Subgroups — C₂×C₅×#5550 #14482502

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	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5550	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#884	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#546	—	3	1	no	maximal, Hall
14	C₂⁴×C₅×D₃	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×#67	C₂²	1	2	yes	complemented
19	C₂²×C₅×#67	C₂²	1	2	yes	complemented
20	C₂×C₅×#235	—	2	8	no	—
21	C₂×C₅×#235	C₂²	1	8	yes	complemented
22	C₂²×C₅×D₁₂	—	2	8	no	—
23	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
25	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
26	C₂²×C₅×D₁₂	C₂²	1	8	yes	complemented
27	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
28	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
29	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#217	C₂²	1	2	yes	—
36	C₅×#937	C₂²	1	16	yes	complemented
37	C₅×#930	C₂²	1	8	yes	complemented
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
40	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
41	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₅×#924	C₂²	1	8	yes	complemented
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
45	C₅×#894	C₂²	1	16	yes	complemented
46	C₅×#884	C₂²	1	16	yes	complemented
47	C₅×D₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
48	C₅×#875	C₂²	1	8	yes	complemented
49	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
50	C₂×#5550	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×#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	D₃	1	1	yes	characteristic, complemented
62	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂³×C₅×D₃	—	2	8	no	—
66	C₂³×C₅×D₃	—	2	8	no	—
67	C₂³×C₅×D₃	—	4	4	no	—
68	C₂³×C₅×D₃	C₂³	1	2	yes	—
69	C₂³×C₅×D₃	C₂³	1	8	yes	—
70	C₂³×C₅×D₃	C₂³	1	2	yes	—
71	C₂×C₃×C₅×D₄	—	2	4	no	—
72	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
73	C₂²×C₃×C₄×C₅	—	2	4	no	—
74	C₂²×C₃×C₄×C₅	—	2	4	no	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
82	C₂×C₅×#67	—	2	8	no	—
83	C₂×C₅×#67	—	4	4	no	—
84	C₂×C₅×#67	C₂³	1	8	yes	complemented
85	C₂×C₅×#67	C₂³	1	8	yes	complemented
86	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
87	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
88	C₅×#235	—	2	32	no	—
89	C₂×C₅×D₁₂	—	2	8	no	—
90	C₂×C₅×D₁₂	—	2	4	no	—
91	C₂×C₅×D₁₂	—	2	32	no	—
92	C₂×C₅×D₁₂	D₄	1	8	yes	complemented
93	C₂×C₅×D₁₂	C₂³	1	4	yes	—
94	C₂×C₅×D₁₂	C₂³	1	8	yes	—
95	C₂×C₅×D₁₂	C₂³	1	4	yes	—
96	C₂×C₄×C₅×D₃	—	2	8	no	—
97	C₂×C₄×C₅×D₃	—	4	4	no	—
98	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
99	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
100	C₂×C₅×Dic₆	—	2	4	no	—
101	C₂×C₅×Dic₆	C₂³	1	4	yes	complemented
102	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
103	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
105	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
106	C₅×#217	C₂³	1	8	yes	—
107	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
108	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
109	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
110	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
111	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
112	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
113	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×#937	C₂×C₅	1	2	yes	complemented
117	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
119	#5550	C₂×C₅	1	16	yes	direct product factor
120	C₂×#894	C₂×C₅	1	2	yes	complemented
121	C₂×#884	C₂×C₅	1	2	yes	complemented
122	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
123	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂⁵×C₅	—	3	2	no	—
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	—	3	2	no	—
130	C₂²×C₅×D₄	—	3	2	no	—
131	C₂²×C₅×D₄	—	3	1	no	—
132	C₂²×C₅×D₄	—	3	2	no	—
133	C₂²×C₅×D₄	—	3	1	no	—
134	C₂²×C₅×D₄	—	3	8	no	—
135	C₂²×C₅×D₄	—	6	8	no	—
136	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
137	C₂³×C₄×C₅	—	3	2	no	—
138	C₂³×C₄×C₅	—	3	2	no	—
139	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
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	C₂×D₃	1	8	yes	complemented
149	C₂×C₅×C₄⋊C₄	—	3	2	no	—
150	C₂×C₅×C₄⋊C₄	—	3	1	no	—
151	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
152	C₂×C₅×C₂²⋊C₄	—	3	2	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	2	no	—
157	C₂×C₅×C₂²⋊C₄	—	3	16	no	—
158	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
161	C₂×#546	—	3	1	no	Sylow
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂³×C₃×C₅	—	2	2	no	—
164	C₂³×C₃×C₅	—	2	2	no	—
165	C₂³×C₃×C₅	—	2	2	no	—
166	C₂³×C₃×C₅	—	2	2	no	—
167	C₂³×C₃×C₅	#41	1	4	yes	complemented
168	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
169	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
170	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
171	C₂²×C₅×D₃	—	2	4	no	—
172	C₂²×C₅×D₃	—	2	4	no	—
173	C₂²×C₅×D₃	—	2	4	no	—
174	C₂²×C₅×D₃	—	2	4	no	—
175	C₂²×C₅×D₃	—	2	16	no	—
176	C₂²×C₅×D₃	—	2	4	no	—
177	C₂²×C₅×D₃	—	2	16	no	—
178	C₂²×C₅×D₃	—	4	8	no	—
179	C₂²×C₅×D₃	—	4	32	no	—
180	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
181	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
182	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
183	C₃×C₅×D₄	—	2	8	no	—
184	C₂×C₃×C₄×C₅	—	2	2	no	—
185	C₂×C₃×C₄×C₅	—	2	2	no	—
186	C₂×C₃×C₄×C₅	—	2	2	no	—
187	C₂×C₃×C₄×C₅	—	2	2	no	—
188	C₂×C₃×C₄×C₅	—	2	8	no	—
189	C₂×C₃×C₄×C₅	—	2	8	no	—
190	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
191	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
192	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
193	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
194	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
195	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
196	C₅×#67	—	2	16	no	—
197	C₅×#67	—	4	8	no	—
198	C₂×C₅×Dic₃	—	2	4	no	—
199	C₂×C₅×Dic₃	—	2	4	no	—
200	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
201	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
202	C₅×D₁₂	—	2	16	no	—
203	C₅×D₁₂	—	2	8	no	—
204	C₅×D₁₂	C₂×D₄	1	16	yes	complemented
205	C₄×C₅×D₃	—	2	16	no	—
206	C₄×C₅×D₃	—	4	8	no	—
207	C₅×Dic₆	—	2	8	no	—
208	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
209	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
210	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
212	C₂²×#67	C₂²×C₅	1	2	yes	complemented
213	C₂²×#67	C₂²×C₅	1	2	yes	complemented
214	C₂×#235	—	2	8	no	—
215	C₂×#235	C₂²×C₅	1	8	yes	complemented
216	C₂²×D₁₂	—	2	8	no	—
217	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
218	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
219	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
220	C₂²×D₁₂	C₂²×C₅	1	8	yes	complemented
221	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
222	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
223	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
224	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
225	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
226	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
228	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
229	C₂×#217	C₂²×C₅	1	2	yes	—
230	#937	C₂²×C₅	1	16	yes	complemented
231	#930	C₂²×C₅	1	8	yes	complemented
232	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
233	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
234	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
235	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
236	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
237	#924	C₂²×C₅	1	8	yes	complemented
238	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
239	#894	C₂²×C₅	1	16	yes	complemented
240	#884	C₂²×C₅	1	16	yes	complemented
241	D₃×C₂²⋊C₄	C₂²×C₅	1	16	yes	complemented
242	#875	C₂²×C₅	1	8	yes	complemented
243	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
244	C₂⁴×C₅	—	3	2	no	—
245	C₂⁴×C₅	—	3	2	no	—
246	C₂⁴×C₅	—	3	8	no	—
247	C₂⁴×C₅	—	6	8	no	—
248	C₂⁴×C₅	—	6	8	no	—
249	C₂⁴×C₅	—	12	4	no	—
250	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
251	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
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	4	no	—
256	C₂×C₅×D₄	—	3	8	no	—
257	C₂×C₅×D₄	—	3	8	no	—
258	C₂×C₅×D₄	—	3	8	no	—
259	C₂×C₅×D₄	—	3	4	no	—
260	C₂×C₅×D₄	—	3	8	no	—
261	C₂×C₅×D₄	—	3	4	no	—
262	C₂×C₅×D₄	—	6	32	no	—
263	C₂×C₅×D₄	—	6	8	no	—
264	C₂×C₅×D₄	—	6	8	no	—
265	C₂×C₅×D₄	—	6	4	no	—
266	C₂×C₅×D₄	—	12	4	no	—
267	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
268	C₂²×C₄×C₅	—	2	4	no	—
269	C₂²×C₄×C₅	—	2	4	no	—
270	C₂²×C₄×C₅	—	3	2	no	—
271	C₂²×C₄×C₅	—	3	2	no	—
272	C₂²×C₄×C₅	—	3	8	no	—
273	C₂²×C₄×C₅	—	3	8	no	—
274	C₂²×C₄×C₅	—	6	8	no	—
275	C₂²×C₄×C₅	—	12	4	no	—
276	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
277	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
278	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
283	C₅×C₄⋊C₄	—	3	4	no	—
284	C₅×C₄⋊C₄	—	3	8	no	—
285	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
286	C₅×C₂²⋊C₄	—	3	8	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	C₂²×D₃	1	4	yes	—
292	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
293	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
294	C₂²×#41	—	3	1	no	—
295	C₂³×D₄	—	3	1	no	—
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	C₅×D₃	1	1	yes	characteristic, complemented
305	C₂²×C₂²⋊C₄	—	3	2	no	—
306	C₂²×C₃×C₅	—	2	8	no	—
307	C₂²×C₃×C₅	—	2	2	no	—
308	C₂²×C₃×C₅	—	2	2	no	—
309	C₂²×C₃×C₅	—	2	2	no	—
310	C₂²×C₃×C₅	—	2	2	no	—
311	C₂²×C₃×C₅	—	2	2	no	—
312	C₂²×C₃×C₅	—	4	4	no	—
313	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
314	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
315	C₂²×C₃×C₅	C₂×#41	1	4	yes	complemented
316	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
317	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
318	C₂×C₅×D₃	—	2	16	no	—
319	C₂×C₅×D₃	—	2	4	no	—
320	C₂×C₅×D₃	—	2	4	no	—
321	C₂×C₅×D₃	—	2	4	no	—
322	C₂×C₅×D₃	—	2	4	no	—
323	C₂×C₅×D₃	—	2	4	no	—
324	C₂×C₅×D₃	—	4	32	no	—
325	C₂×C₅×D₃	—	4	8	no	—
326	C₂×C₅×D₃	C₂²×D₄	1	8	yes	—
327	C₃×C₄×C₅	—	2	2	no	—
328	C₃×C₄×C₅	—	2	2	no	—
329	C₃×C₄×C₅	—	2	2	no	—
330	C₃×C₄×C₅	—	2	2	no	—
331	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
332	C₅×Dic₃	—	2	4	no	—
333	C₅×Dic₃	—	2	4	no	—
334	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
335	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
336	C₂³×D₃	—	2	8	no	—
337	C₂³×D₃	—	2	8	no	—
338	C₂³×D₃	—	4	4	no	—
339	C₂³×D₃	C₂³×C₅	1	2	yes	—
340	C₂³×D₃	C₂³×C₅	1	8	yes	—
341	C₂³×D₃	C₂³×C₅	1	2	yes	—
342	C₂×C₃×D₄	—	2	4	no	—
343	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
344	C₂²×C₃×C₄	—	2	4	no	—
345	C₂²×C₃×C₄	—	2	4	no	—
346	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
348	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
353	C₂×#67	—	2	8	no	—
354	C₂×#67	—	4	4	no	—
355	C₂×#67	C₂³×C₅	1	8	yes	complemented
356	C₂×#67	C₂³×C₅	1	8	yes	complemented
357	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
358	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
359	#235	—	2	32	no	—
360	C₂×D₁₂	—	2	8	no	—
361	C₂×D₁₂	—	2	4	no	—
362	C₂×D₁₂	—	2	32	no	—
363	C₂×D₁₂	C₅×D₄	1	8	yes	complemented
364	C₂×D₁₂	C₂³×C₅	1	4	yes	—
365	C₂×D₁₂	C₂³×C₅	1	8	yes	—
366	C₂×D₁₂	C₂³×C₅	1	4	yes	—
367	C₂×C₄×D₃	—	2	8	no	—
368	C₂×C₄×D₃	—	4	4	no	—
369	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
370	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
371	C₂×Dic₆	—	2	4	no	—
372	C₂×Dic₆	C₂³×C₅	1	4	yes	complemented
373	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
374	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
375	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
376	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
377	#217	C₂³×C₅	1	8	yes	—
378	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
379	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
380	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
381	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
382	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
383	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
384	C₂³×C₅	—	2	2	no	—
385	C₂³×C₅	—	2	2	no	—
386	C₂³×C₅	—	2	2	no	—
387	C₂³×C₅	—	2	2	no	—
388	C₂³×C₅	—	2	2	no	—
389	C₂³×C₅	—	3	8	no	—
390	C₂³×C₅	—	3	4	no	—
391	C₂³×C₅	—	3	4	no	—
392	C₂³×C₅	—	6	16	no	—
393	C₂³×C₅	—	6	4	no	—
394	C₂³×C₅	—	6	4	no	—
395	C₂³×C₅	—	6	4	no	—
396	C₂³×C₅	—	6	16	no	—
397	C₂³×C₅	—	6	4	no	—
398	C₂³×C₅	—	6	4	no	—
399	C₂³×C₅	—	12	8	no	—
400	C₂³×C₅	—	12	32	no	—
401	C₂³×C₅	#235	1	4	yes	complemented
402	C₂³×C₅	C₂³×D₃	1	2	yes	—
403	C₂³×C₅	C₂³×D₃	1	2	yes	—
404	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
405	C₅×Q₈	—	6	8	no	—
406	C₅×D₄	—	2	8	no	—
407	C₅×D₄	—	3	16	no	—
408	C₅×D₄	—	6	16	no	—
409	C₅×D₄	—	6	16	no	—
410	C₅×D₄	—	6	8	no	—
411	C₅×D₄	—	12	8	no	—
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	—	2	2	no	—
414	C₂×C₄×C₅	—	2	2	no	—
415	C₂×C₄×C₅	—	2	2	no	—
416	C₂×C₄×C₅	—	2	8	no	—
417	C₂×C₄×C₅	—	2	8	no	—
418	C₂×C₄×C₅	—	3	4	no	—
419	C₂×C₄×C₅	—	3	4	no	—
420	C₂×C₄×C₅	—	6	16	no	—
421	C₂×C₄×C₅	—	6	4	no	—
422	C₂×C₄×C₅	—	6	4	no	—
423	C₂×C₄×C₅	—	12	8	no	—
424	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
425	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
426	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
427	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
428	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
429	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
430	C₂⁵	—	3	2	no	—
431	C₂×#41	—	3	8	no	—
432	C₂×#41	—	6	8	no	—
433	C₂²×Q₈	—	3	1	no	—
434	C₂²×D₄	—	3	2	no	—
435	C₂²×D₄	—	3	2	no	—
436	C₂²×D₄	—	3	1	no	—
437	C₂²×D₄	—	3	2	no	—
438	C₂²×D₄	—	3	1	no	—
439	C₂²×D₄	—	3	8	no	—
440	C₂²×D₄	—	6	8	no	—
441	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
442	C₂³×C₄	—	3	2	no	—
443	C₂³×C₄	—	3	2	no	—
444	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
445	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
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	C₂×C₅×D₃	1	8	yes	complemented
454	C₂×C₄⋊C₄	—	3	1	no	—
455	C₂×C₄⋊C₄	—	3	2	no	—
456	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
457	C₂×C₂²⋊C₄	—	3	2	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	2	no	—
462	C₂×C₂²⋊C₄	—	3	16	no	—
463	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
465	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
466	C₂×C₃×C₅	—	2	4	no	—
467	C₂×C₃×C₅	—	4	2	no	—
468	C₂×C₃×C₅	#546	1	4	yes	complemented
469	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
470	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
471	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₅×D₃	—	2	8	no	—
473	C₅×D₃	—	4	4	no	—
474	C₂³×C₃	—	2	2	no	—
475	C₂³×C₃	—	2	2	no	—
476	C₂³×C₃	—	2	2	no	—
477	C₂³×C₃	—	2	2	no	—
478	C₂³×C₃	—	2	2	no	—
479	C₂³×C₃	C₅×#41	1	4	yes	complemented
480	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
481	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
482	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
483	C₂²×D₃	—	2	4	no	—
484	C₂²×D₃	—	2	4	no	—
485	C₂²×D₃	—	2	4	no	—
486	C₂²×D₃	—	2	4	no	—
487	C₂²×D₃	—	2	16	no	—
488	C₂²×D₃	—	2	4	no	—
489	C₂²×D₃	—	2	16	no	—
490	C₂²×D₃	—	4	8	no	—
491	C₂²×D₃	—	4	32	no	—
492	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
493	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
494	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
495	C₃×D₄	—	2	8	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	2	no	—
498	C₂×C₃×C₄	—	2	2	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	8	no	—
501	C₂×C₃×C₄	—	2	8	no	—
502	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
503	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
504	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
505	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
506	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
507	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
508	#67	—	2	16	no	—
509	#67	—	4	8	no	—
510	C₂×Dic₃	—	2	4	no	—
511	C₂×Dic₃	—	2	4	no	—
512	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
513	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
514	D₁₂	—	2	16	no	—
515	D₁₂	—	2	8	no	—
516	D₁₂	C₂×C₅×D₄	1	16	yes	complemented
517	C₄×D₃	—	2	16	no	—
518	C₄×D₃	—	4	8	no	—
519	Dic₆	—	2	8	no	—
520	C₂²×C₅	—	2	2	no	—
521	C₂²×C₅	—	2	2	no	—
522	C₂²×C₅	—	2	8	no	—
523	C₂²×C₅	—	2	2	no	—
524	C₂²×C₅	—	2	2	no	—
525	C₂²×C₅	—	2	2	no	—
526	C₂²×C₅	—	3	8	no	—
527	C₂²×C₅	—	4	4	no	—
528	C₂²×C₅	—	6	4	no	—
529	C₂²×C₅	—	6	4	no	—
530	C₂²×C₅	—	6	16	no	—
531	C₂²×C₅	—	6	4	no	—
532	C₂²×C₅	—	6	4	no	—
533	C₂²×C₅	—	6	4	no	—
534	C₂²×C₅	—	12	32	no	—
535	C₂²×C₅	—	12	8	no	—
536	C₂²×C₅	C₂×#235	1	2	yes	—
537	C₂²×C₅	C₂×#235	1	4	yes	complemented
538	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
539	C₂²×C₅	#1009	1	2	yes	—
540	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
541	C₄×C₅	—	2	2	no	—
542	C₄×C₅	—	2	2	no	—
543	C₄×C₅	—	2	2	no	—
544	C₄×C₅	—	2	2	no	—
545	C₄×C₅	—	6	4	no	—
546	C₄×C₅	—	6	4	no	—
547	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
548	C₂⁴	—	3	2	no	—
549	C₂⁴	—	3	2	no	—
550	C₂⁴	—	3	8	no	—
551	C₂⁴	—	6	8	no	—
552	C₂⁴	—	6	8	no	—
553	C₂⁴	—	12	4	no	—
554	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
555	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
556	#41	—	6	32	no	—
557	C₂×Q₈	—	3	4	no	—
558	C₂×Q₈	—	6	4	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	3	8	no	—
561	C₂×D₄	—	3	8	no	—
562	C₂×D₄	—	3	8	no	—
563	C₂×D₄	—	3	4	no	—
564	C₂×D₄	—	3	8	no	—
565	C₂×D₄	—	3	4	no	—
566	C₂×D₄	—	6	32	no	—
567	C₂×D₄	—	6	8	no	—
568	C₂×D₄	—	6	8	no	—
569	C₂×D₄	—	6	4	no	—
570	C₂×D₄	—	12	4	no	—
571	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	3	2	no	—
575	C₂²×C₄	—	3	2	no	—
576	C₂²×C₄	—	3	8	no	—
577	C₂²×C₄	—	3	8	no	—
578	C₂²×C₄	—	6	8	no	—
579	C₂²×C₄	—	12	4	no	—
580	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
581	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
582	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
584	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
585	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
586	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
587	C₄⋊C₄	—	3	4	no	—
588	C₄⋊C₄	—	3	8	no	—
589	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
590	C₂²⋊C₄	—	3	8	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	C₂²×C₅×D₃	1	4	yes	—
596	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
597	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
598	C₃×C₅	C₂×#546	1	1	yes	characteristic, complemented, Hall
599	C₂²×C₃	—	2	8	no	—
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	2	2	no	—
602	C₂²×C₃	—	2	2	no	—
603	C₂²×C₃	—	2	2	no	—
604	C₂²×C₃	—	2	2	no	—
605	C₂²×C₃	—	4	4	no	—
606	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
607	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
608	C₂²×C₃	C₂×C₅×#41	1	4	yes	complemented
609	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
610	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
611	C₂×D₃	—	2	16	no	—
612	C₂×D₃	—	2	4	no	—
613	C₂×D₃	—	2	4	no	—
614	C₂×D₃	—	2	4	no	—
615	C₂×D₃	—	2	4	no	—
616	C₂×D₃	—	2	4	no	—
617	C₂×D₃	—	4	32	no	—
618	C₂×D₃	—	4	8	no	—
619	C₂×D₃	C₂²×C₅×D₄	1	8	yes	—
620	C₃×C₄	—	2	2	no	—
621	C₃×C₄	—	2	2	no	—
622	C₃×C₄	—	2	2	no	—
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
625	Dic₃	—	2	4	no	—
626	Dic₃	—	2	4	no	—
627	C₂×C₅	—	2	4	no	—
628	C₂×C₅	—	4	2	no	—
629	C₂×C₅	—	6	8	no	—
630	C₂×C₅	—	12	4	no	—
631	C₂×C₅	#5550	1	4	yes	direct product factor
632	C₂×C₅	C₂²×#235	1	1	yes	characteristic
633	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
634	C₂×C₅	C₂×#1009	1	1	yes	characteristic
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	3	8	no	—
641	C₂³	—	3	4	no	—
642	C₂³	—	3	4	no	—
643	C₂³	—	6	16	no	—
644	C₂³	—	6	4	no	—
645	C₂³	—	6	4	no	—
646	C₂³	—	6	4	no	—
647	C₂³	—	6	16	no	—
648	C₂³	—	6	4	no	—
649	C₂³	—	6	4	no	—
650	C₂³	—	12	8	no	—
651	C₂³	—	12	32	no	—
652	C₂³	C₅×#235	1	4	yes	complemented
653	C₂³	C₂³×C₅×D₃	1	2	yes	—
654	C₂³	C₂³×C₅×D₃	1	2	yes	—
655	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
656	Q₈	—	6	8	no	—
657	D₄	—	2	8	no	—
658	D₄	—	3	16	no	—
659	D₄	—	6	16	no	—
660	D₄	—	6	16	no	—
661	D₄	—	6	8	no	—
662	D₄	—	12	8	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	8	no	—
668	C₂×C₄	—	2	8	no	—
669	C₂×C₄	—	3	4	no	—
670	C₂×C₄	—	3	4	no	—
671	C₂×C₄	—	6	16	no	—
672	C₂×C₄	—	6	4	no	—
673	C₂×C₄	—	6	4	no	—
674	C₂×C₄	—	12	8	no	—
675	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
676	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
677	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
678	C₂×C₄	C₂³×C₅×D₃	1	2	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	—	4	2	no	—
683	C₂×C₃	C₅×#546	1	4	yes	complemented
684	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
685	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
686	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
687	D₃	—	2	8	no	—
688	D₃	—	4	4	no	—
689	C₅	C₂×#5550	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	8	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	3	8	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	6	4	no	—
699	C₂²	—	6	4	no	—
700	C₂²	—	6	16	no	—
701	C₂²	—	6	4	no	—
702	C₂²	—	6	4	no	—
703	C₂²	—	6	4	no	—
704	C₂²	—	12	32	no	—
705	C₂²	—	12	8	no	—
706	C₂²	C₂×C₅×#235	1	2	yes	—
707	C₂²	C₂×C₅×#235	1	4	yes	complemented
708	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
709	C₂²	C₅×#1009	1	2	yes	—
710	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	6	4	no	—
716	C₄	—	6	4	no	—
717	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
718	C₃	C₂×C₅×#546	1	1	yes	characteristic, complemented, Sylow
719	C₂	—	2	4	no	—
720	C₂	—	4	2	no	—
721	C₂	—	6	8	no	—
722	C₂	—	12	4	no	—
723	C₂	C₅×#5550	1	4	yes	direct product factor
724	C₂	C₂²×C₅×#235	1	1	yes	characteristic
725	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
726	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×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#235	C₂	semidirect
2. C₂³×C₅×D₁₂	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
4. C₂×C₅×#937	C₂	semidirect
5. C₂×C₅×#930	C₂	semidirect
6. C₂×C₅×#924	C₂	semidirect
7. C₅×#5550	C₂	direct (N × H)
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×#884	C₂	semidirect
10. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
11. C₂×C₅×#875	C₂	semidirect
12. C₂×C₄×C₅×D₁₂	C₂	semidirect
17. C₂³×C₃×C₄×C₅	C₂²	semidirect
18. C₂²×C₅×#67	C₂²	semidirect
19. C₂²×C₅×#67	C₂²	semidirect
21. C₂×C₅×#235	C₂²	semidirect
26. C₂²×C₅×D₁₂	C₂²	semidirect
27. C₂²×C₄×C₅×D₃	C₂²	semidirect
28. C₂²×C₄×C₅×D₃	C₂²	semidirect
29. C₂²×C₅×Dic₆	C₂²	semidirect
30. C₃×C₄×C₅×D₄	C₂²	semidirect
31. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
33. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₂×C₃×C₄²×C₅	C₂²	semidirect
36. C₅×#937	C₂²	semidirect
37. C₅×#930	C₂²	semidirect
38. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
39. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
40. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
42. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
43. C₅×#924	C₂²	semidirect
44. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
45. C₅×#894	C₂²	semidirect
46. C₅×#884	C₂²	semidirect
47. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
48. C₅×#875	C₂²	semidirect
49. C₄×C₅×D₁₂	C₂²	semidirect
50. C₂×#5550	C₅	direct (N × H)
61. C₂×C₄×C₅×D₄	D₃	semidirect
81. C₂²×C₃×C₄×C₅	C₂³	semidirect
84. C₂×C₅×#67	C₂³	semidirect
85. C₂×C₅×#67	C₂³	semidirect
92. C₂×C₅×D₁₂	D₄	semidirect
98. C₂×C₄×C₅×D₃	C₂³	semidirect
99. C₂×C₄×C₅×D₃	C₂³	semidirect
101. C₂×C₅×Dic₆	C₂³	semidirect
102. C₃×C₅×C₄⋊C₄	C₂³	semidirect
104. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
105. C₃×C₄²×C₅	C₂³	semidirect
107. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
108. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
109. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
110. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
111. C₅×C₄⋊Dic₃	C₂³	semidirect
112. C₅×Dic₃⋊C₄	C₂³	semidirect
113. C₂²×#235	C₂×C₅	semidirect
114. C₂³×D₁₂	C₂×C₅	semidirect
115. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
116. C₂×#937	C₂×C₅	semidirect
117. C₂×#930	C₂×C₅	semidirect
118. C₂×#924	C₂×C₅	semidirect
119. #5550	C₂×C₅	direct (N × H)
120. C₂×#894	C₂×C₅	semidirect
121. C₂×#884	C₂×C₅	semidirect
122. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
123. C₂×#875	C₂×C₅	semidirect
124. C₂×C₄×D₁₂	C₂×C₅	semidirect
140. C₂³×C₄×C₅	C₂×D₃	semidirect
148. C₄×C₅×D₄	C₂×D₃	semidirect
151. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
159. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
160. C₂×C₄²×C₅	C₂×D₃	semidirect
167. C₂³×C₃×C₅	#41	semidirect
204. C₅×D₁₂	C₂×D₄	semidirect
211. C₂³×C₃×C₄	C₂²×C₅	semidirect
212. C₂²×#67	C₂²×C₅	semidirect
213. C₂²×#67	C₂²×C₅	semidirect
215. C₂×#235	C₂²×C₅	semidirect
220. C₂²×D₁₂	C₂²×C₅	semidirect
221. C₂²×C₄×D₃	C₂²×C₅	semidirect
222. C₂²×C₄×D₃	C₂²×C₅	semidirect
223. C₂²×Dic₆	C₂²×C₅	semidirect
224. C₃×C₄×D₄	C₂²×C₅	semidirect
225. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
227. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
228. C₂×C₃×C₄²	C₂²×C₅	semidirect
230. #937	C₂²×C₅	semidirect
231. #930	C₂²×C₅	semidirect
232. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
233. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
234. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
235. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
236. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
237. #924	C₂²×C₅	semidirect
238. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
239. #894	C₂²×C₅	semidirect
240. #884	C₂²×C₅	semidirect
241. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
242. #875	C₂²×C₅	semidirect
243. C₄×D₁₂	C₂²×C₅	semidirect
282. C₂²×C₄×C₅	C₂²×D₃	semidirect
285. C₅×C₄⋊C₄	C₂²×D₃	semidirect
292. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
293. C₄²×C₅	C₂²×D₃	semidirect
304. C₂×C₄×D₄	C₅×D₃	semidirect
315. C₂²×C₃×C₅	C₂×#41	semidirect
352. C₂²×C₃×C₄	C₂³×C₅	semidirect
355. C₂×#67	C₂³×C₅	semidirect
356. C₂×#67	C₂³×C₅	semidirect
363. C₂×D₁₂	C₅×D₄	semidirect
369. C₂×C₄×D₃	C₂³×C₅	semidirect
370. C₂×C₄×D₃	C₂³×C₅	semidirect
372. C₂×Dic₆	C₂³×C₅	semidirect
373. C₃×C₄⋊C₄	C₂³×C₅	semidirect
375. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
376. C₃×C₄²	C₂³×C₅	semidirect
378. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
379. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
380. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
381. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
382. C₄⋊Dic₃	C₂³×C₅	semidirect
383. Dic₃⋊C₄	C₂³×C₅	semidirect
401. C₂³×C₅	#235	semidirect
445. C₂³×C₄	C₂×C₅×D₃	semidirect
453. C₄×D₄	C₂×C₅×D₃	semidirect
456. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
464. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
465. C₂×C₄²	C₂×C₅×D₃	semidirect
468. C₂×C₃×C₅	#546	semidirect
479. C₂³×C₃	C₅×#41	semidirect
516. D₁₂	C₂×C₅×D₄	semidirect
537. C₂²×C₅	C₂×#235	semidirect
586. C₂²×C₄	C₂²×C₅×D₃	semidirect
589. C₄⋊C₄	C₂²×C₅×D₃	semidirect
596. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
597. C₄²	C₂²×C₅×D₃	semidirect
598. C₃×C₅	C₂×#546	semidirect
608. C₂²×C₃	C₂×C₅×#41	semidirect
631. C₂×C₅	#5550	direct (N × H)
652. C₂³	C₅×#235	semidirect
683. C₂×C₃	C₅×#546	semidirect
689. C₅	C₂×#5550	direct (N × H)
707. C₂²	C₂×C₅×#235	semidirect
718. C₃	C₂×C₅×#546	semidirect
723. C₂	C₅×#5550	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×#235	2
C₂³×C₅×D₁₂	2
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#937	2
C₂×C₅×#930	2
C₂×C₅×#924	2
C₅×#5550	2
C₂×C₅×#894	2
C₂×C₅×#884	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#875	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#546	3
C₂×#5550	5

Subgroups — C2×C5×#5550 #14482502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5550 #14482502