no	—
746	C₂²	—	12	16	no	—
747	C₂²	—	12	4	no	—
748	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
749	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
750	C₂²	C₅×#1004	1	4	yes	—
751	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
752	C₄	—	2	2	no	—
753	C₄	—	2	4	no	—
754	C₄	—	6	2	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	—	4	4	no	—
760	C₂	—	4	2	no	—
761	C₂	—	6	4	no	—
762	C₂	—	6	4	no	—
763	C₂	—	12	2	no	—
764	C₂	C₅×#5589	1	4	yes	direct product factor
765	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
766	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×#120	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#120	D₃
hypocenter	C₃	C₂×C₅×#534
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×#67	C₂	semidirect
2. C₂²×C₅×D₃×D₄	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₅×#953	C₂	semidirect
5. C₂×C₅×#938	C₂	semidirect
6. C₂×C₅×#937	C₂	semidirect
7. C₂×C₅×#935	C₂	semidirect
8. C₅×#5589	C₂	direct (N × H)
9. C₂×C₅×#886	C₂	semidirect
10. C₂×C₅×#884	C₂	semidirect
11. C₂×C₅×#883	C₂	semidirect
12. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂⁵×C₃×C₅	C₂²	semidirect
16. C₂⁴×C₅×D₃	C₂²	semidirect
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂²×C₅×#67	C₂²	semidirect
23. C₂²×C₅×#67	C₂²	semidirect
24. C₂²×C₅×#67	C₂²	semidirect
25. C₂²×C₅×#67	C₂²	semidirect
26. C₂³×C₅×Dic₃	C₂²	semidirect
28. C₂×C₅×D₃×D₄	C₂²	semidirect
29. C₂²×C₅×D₁₂	C₂²	semidirect
30. C₂²×C₄×C₅×D₃	C₂²	semidirect
31. C₂²×C₄×C₅×D₃	C₂²	semidirect
32. C₃×C₅×#120	C₂²	semidirect
33. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₅×#953	C₂²	semidirect
36. C₂×C₅×#217	C₂²	semidirect
37. C₂×C₅×#217	C₂²	semidirect
38. C₂×C₅×#217	C₂²	semidirect
39. C₅×#938	C₂²	semidirect
40. C₅×#937	C₂²	semidirect
41. C₅×#935	C₂²	semidirect
42. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
43. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
45. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
46. C₅×#886	C₂²	semidirect
47. C₅×#884	C₂²	semidirect
48. C₅×#883	C₂²	semidirect
49. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
50. C₂×#5589	C₅	direct (N × H)
61. C₂×C₅×#120	D₃	semidirect
68. C₂⁴×C₃×C₅	C₂³	semidirect
72. C₂³×C₅×D₃	D₄	semidirect
77. C₂³×C₅×D₃	C₂³	semidirect
81. C₂×C₃×C₅×D₄	C₂³	semidirect
92. C₂×C₅×#67	C₂³	semidirect
93. C₂×C₅×#67	C₂³	semidirect
94. C₂×C₅×#67	C₂³	semidirect
99. C₂²×C₅×Dic₃	C₂³	semidirect
102. C₂×C₅×D₁₂	C₂³	semidirect
105. C₂×C₄×C₅×D₃	C₂³	semidirect
106. C₂×C₄×C₅×D₃	C₂³	semidirect
107. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
108. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
109. C₅×#217	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×C₄⋊Dic₃	C₂³	semidirect
115. C₅×Dic₃⋊C₄	C₂³	semidirect
116. C₂³×#67	C₂×C₅	semidirect
117. C₂²×D₃×D₄	C₂×C₅	semidirect
118. C₂×C₃×#120	C₂×C₅	semidirect
119. C₂×#953	C₂×C₅	semidirect
120. C₂×#938	C₂×C₅	semidirect
121. C₂×#937	C₂×C₅	semidirect
122. C₂×#935	C₂×C₅	semidirect
123. #5589	C₂×C₅	direct (N × H)
124. C₂×#886	C₂×C₅	semidirect
125. C₂×#884	C₂×C₅	semidirect
126. C₂×#883	C₂×C₅	semidirect
127. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
130. C₂⁵×C₅	C₂×D₃	semidirect
142. C₂²×C₅×D₄	C₂×D₃	semidirect
153. C₅×#120	C₂×D₃	semidirect
162. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
163. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
190. C₂²×C₅×D₃	C₂×D₄	semidirect
215. C₂⁵×C₃	C₂²×C₅	semidirect
217. C₂⁴×D₃	C₂²×C₅	semidirect
219. C₂²×C₃×D₄	C₂²×C₅	semidirect
223. C₂²×#67	C₂²×C₅	semidirect
224. C₂²×#67	C₂²×C₅	semidirect
225. C₂²×#67	C₂²×C₅	semidirect
226. C₂²×#67	C₂²×C₅	semidirect
227. C₂³×Dic₃	C₂²×C₅	semidirect
229. C₂×D₃×D₄	C₂²×C₅	semidirect
230. C₂²×D₁₂	C₂²×C₅	semidirect
231. C₂²×C₄×D₃	C₂²×C₅	semidirect
232. C₂²×C₄×D₃	C₂²×C₅	semidirect
233. C₃×#120	C₂²×C₅	semidirect
234. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
235. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
236. #953	C₂²×C₅	semidirect
237. C₂×#217	C₂²×C₅	semidirect
238. C₂×#217	C₂²×C₅	semidirect
239. C₂×#217	C₂²×C₅	semidirect
240. #938	C₂²×C₅	semidirect
241. #937	C₂²×C₅	semidirect
242. #935	C₂²×C₅	semidirect
243. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
244. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
245. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
246. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
247. #886	C₂²×C₅	semidirect
248. #884	C₂²×C₅	semidirect
249. #883	C₂²×C₅	semidirect
250. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
265. C₂⁴×C₅	C₂²×D₃	semidirect
283. C₂×C₅×D₄	C₂²×D₃	semidirect
302. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
303. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
314. C₂×#120	C₅×D₃	semidirect
351. C₂⁴×C₃	C₂³×C₅	semidirect
355. C₂³×D₃	C₅×D₄	semidirect
360. C₂³×D₃	C₂³×C₅	semidirect
364. C₂×C₃×D₄	C₂³×C₅	semidirect
375. C₂×#67	C₂³×C₅	semidirect
376. C₂×#67	C₂³×C₅	semidirect
377. C₂×#67	C₂³×C₅	semidirect
382. C₂²×Dic₃	C₂³×C₅	semidirect
385. C₂×D₁₂	C₂³×C₅	semidirect
388. C₂×C₄×D₃	C₂³×C₅	semidirect
389. C₂×C₄×D₃	C₂³×C₅	semidirect
390. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
391. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
392. #217	C₂³×C₅	semidirect
393. #217	C₂³×C₅	semidirect
394. #217	C₂³×C₅	semidirect
395. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
396. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
397. C₄⋊Dic₃	C₂³×C₅	semidirect
398. Dic₃⋊C₄	C₂³×C₅	semidirect
451. C₂⁵	C₂×C₅×D₃	semidirect
463. C₂²×D₄	C₂×C₅×D₃	semidirect
474. #120	C₂×C₅×D₃	semidirect
483. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
484. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
488. C₂×C₃×C₅	#534	semidirect
519. C₂²×D₃	C₂×C₅×D₄	semidirect
588. C₂⁴	C₂²×C₅×D₃	semidirect
606. C₂×D₄	C₂²×C₅×D₃	semidirect
625. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
626. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
627. C₃×C₅	C₂×#534	semidirect
664. C₂×C₅	#5589	direct (N × H)
720. C₂×C₃	C₅×#534	semidirect
726. C₅	C₂×#5589	direct (N × H)
757. C₃	C₂×C₅×#534	semidirect
764. C₂	C₅×#5589	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×#67	2
C₂²×C₅×D₃×D₄	2
C₂×C₃×C₅×#120	2
C₂×C₅×#953	2
C₂×C₅×#938	2
C₂×C₅×#937	2
C₂×C₅×#935	2
C₅×#5589	2
C₂×C₅×#886	2
C₂×C₅×#884	2
C₂×C₅×#883	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#534	3
C₂×#5589	5

Subgroups — C2×C5×#5589 #14480296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5589 #14480296