Subgroups — C₂×C₅×#5592 #14480368

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 752 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×#237	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×#940	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5592	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₅×#885	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#535	—	3	1	no	maximal, Hall
14	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
15	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
18	C₂²×C₅×#67	—	2	8	no	—
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	C₂²	1	2	yes	—
21	C₂²×C₅×#67	C₂²	1	2	yes	—
22	C₂²×C₅×#67	C₂²	1	8	yes	complemented
23	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₅×#67	C₂²	1	2	yes	complemented
25	C₂²×C₅×#67	C₂²	1	2	yes	complemented
26	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#237	—	2	8	no	—
29	C₂×C₅×#237	C₂²	1	8	yes	complemented
30	C₂²×C₅×D₁₂	C₂²	1	2	yes	complemented
31	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#120	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₅×#953	C₂²	1	8	yes	complemented
37	C₂×C₅×#217	C₂²	1	1	yes	characteristic
38	C₂×C₅×#217	C₂²	1	2	yes	complemented
39	C₅×#940	C₂²	1	16	yes	complemented
40	C₅×#939	C₂²	1	16	yes	complemented
41	C₅×#937	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×Dic₃⋊C₄	C₂²	1	2	yes	complemented
45	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
46	C₅×#885	C₂²	1	16	yes	complemented
47	C₅×#884	C₂²	1	16	yes	complemented
48	C₅×#882	C₂²	1	8	yes	complemented
49	C₅×#877	C₂²	1	8	yes	complemented
50	C₂×#5592	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	2	no	—
57	C₂×C₅×#121	—	3	2	no	—
58	C₂×C₅×#120	—	3	1	no	—
59	C₂×C₅×#120	—	3	1	no	—
60	C₂×C₅×#120	—	3	1	no	—
61	C₂×C₅×#120	D₃	1	1	yes	characteristic, complemented
62	C₂×C₅×#117	—	3	1	no	—
63	C₂⁴×C₃×C₅	—	2	4	no	—
64	C₂⁴×C₃×C₅	—	4	4	no	—
65	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
66	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
67	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
68	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
69	C₂³×C₅×D₃	—	2	4	no	—
70	C₂³×C₅×D₃	—	4	4	no	—
71	C₂³×C₅×D₃	C₂³	1	2	yes	—
72	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂³×C₅×D₃	C₂³	1	4	yes	—
74	C₂×C₃×C₅×D₄	—	2	4	no	—
75	C₂×C₃×C₅×D₄	—	4	4	no	—
76	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
77	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
78	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₅×#67	—	2	4	no	—
81	C₂×C₅×#67	—	2	4	no	—
82	C₂×C₅×#67	—	2	8	no	—
83	C₂×C₅×#67	—	2	8	no	—
84	C₂×C₅×#67	—	2	32	no	—
85	C₂×C₅×#67	—	4	4	no	—
86	C₂×C₅×#67	—	4	4	no	—
87	C₂×C₅×#67	C₂³	1	4	yes	—
88	C₂×C₅×#67	C₂³	1	8	yes	—
89	C₂×C₅×#67	C₂³	1	8	yes	—
90	C₂×C₅×#67	C₂³	1	4	yes	complemented
91	C₂×C₅×#67	C₂³	1	8	yes	complemented
92	C₂×C₅×#67	C₂³	1	8	yes	complemented
93	C₂²×C₅×Dic₃	—	2	4	no	—
94	C₂²×C₅×Dic₃	D₄	1	8	yes	complemented
95	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
100	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
101	C₅×#237	—	2	32	no	—
102	C₂×C₅×D₁₂	—	4	4	no	—
103	C₂×C₅×D₁₂	C₂³	1	8	yes	complemented
104	C₂×C₄×C₅×D₃	—	2	4	no	—
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×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₅×#217	C₂³	1	4	yes	—
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×Dic₃⋊C₄	C₂³	1	8	yes	complemented
115	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
116	C₂³×#67	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂²×#237	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×#940	C₂×C₅	1	2	yes	complemented
121	C₂×#939	C₂×C₅	1	2	yes	complemented
122	C₂×#937	C₂×C₅	1	1	yes	characteristic, complemented
123	#5592	C₂×C₅	1	16	yes	direct product factor
124	C₂×#885	C₂×C₅	1	2	yes	complemented
125	C₂×#884	C₂×C₅	1	2	yes	complemented
126	C₂×#882	C₂×C₅	1	1	yes	characteristic, complemented
127	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
128	C₂⁵×C₅	—	3	1	no	—
129	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
130	C₂×C₅×#41	—	3	8	no	—
131	C₂×C₅×#41	—	6	8	no	—
132	C₂²×C₅×Q₈	—	3	1	no	—
133	C₂²×C₅×D₄	—	3	1	no	—
134	C₂²×C₅×D₄	—	3	2	no	—
135	C₂²×C₅×D₄	—	3	2	no	—
136	C₂²×C₅×D₄	—	3	1	no	—
137	C₂²×C₅×D₄	—	3	8	no	—
138	C₂²×C₅×D₄	—	3	2	no	—
139	C₂²×C₅×D₄	—	3	2	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	—	3	1	no	—
147	C₅×#127	—	3	16	no	—
148	C₅×#124	—	3	16	no	—
149	C₅×#121	—	3	16	no	—
150	C₅×#121	—	3	16	no	—
151	C₅×#120	—	3	8	no	—
152	C₅×#120	—	3	8	no	—
153	C₅×#120	—	3	8	no	—
154	C₅×#120	C₂×D₃	1	8	yes	complemented
155	C₅×#117	—	3	8	no	—
156	C₂×C₅×C₄⋊C₄	—	3	2	no	—
157	C₂×C₅×C₂²⋊C₄	—	3	1	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	C₂×D₃	1	1	yes	characteristic
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	4	no	—
166	C₂³×C₃×C₅	—	2	2	no	—
167	C₂³×C₃×C₅	—	2	8	no	—
168	C₂³×C₃×C₅	—	2	4	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	4	yes	—
176	C₂³×C₃×C₅	C₂⁴	1	2	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	8	no	—
181	C₂²×C₅×D₃	—	2	4	no	—
182	C₂²×C₅×D₃	—	2	4	no	—
183	C₂²×C₅×D₃	—	2	4	no	—
184	C₂²×C₅×D₃	—	2	4	no	—
185	C₂²×C₅×D₃	—	4	8	no	—
186	C₂²×C₅×D₃	—	4	16	no	—
187	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
188	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
189	C₃×C₅×D₄	—	2	8	no	—
190	C₃×C₅×D₄	—	4	8	no	—
191	C₂×C₃×C₄×C₅	—	2	2	no	—
192	C₂×C₃×C₄×C₅	—	2	4	no	—
193	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
194	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
195	C₅×#67	—	2	8	no	—
196	C₅×#67	—	2	8	no	—
197	C₅×#67	—	2	16	no	—
198	C₅×#67	—	2	16	no	—
199	C₅×#67	—	4	8	no	—
200	C₅×#67	—	4	8	no	—
201	C₂×C₅×Dic₃	—	2	2	no	—
202	C₂×C₅×Dic₃	—	2	4	no	—
203	C₂×C₅×Dic₃	—	2	8	no	—
204	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
205	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
206	C₂×C₅×Dic₃	C₂×D₄	1	16	yes	complemented
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	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
211	C₅×D₁₂	—	4	8	no	—
212	C₄×C₅×D₃	—	2	8	no	—
213	C₅×Dic₆	—	2	8	no	—
214	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
215	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
216	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
217	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
218	C₂²×#67	—	2	8	no	—
219	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
220	C₂²×#67	C₂²×C₅	1	2	yes	—
221	C₂²×#67	C₂²×C₅	1	2	yes	—
222	C₂²×#67	C₂²×C₅	1	8	yes	complemented
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	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
227	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₂×#237	—	2	8	no	—
229	C₂×#237	C₂²×C₅	1	8	yes	complemented
230	C₂²×D₁₂	C₂²×C₅	1	2	yes	complemented
231	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
232	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₃×#120	C₂²×C₅	1	8	yes	complemented
234	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
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
238	C₂×#217	C₂²×C₅	1	2	yes	complemented
239	#940	C₂²×C₅	1	16	yes	complemented
240	#939	C₂²×C₅	1	16	yes	complemented
241	#937	C₂²×C₅	1	8	yes	complemented
242	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
243	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
244	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
245	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
246	#885	C₂²×C₅	1	16	yes	complemented
247	#884	C₂²×C₅	1	16	yes	complemented
248	#882	C₂²×C₅	1	8	yes	complemented
249	#877	C₂²×C₅	1	8	yes	complemented
250	C₂⁴×C₅	—	2	4	no	—
251	C₂⁴×C₅	—	3	2	no	—
252	C₂⁴×C₅	—	3	1	no	—
253	C₂⁴×C₅	—	3	4	no	—
254	C₂⁴×C₅	—	4	4	no	—
255	C₂⁴×C₅	—	6	4	no	—
256	C₂⁴×C₅	—	12	4	no	—
257	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
258	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
259	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
260	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
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	8	no	—
268	C₂×C₅×D₄	—	3	4	no	—
269	C₂×C₅×D₄	—	3	8	no	—
270	C₂×C₅×D₄	—	3	8	no	—
271	C₂×C₅×D₄	—	3	8	no	—
272	C₂×C₅×D₄	—	4	4	no	—
273	C₂×C₅×D₄	—	6	8	no	—
274	C₂×C₅×D₄	—	6	8	no	—
275	C₂×C₅×D₄	—	6	32	no	—
276	C₂×C₅×D₄	—	6	4	no	—
277	C₂×C₅×D₄	—	6	4	no	—
278	C₂×C₅×D₄	—	12	4	no	—
279	C₂×C₅×D₄	—	12	4	no	—
280	C₂×C₅×D₄	—	12	4	no	—
281	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
282	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
283	C₂²×C₄×C₅	—	3	8	no	—
284	C₂²×C₄×C₅	—	3	4	no	—
285	C₂²×C₄×C₅	—	3	1	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	4	no	—
288	C₂²×C₄×C₅	—	3	2	no	—
289	C₂²×C₄×C₅	—	3	1	no	—
290	C₂²×C₄×C₅	—	3	4	no	—
291	C₂²×C₄×C₅	—	6	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	C₅×C₄⋊C₄	—	3	8	no	—
296	C₅×C₂²⋊C₄	—	3	4	no	—
297	C₅×C₂²⋊C₄	—	3	8	no	—
298	C₅×C₂²⋊C₄	—	3	8	no	—
299	C₅×C₂²⋊C₄	—	3	8	no	—
300	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
301	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
302	C₄²×C₅	—	3	8	no	—
303	C₂²×#41	—	3	1	no	—
304	C₂³×D₄	—	3	1	no	—
305	#535	—	3	16	no	—
306	C₂×#127	—	3	2	no	—
307	C₂×#124	—	3	2	no	—
308	C₂×#121	—	3	2	no	—
309	C₂×#121	—	3	2	no	—
310	C₂×#120	—	3	1	no	—
311	C₂×#120	—	3	1	no	—
312	C₂×#120	—	3	1	no	—
313	C₂×#120	C₅×D₃	1	1	yes	characteristic, complemented
314	C₂×#117	—	3	1	no	—
315	C₂²×C₃×C₅	—	2	8	no	—
316	C₂²×C₃×C₅	—	2	4	no	—
317	C₂²×C₃×C₅	—	2	2	no	—
318	C₂²×C₃×C₅	—	2	4	no	—
319	C₂²×C₃×C₅	—	2	4	no	—
320	C₂²×C₃×C₅	—	2	4	no	—
321	C₂²×C₃×C₅	—	2	4	no	—
322	C₂²×C₃×C₅	—	4	16	no	—
323	C₂²×C₃×C₅	—	4	4	no	—
324	C₂²×C₃×C₅	—	4	8	no	—
325	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
326	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
327	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
328	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
329	C₂×C₅×D₃	—	2	2	no	—
330	C₂×C₅×D₃	—	2	4	no	—
331	C₂×C₅×D₃	—	2	4	no	—
332	C₂×C₅×D₃	—	2	4	no	—
333	C₂×C₅×D₃	—	2	4	no	—
334	C₂×C₅×D₃	—	4	16	no	—
335	C₂×C₅×D₃	—	4	4	no	—
336	C₂×C₅×D₃	—	4	8	no	—
337	C₃×C₄×C₅	—	2	2	no	—
338	C₃×C₄×C₅	—	2	4	no	—
339	C₅×Dic₃	—	2	2	no	—
340	C₅×Dic₃	—	2	4	no	—
341	C₅×Dic₃	C₂²×D₄	1	4	yes	—
342	C₅×Dic₃	C₂²×D₄	1	4	yes	—
343	C₂⁴×C₃	—	2	4	no	—
344	C₂⁴×C₃	—	4	4	no	—
345	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
346	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
347	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
348	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
349	C₂³×D₃	—	2	4	no	—
350	C₂³×D₃	—	4	4	no	—
351	C₂³×D₃	C₂³×C₅	1	2	yes	—
352	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
353	C₂³×D₃	C₂³×C₅	1	4	yes	—
354	C₂×C₃×D₄	—	2	4	no	—
355	C₂×C₃×D₄	—	4	4	no	—
356	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
357	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
358	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
359	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂×#67	—	2	4	no	—
361	C₂×#67	—	2	4	no	—
362	C₂×#67	—	2	8	no	—
363	C₂×#67	—	2	8	no	—
364	C₂×#67	—	2	32	no	—
365	C₂×#67	—	4	4	no	—
366	C₂×#67	—	4	4	no	—
367	C₂×#67	C₂³×C₅	1	4	yes	—
368	C₂×#67	C₂³×C₅	1	8	yes	—
369	C₂×#67	C₂³×C₅	1	8	yes	—
370	C₂×#67	C₂³×C₅	1	4	yes	complemented
371	C₂×#67	C₂³×C₅	1	8	yes	complemented
372	C₂×#67	C₂³×C₅	1	8	yes	complemented
373	C₂²×Dic₃	—	2	4	no	—
374	C₂²×Dic₃	C₅×D₄	1	8	yes	complemented
375	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
376	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
377	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
379	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
380	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
381	#237	—	2	32	no	—
382	C₂×D₁₂	—	4	4	no	—
383	C₂×D₁₂	C₂³×C₅	1	8	yes	complemented
384	C₂×C₄×D₃	—	2	4	no	—
385	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
386	C₂×Dic₆	—	2	4	no	—
387	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
388	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
389	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
390	#217	C₂³×C₅	1	4	yes	—
391	#217	C₂³×C₅	1	8	yes	complemented
392	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
393	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
394	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
395	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
396	C₂³×C₅	—	2	4	no	—
397	C₂³×C₅	—	2	2	no	—
398	C₂³×C₅	—	2	8	no	—
399	C₂³×C₅	—	2	4	no	—
400	C₂³×C₅	—	2	4	no	—
401	C₂³×C₅	—	2	4	no	—
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	3	4	no	—
404	C₂³×C₅	—	3	2	no	—
405	C₂³×C₅	—	4	8	no	—
406	C₂³×C₅	—	4	16	no	—
407	C₂³×C₅	—	6	2	no	—
408	C₂³×C₅	—	6	8	no	—
409	C₂³×C₅	—	6	4	no	—
410	C₂³×C₅	—	6	4	no	—
411	C₂³×C₅	—	6	4	no	—
412	C₂³×C₅	—	6	4	no	—
413	C₂³×C₅	—	12	8	no	—
414	C₂³×C₅	—	12	16	no	—
415	C₂³×C₅	D₃×D₄	1	4	yes	—
416	C₂³×C₅	C₂³×D₃	1	4	yes	—
417	C₂³×C₅	C₂³×D₃	1	2	yes	—
418	C₂³×C₅	C₂³×D₃	1	2	yes	—
419	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
420	C₅×Q₈	—	6	8	no	—
421	C₅×D₄	—	2	8	no	—
422	C₅×D₄	—	4	8	no	—
423	C₅×D₄	—	6	16	no	—
424	C₅×D₄	—	6	16	no	—
425	C₅×D₄	—	6	8	no	—
426	C₅×D₄	—	6	8	no	—
427	C₅×D₄	—	12	8	no	—
428	C₅×D₄	—	12	8	no	—
429	C₅×D₄	—	12	8	no	—
430	C₂×C₄×C₅	—	2	2	no	—
431	C₂×C₄×C₅	—	2	4	no	—
432	C₂×C₄×C₅	—	3	4	no	—
433	C₂×C₄×C₅	—	3	4	no	—
434	C₂×C₄×C₅	—	3	16	no	—
435	C₂×C₄×C₅	—	3	2	no	—
436	C₂×C₄×C₅	—	3	2	no	—
437	C₂×C₄×C₅	—	3	4	no	—
438	C₂×C₄×C₅	—	3	2	no	—
439	C₂×C₄×C₅	—	6	8	no	—
440	C₂×C₄×C₅	—	6	8	no	—
441	C₂×C₄×C₅	—	6	2	no	—
442	C₂×C₄×C₅	—	6	4	no	—
443	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
444	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
445	C₂⁵	—	3	1	no	—
446	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
447	C₂×#41	—	3	8	no	—
448	C₂×#41	—	6	8	no	—
449	C₂²×Q₈	—	3	1	no	—
450	C₂²×D₄	—	3	1	no	—
451	C₂²×D₄	—	3	2	no	—
452	C₂²×D₄	—	3	2	no	—
453	C₂²×D₄	—	3	1	no	—
454	C₂²×D₄	—	3	8	no	—
455	C₂²×D₄	—	3	2	no	—
456	C₂²×D₄	—	3	2	no	—
457	C₂²×D₄	—	3	2	no	—
458	C₂²×D₄	—	6	8	no	—
459	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
460	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
461	C₂³×C₄	—	3	1	no	—
462	C₂³×C₄	—	3	1	no	—
463	C₂³×C₄	—	3	1	no	—
464	#127	—	3	16	no	—
465	#124	—	3	16	no	—
466	#121	—	3	16	no	—
467	#121	—	3	16	no	—
468	#120	—	3	8	no	—
469	#120	—	3	8	no	—
470	#120	—	3	8	no	—
471	#120	C₂×C₅×D₃	1	8	yes	complemented
472	#117	—	3	8	no	—
473	C₂×C₄⋊C₄	—	3	2	no	—
474	C₂×C₂²⋊C₄	—	3	1	no	—
475	C₂×C₂²⋊C₄	—	3	2	no	—
476	C₂×C₂²⋊C₄	—	3	2	no	—
477	C₂×C₂²⋊C₄	—	3	2	no	—
478	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
480	C₂×C₄²	—	3	2	no	—
481	C₂×C₃×C₅	—	2	4	no	—
482	C₂×C₃×C₅	—	4	2	no	—
483	C₂×C₃×C₅	—	4	4	no	—
484	C₂×C₃×C₅	#535	1	4	yes	complemented
485	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
486	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
487	C₅×D₃	—	4	2	no	—
488	C₅×D₃	—	4	4	no	—
489	C₂³×C₃	—	2	4	no	—
490	C₂³×C₃	—	2	2	no	—
491	C₂³×C₃	—	2	8	no	—
492	C₂³×C₃	—	2	4	no	—
493	C₂³×C₃	—	2	4	no	—
494	C₂³×C₃	—	2	4	no	—
495	C₂³×C₃	—	2	4	no	—
496	C₂³×C₃	—	4	8	no	—
497	C₂³×C₃	—	4	16	no	—
498	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
499	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
500	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
501	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
502	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
503	C₂²×D₃	—	2	2	no	—
504	C₂²×D₃	—	2	8	no	—
505	C₂²×D₃	—	2	4	no	—
506	C₂²×D₃	—	2	4	no	—
507	C₂²×D₃	—	2	4	no	—
508	C₂²×D₃	—	2	4	no	—
509	C₂²×D₃	—	4	8	no	—
510	C₂²×D₃	—	4	16	no	—
511	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
512	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
513	C₃×D₄	—	2	8	no	—
514	C₃×D₄	—	4	8	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	2	4	no	—
517	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
518	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
519	#67	—	2	8	no	—
520	#67	—	2	8	no	—
521	#67	—	2	16	no	—
522	#67	—	2	16	no	—
523	#67	—	4	8	no	—
524	#67	—	4	8	no	—
525	C₂×Dic₃	—	2	2	no	—
526	C₂×Dic₃	—	2	4	no	—
527	C₂×Dic₃	—	2	8	no	—
528	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
529	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
530	C₂×Dic₃	C₂×C₅×D₄	1	16	yes	complemented
531	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
532	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
533	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
534	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
535	D₁₂	—	4	8	no	—
536	C₄×D₃	—	2	8	no	—
537	Dic₆	—	2	8	no	—
538	C₂²×C₅	—	2	4	no	—
539	C₂²×C₅	—	2	8	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	2	4	no	—
542	C₂²×C₅	—	2	4	no	—
543	C₂²×C₅	—	2	4	no	—
544	C₂²×C₅	—	2	4	no	—
545	C₂²×C₅	—	4	16	no	—
546	C₂²×C₅	—	4	4	no	—
547	C₂²×C₅	—	4	8	no	—
548	C₂²×C₅	—	6	2	no	—
549	C₂²×C₅	—	6	4	no	—
550	C₂²×C₅	—	6	4	no	—
551	C₂²×C₅	—	6	4	no	—
552	C₂²×C₅	—	6	4	no	—
553	C₂²×C₅	—	12	16	no	—
554	C₂²×C₅	—	12	4	no	—
555	C₂²×C₅	—	12	8	no	—
556	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
557	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
558	C₂²×C₅	#1004	1	4	yes	—
559	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
560	C₄×C₅	—	2	2	no	—
561	C₄×C₅	—	2	4	no	—
562	C₄×C₅	—	3	4	no	—
563	C₄×C₅	—	3	4	no	—
564	C₄×C₅	—	6	2	no	—
565	C₄×C₅	—	6	4	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	3	2	no	—
568	C₂⁴	—	3	1	no	—
569	C₂⁴	—	3	4	no	—
570	C₂⁴	—	4	4	no	—
571	C₂⁴	—	6	4	no	—
572	C₂⁴	—	12	4	no	—
573	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
574	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
575	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
576	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
577	#41	—	6	32	no	—
578	C₂×Q₈	—	3	4	no	—
579	C₂×Q₈	—	6	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	3	4	no	—
582	C₂×D₄	—	3	8	no	—
583	C₂×D₄	—	3	8	no	—
584	C₂×D₄	—	3	4	no	—
585	C₂×D₄	—	3	8	no	—
586	C₂×D₄	—	3	8	no	—
587	C₂×D₄	—	3	8	no	—
588	C₂×D₄	—	4	4	no	—
589	C₂×D₄	—	6	8	no	—
590	C₂×D₄	—	6	8	no	—
591	C₂×D₄	—	6	32	no	—
592	C₂×D₄	—	6	4	no	—
593	C₂×D₄	—	6	4	no	—
594	C₂×D₄	—	12	4	no	—
595	C₂×D₄	—	12	4	no	—
596	C₂×D₄	—	12	4	no	—
597	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
598	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
599	C₂²×C₄	—	3	8	no	—
600	C₂²×C₄	—	3	1	no	—
601	C₂²×C₄	—	3	1	no	—
602	C₂²×C₄	—	3	4	no	—
603	C₂²×C₄	—	3	2	no	—
604	C₂²×C₄	—	3	1	no	—
605	C₂²×C₄	—	3	4	no	—
606	C₂²×C₄	—	3	4	no	—
607	C₂²×C₄	—	6	4	no	—
608	C₂²×C₄	—	6	4	no	—
609	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
610	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
611	C₄⋊C₄	—	3	8	no	—
612	C₂²⋊C₄	—	3	4	no	—
613	C₂²⋊C₄	—	3	8	no	—
614	C₂²⋊C₄	—	3	8	no	—
615	C₂²⋊C₄	—	3	8	no	—
616	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
617	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
618	C₄²	—	3	8	no	—
619	C₃×C₅	C₂×#535	1	1	yes	characteristic, complemented, Hall
620	C₂²×C₃	—	2	8	no	—
621	C₂²×C₃	—	2	4	no	—
622	C₂²×C₃	—	2	2	no	—
623	C₂²×C₃	—	2	4	no	—
624	C₂²×C₃	—	2	4	no	—
625	C₂²×C₃	—	2	4	no	—
626	C₂²×C₃	—	2	4	no	—
627	C₂²×C₃	—	4	16	no	—
628	C₂²×C₃	—	4	4	no	—
629	C₂²×C₃	—	4	8	no	—
630	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
631	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
632	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
633	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
634	C₂×D₃	—	2	2	no	—
635	C₂×D₃	—	2	4	no	—
636	C₂×D₃	—	2	4	no	—
637	C₂×D₃	—	2	4	no	—
638	C₂×D₃	—	2	4	no	—
639	C₂×D₃	—	4	16	no	—
640	C₂×D₃	—	4	4	no	—
641	C₂×D₃	—	4	8	no	—
642	C₃×C₄	—	2	2	no	—
643	C₃×C₄	—	2	4	no	—
644	Dic₃	—	2	2	no	—
645	Dic₃	—	2	4	no	—
646	Dic₃	C₂²×C₅×D₄	1	4	yes	—
647	Dic₃	C₂²×C₅×D₄	1	4	yes	—
648	C₂×C₅	—	2	4	no	—
649	C₂×C₅	—	4	4	no	—
650	C₂×C₅	—	4	2	no	—
651	C₂×C₅	—	12	4	no	—
652	C₂×C₅	—	12	2	no	—
653	C₂×C₅	#5592	1	4	yes	direct product factor
654	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
655	C₂×C₅	C₂×#1004	1	2	yes	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	8	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	2	4	no	—
663	C₂³	—	3	4	no	—
664	C₂³	—	3	2	no	—
665	C₂³	—	4	8	no	—
666	C₂³	—	4	16	no	—
667	C₂³	—	6	2	no	—
668	C₂³	—	6	8	no	—
669	C₂³	—	6	4	no	—
670	C₂³	—	6	4	no	—
671	C₂³	—	6	4	no	—
672	C₂³	—	6	4	no	—
673	C₂³	—	12	8	no	—
674	C₂³	—	12	16	no	—
675	C₂³	C₅×D₃×D₄	1	4	yes	—
676	C₂³	C₂³×C₅×D₃	1	4	yes	—
677	C₂³	C₂³×C₅×D₃	1	2	yes	—
678	C₂³	C₂³×C₅×D₃	1	2	yes	—
679	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
680	Q₈	—	6	8	no	—
681	D₄	—	2	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	6	16	no	—
684	D₄	—	6	16	no	—
685	D₄	—	6	8	no	—
686	D₄	—	6	8	no	—
687	D₄	—	12	8	no	—
688	D₄	—	12	8	no	—
689	D₄	—	12	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	3	4	no	—
693	C₂×C₄	—	3	4	no	—
694	C₂×C₄	—	3	16	no	—
695	C₂×C₄	—	3	2	no	—
696	C₂×C₄	—	3	2	no	—
697	C₂×C₄	—	3	4	no	—
698	C₂×C₄	—	3	2	no	—
699	C₂×C₄	—	6	8	no	—
700	C₂×C₄	—	6	8	no	—
701	C₂×C₄	—	6	2	no	—
702	C₂×C₄	—	6	4	no	—
703	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
704	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
705	C₂×C₃	—	2	4	no	—
706	C₂×C₃	—	4	4	no	—
707	C₂×C₃	—	4	2	no	—
708	C₂×C₃	C₅×#535	1	4	yes	complemented
709	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
710	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
711	D₃	—	4	4	no	—
712	D₃	—	4	2	no	—
713	C₅	C₂×#5592	1	1	yes	characteristic, direct product factor, Sylow
714	C₂²	—	2	4	no	—
715	C₂²	—	2	8	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	4	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	4	16	no	—
722	C₂²	—	4	8	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	6	2	no	—
725	C₂²	—	6	4	no	—
726	C₂²	—	6	4	no	—
727	C₂²	—	6	4	no	—
728	C₂²	—	6	4	no	—
729	C₂²	—	12	16	no	—
730	C₂²	—	12	8	no	—
731	C₂²	—	12	4	no	—
732	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
733	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
734	C₂²	C₅×#1004	1	4	yes	—
735	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
736	C₄	—	2	2	no	—
737	C₄	—	2	4	no	—
738	C₄	—	3	4	no	—
739	C₄	—	3	4	no	—
740	C₄	—	6	2	no	—
741	C₄	—	6	4	no	—
742	C₃	C₂×C₅×#535	1	1	yes	characteristic, complemented, Sylow
743	C₂	—	2	4	no	—
744	C₂	—	4	4	no	—
745	C₂	—	4	2	no	—
746	C₂	—	12	4	no	—
747	C₂	—	12	2	no	—
748	C₂	C₅×#5592	1	4	yes	direct product factor
749	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
750	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×#535
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×#237	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₅×#953	C₂	semidirect
5. C₂×C₅×#940	C₂	semidirect
6. C₂×C₅×#939	C₂	semidirect
7. C₂×C₅×#937	C₂	semidirect
8. C₅×#5592	C₂	direct (N × H)
9. C₂×C₅×#885	C₂	semidirect
10. C₂×C₅×#884	C₂	semidirect
11. C₂×C₅×#882	C₂	semidirect
12. C₂×C₅×#877	C₂	semidirect
17. 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
27. C₂³×C₅×Dic₃	C₂²	semidirect
29. C₂×C₅×#237	C₂²	semidirect
30. C₂²×C₅×D₁₂	C₂²	semidirect
31. C₂²×C₄×C₅×D₃	C₂²	semidirect
32. C₂²×C₅×Dic₆	C₂²	semidirect
33. C₃×C₅×#120	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₅×#953	C₂²	semidirect
38. C₂×C₅×#217	C₂²	semidirect
39. C₅×#940	C₂²	semidirect
40. C₅×#939	C₂²	semidirect
41. C₅×#937	C₂²	semidirect
42. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
43. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
45. C₂×C₄×C₅×Dic₃	C₂²	semidirect
46. C₅×#885	C₂²	semidirect
47. C₅×#884	C₂²	semidirect
48. C₅×#882	C₂²	semidirect
49. C₅×#877	C₂²	semidirect
50. C₂×#5592	C₅	direct (N × H)
61. C₂×C₅×#120	D₃	semidirect
77. C₂×C₃×C₅×D₄	C₂³	semidirect
90. C₂×C₅×#67	C₂³	semidirect
91. C₂×C₅×#67	C₂³	semidirect
92. C₂×C₅×#67	C₂³	semidirect
94. C₂²×C₅×Dic₃	D₄	semidirect
100. C₂²×C₅×Dic₃	C₂³	semidirect
103. C₂×C₅×D₁₂	C₂³	semidirect
105. C₂×C₄×C₅×D₃	C₂³	semidirect
107. C₂×C₅×Dic₆	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
111. C₅×#217	C₂³	semidirect
112. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
113. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
114. C₅×Dic₃⋊C₄	C₂³	semidirect
115. C₄×C₅×Dic₃	C₂³	semidirect
116. C₂³×#67	C₂×C₅	semidirect
117. C₂²×#237	C₂×C₅	semidirect
118. C₂×C₃×#120	C₂×C₅	semidirect
119. C₂×#953	C₂×C₅	semidirect
120. C₂×#940	C₂×C₅	semidirect
121. C₂×#939	C₂×C₅	semidirect
122. C₂×#937	C₂×C₅	semidirect
123. #5592	C₂×C₅	direct (N × H)
124. C₂×#885	C₂×C₅	semidirect
125. C₂×#884	C₂×C₅	semidirect
126. C₂×#882	C₂×C₅	semidirect
127. C₂×#877	C₂×C₅	semidirect
143. C₂²×C₅×D₄	C₂×D₃	semidirect
154. C₅×#120	C₂×D₃	semidirect
162. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
206. C₂×C₅×Dic₃	C₂×D₄	semidirect
217. C₂²×C₃×D₄	C₂²×C₅	semidirect
222. C₂²×#67	C₂²×C₅	semidirect
223. C₂²×#67	C₂²×C₅	semidirect
224. C₂²×#67	C₂²×C₅	semidirect
225. C₂²×#67	C₂²×C₅	semidirect
227. C₂³×Dic₃	C₂²×C₅	semidirect
229. C₂×#237	C₂²×C₅	semidirect
230. C₂²×D₁₂	C₂²×C₅	semidirect
231. C₂²×C₄×D₃	C₂²×C₅	semidirect
232. C₂²×Dic₆	C₂²×C₅	semidirect
233. C₃×#120	C₂²×C₅	semidirect
235. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
236. #953	C₂²×C₅	semidirect
238. C₂×#217	C₂²×C₅	semidirect
239. #940	C₂²×C₅	semidirect
240. #939	C₂²×C₅	semidirect
241. #937	C₂²×C₅	semidirect
242. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
243. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
244. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
245. C₂×C₄×Dic₃	C₂²×C₅	semidirect
246. #885	C₂²×C₅	semidirect
247. #884	C₂²×C₅	semidirect
248. #882	C₂²×C₅	semidirect
249. #877	C₂²×C₅	semidirect
282. C₂×C₅×D₄	C₂²×D₃	semidirect
301. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
313. C₂×#120	C₅×D₃	semidirect
357. C₂×C₃×D₄	C₂³×C₅	semidirect
370. C₂×#67	C₂³×C₅	semidirect
371. C₂×#67	C₂³×C₅	semidirect
372. C₂×#67	C₂³×C₅	semidirect
374. C₂²×Dic₃	C₅×D₄	semidirect
380. C₂²×Dic₃	C₂³×C₅	semidirect
383. C₂×D₁₂	C₂³×C₅	semidirect
385. C₂×C₄×D₃	C₂³×C₅	semidirect
387. C₂×Dic₆	C₂³×C₅	semidirect
389. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
391. #217	C₂³×C₅	semidirect
392. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
393. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
394. Dic₃⋊C₄	C₂³×C₅	semidirect
395. C₄×Dic₃	C₂³×C₅	semidirect
460. C₂²×D₄	C₂×C₅×D₃	semidirect
471. #120	C₂×C₅×D₃	semidirect
479. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
484. C₂×C₃×C₅	#535	semidirect
530. C₂×Dic₃	C₂×C₅×D₄	semidirect
598. C₂×D₄	C₂²×C₅×D₃	semidirect
617. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
619. C₃×C₅	C₂×#535	semidirect
653. C₂×C₅	#5592	direct (N × H)
708. C₂×C₃	C₅×#535	semidirect
713. C₅	C₂×#5592	direct (N × H)
742. C₃	C₂×C₅×#535	semidirect
748. C₂	C₅×#5592	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×#237	2
C₂×C₃×C₅×#120	2
C₂×C₅×#953	2
C₂×C₅×#940	2
C₂×C₅×#939	2
C₂×C₅×#937	2
C₅×#5592	2
C₂×C₅×#885	2
C₂×C₅×#884	2
C₂×C₅×#882	2
C₂×C₅×#877	2
C₂×C₅×#535	3
C₂×#5592	5

Subgroups — C2×C5×#5592 #14480368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5592 #14480368