Subgroups — C₂×C₅×#5806 #14482496

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#953	C₂	1	2	yes	maximal, complemented
4	C₂²×C₅×#217	C₂	1	2	yes	maximal, complemented
5	C₅×#5806	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#935	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#546	—	3	1	no	maximal, Hall
14	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	—	2	8	no	—
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂²×C₅×#67	C₂²	1	2	yes	complemented
23	C₂²×C₅×#67	C₂²	1	2	yes	complemented
24	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
25	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
26	C₂×C₅×#237	—	2	8	no	—
27	C₂×C₅×#237	C₂²	1	8	yes	complemented
28	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
30	C₅×#953	C₂²	1	16	yes	complemented
31	C₂×C₅×#217	C₂²	1	2	yes	—
32	C₂×C₅×#217	C₂²	1	1	yes	characteristic
33	C₂×C₅×#217	C₂²	1	16	yes	complemented
34	C₂×C₅×#217	C₂²	1	2	yes	complemented
35	C₂×C₅×#217	C₂²	1	2	yes	complemented
36	C₂×C₅×#217	C₂²	1	2	yes	complemented
37	C₂×C₅×#217	C₂²	1	2	yes	complemented
38	C₅×#939	C₂²	1	16	yes	complemented
39	C₅×#938	C₂²	1	8	yes	complemented
40	C₅×#936	C₂²	1	8	yes	complemented
41	C₅×#935	C₂²	1	16	yes	complemented
42	C₅×D₄×Dic₃	C₂²	1	8	yes	complemented
43	C₄×C₅×#67	C₂²	1	8	yes	complemented
44	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₅×#924	C₂²	1	8	yes	complemented
47	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
48	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#5806	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂²×C₅×#41	—	3	1	no	—
52	C₂³×C₅×D₄	D₃	1	1	yes	characteristic, complemented
53	C₅×#546	—	3	16	no	—
54	C₂×C₅×#124	—	3	1	no	—
55	C₂×C₅×#123	—	3	2	no	—
56	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
57	C₂×C₅×#121	—	3	1	no	—
58	C₂×C₅×#121	—	3	2	no	—
59	C₂×C₅×#120	—	3	2	no	—
60	C₂×C₄×C₅×D₄	—	3	1	no	—
61	C₂×C₄×C₅×D₄	—	3	1	no	—
62	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
63	C₂⁴×C₃×C₅	—	2	8	no	—
64	C₂⁴×C₃×C₅	—	2	8	no	—
65	C₂⁴×C₃×C₅	—	4	4	no	—
66	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
67	C₂⁴×C₃×C₅	C₂³	1	8	yes	—
68	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×D₄	—	2	8	no	—
72	C₂×C₃×C₅×D₄	—	2	32	no	—
73	C₂×C₃×C₅×D₄	—	2	4	no	—
74	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
75	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
76	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
77	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
78	C₂²×C₃×C₄×C₅	—	2	4	no	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	—	2	8	no	—
83	C₂×C₅×#67	—	2	4	no	—
84	C₂×C₅×#67	—	4	4	no	—
85	C₂×C₅×#67	C₂³	1	4	yes	—
86	C₂×C₅×#67	C₂³	1	8	yes	complemented
87	C₂×C₅×#67	C₂³	1	8	yes	complemented
88	C₂²×C₅×Dic₃	—	2	8	no	—
89	C₂²×C₅×Dic₃	—	4	4	no	—
90	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
93	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	8	yes	complemented
96	C₂²×C₅×Dic₃	C₂³	1	8	yes	complemented
97	C₅×#237	—	2	32	no	—
98	C₂×C₄×C₅×D₃	—	2	4	no	—
99	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
100	C₂×C₅×Dic₆	—	2	4	no	—
101	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
102	C₅×#217	C₂³	1	8	yes	—
103	C₅×#217	C₂³	1	4	yes	—
104	C₅×#217	C₂³	1	8	yes	complemented
105	C₅×#217	C₂³	1	8	yes	complemented
106	C₅×#217	C₂³	1	8	yes	complemented
107	C₅×#217	C₂³	1	8	yes	complemented
108	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
109	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
110	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
111	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
112	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
113	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂²×#237	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#953	C₂×C₅	1	2	yes	complemented
116	C₂²×#217	C₂×C₅	1	2	yes	complemented
117	#5806	C₂×C₅	1	16	yes	direct product factor
118	C₂×#939	C₂×C₅	1	2	yes	complemented
119	C₂×#938	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#936	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×#935	C₂×C₅	1	2	yes	complemented
122	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂⁵×C₅	C₂×D₃	1	2	yes	—
126	C₂×C₅×#41	—	3	8	no	—
127	C₂×C₅×#41	—	6	8	no	—
128	C₂²×C₅×Q₈	—	3	1	no	—
129	C₂²×C₅×D₄	—	2	8	no	—
130	C₂²×C₅×D₄	—	3	1	no	—
131	C₂²×C₅×D₄	—	3	2	no	—
132	C₂²×C₅×D₄	—	3	2	no	—
133	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
134	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
135	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
136	C₂²×C₅×D₄	C₂×D₃	1	8	yes	complemented
137	C₂³×C₄×C₅	—	3	2	no	—
138	C₂³×C₄×C₅	—	3	2	no	—
139	C₂³×C₄×C₅	—	3	1	no	—
140	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
141	C₅×#124	—	3	8	no	—
142	C₅×#123	—	3	16	no	—
143	C₅×C₂²⋊Q₈	—	3	8	no	—
144	C₅×#121	—	3	8	no	—
145	C₅×#121	—	3	16	no	—
146	C₅×#120	—	3	16	no	—
147	C₄×C₅×D₄	—	3	8	no	—
148	C₄×C₅×D₄	—	3	8	no	—
149	C₂×C₅×C₄⋊C₄	—	3	1	no	—
150	C₂×C₅×C₄⋊C₄	—	3	2	no	—
151	C₂×C₅×C₄⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
155	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
156	C₂×C₅×C₂²⋊C₄	—	3	16	no	—
157	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
158	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
159	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
160	C₂×C₄²×C₅	—	3	1	no	—
161	C₂×#546	—	3	1	no	Sylow
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂³×C₃×C₅	—	2	4	no	—
164	C₂³×C₃×C₅	—	2	4	no	—
165	C₂³×C₃×C₅	—	2	2	no	—
166	C₂³×C₃×C₅	—	2	16	no	—
167	C₂³×C₃×C₅	—	2	4	no	—
168	C₂³×C₃×C₅	—	2	4	no	—
169	C₂³×C₃×C₅	—	2	16	no	—
170	C₂³×C₃×C₅	—	2	4	no	—
171	C₂³×C₃×C₅	—	4	8	no	—
172	C₂³×C₃×C₅	—	4	32	no	—
173	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
174	C₂³×C₃×C₅	#41	1	4	yes	complemented
175	C₂³×C₃×C₅	C₂⁴	1	4	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	2	no	—
180	C₂²×C₅×D₃	—	2	2	no	—
181	C₂²×C₅×D₃	—	2	2	no	—
182	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
183	C₃×C₅×D₄	—	2	16	no	—
184	C₃×C₅×D₄	—	2	8	no	—
185	C₃×C₅×D₄	C₂×D₄	1	16	yes	complemented
186	C₂×C₃×C₄×C₅	—	2	2	no	—
187	C₂×C₃×C₄×C₅	—	2	8	no	—
188	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
189	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
190	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
191	C₅×#67	—	2	16	no	—
192	C₅×#67	—	2	8	no	—
193	C₅×#67	—	4	8	no	—
194	C₂×C₅×Dic₃	—	2	4	no	—
195	C₂×C₅×Dic₃	—	2	2	no	—
196	C₂×C₅×Dic₃	—	2	16	no	—
197	C₂×C₅×Dic₃	—	2	2	no	—
198	C₂×C₅×Dic₃	—	2	2	no	—
199	C₂×C₅×Dic₃	—	2	4	no	—
200	C₂×C₅×Dic₃	—	4	8	no	—
201	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
202	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
203	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
204	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
205	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
206	C₄×C₅×D₃	—	2	8	no	—
207	C₅×Dic₆	—	2	8	no	—
208	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
209	C₂²×C₃×D₄	—	2	8	no	—
210	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
211	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
212	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
213	C₂²×C₃×D₄	C₂²×C₅	1	8	yes	complemented
214	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
216	C₂²×#67	C₂²×C₅	1	2	yes	complemented
217	C₂²×#67	C₂²×C₅	1	2	yes	complemented
218	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
219	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
220	C₂×#237	—	2	8	no	—
221	C₂×#237	C₂²×C₅	1	8	yes	complemented
222	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
223	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
224	#953	C₂²×C₅	1	16	yes	complemented
225	C₂×#217	C₂²×C₅	1	2	yes	—
226	C₂×#217	C₂²×C₅	1	1	yes	characteristic
227	C₂×#217	C₂²×C₅	1	16	yes	complemented
228	C₂×#217	C₂²×C₅	1	2	yes	complemented
229	C₂×#217	C₂²×C₅	1	2	yes	complemented
230	C₂×#217	C₂²×C₅	1	2	yes	complemented
231	C₂×#217	C₂²×C₅	1	2	yes	complemented
232	#939	C₂²×C₅	1	16	yes	complemented
233	#938	C₂²×C₅	1	8	yes	complemented
234	#936	C₂²×C₅	1	8	yes	complemented
235	#935	C₂²×C₅	1	16	yes	complemented
236	D₄×Dic₃	C₂²×C₅	1	8	yes	complemented
237	C₄×#67	C₂²×C₅	1	8	yes	complemented
238	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
240	#924	C₂²×C₅	1	8	yes	complemented
241	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
242	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
244	C₂⁴×C₅	—	2	8	no	—
245	C₂⁴×C₅	—	2	8	no	—
246	C₂⁴×C₅	—	3	1	no	—
247	C₂⁴×C₅	—	4	4	no	—
248	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
249	C₂⁴×C₅	C₂²×D₃	1	8	yes	—
250	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
251	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
252	C₅×#41	—	6	32	no	—
253	C₂×C₅×Q₈	—	3	4	no	—
254	C₂×C₅×Q₈	—	6	4	no	—
255	C₂×C₅×D₄	—	2	8	no	—
256	C₂×C₅×D₄	—	2	32	no	—
257	C₂×C₅×D₄	—	2	4	no	—
258	C₂×C₅×D₄	—	3	4	no	—
259	C₂×C₅×D₄	—	3	8	no	—
260	C₂×C₅×D₄	—	3	8	no	—
261	C₂×C₅×D₄	—	6	4	no	—
262	C₂×C₅×D₄	—	6	8	no	—
263	C₂×C₅×D₄	—	12	4	no	—
264	C₂×C₅×D₄	#67	1	8	yes	complemented
265	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
266	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
267	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
268	C₂²×C₄×C₅	—	2	4	no	—
269	C₂²×C₄×C₅	—	3	8	no	—
270	C₂²×C₄×C₅	—	3	1	no	—
271	C₂²×C₄×C₅	—	3	1	no	—
272	C₂²×C₄×C₅	—	3	2	no	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	3	2	no	—
275	C₂²×C₄×C₅	—	3	8	no	—
276	C₂²×C₄×C₅	—	3	4	no	—
277	C₂²×C₄×C₅	—	6	8	no	—
278	C₂²×C₄×C₅	—	6	4	no	—
279	C₂²×C₄×C₅	—	12	4	no	—
280	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
281	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
283	C₅×C₄⋊C₄	—	3	4	no	—
284	C₅×C₄⋊C₄	—	3	4	no	—
285	C₅×C₄⋊C₄	—	3	8	no	—
286	C₅×C₂²⋊C₄	—	3	4	no	—
287	C₅×C₂²⋊C₄	—	3	8	no	—
288	C₅×C₂²⋊C₄	—	3	8	no	—
289	C₅×C₂²⋊C₄	—	3	8	no	—
290	C₅×C₂²⋊C₄	—	3	8	no	—
291	C₅×C₂²⋊C₄	—	3	8	no	—
292	C₅×C₂²⋊C₄	—	3	4	no	—
293	C₄²×C₅	—	3	4	no	—
294	C₂²×#41	—	3	1	no	—
295	C₂³×D₄	C₅×D₃	1	1	yes	characteristic, complemented
296	#546	—	3	16	no	—
297	C₂×#124	—	3	1	no	—
298	C₂×#123	—	3	2	no	—
299	C₂×C₂²⋊Q₈	—	3	1	no	—
300	C₂×#121	—	3	1	no	—
301	C₂×#121	—	3	2	no	—
302	C₂×#120	—	3	2	no	—
303	C₂×C₄×D₄	—	3	1	no	—
304	C₂×C₄×D₄	—	3	1	no	—
305	C₂²×C₂²⋊C₄	—	3	2	no	—
306	C₂²×C₃×C₅	—	2	8	no	—
307	C₂²×C₃×C₅	—	2	16	no	—
308	C₂²×C₃×C₅	—	2	2	no	—
309	C₂²×C₃×C₅	—	2	4	no	—
310	C₂²×C₃×C₅	—	2	4	no	—
311	C₂²×C₃×C₅	—	2	2	no	—
312	C₂²×C₃×C₅	—	2	4	no	—
313	C₂²×C₃×C₅	—	2	4	no	—
314	C₂²×C₃×C₅	—	2	4	no	—
315	C₂²×C₃×C₅	—	4	32	no	—
316	C₂²×C₃×C₅	—	4	8	no	—
317	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	—
318	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
319	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
320	C₂²×C₃×C₅	C₂×#41	1	4	yes	complemented
321	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
322	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
323	C₂×C₅×D₃	—	2	2	no	—
324	C₂×C₅×D₃	—	2	2	no	—
325	C₂×C₅×D₃	—	2	2	no	—
326	C₂×C₅×D₃	—	4	4	no	—
327	C₃×C₄×C₅	—	2	2	no	—
328	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
329	C₅×Dic₃	—	2	4	no	—
330	C₅×Dic₃	—	2	2	no	—
331	C₅×Dic₃	—	2	2	no	—
332	C₅×Dic₃	—	2	2	no	—
333	C₅×Dic₃	—	2	4	no	—
334	C₂⁴×C₃	—	2	8	no	—
335	C₂⁴×C₃	—	2	8	no	—
336	C₂⁴×C₃	—	4	4	no	—
337	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
338	C₂⁴×C₃	C₂³×C₅	1	8	yes	—
339	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
340	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
341	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₃×D₄	—	2	8	no	—
343	C₂×C₃×D₄	—	2	32	no	—
344	C₂×C₃×D₄	—	2	4	no	—
345	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
346	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
347	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
348	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
349	C₂²×C₃×C₄	—	2	4	no	—
350	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
352	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
353	C₂×#67	—	2	8	no	—
354	C₂×#67	—	2	4	no	—
355	C₂×#67	—	4	4	no	—
356	C₂×#67	C₂³×C₅	1	4	yes	—
357	C₂×#67	C₂³×C₅	1	8	yes	complemented
358	C₂×#67	C₂³×C₅	1	8	yes	complemented
359	C₂²×Dic₃	—	2	8	no	—
360	C₂²×Dic₃	—	4	4	no	—
361	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
362	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
363	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
364	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
365	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
366	C₂²×Dic₃	C₂³×C₅	1	8	yes	complemented
367	C₂²×Dic₃	C₂³×C₅	1	8	yes	complemented
368	#237	—	2	32	no	—
369	C₂×C₄×D₃	—	2	4	no	—
370	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
371	C₂×Dic₆	—	2	4	no	—
372	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
373	#217	C₂³×C₅	1	8	yes	—
374	#217	C₂³×C₅	1	4	yes	—
375	#217	C₂³×C₅	1	8	yes	complemented
376	#217	C₂³×C₅	1	8	yes	complemented
377	#217	C₂³×C₅	1	8	yes	complemented
378	#217	C₂³×C₅	1	8	yes	complemented
379	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
380	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
381	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
382	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
383	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
384	C₂³×C₅	—	2	4	no	—
385	C₂³×C₅	—	2	4	no	—
386	C₂³×C₅	—	2	2	no	—
387	C₂³×C₅	—	2	2	no	—
388	C₂³×C₅	—	2	4	no	—
389	C₂³×C₅	—	2	16	no	—
390	C₂³×C₅	—	2	4	no	—
391	C₂³×C₅	—	2	16	no	—
392	C₂³×C₅	—	2	4	no	—
393	C₂³×C₅	—	3	2	no	—
394	C₂³×C₅	—	4	8	no	—
395	C₂³×C₅	—	4	32	no	—
396	C₂³×C₅	—	6	2	no	—
397	C₂³×C₅	—	6	2	no	—
398	C₂³×C₅	—	6	2	no	—
399	C₂³×C₅	#237	1	4	yes	complemented
400	C₂³×C₅	C₂×#67	1	8	yes	—
401	C₂³×C₅	C₂³×D₃	1	4	yes	—
402	C₂³×C₅	C₂³×D₃	1	2	yes	—
403	C₂³×C₅	C₂³×D₃	1	4	yes	—
404	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
405	C₅×Q₈	—	6	8	no	—
406	C₅×D₄	—	2	16	no	—
407	C₅×D₄	—	2	8	no	—
408	C₅×D₄	—	6	8	no	—
409	C₅×D₄	—	6	16	no	—
410	C₅×D₄	—	12	8	no	—
411	C₅×D₄	C₂×#67	1	16	yes	complemented
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	—	2	8	no	—
414	C₂×C₄×C₅	—	3	2	no	—
415	C₂×C₄×C₅	—	3	2	no	—
416	C₂×C₄×C₅	—	3	4	no	—
417	C₂×C₄×C₅	—	3	2	no	—
418	C₂×C₄×C₅	—	3	4	no	—
419	C₂×C₄×C₅	—	6	2	no	—
420	C₂×C₄×C₅	—	6	2	no	—
421	C₂×C₄×C₅	—	6	4	no	—
422	C₂×C₄×C₅	—	6	2	no	—
423	C₂×C₄×C₅	—	6	4	no	—
424	C₂×C₄×C₅	—	6	16	no	—
425	C₂×C₄×C₅	—	6	8	no	—
426	C₂×C₄×C₅	—	12	8	no	—
427	C₂×C₄×C₅	C₂×#67	1	4	yes	—
428	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
429	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
430	C₂⁵	C₂×C₅×D₃	1	2	yes	—
431	C₂×#41	—	3	8	no	—
432	C₂×#41	—	6	8	no	—
433	C₂²×Q₈	—	3	1	no	—
434	C₂²×D₄	—	2	8	no	—
435	C₂²×D₄	—	3	1	no	—
436	C₂²×D₄	—	3	2	no	—
437	C₂²×D₄	—	3	2	no	—
438	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
439	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
440	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
441	C₂²×D₄	C₂×C₅×D₃	1	8	yes	complemented
442	C₂³×C₄	—	3	2	no	—
443	C₂³×C₄	—	3	2	no	—
444	C₂³×C₄	—	3	1	no	—
445	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
446	#124	—	3	8	no	—
447	#123	—	3	16	no	—
448	C₂²⋊Q₈	—	3	8	no	—
449	#121	—	3	8	no	—
450	#121	—	3	16	no	—
451	#120	—	3	16	no	—
452	C₄×D₄	—	3	8	no	—
453	C₄×D₄	—	3	8	no	—
454	C₂×C₄⋊C₄	—	3	1	no	—
455	C₂×C₄⋊C₄	—	3	1	no	—
456	C₂×C₄⋊C₄	—	3	2	no	—
457	C₂×C₂²⋊C₄	—	3	1	no	—
458	C₂×C₂²⋊C₄	—	3	2	no	—
459	C₂×C₂²⋊C₄	—	3	2	no	—
460	C₂×C₂²⋊C₄	—	3	2	no	—
461	C₂×C₂²⋊C₄	—	3	16	no	—
462	C₂×C₂²⋊C₄	—	3	2	no	—
463	C₂×C₂²⋊C₄	—	3	2	no	—
464	C₂×C₂²⋊C₄	—	3	1	no	—
465	C₂×C₄²	—	3	1	no	—
466	C₂×C₃×C₅	—	2	4	no	—
467	C₂×C₃×C₅	—	2	8	no	—
468	C₂×C₃×C₅	—	4	4	no	—
469	C₂×C₃×C₅	#546	1	4	yes	complemented
470	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
471	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
472	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₅×D₃	—	4	2	no	—
474	C₂³×C₃	—	2	2	no	—
475	C₂³×C₃	—	2	4	no	—
476	C₂³×C₃	—	2	4	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	16	no	—
479	C₂³×C₃	—	2	4	no	—
480	C₂³×C₃	—	2	4	no	—
481	C₂³×C₃	—	2	16	no	—
482	C₂³×C₃	—	2	4	no	—
483	C₂³×C₃	—	4	8	no	—
484	C₂³×C₃	—	4	32	no	—
485	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
486	C₂³×C₃	C₅×#41	1	4	yes	complemented
487	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
488	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
489	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
490	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
491	C₂²×D₃	—	2	2	no	—
492	C₂²×D₃	—	2	2	no	—
493	C₂²×D₃	—	2	2	no	—
494	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
495	C₃×D₄	—	2	16	no	—
496	C₃×D₄	—	2	8	no	—
497	C₃×D₄	C₂×C₅×D₄	1	16	yes	complemented
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	8	no	—
500	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
501	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
502	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
503	#67	—	2	16	no	—
504	#67	—	2	8	no	—
505	#67	—	4	8	no	—
506	C₂×Dic₃	—	2	4	no	—
507	C₂×Dic₃	—	2	2	no	—
508	C₂×Dic₃	—	2	16	no	—
509	C₂×Dic₃	—	2	2	no	—
510	C₂×Dic₃	—	2	2	no	—
511	C₂×Dic₃	—	2	4	no	—
512	C₂×Dic₃	—	4	8	no	—
513	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
514	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
515	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
516	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
517	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
518	C₄×D₃	—	2	8	no	—
519	Dic₆	—	2	8	no	—
520	C₂²×C₅	—	2	4	no	—
521	C₂²×C₅	—	2	4	no	—
522	C₂²×C₅	—	2	2	no	—
523	C₂²×C₅	—	2	2	no	—
524	C₂²×C₅	—	2	8	no	—
525	C₂²×C₅	—	2	16	no	—
526	C₂²×C₅	—	2	4	no	—
527	C₂²×C₅	—	2	4	no	—
528	C₂²×C₅	—	2	4	no	—
529	C₂²×C₅	—	4	32	no	—
530	C₂²×C₅	—	4	8	no	—
531	C₂²×C₅	—	6	2	no	—
532	C₂²×C₅	—	6	2	no	—
533	C₂²×C₅	—	6	2	no	—
534	C₂²×C₅	—	12	4	no	—
535	C₂²×C₅	C₂×#237	1	2	yes	—
536	C₂²×C₅	C₂×#237	1	4	yes	complemented
537	C₂²×C₅	#1004	1	2	yes	—
538	C₂²×C₅	C₂²×#67	1	8	yes	—
539	C₂²×C₅	C₂²×#67	1	2	yes	—
540	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
541	C₄×C₅	—	2	2	no	—
542	C₄×C₅	—	6	2	no	—
543	C₄×C₅	—	6	2	no	—
544	C₄×C₅	—	6	4	no	—
545	C₄×C₅	—	6	2	no	—
546	C₄×C₅	—	6	4	no	—
547	C₄×C₅	C₂²×#67	1	4	yes	—
548	C₂⁴	—	2	8	no	—
549	C₂⁴	—	2	8	no	—
550	C₂⁴	—	3	1	no	—
551	C₂⁴	—	4	4	no	—
552	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
553	C₂⁴	C₂²×C₅×D₃	1	8	yes	—
554	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
555	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
556	#41	—	6	32	no	—
557	C₂×Q₈	—	3	4	no	—
558	C₂×Q₈	—	6	4	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	32	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	3	4	no	—
563	C₂×D₄	—	3	8	no	—
564	C₂×D₄	—	3	8	no	—
565	C₂×D₄	—	6	4	no	—
566	C₂×D₄	—	6	8	no	—
567	C₂×D₄	—	12	4	no	—
568	C₂×D₄	C₅×#67	1	8	yes	complemented
569	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
570	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
571	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	3	1	no	—
574	C₂²×C₄	—	3	1	no	—
575	C₂²×C₄	—	3	2	no	—
576	C₂²×C₄	—	3	1	no	—
577	C₂²×C₄	—	3	2	no	—
578	C₂²×C₄	—	3	8	no	—
579	C₂²×C₄	—	3	8	no	—
580	C₂²×C₄	—	3	4	no	—
581	C₂²×C₄	—	6	8	no	—
582	C₂²×C₄	—	6	4	no	—
583	C₂²×C₄	—	12	4	no	—
584	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
585	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
586	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₄⋊C₄	—	3	4	no	—
588	C₄⋊C₄	—	3	4	no	—
589	C₄⋊C₄	—	3	8	no	—
590	C₂²⋊C₄	—	3	4	no	—
591	C₂²⋊C₄	—	3	8	no	—
592	C₂²⋊C₄	—	3	8	no	—
593	C₂²⋊C₄	—	3	8	no	—
594	C₂²⋊C₄	—	3	8	no	—
595	C₂²⋊C₄	—	3	8	no	—
596	C₂²⋊C₄	—	3	4	no	—
597	C₄²	—	3	4	no	—
598	C₃×C₅	C₂×#546	1	1	yes	characteristic, complemented, Hall
599	C₂²×C₃	—	2	8	no	—
600	C₂²×C₃	—	2	16	no	—
601	C₂²×C₃	—	2	2	no	—
602	C₂²×C₃	—	2	4	no	—
603	C₂²×C₃	—	2	4	no	—
604	C₂²×C₃	—	2	2	no	—
605	C₂²×C₃	—	2	4	no	—
606	C₂²×C₃	—	2	4	no	—
607	C₂²×C₃	—	2	4	no	—
608	C₂²×C₃	—	4	32	no	—
609	C₂²×C₃	—	4	8	no	—
610	C₂²×C₃	C₂²×C₅×D₄	1	8	yes	—
611	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
612	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
613	C₂²×C₃	C₂×C₅×#41	1	4	yes	complemented
614	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
615	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
616	C₂×D₃	—	2	2	no	—
617	C₂×D₃	—	2	2	no	—
618	C₂×D₃	—	2	2	no	—
619	C₂×D₃	—	4	4	no	—
620	C₃×C₄	—	2	2	no	—
621	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
622	Dic₃	—	2	4	no	—
623	Dic₃	—	2	2	no	—
624	Dic₃	—	2	2	no	—
625	Dic₃	—	2	2	no	—
626	Dic₃	—	2	4	no	—
627	C₂×C₅	—	2	4	no	—
628	C₂×C₅	—	2	8	no	—
629	C₂×C₅	—	4	4	no	—
630	C₂×C₅	—	12	2	no	—
631	C₂×C₅	#5806	1	4	yes	direct product factor
632	C₂×C₅	C₂²×#237	1	1	yes	characteristic
633	C₂×C₅	C₂×#1004	1	1	yes	characteristic
634	C₂×C₅	C₂³×#67	1	1	yes	characteristic
635	C₂³	—	2	4	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	16	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	2	16	no	—
643	C₂³	—	2	4	no	—
644	C₂³	—	3	2	no	—
645	C₂³	—	4	8	no	—
646	C₂³	—	4	32	no	—
647	C₂³	—	6	2	no	—
648	C₂³	—	6	2	no	—
649	C₂³	—	6	2	no	—
650	C₂³	C₅×#237	1	4	yes	complemented
651	C₂³	C₂×C₅×#67	1	8	yes	—
652	C₂³	C₂³×C₅×D₃	1	4	yes	—
653	C₂³	C₂³×C₅×D₃	1	2	yes	—
654	C₂³	C₂³×C₅×D₃	1	4	yes	—
655	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
656	Q₈	—	6	8	no	—
657	D₄	—	2	16	no	—
658	D₄	—	2	8	no	—
659	D₄	—	6	8	no	—
660	D₄	—	6	16	no	—
661	D₄	—	12	8	no	—
662	D₄	C₂×C₅×#67	1	16	yes	complemented
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	8	no	—
665	C₂×C₄	—	3	2	no	—
666	C₂×C₄	—	3	2	no	—
667	C₂×C₄	—	3	4	no	—
668	C₂×C₄	—	3	2	no	—
669	C₂×C₄	—	3	4	no	—
670	C₂×C₄	—	6	2	no	—
671	C₂×C₄	—	6	2	no	—
672	C₂×C₄	—	6	4	no	—
673	C₂×C₄	—	6	2	no	—
674	C₂×C₄	—	6	4	no	—
675	C₂×C₄	—	6	16	no	—
676	C₂×C₄	—	6	8	no	—
677	C₂×C₄	—	12	8	no	—
678	C₂×C₄	C₂×C₅×#67	1	4	yes	—
679	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
680	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
681	C₂×C₃	—	2	4	no	—
682	C₂×C₃	—	2	8	no	—
683	C₂×C₃	—	4	4	no	—
684	C₂×C₃	C₅×#546	1	4	yes	complemented
685	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
686	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
687	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
688	D₃	—	4	2	no	—
689	C₅	C₂×#5806	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²	—	2	4	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	8	no	—
695	C₂²	—	2	16	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	32	no	—
700	C₂²	—	4	8	no	—
701	C₂²	—	6	2	no	—
702	C₂²	—	6	2	no	—
703	C₂²	—	6	2	no	—
704	C₂²	—	12	4	no	—
705	C₂²	C₂×C₅×#237	1	2	yes	—
706	C₂²	C₂×C₅×#237	1	4	yes	complemented
707	C₂²	C₅×#1004	1	2	yes	—
708	C₂²	C₂²×C₅×#67	1	8	yes	—
709	C₂²	C₂²×C₅×#67	1	2	yes	—
710	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
711	C₄	—	2	2	no	—
712	C₄	—	6	2	no	—
713	C₄	—	6	2	no	—
714	C₄	—	6	4	no	—
715	C₄	—	6	2	no	—
716	C₄	—	6	4	no	—
717	C₄	C₂²×C₅×#67	1	4	yes	—
718	C₃	C₂×C₅×#546	1	1	yes	characteristic, complemented, Sylow
719	C₂	—	2	4	no	—
720	C₂	—	2	8	no	—
721	C₂	—	4	4	no	—
722	C₂	—	12	2	no	—
723	C₂	C₅×#5806	1	4	yes	direct product factor
724	C₂	C₂²×C₅×#237	1	1	yes	characteristic
725	C₂	C₂×C₅×#1004	1	1	yes	characteristic
726	C₂	C₂³×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂³×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂²×C₅×#237	C₂	semidirect
3. C₂×C₅×#953	C₂	semidirect
4. C₂²×C₅×#217	C₂	semidirect
5. C₅×#5806	C₂	direct (N × H)
6. C₂×C₅×#939	C₂	semidirect
7. C₂×C₅×#938	C₂	semidirect
8. C₂×C₅×#936	C₂	semidirect
9. C₂×C₅×#935	C₂	semidirect
10. C₂×C₅×D₄×Dic₃	C₂	semidirect
11. C₂×C₄×C₅×#67	C₂	semidirect
12. C₂×C₅×#924	C₂	semidirect
19. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂²×C₅×#67	C₂²	semidirect
23. C₂²×C₅×#67	C₂²	semidirect
24. C₂³×C₅×Dic₃	C₂²	semidirect
25. C₂³×C₅×Dic₃	C₂²	semidirect
27. C₂×C₅×#237	C₂²	semidirect
28. C₂²×C₄×C₅×D₃	C₂²	semidirect
29. C₂²×C₅×Dic₆	C₂²	semidirect
30. C₅×#953	C₂²	semidirect
33. C₂×C₅×#217	C₂²	semidirect
34. C₂×C₅×#217	C₂²	semidirect
35. C₂×C₅×#217	C₂²	semidirect
36. C₂×C₅×#217	C₂²	semidirect
37. C₂×C₅×#217	C₂²	semidirect
38. C₅×#939	C₂²	semidirect
39. C₅×#938	C₂²	semidirect
40. C₅×#936	C₂²	semidirect
41. C₅×#935	C₂²	semidirect
42. C₅×D₄×Dic₃	C₂²	semidirect
43. C₄×C₅×#67	C₂²	semidirect
44. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
45. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
46. C₅×#924	C₂²	semidirect
47. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
48. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
49. C₂×C₄×C₅×Dic₃	C₂²	semidirect
50. C₂×#5806	C₅	direct (N × H)
52. C₂³×C₅×D₄	D₃	semidirect
74. C₂×C₃×C₅×D₄	D₄	semidirect
86. C₂×C₅×#67	C₂³	semidirect
87. C₂×C₅×#67	C₂³	semidirect
95. C₂²×C₅×Dic₃	C₂³	semidirect
96. C₂²×C₅×Dic₃	C₂³	semidirect
99. C₂×C₄×C₅×D₃	C₂³	semidirect
101. C₂×C₅×Dic₆	C₂³	semidirect
104. C₅×#217	C₂³	semidirect
105. C₅×#217	C₂³	semidirect
106. C₅×#217	C₂³	semidirect
107. C₅×#217	C₂³	semidirect
108. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
109. C₅×C₄⋊Dic₃	C₂³	semidirect
110. C₅×Dic₃⋊C₄	C₂³	semidirect
111. C₅×Dic₃⋊C₄	C₂³	semidirect
112. C₄×C₅×Dic₃	C₂³	semidirect
113. C₂³×C₃×D₄	C₂×C₅	semidirect
114. C₂²×#237	C₂×C₅	semidirect
115. C₂×#953	C₂×C₅	semidirect
116. C₂²×#217	C₂×C₅	semidirect
117. #5806	C₂×C₅	direct (N × H)
118. C₂×#939	C₂×C₅	semidirect
119. C₂×#938	C₂×C₅	semidirect
120. C₂×#936	C₂×C₅	semidirect
121. C₂×#935	C₂×C₅	semidirect
122. C₂×D₄×Dic₃	C₂×C₅	semidirect
123. C₂×C₄×#67	C₂×C₅	semidirect
124. C₂×#924	C₂×C₅	semidirect
136. C₂²×C₅×D₄	C₂×D₃	semidirect
174. C₂³×C₃×C₅	#41	semidirect
185. C₃×C₅×D₄	C₂×D₄	semidirect
213. C₂²×C₃×D₄	C₂²×C₅	semidirect
216. C₂²×#67	C₂²×C₅	semidirect
217. C₂²×#67	C₂²×C₅	semidirect
218. C₂³×Dic₃	C₂²×C₅	semidirect
219. C₂³×Dic₃	C₂²×C₅	semidirect
221. C₂×#237	C₂²×C₅	semidirect
222. C₂²×C₄×D₃	C₂²×C₅	semidirect
223. C₂²×Dic₆	C₂²×C₅	semidirect
224. #953	C₂²×C₅	semidirect
227. C₂×#217	C₂²×C₅	semidirect
228. C₂×#217	C₂²×C₅	semidirect
229. C₂×#217	C₂²×C₅	semidirect
230. C₂×#217	C₂²×C₅	semidirect
231. C₂×#217	C₂²×C₅	semidirect
232. #939	C₂²×C₅	semidirect
233. #938	C₂²×C₅	semidirect
234. #936	C₂²×C₅	semidirect
235. #935	C₂²×C₅	semidirect
236. D₄×Dic₃	C₂²×C₅	semidirect
237. C₄×#67	C₂²×C₅	semidirect
238. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
239. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
240. #924	C₂²×C₅	semidirect
241. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
242. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
243. C₂×C₄×Dic₃	C₂²×C₅	semidirect
264. C₂×C₅×D₄	#67	semidirect
295. C₂³×D₄	C₅×D₃	semidirect
320. C₂²×C₃×C₅	C₂×#41	semidirect
345. C₂×C₃×D₄	C₅×D₄	semidirect
357. C₂×#67	C₂³×C₅	semidirect
358. C₂×#67	C₂³×C₅	semidirect
366. C₂²×Dic₃	C₂³×C₅	semidirect
367. C₂²×Dic₃	C₂³×C₅	semidirect
370. C₂×C₄×D₃	C₂³×C₅	semidirect
372. C₂×Dic₆	C₂³×C₅	semidirect
375. #217	C₂³×C₅	semidirect
376. #217	C₂³×C₅	semidirect
377. #217	C₂³×C₅	semidirect
378. #217	C₂³×C₅	semidirect
379. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
380. C₄⋊Dic₃	C₂³×C₅	semidirect
381. Dic₃⋊C₄	C₂³×C₅	semidirect
382. Dic₃⋊C₄	C₂³×C₅	semidirect
383. C₄×Dic₃	C₂³×C₅	semidirect
399. C₂³×C₅	#237	semidirect
411. C₅×D₄	C₂×#67	semidirect
441. C₂²×D₄	C₂×C₅×D₃	semidirect
469. C₂×C₃×C₅	#546	semidirect
486. C₂³×C₃	C₅×#41	semidirect
497. C₃×D₄	C₂×C₅×D₄	semidirect
536. C₂²×C₅	C₂×#237	semidirect
568. C₂×D₄	C₅×#67	semidirect
598. C₃×C₅	C₂×#546	semidirect
613. C₂²×C₃	C₂×C₅×#41	semidirect
631. C₂×C₅	#5806	direct (N × H)
650. C₂³	C₅×#237	semidirect
662. D₄	C₂×C₅×#67	semidirect
684. C₂×C₃	C₅×#546	semidirect
689. C₅	C₂×#5806	direct (N × H)
706. C₂²	C₂×C₅×#237	semidirect
718. C₃	C₂×C₅×#546	semidirect
723. C₂	C₅×#5806	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×C₃×C₅×D₄	2
C₂²×C₅×#237	2
C₂×C₅×#953	2
C₂²×C₅×#217	2
C₅×#5806	2
C₂×C₅×#939	2
C₂×C₅×#938	2
C₂×C₅×#936	2
C₂×C₅×#935	2
C₂×C₅×D₄×Dic₃	2
C₂×C₄×C₅×#67	2
C₂×C₅×#924	2
C₂×C₅×#546	3
C₂×#5806	5

Subgroups — C2×C5×#5806 #14482496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5806 #14482496