Subgroups — C₂×C₅×#5607 #14480371

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 776 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#940	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5607	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#885	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#882	C₂	1	2	yes	maximal, complemented
13	C₂×C₅×#535	—	3	1	no	maximal, Hall
14	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	C₂²	1	2	yes	—
20	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₅×#67	C₂²	1	2	yes	complemented
22	C₂²×C₅×#67	C₂²	1	2	yes	complemented
23	C₂×C₅×D₃×D₄	—	2	8	no	—
24	C₂×C₅×D₃×D₄	C₂²	1	8	yes	complemented
25	C₂×C₅×#235	—	2	8	no	—
26	C₂×C₅×#235	C₂²	1	8	yes	complemented
27	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
30	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₅×#217	C₂²	1	2	yes	complemented
37	C₅×#940	C₂²	1	16	yes	complemented
38	C₅×#938	C₂²	1	8	yes	complemented
39	C₅×#937	C₂²	1	16	yes	complemented
40	C₅×#930	C₂²	1	8	yes	complemented
41	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
45	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
46	C₅×#895	C₂²	1	8	yes	complemented
47	C₅×#892	C₂²	1	8	yes	complemented
48	C₅×#885	C₂²	1	16	yes	complemented
49	C₅×#882	C₂²	1	16	yes	complemented
50	C₂×#5607	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
51	C₂²×C₅×#41	—	3	1	no	—
52	C₂³×C₅×D₄	—	3	1	no	—
53	C₅×#535	—	3	16	no	—
54	C₂×C₅×#127	—	3	2	no	—
55	C₂×C₅×#124	—	3	2	no	—
56	C₂×C₅×#121	—	3	1	no	—
57	C₂×C₅×#121	—	3	1	no	—
58	C₂×C₅×#121	—	3	1	no	—
59	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
60	C₂×C₅×#120	—	3	2	no	—
61	C₂×C₅×#120	—	3	2	no	—
62	C₂×C₅×#117	—	3	1	no	—
63	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₅×D₃	—	2	8	no	—
66	C₂³×C₅×D₃	—	4	4	no	—
67	C₂³×C₅×D₃	—	4	4	no	—
68	C₂³×C₅×D₃	C₂³	1	2	yes	—
69	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂³×C₅×D₃	C₂³	1	8	yes	—
72	C₂×C₃×C₅×D₄	—	2	4	no	—
73	C₂×C₃×C₅×D₄	—	4	4	no	—
74	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
75	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
76	C₂²×C₃×C₄×C₅	—	2	4	no	—
77	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
81	C₂×C₅×#67	—	2	4	no	—
82	C₂×C₅×#67	—	2	4	no	—
83	C₂×C₅×#67	—	2	8	no	—
84	C₂×C₅×#67	—	4	4	no	—
85	C₂×C₅×#67	—	4	4	no	—
86	C₂×C₅×#67	C₂³	1	8	yes	—
87	C₂×C₅×#67	C₂³	1	4	yes	—
88	C₂×C₅×#67	C₂³	1	4	yes	complemented
89	C₂×C₅×#67	C₂³	1	8	yes	complemented
90	C₂×C₅×#67	C₂³	1	8	yes	complemented
91	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
92	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₅×D₃×D₄	—	2	32	no	—
95	C₅×#235	—	2	32	no	—
96	C₂×C₅×D₁₂	—	2	4	no	—
97	C₂×C₅×D₁₂	—	2	4	no	—
98	C₂×C₅×D₁₂	—	4	4	no	—
99	C₂×C₅×D₁₂	C₂³	1	4	yes	—
100	C₂×C₅×D₁₂	C₂³	1	4	yes	—
101	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
102	C₂×C₄×C₅×D₃	—	2	4	no	—
103	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
104	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
105	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
106	C₂×C₅×Dic₆	—	2	4	no	—
107	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
108	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₅×#217	C₂³	1	8	yes	complemented
111	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
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	4	yes	complemented
115	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
116	C₂²×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#940	C₂×C₅	1	2	yes	complemented
120	C₂×#938	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×#937	C₂×C₅	1	2	yes	complemented
122	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
123	#5607	C₂×C₅	1	16	yes	direct product factor
124	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
126	C₂×#885	C₂×C₅	1	2	yes	complemented
127	C₂×#882	C₂×C₅	1	2	yes	complemented
128	C₂⁵×C₅	—	3	2	no	—
129	C₂×C₅×#41	—	3	8	no	—
130	C₂×C₅×#41	—	6	8	no	—
131	C₂²×C₅×Q₈	—	3	1	no	—
132	C₂²×C₅×D₄	—	3	1	no	—
133	C₂²×C₅×D₄	—	3	2	no	—
134	C₂²×C₅×D₄	—	3	1	no	—
135	C₂²×C₅×D₄	—	3	2	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	—	3	1	no	—
140	C₂²×C₅×D₄	—	3	2	no	—
141	C₂²×C₅×D₄	—	6	8	no	—
142	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
143	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
144	C₂³×C₄×C₅	—	3	1	no	—
145	C₂³×C₄×C₅	—	3	1	no	—
146	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
147	C₅×#127	—	3	16	no	—
148	C₅×#124	—	3	16	no	—
149	C₅×#121	—	3	8	no	—
150	C₅×#121	—	3	8	no	—
151	C₅×#121	—	3	8	no	—
152	C₅×#121	C₂×D₃	1	8	yes	complemented
153	C₅×#120	—	3	16	no	—
154	C₅×#120	—	3	16	no	—
155	C₅×#117	—	3	8	no	—
156	C₂×C₅×C₄⋊C₄	—	3	1	no	—
157	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	2	no	—
162	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
163	C₂×C₄²×C₅	—	3	2	no	—
164	C₂×#535	—	3	1	no	Sylow
165	C₂³×C₃×C₅	—	2	2	no	—
166	C₂³×C₃×C₅	—	2	4	no	—
167	C₂³×C₃×C₅	—	2	2	no	—
168	C₂³×C₃×C₅	—	2	4	no	—
169	C₂³×C₃×C₅	—	2	2	no	—
170	C₂³×C₃×C₅	—	2	4	no	—
171	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
172	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
173	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
174	C₂²×C₅×D₃	—	2	2	no	—
175	C₂²×C₅×D₃	—	2	2	no	—
176	C₂²×C₅×D₃	—	2	2	no	—
177	C₂²×C₅×D₃	—	2	4	no	—
178	C₂²×C₅×D₃	—	2	2	no	—
179	C₂²×C₅×D₃	—	2	4	no	—
180	C₂²×C₅×D₃	—	2	2	no	—
181	C₂²×C₅×D₃	—	2	4	no	—
182	C₂²×C₅×D₃	—	2	16	no	—
183	C₂²×C₅×D₃	—	4	8	no	—
184	C₂²×C₅×D₃	—	4	8	no	—
185	C₂²×C₅×D₃	—	4	32	no	—
186	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
187	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
188	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
189	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
190	C₃×C₅×D₄	—	2	8	no	—
191	C₃×C₅×D₄	—	4	8	no	—
192	C₂×C₃×C₄×C₅	—	2	2	no	—
193	C₂×C₃×C₄×C₅	—	2	4	no	—
194	C₂×C₃×C₄×C₅	—	2	8	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
196	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
197	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
198	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
199	C₅×#67	—	2	8	no	—
200	C₅×#67	—	2	8	no	—
201	C₅×#67	—	2	16	no	—
202	C₅×#67	—	4	8	no	—
203	C₅×#67	—	4	8	no	—
204	C₂×C₅×Dic₃	—	2	2	no	—
205	C₂×C₅×Dic₃	—	2	4	no	—
206	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
207	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
208	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
209	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
210	C₅×D₁₂	—	2	8	no	—
211	C₅×D₁₂	—	2	8	no	—
212	C₅×D₁₂	—	4	8	no	—
213	C₄×C₅×D₃	—	2	8	no	—
214	C₄×C₅×D₃	C₂×D₄	1	16	yes	complemented
215	C₅×Dic₆	—	2	8	no	—
216	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
217	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
218	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
219	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
220	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
221	C₂²×#67	C₂²×C₅	1	2	yes	—
222	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
223	C₂²×#67	C₂²×C₅	1	2	yes	complemented
224	C₂²×#67	C₂²×C₅	1	2	yes	complemented
225	C₂×D₃×D₄	—	2	8	no	—
226	C₂×D₃×D₄	C₂²×C₅	1	8	yes	complemented
227	C₂×#235	—	2	8	no	—
228	C₂×#235	C₂²×C₅	1	8	yes	complemented
229	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
230	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
231	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
232	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
233	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
234	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₃×#121	C₂²×C₅	1	8	yes	complemented
236	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
237	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
238	C₂×#217	C₂²×C₅	1	2	yes	complemented
239	#940	C₂²×C₅	1	16	yes	complemented
240	#938	C₂²×C₅	1	8	yes	complemented
241	#937	C₂²×C₅	1	16	yes	complemented
242	#930	C₂²×C₅	1	8	yes	complemented
243	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
244	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
245	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
246	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
248	#895	C₂²×C₅	1	8	yes	complemented
249	#892	C₂²×C₅	1	8	yes	complemented
250	#885	C₂²×C₅	1	16	yes	complemented
251	#882	C₂²×C₅	1	16	yes	complemented
252	C₂⁴×C₅	—	3	1	no	—
253	C₂⁴×C₅	—	3	2	no	—
254	C₂⁴×C₅	—	3	1	no	—
255	C₂⁴×C₅	—	3	8	no	—
256	C₂⁴×C₅	—	6	8	no	—
257	C₂⁴×C₅	—	12	4	no	—
258	C₂⁴×C₅	—	12	4	no	—
259	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
260	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
261	C₅×#41	—	6	32	no	—
262	C₂×C₅×Q₈	—	3	4	no	—
263	C₂×C₅×Q₈	—	6	4	no	—
264	C₂×C₅×D₄	—	2	4	no	—
265	C₂×C₅×D₄	—	3	4	no	—
266	C₂×C₅×D₄	—	3	8	no	—
267	C₂×C₅×D₄	—	3	4	no	—
268	C₂×C₅×D₄	—	3	8	no	—
269	C₂×C₅×D₄	—	3	8	no	—
270	C₂×C₅×D₄	—	3	4	no	—
271	C₂×C₅×D₄	—	3	4	no	—
272	C₂×C₅×D₄	—	3	8	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	8	no	—
277	C₂×C₅×D₄	—	6	4	no	—
278	C₂×C₅×D₄	—	6	4	no	—
279	C₂×C₅×D₄	—	6	4	no	—
280	C₂×C₅×D₄	—	12	4	no	—
281	C₂×C₅×D₄	—	12	4	no	—
282	C₂×C₅×D₄	—	12	4	no	—
283	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
284	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
285	C₂²×C₄×C₅	—	2	4	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	8	no	—
288	C₂²×C₄×C₅	—	3	4	no	—
289	C₂²×C₄×C₅	—	3	2	no	—
290	C₂²×C₄×C₅	—	3	1	no	—
291	C₂²×C₄×C₅	—	3	4	no	—
292	C₂²×C₄×C₅	—	6	4	no	—
293	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
294	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
297	C₅×C₄⋊C₄	—	3	4	no	—
298	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
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	—	3	8	no	—
303	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
304	C₄²×C₅	—	3	8	no	—
305	C₂²×#41	—	3	1	no	—
306	C₂³×D₄	—	3	1	no	—
307	#535	—	3	16	no	—
308	C₂×#127	—	3	2	no	—
309	C₂×#124	—	3	2	no	—
310	C₂×#121	—	3	1	no	—
311	C₂×#121	—	3	1	no	—
312	C₂×#121	—	3	1	no	—
313	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
314	C₂×#120	—	3	2	no	—
315	C₂×#120	—	3	2	no	—
316	C₂×#117	—	3	1	no	—
317	C₂²×C₃×C₅	—	2	2	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	2	no	—
322	C₂²×C₃×C₅	—	2	4	no	—
323	C₂²×C₃×C₅	—	4	8	no	—
324	C₂²×C₃×C₅	—	4	4	no	—
325	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
326	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
328	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
329	C₂×C₅×D₃	—	2	8	no	—
330	C₂×C₅×D₃	—	2	2	no	—
331	C₂×C₅×D₃	—	2	2	no	—
332	C₂×C₅×D₃	—	2	2	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	—	2	2	no	—
337	C₂×C₅×D₃	—	2	4	no	—
338	C₂×C₅×D₃	—	4	32	no	—
339	C₂×C₅×D₃	—	4	4	no	—
340	C₂×C₅×D₃	—	4	8	no	—
341	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
342	C₃×C₄×C₅	—	2	2	no	—
343	C₃×C₄×C₅	—	2	4	no	—
344	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
345	C₅×Dic₃	—	2	2	no	—
346	C₅×Dic₃	—	2	4	no	—
347	C₅×Dic₃	C₂²×D₄	1	4	yes	—
348	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
349	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
350	C₂³×D₃	—	2	8	no	—
351	C₂³×D₃	—	4	4	no	—
352	C₂³×D₃	—	4	4	no	—
353	C₂³×D₃	C₂³×C₅	1	2	yes	—
354	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
355	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
356	C₂³×D₃	C₂³×C₅	1	8	yes	—
357	C₂×C₃×D₄	—	2	4	no	—
358	C₂×C₃×D₄	—	4	4	no	—
359	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
360	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
361	C₂²×C₃×C₄	—	2	4	no	—
362	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
363	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
366	C₂×#67	—	2	4	no	—
367	C₂×#67	—	2	4	no	—
368	C₂×#67	—	2	8	no	—
369	C₂×#67	—	4	4	no	—
370	C₂×#67	—	4	4	no	—
371	C₂×#67	C₂³×C₅	1	8	yes	—
372	C₂×#67	C₂³×C₅	1	4	yes	—
373	C₂×#67	C₂³×C₅	1	4	yes	complemented
374	C₂×#67	C₂³×C₅	1	8	yes	complemented
375	C₂×#67	C₂³×C₅	1	8	yes	complemented
376	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
377	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
379	D₃×D₄	—	2	32	no	—
380	#235	—	2	32	no	—
381	C₂×D₁₂	—	2	4	no	—
382	C₂×D₁₂	—	2	4	no	—
383	C₂×D₁₂	—	4	4	no	—
384	C₂×D₁₂	C₂³×C₅	1	4	yes	—
385	C₂×D₁₂	C₂³×C₅	1	4	yes	—
386	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
387	C₂×C₄×D₃	—	2	4	no	—
388	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
389	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
390	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
391	C₂×Dic₆	—	2	4	no	—
392	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
393	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
394	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
395	#217	C₂³×C₅	1	8	yes	complemented
396	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
397	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
398	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
399	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
400	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
401	C₂³×C₅	—	2	2	no	—
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	2	2	no	—
404	C₂³×C₅	—	2	4	no	—
405	C₂³×C₅	—	2	2	no	—
406	C₂³×C₅	—	2	4	no	—
407	C₂³×C₅	—	3	4	no	—
408	C₂³×C₅	—	3	2	no	—
409	C₂³×C₅	—	3	4	no	—
410	C₂³×C₅	—	3	2	no	—
411	C₂³×C₅	—	6	16	no	—
412	C₂³×C₅	—	6	2	no	—
413	C₂³×C₅	—	6	2	no	—
414	C₂³×C₅	—	6	2	no	—
415	C₂³×C₅	—	6	4	no	—
416	C₂³×C₅	—	6	2	no	—
417	C₂³×C₅	—	6	4	no	—
418	C₂³×C₅	—	6	2	no	—
419	C₂³×C₅	—	6	4	no	—
420	C₂³×C₅	—	12	8	no	—
421	C₂³×C₅	—	12	8	no	—
422	C₂³×C₅	—	12	32	no	—
423	C₂³×C₅	C₂³×D₃	1	4	yes	—
424	C₂³×C₅	C₂³×D₃	1	2	yes	—
425	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
426	C₅×Q₈	—	6	8	no	—
427	C₅×D₄	—	2	8	no	—
428	C₅×D₄	—	4	8	no	—
429	C₅×D₄	—	6	8	no	—
430	C₅×D₄	—	6	16	no	—
431	C₅×D₄	—	6	8	no	—
432	C₅×D₄	—	6	8	no	—
433	C₅×D₄	—	6	8	no	—
434	C₅×D₄	—	12	8	no	—
435	C₅×D₄	—	12	8	no	—
436	C₅×D₄	—	12	8	no	—
437	C₂×C₄×C₅	—	2	2	no	—
438	C₂×C₄×C₅	—	2	4	no	—
439	C₂×C₄×C₅	—	2	8	no	—
440	C₂×C₄×C₅	—	3	4	no	—
441	C₂×C₄×C₅	—	3	2	no	—
442	C₂×C₄×C₅	—	3	16	no	—
443	C₂×C₄×C₅	—	3	4	no	—
444	C₂×C₄×C₅	—	3	2	no	—
445	C₂×C₄×C₅	—	6	2	no	—
446	C₂×C₄×C₅	—	6	4	no	—
447	C₂×C₄×C₅	—	6	8	no	—
448	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
449	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
450	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
451	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
452	C₂⁵	—	3	2	no	—
453	C₂×#41	—	3	8	no	—
454	C₂×#41	—	6	8	no	—
455	C₂²×Q₈	—	3	1	no	—
456	C₂²×D₄	—	3	1	no	—
457	C₂²×D₄	—	3	2	no	—
458	C₂²×D₄	—	3	1	no	—
459	C₂²×D₄	—	3	2	no	—
460	C₂²×D₄	—	3	2	no	—
461	C₂²×D₄	—	3	8	no	—
462	C₂²×D₄	—	3	1	no	—
463	C₂²×D₄	—	3	1	no	—
464	C₂²×D₄	—	3	2	no	—
465	C₂²×D₄	—	6	8	no	—
466	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
467	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
468	C₂³×C₄	—	3	1	no	—
469	C₂³×C₄	—	3	1	no	—
470	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
471	#127	—	3	16	no	—
472	#124	—	3	16	no	—
473	#121	—	3	8	no	—
474	#121	—	3	8	no	—
475	#121	—	3	8	no	—
476	#121	C₂×C₅×D₃	1	8	yes	complemented
477	#120	—	3	16	no	—
478	#120	—	3	16	no	—
479	#117	—	3	8	no	—
480	C₂×C₄⋊C₄	—	3	1	no	—
481	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
482	C₂×C₂²⋊C₄	—	3	2	no	—
483	C₂×C₂²⋊C₄	—	3	2	no	—
484	C₂×C₂²⋊C₄	—	3	2	no	—
485	C₂×C₂²⋊C₄	—	3	2	no	—
486	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
487	C₂×C₄²	—	3	2	no	—
488	C₂×C₃×C₅	—	4	4	no	—
489	C₂×C₃×C₅	—	4	2	no	—
490	C₂×C₃×C₅	#535	1	4	yes	complemented
491	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
492	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₅×D₃	—	2	4	no	—
495	C₅×D₃	—	4	2	no	—
496	C₅×D₃	—	4	4	no	—
497	C₂³×C₃	—	2	2	no	—
498	C₂³×C₃	—	2	4	no	—
499	C₂³×C₃	—	2	2	no	—
500	C₂³×C₃	—	2	4	no	—
501	C₂³×C₃	—	2	2	no	—
502	C₂³×C₃	—	2	4	no	—
503	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
504	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
505	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
506	C₂²×D₃	—	2	2	no	—
507	C₂²×D₃	—	2	2	no	—
508	C₂²×D₃	—	2	2	no	—
509	C₂²×D₃	—	2	4	no	—
510	C₂²×D₃	—	2	2	no	—
511	C₂²×D₃	—	2	4	no	—
512	C₂²×D₃	—	2	2	no	—
513	C₂²×D₃	—	2	4	no	—
514	C₂²×D₃	—	2	16	no	—
515	C₂²×D₃	—	4	8	no	—
516	C₂²×D₃	—	4	8	no	—
517	C₂²×D₃	—	4	32	no	—
518	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
519	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
520	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
521	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
522	C₃×D₄	—	2	8	no	—
523	C₃×D₄	—	4	8	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	4	no	—
526	C₂×C₃×C₄	—	2	8	no	—
527	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
528	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
529	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
530	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
531	#67	—	2	8	no	—
532	#67	—	2	8	no	—
533	#67	—	2	16	no	—
534	#67	—	4	8	no	—
535	#67	—	4	8	no	—
536	C₂×Dic₃	—	2	2	no	—
537	C₂×Dic₃	—	2	4	no	—
538	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
539	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
540	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
541	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
542	D₁₂	—	2	8	no	—
543	D₁₂	—	2	8	no	—
544	D₁₂	—	4	8	no	—
545	C₄×D₃	—	2	8	no	—
546	C₄×D₃	C₂×C₅×D₄	1	16	yes	complemented
547	Dic₆	—	2	8	no	—
548	C₂²×C₅	—	2	2	no	—
549	C₂²×C₅	—	2	4	no	—
550	C₂²×C₅	—	2	2	no	—
551	C₂²×C₅	—	2	4	no	—
552	C₂²×C₅	—	2	2	no	—
553	C₂²×C₅	—	2	4	no	—
554	C₂²×C₅	—	3	4	no	—
555	C₂²×C₅	—	4	4	no	—
556	C₂²×C₅	—	4	8	no	—
557	C₂²×C₅	—	6	2	no	—
558	C₂²×C₅	—	6	2	no	—
559	C₂²×C₅	—	6	8	no	—
560	C₂²×C₅	—	6	2	no	—
561	C₂²×C₅	—	6	4	no	—
562	C₂²×C₅	—	6	2	no	—
563	C₂²×C₅	—	6	4	no	—
564	C₂²×C₅	—	6	2	no	—
565	C₂²×C₅	—	6	4	no	—
566	C₂²×C₅	—	12	32	no	—
567	C₂²×C₅	—	12	4	no	—
568	C₂²×C₅	—	12	8	no	—
569	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
570	C₂²×C₅	#1004	1	2	yes	—
571	C₂²×C₅	#1009	1	2	yes	—
572	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
573	C₄×C₅	—	2	2	no	—
574	C₄×C₅	—	2	4	no	—
575	C₄×C₅	—	3	4	no	—
576	C₄×C₅	—	6	2	no	—
577	C₄×C₅	—	6	4	no	—
578	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
579	C₂⁴	—	3	1	no	—
580	C₂⁴	—	3	2	no	—
581	C₂⁴	—	3	1	no	—
582	C₂⁴	—	3	8	no	—
583	C₂⁴	—	6	8	no	—
584	C₂⁴	—	12	4	no	—
585	C₂⁴	—	12	4	no	—
586	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
587	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
588	#41	—	6	32	no	—
589	C₂×Q₈	—	3	4	no	—
590	C₂×Q₈	—	6	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	3	4	no	—
593	C₂×D₄	—	3	8	no	—
594	C₂×D₄	—	3	4	no	—
595	C₂×D₄	—	3	8	no	—
596	C₂×D₄	—	3	8	no	—
597	C₂×D₄	—	3	4	no	—
598	C₂×D₄	—	3	4	no	—
599	C₂×D₄	—	3	8	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	6	4	no	—
602	C₂×D₄	—	6	32	no	—
603	C₂×D₄	—	6	8	no	—
604	C₂×D₄	—	6	4	no	—
605	C₂×D₄	—	6	4	no	—
606	C₂×D₄	—	6	4	no	—
607	C₂×D₄	—	12	4	no	—
608	C₂×D₄	—	12	4	no	—
609	C₂×D₄	—	12	4	no	—
610	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
611	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	3	1	no	—
614	C₂²×C₄	—	3	8	no	—
615	C₂²×C₄	—	3	4	no	—
616	C₂²×C₄	—	3	2	no	—
617	C₂²×C₄	—	3	1	no	—
618	C₂²×C₄	—	3	4	no	—
619	C₂²×C₄	—	6	4	no	—
620	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
621	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
624	C₄⋊C₄	—	3	4	no	—
625	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
626	C₂²⋊C₄	—	3	8	no	—
627	C₂²⋊C₄	—	3	8	no	—
628	C₂²⋊C₄	—	3	8	no	—
629	C₂²⋊C₄	—	3	8	no	—
630	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
631	C₄²	—	3	8	no	—
632	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
633	C₂²×C₃	—	2	2	no	—
634	C₂²×C₃	—	2	4	no	—
635	C₂²×C₃	—	2	2	no	—
636	C₂²×C₃	—	2	4	no	—
637	C₂²×C₃	—	2	2	no	—
638	C₂²×C₃	—	2	4	no	—
639	C₂²×C₃	—	4	8	no	—
640	C₂²×C₃	—	4	4	no	—
641	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
642	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
643	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
644	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
645	C₂×D₃	—	2	8	no	—
646	C₂×D₃	—	2	2	no	—
647	C₂×D₃	—	2	2	no	—
648	C₂×D₃	—	2	2	no	—
649	C₂×D₃	—	2	4	no	—
650	C₂×D₃	—	2	2	no	—
651	C₂×D₃	—	2	4	no	—
652	C₂×D₃	—	2	2	no	—
653	C₂×D₃	—	2	4	no	—
654	C₂×D₃	—	4	32	no	—
655	C₂×D₃	—	4	4	no	—
656	C₂×D₃	—	4	8	no	—
657	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	4	no	—
660	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
661	Dic₃	—	2	2	no	—
662	Dic₃	—	2	4	no	—
663	Dic₃	C₂²×C₅×D₄	1	4	yes	—
664	C₂×C₅	—	4	4	no	—
665	C₂×C₅	—	4	2	no	—
666	C₂×C₅	—	6	4	no	—
667	C₂×C₅	—	12	4	no	—
668	C₂×C₅	—	12	2	no	—
669	C₂×C₅	#5607	1	4	yes	direct product factor
670	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
671	C₂×C₅	C₂×#1004	1	1	yes	characteristic
672	C₂×C₅	C₂×#1009	1	1	yes	characteristic
673	C₂³	—	2	2	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	3	4	no	—
680	C₂³	—	3	2	no	—
681	C₂³	—	3	4	no	—
682	C₂³	—	3	2	no	—
683	C₂³	—	6	16	no	—
684	C₂³	—	6	2	no	—
685	C₂³	—	6	2	no	—
686	C₂³	—	6	2	no	—
687	C₂³	—	6	4	no	—
688	C₂³	—	6	2	no	—
689	C₂³	—	6	4	no	—
690	C₂³	—	6	2	no	—
691	C₂³	—	6	4	no	—
692	C₂³	—	12	8	no	—
693	C₂³	—	12	8	no	—
694	C₂³	—	12	32	no	—
695	C₂³	C₂³×C₅×D₃	1	4	yes	—
696	C₂³	C₂³×C₅×D₃	1	2	yes	—
697	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
698	Q₈	—	6	8	no	—
699	D₄	—	2	8	no	—
700	D₄	—	4	8	no	—
701	D₄	—	6	8	no	—
702	D₄	—	6	16	no	—
703	D₄	—	6	8	no	—
704	D₄	—	6	8	no	—
705	D₄	—	6	8	no	—
706	D₄	—	12	8	no	—
707	D₄	—	12	8	no	—
708	D₄	—	12	8	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	3	4	no	—
713	C₂×C₄	—	3	2	no	—
714	C₂×C₄	—	3	16	no	—
715	C₂×C₄	—	3	4	no	—
716	C₂×C₄	—	3	2	no	—
717	C₂×C₄	—	6	2	no	—
718	C₂×C₄	—	6	4	no	—
719	C₂×C₄	—	6	8	no	—
720	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
721	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
722	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
723	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
724	C₂×C₃	—	4	4	no	—
725	C₂×C₃	—	4	2	no	—
726	C₂×C₃	C₅×#535	1	4	yes	complemented
727	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
728	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
730	D₃	—	2	4	no	—
731	D₃	—	4	4	no	—
732	D₃	—	4	2	no	—
733	C₅	C₂×#5607	1	1	yes	characteristic, direct product factor, Sylow
734	C₂²	—	2	2	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	3	4	no	—
741	C₂²	—	4	8	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	6	2	no	—
744	C₂²	—	6	2	no	—
745	C₂²	—	6	8	no	—
746	C₂²	—	6	2	no	—
747	C₂²	—	6	4	no	—
748	C₂²	—	6	2	no	—
749	C₂²	—	6	4	no	—
750	C₂²	—	6	2	no	—
751	C₂²	—	6	4	no	—
752	C₂²	—	12	32	no	—
753	C₂²	—	12	8	no	—
754	C₂²	—	12	4	no	—
755	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
756	C₂²	C₅×#1004	1	2	yes	—
757	C₂²	C₅×#1009	1	2	yes	—
758	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
759	C₄	—	2	2	no	—
760	C₄	—	2	4	no	—
761	C₄	—	3	4	no	—
762	C₄	—	6	2	no	—
763	C₄	—	6	4	no	—
764	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
765	C₃	C₂×C₅×#535	1	1	yes	characteristic, complemented, Sylow
766	C₂	—	4	4	no	—
767	C₂	—	4	2	no	—
768	C₂	—	6	4	no	—
769	C₂	—	12	4	no	—
770	C₂	—	12	2	no	—
771	C₂	C₅×#5607	1	4	yes	direct product factor
772	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
773	C₂	C₂×C₅×#1004	1	1	yes	characteristic
774	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×D₄	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₅×#940	C₂	semidirect
5. C₂×C₅×#938	C₂	semidirect
6. C₂×C₅×#937	C₂	semidirect
7. C₂×C₅×#930	C₂	semidirect
8. C₅×#5607	C₂	direct (N × H)
9. C₂×C₅×#895	C₂	semidirect
10. C₂×C₅×#892	C₂	semidirect
11. C₂×C₅×#885	C₂	semidirect
12. C₂×C₅×#882	C₂	semidirect
16. C₂²×C₃×C₅×D₄	C₂²	semidirect
17. C₂³×C₃×C₄×C₅	C₂²	semidirect
20. C₂²×C₅×#67	C₂²	semidirect
21. C₂²×C₅×#67	C₂²	semidirect
22. C₂²×C₅×#67	C₂²	semidirect
24. C₂×C₅×D₃×D₄	C₂²	semidirect
26. C₂×C₅×#235	C₂²	semidirect
29. C₂²×C₅×D₁₂	C₂²	semidirect
31. C₂²×C₄×C₅×D₃	C₂²	semidirect
32. C₂²×C₅×Dic₆	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
34. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₅×#217	C₂²	semidirect
37. C₅×#940	C₂²	semidirect
38. C₅×#938	C₂²	semidirect
39. C₅×#937	C₂²	semidirect
40. C₅×#930	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×C₄×C₅×Dic₃	C₂²	semidirect
46. C₅×#895	C₂²	semidirect
47. C₅×#892	C₂²	semidirect
48. C₅×#885	C₂²	semidirect
49. C₅×#882	C₂²	semidirect
50. C₂×#5607	C₅	direct (N × H)
59. C₂×C₅×#121	D₃	semidirect
75. C₂×C₃×C₅×D₄	C₂³	semidirect
80. C₂²×C₃×C₄×C₅	C₂³	semidirect
88. C₂×C₅×#67	C₂³	semidirect
89. C₂×C₅×#67	C₂³	semidirect
90. C₂×C₅×#67	C₂³	semidirect
101. C₂×C₅×D₁₂	C₂³	semidirect
103. C₂×C₄×C₅×D₃	D₄	semidirect
105. C₂×C₄×C₅×D₃	C₂³	semidirect
107. C₂×C₅×Dic₆	C₂³	semidirect
108. C₃×C₅×C₄⋊C₄	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
110. 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. C₄×C₅×Dic₃	C₂³	semidirect
116. C₂²×D₃×D₄	C₂×C₅	semidirect
117. C₂²×#235	C₂×C₅	semidirect
118. C₂×C₃×#121	C₂×C₅	semidirect
119. C₂×#940	C₂×C₅	semidirect
120. C₂×#938	C₂×C₅	semidirect
121. C₂×#937	C₂×C₅	semidirect
122. C₂×#930	C₂×C₅	semidirect
123. #5607	C₂×C₅	direct (N × H)
124. C₂×#895	C₂×C₅	semidirect
125. C₂×#892	C₂×C₅	semidirect
126. C₂×#885	C₂×C₅	semidirect
127. C₂×#882	C₂×C₅	semidirect
143. C₂²×C₅×D₄	C₂×D₃	semidirect
146. C₂³×C₄×C₅	C₂×D₃	semidirect
152. C₅×#121	C₂×D₃	semidirect
157. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
162. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
214. C₄×C₅×D₃	C₂×D₄	semidirect
218. C₂²×C₃×D₄	C₂²×C₅	semidirect
219. C₂³×C₃×C₄	C₂²×C₅	semidirect
222. C₂²×#67	C₂²×C₅	semidirect
223. C₂²×#67	C₂²×C₅	semidirect
224. C₂²×#67	C₂²×C₅	semidirect
226. C₂×D₃×D₄	C₂²×C₅	semidirect
228. C₂×#235	C₂²×C₅	semidirect
231. C₂²×D₁₂	C₂²×C₅	semidirect
233. C₂²×C₄×D₃	C₂²×C₅	semidirect
234. C₂²×Dic₆	C₂²×C₅	semidirect
235. C₃×#121	C₂²×C₅	semidirect
236. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
237. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
238. C₂×#217	C₂²×C₅	semidirect
239. #940	C₂²×C₅	semidirect
240. #938	C₂²×C₅	semidirect
241. #937	C₂²×C₅	semidirect
242. #930	C₂²×C₅	semidirect
244. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
245. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
246. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
247. C₂×C₄×Dic₃	C₂²×C₅	semidirect
248. #895	C₂²×C₅	semidirect
249. #892	C₂²×C₅	semidirect
250. #885	C₂²×C₅	semidirect
251. #882	C₂²×C₅	semidirect
284. C₂×C₅×D₄	C₂²×D₃	semidirect
296. C₂²×C₄×C₅	C₂²×D₃	semidirect
298. C₅×C₄⋊C₄	C₂²×D₃	semidirect
303. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
313. C₂×#121	C₅×D₃	semidirect
360. C₂×C₃×D₄	C₂³×C₅	semidirect
365. C₂²×C₃×C₄	C₂³×C₅	semidirect
373. C₂×#67	C₂³×C₅	semidirect
374. C₂×#67	C₂³×C₅	semidirect
375. C₂×#67	C₂³×C₅	semidirect
386. C₂×D₁₂	C₂³×C₅	semidirect
388. C₂×C₄×D₃	C₅×D₄	semidirect
390. C₂×C₄×D₃	C₂³×C₅	semidirect
392. C₂×Dic₆	C₂³×C₅	semidirect
393. C₃×C₄⋊C₄	C₂³×C₅	semidirect
394. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
395. #217	C₂³×C₅	semidirect
397. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
398. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
399. C₄⋊Dic₃	C₂³×C₅	semidirect
400. C₄×Dic₃	C₂³×C₅	semidirect
467. C₂²×D₄	C₂×C₅×D₃	semidirect
470. C₂³×C₄	C₂×C₅×D₃	semidirect
476. #121	C₂×C₅×D₃	semidirect
481. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
486. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
490. C₂×C₃×C₅	#535	semidirect
546. C₄×D₃	C₂×C₅×D₄	semidirect
611. C₂×D₄	C₂²×C₅×D₃	semidirect
623. C₂²×C₄	C₂²×C₅×D₃	semidirect
625. C₄⋊C₄	C₂²×C₅×D₃	semidirect
630. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
632. C₃×C₅	C₂×#535	semidirect
669. C₂×C₅	#5607	direct (N × H)
726. C₂×C₃	C₅×#535	semidirect
733. C₅	C₂×#5607	direct (N × H)
765. C₃	C₂×C₅×#535	semidirect
771. C₂	C₅×#5607	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×C₅×D₃×D₄	2
C₂²×C₅×#235	2
C₂×C₃×C₅×#121	2
C₂×C₅×#940	2
C₂×C₅×#938	2
C₂×C₅×#937	2
C₂×C₅×#930	2
C₅×#5607	2
C₂×C₅×#895	2
C₂×C₅×#892	2
C₂×C₅×#885	2
C₂×C₅×#882	2
C₂×C₅×#535	3
C₂×#5607	5

Subgroups — C2×C5×#5607 #14480371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5607 #14480371