Subgroups — C₂×C₅×#5605 #14480290

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 680 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	2	yes	maximal, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#939	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5605	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#883	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#882	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#534	—	3	1	no	maximal, Hall
12	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₅×D₃	C₂²	1	2	yes	complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₅×#67	C₂²	1	2	yes	—
18	C₂²×C₅×#67	C₂²	1	2	yes	complemented
19	C₂²×C₅×#67	C₂²	1	2	yes	complemented
20	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×D₃×D₄	—	2	16	no	—
22	C₂×C₅×D₃×D₄	C₂²	1	16	yes	complemented
23	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
24	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
26	C₃×C₅×#121	C₂²	1	8	yes	complemented
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₂×C₅×#217	C₂²	1	2	yes	complemented
30	C₅×#939	C₂²	1	16	yes	complemented
31	C₅×#937	C₂²	1	16	yes	complemented
32	C₅×#930	C₂²	1	8	yes	complemented
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
38	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
40	C₅×#894	C₂²	1	16	yes	complemented
41	C₅×#883	C₂²	1	16	yes	complemented
42	C₅×#882	C₂²	1	16	yes	complemented
43	C₂×#5605	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂³×C₅×D₄	—	3	2	no	—
45	C₅×#534	—	3	16	no	—
46	C₂×C₅×#123	—	3	2	no	—
47	C₂×C₅×#123	—	3	2	no	—
48	C₂×C₅×#121	—	3	2	no	—
49	C₂×C₅×#121	—	3	1	no	—
50	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
51	C₂×C₅×#120	—	3	2	no	—
52	C₂×C₅×#120	—	3	2	no	—
53	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
54	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
55	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
56	C₂³×C₅×D₃	—	2	8	no	—
57	C₂³×C₅×D₃	—	4	2	no	—
58	C₂³×C₅×D₃	—	4	2	no	—
59	C₂³×C₅×D₃	—	4	4	no	—
60	C₂³×C₅×D₃	—	4	4	no	—
61	C₂³×C₅×D₃	D₄	1	8	yes	complemented
62	C₂³×C₅×D₃	C₂³	1	2	yes	—
63	C₂³×C₅×D₃	C₂³	1	2	yes	—
64	C₂³×C₅×D₃	C₂³	1	4	yes	—
65	C₂³×C₅×D₃	C₂³	1	8	yes	complemented
66	C₂×C₃×C₅×D₄	—	2	8	no	—
67	C₂×C₃×C₅×D₄	—	4	2	no	—
68	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
69	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
70	C₂²×C₃×C₄×C₅	—	4	2	no	—
71	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
75	C₂×C₅×#67	—	2	8	no	—
76	C₂×C₅×#67	—	2	8	no	—
77	C₂×C₅×#67	—	4	4	no	—
78	C₂×C₅×#67	C₂³	1	8	yes	—
79	C₂×C₅×#67	C₂³	1	8	yes	complemented
80	C₂×C₅×#67	C₂³	1	8	yes	complemented
81	C₂²×C₅×Dic₃	—	4	2	no	—
82	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
83	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
84	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
85	C₅×D₃×D₄	—	2	64	no	—
86	C₂×C₅×D₁₂	—	2	8	no	—
87	C₂×C₅×D₁₂	—	4	2	no	—
88	C₂×C₅×D₁₂	C₂³	1	8	yes	—
89	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
90	C₂×C₄×C₅×D₃	—	2	8	no	—
91	C₂×C₄×C₅×D₃	C₂³	1	8	yes	complemented
92	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
93	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
94	C₅×#217	C₂³	1	8	yes	complemented
95	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
96	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
97	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
98	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	complemented
99	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
100	C₅×Dic₃⋊C₄	C₂³	1	8	yes	complemented
101	C₂²×D₃×D₄	C₂×C₅	1	2	yes	complemented
102	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#939	C₂×C₅	1	2	yes	complemented
104	C₂×#937	C₂×C₅	1	2	yes	complemented
105	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
107	#5605	C₂×C₅	1	16	yes	direct product factor
108	C₂×#894	C₂×C₅	1	2	yes	complemented
109	C₂×#883	C₂×C₅	1	2	yes	complemented
110	C₂×#882	C₂×C₅	1	2	yes	complemented
111	C₂⁵×C₅	—	3	1	no	—
112	C₂⁵×C₅	—	3	2	no	—
113	C₂²×C₅×D₄	—	3	2	no	—
114	C₂²×C₅×D₄	—	3	2	no	—
115	C₂²×C₅×D₄	—	3	2	no	—
116	C₂²×C₅×D₄	—	3	16	no	—
117	C₂²×C₅×D₄	—	3	2	no	—
118	C₂²×C₅×D₄	—	3	1	no	—
119	C₂²×C₅×D₄	—	6	16	no	—
120	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
121	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
122	C₂³×C₄×C₅	—	3	1	no	—
123	C₂³×C₄×C₅	—	3	2	no	—
124	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
125	C₅×#123	—	3	16	no	—
126	C₅×#123	—	3	16	no	—
127	C₅×#121	—	3	16	no	—
128	C₅×#121	—	3	8	no	—
129	C₅×#121	C₂×D₃	1	8	yes	complemented
130	C₅×#120	—	3	16	no	—
131	C₅×#120	—	3	16	no	—
132	C₂×C₅×C₄⋊C₄	—	3	2	no	—
133	C₂×C₅×C₄⋊C₄	—	3	1	no	—
134	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
135	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
136	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
137	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
138	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
139	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
141	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
142	C₂×#534	—	3	1	no	Sylow
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	4	no	—
146	C₂³×C₃×C₅	—	2	4	no	—
147	C₂³×C₃×C₅	—	2	4	no	—
148	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
149	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
150	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
151	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
152	C₂²×C₅×D₃	—	2	4	no	—
153	C₂²×C₅×D₃	—	2	4	no	—
154	C₂²×C₅×D₃	—	2	4	no	—
155	C₂²×C₅×D₃	—	2	4	no	—
156	C₂²×C₅×D₃	—	2	4	no	—
157	C₂²×C₅×D₃	—	2	16	no	—
158	C₂²×C₅×D₃	—	4	16	no	—
159	C₂²×C₅×D₃	—	4	4	no	—
160	C₂²×C₅×D₃	—	4	4	no	—
161	C₂²×C₅×D₃	—	4	8	no	—
162	C₂²×C₅×D₃	—	4	8	no	—
163	C₂²×C₅×D₃	—	4	32	no	—
164	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
165	C₂²×C₅×D₃	C₂×D₄	1	16	yes	complemented
166	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
167	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
168	C₃×C₅×D₄	—	2	16	no	—
169	C₃×C₅×D₄	—	4	4	no	—
170	C₂×C₃×C₄×C₅	—	2	4	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	2	2	no	—
173	C₂×C₃×C₄×C₅	—	4	4	no	—
174	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
177	C₅×#67	—	2	16	no	—
178	C₅×#67	—	2	16	no	—
179	C₅×#67	—	4	8	no	—
180	C₂×C₅×Dic₃	—	2	4	no	—
181	C₂×C₅×Dic₃	—	2	4	no	—
182	C₂×C₅×Dic₃	—	4	4	no	—
183	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
184	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
185	C₅×D₁₂	—	2	16	no	—
186	C₅×D₁₂	—	4	4	no	—
187	C₄×C₅×D₃	—	2	16	no	—
188	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
189	C₂⁴×D₃	C₂²×C₅	1	2	yes	complemented
190	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
191	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂²×#67	C₂²×C₅	1	2	yes	—
194	C₂²×#67	C₂²×C₅	1	2	yes	complemented
195	C₂²×#67	C₂²×C₅	1	2	yes	complemented
196	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂×D₃×D₄	—	2	16	no	—
198	C₂×D₃×D₄	C₂²×C₅	1	16	yes	complemented
199	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
200	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
201	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
202	C₃×#121	C₂²×C₅	1	8	yes	complemented
203	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
205	C₂×#217	C₂²×C₅	1	2	yes	complemented
206	#939	C₂²×C₅	1	16	yes	complemented
207	#937	C₂²×C₅	1	16	yes	complemented
208	#930	C₂²×C₅	1	8	yes	complemented
209	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
210	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
211	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
212	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
213	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
214	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
215	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
216	#894	C₂²×C₅	1	16	yes	complemented
217	#883	C₂²×C₅	1	16	yes	complemented
218	#882	C₂²×C₅	1	16	yes	complemented
219	C₂⁴×C₅	—	3	2	no	—
220	C₂⁴×C₅	—	3	8	no	—
221	C₂⁴×C₅	—	3	4	no	—
222	C₂⁴×C₅	—	3	2	no	—
223	C₂⁴×C₅	—	3	8	no	—
224	C₂⁴×C₅	—	6	8	no	—
225	C₂⁴×C₅	—	12	2	no	—
226	C₂⁴×C₅	—	12	2	no	—
227	C₂⁴×C₅	—	12	4	no	—
228	C₂⁴×C₅	—	12	4	no	—
229	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
230	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₅×D₄	—	2	8	no	—
232	C₂×C₅×D₄	—	3	8	no	—
233	C₂×C₅×D₄	—	3	8	no	—
234	C₂×C₅×D₄	—	3	8	no	—
235	C₂×C₅×D₄	—	3	8	no	—
236	C₂×C₅×D₄	—	3	4	no	—
237	C₂×C₅×D₄	—	4	2	no	—
238	C₂×C₅×D₄	—	6	8	no	—
239	C₂×C₅×D₄	—	6	64	no	—
240	C₂×C₅×D₄	—	6	8	no	—
241	C₂×C₅×D₄	—	6	8	no	—
242	C₂×C₅×D₄	—	12	2	no	—
243	C₂×C₅×D₄	—	12	4	no	—
244	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
245	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
246	C₂²×C₄×C₅	—	3	2	no	—
247	C₂²×C₄×C₅	—	3	2	no	—
248	C₂²×C₄×C₅	—	3	4	no	—
249	C₂²×C₄×C₅	—	3	8	no	—
250	C₂²×C₄×C₅	—	4	2	no	—
251	C₂²×C₄×C₅	—	6	8	no	—
252	C₂²×C₄×C₅	—	12	2	no	—
253	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
256	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
257	C₅×C₄⋊C₄	—	3	8	no	—
258	C₅×C₄⋊C₄	—	3	4	no	—
259	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
260	C₅×C₂²⋊C₄	—	3	8	no	—
261	C₅×C₂²⋊C₄	—	3	8	no	—
262	C₅×C₂²⋊C₄	—	3	8	no	—
263	C₅×C₂²⋊C₄	—	3	8	no	—
264	C₅×C₂²⋊C₄	—	3	8	no	—
265	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	complemented
266	C₂³×D₄	—	3	2	no	—
267	#534	—	3	16	no	—
268	C₂×#123	—	3	2	no	—
269	C₂×#123	—	3	2	no	—
270	C₂×#121	—	3	2	no	—
271	C₂×#121	—	3	1	no	—
272	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
273	C₂×#120	—	3	2	no	—
274	C₂×#120	—	3	2	no	—
275	C₂²×C₂²⋊C₄	—	3	1	no	—
276	C₂²×C₃×C₅	—	2	8	no	—
277	C₂²×C₃×C₅	—	2	2	no	—
278	C₂²×C₃×C₅	—	2	2	no	—
279	C₂²×C₃×C₅	—	2	4	no	—
280	C₂²×C₃×C₅	—	2	4	no	—
281	C₂²×C₃×C₅	—	2	4	no	—
282	C₂²×C₃×C₅	—	4	8	no	—
283	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
284	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
285	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
286	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
288	C₂×C₅×D₃	—	2	16	no	—
289	C₂×C₅×D₃	—	2	4	no	—
290	C₂×C₅×D₃	—	2	4	no	—
291	C₂×C₅×D₃	—	2	4	no	—
292	C₂×C₅×D₃	—	2	4	no	—
293	C₂×C₅×D₃	—	2	4	no	—
294	C₂×C₅×D₃	—	4	16	no	—
295	C₂×C₅×D₃	—	4	32	no	—
296	C₂×C₅×D₃	—	4	8	no	—
297	C₂×C₅×D₃	C₂²×D₄	1	8	yes	—
298	C₃×C₄×C₅	—	2	4	no	—
299	C₃×C₄×C₅	—	2	2	no	—
300	C₃×C₄×C₅	—	2	2	no	—
301	C₅×Dic₃	—	2	4	no	—
302	C₅×Dic₃	—	2	4	no	—
303	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
304	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
305	C₂³×D₃	—	2	8	no	—
306	C₂³×D₃	—	4	2	no	—
307	C₂³×D₃	—	4	2	no	—
308	C₂³×D₃	—	4	4	no	—
309	C₂³×D₃	—	4	4	no	—
310	C₂³×D₃	C₅×D₄	1	8	yes	complemented
311	C₂³×D₃	C₂³×C₅	1	2	yes	—
312	C₂³×D₃	C₂³×C₅	1	2	yes	—
313	C₂³×D₃	C₂³×C₅	1	4	yes	—
314	C₂³×D₃	C₂³×C₅	1	8	yes	complemented
315	C₂×C₃×D₄	—	2	8	no	—
316	C₂×C₃×D₄	—	4	2	no	—
317	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
318	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
319	C₂²×C₃×C₄	—	4	2	no	—
320	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
321	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
324	C₂×#67	—	2	8	no	—
325	C₂×#67	—	2	8	no	—
326	C₂×#67	—	4	4	no	—
327	C₂×#67	C₂³×C₅	1	8	yes	—
328	C₂×#67	C₂³×C₅	1	8	yes	complemented
329	C₂×#67	C₂³×C₅	1	8	yes	complemented
330	C₂²×Dic₃	—	4	2	no	—
331	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
332	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
333	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
334	D₃×D₄	—	2	64	no	—
335	C₂×D₁₂	—	2	8	no	—
336	C₂×D₁₂	—	4	2	no	—
337	C₂×D₁₂	C₂³×C₅	1	8	yes	—
338	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
339	C₂×C₄×D₃	—	2	8	no	—
340	C₂×C₄×D₃	C₂³×C₅	1	8	yes	complemented
341	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
342	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
343	#217	C₂³×C₅	1	8	yes	complemented
344	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
345	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
346	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
347	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	complemented
348	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
349	Dic₃⋊C₄	C₂³×C₅	1	8	yes	complemented
350	C₂³×C₅	—	2	2	no	—
351	C₂³×C₅	—	2	2	no	—
352	C₂³×C₅	—	2	4	no	—
353	C₂³×C₅	—	2	4	no	—
354	C₂³×C₅	—	2	4	no	—
355	C₂³×C₅	—	3	8	no	—
356	C₂³×C₅	—	3	4	no	—
357	C₂³×C₅	—	3	16	no	—
358	C₂³×C₅	—	3	4	no	—
359	C₂³×C₅	—	6	16	no	—
360	C₂³×C₅	—	6	4	no	—
361	C₂³×C₅	—	6	4	no	—
362	C₂³×C₅	—	6	4	no	—
363	C₂³×C₅	—	6	4	no	—
364	C₂³×C₅	—	6	4	no	—
365	C₂³×C₅	—	12	4	no	—
366	C₂³×C₅	—	12	4	no	—
367	C₂³×C₅	—	12	16	no	—
368	C₂³×C₅	—	12	8	no	—
369	C₂³×C₅	—	12	8	no	—
370	C₂³×C₅	—	12	32	no	—
371	C₂³×C₅	D₃×D₄	1	4	yes	—
372	C₂³×C₅	C₂³×D₃	1	4	yes	—
373	C₂³×C₅	C₂³×D₃	1	2	yes	—
374	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
375	C₅×D₄	—	2	16	no	—
376	C₅×D₄	—	4	4	no	—
377	C₅×D₄	—	6	16	no	—
378	C₅×D₄	—	6	16	no	—
379	C₅×D₄	—	6	16	no	—
380	C₅×D₄	—	12	4	no	—
381	C₅×D₄	—	12	8	no	—
382	C₂×C₄×C₅	—	2	4	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	2	no	—
385	C₂×C₄×C₅	—	3	4	no	—
386	C₂×C₄×C₅	—	3	4	no	—
387	C₂×C₄×C₅	—	4	4	no	—
388	C₂×C₄×C₅	—	6	16	no	—
389	C₂×C₄×C₅	—	6	4	no	—
390	C₂×C₄×C₅	—	6	4	no	—
391	C₂×C₄×C₅	—	12	4	no	—
392	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
393	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
394	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
395	C₂⁵	—	3	1	no	—
396	C₂⁵	—	3	2	no	—
397	C₂²×D₄	—	3	2	no	—
398	C₂²×D₄	—	3	2	no	—
399	C₂²×D₄	—	3	2	no	—
400	C₂²×D₄	—	3	16	no	—
401	C₂²×D₄	—	3	2	no	—
402	C₂²×D₄	—	3	1	no	—
403	C₂²×D₄	—	6	16	no	—
404	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
405	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
406	C₂³×C₄	—	3	1	no	—
407	C₂³×C₄	—	3	2	no	—
408	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
409	#123	—	3	16	no	—
410	#123	—	3	16	no	—
411	#121	—	3	16	no	—
412	#121	—	3	8	no	—
413	#121	C₂×C₅×D₃	1	8	yes	complemented
414	#120	—	3	16	no	—
415	#120	—	3	16	no	—
416	C₂×C₄⋊C₄	—	3	2	no	—
417	C₂×C₄⋊C₄	—	3	1	no	—
418	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
419	C₂×C₂²⋊C₄	—	3	2	no	—
420	C₂×C₂²⋊C₄	—	3	2	no	—
421	C₂×C₂²⋊C₄	—	3	2	no	—
422	C₂×C₂²⋊C₄	—	3	2	no	—
423	C₂×C₂²⋊C₄	—	3	2	no	—
424	C₂×C₂²⋊C₄	—	3	8	no	—
425	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
426	C₂×C₃×C₅	—	2	4	no	—
427	C₂×C₃×C₅	—	4	4	no	—
428	C₂×C₃×C₅	#534	1	4	yes	complemented
429	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
430	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
432	C₅×D₃	—	2	8	no	—
433	C₅×D₃	—	4	4	no	—
434	C₂³×C₃	—	2	2	no	—
435	C₂³×C₃	—	2	2	no	—
436	C₂³×C₃	—	2	4	no	—
437	C₂³×C₃	—	2	4	no	—
438	C₂³×C₃	—	2	4	no	—
439	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
440	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
441	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
442	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
443	C₂²×D₃	—	2	4	no	—
444	C₂²×D₃	—	2	4	no	—
445	C₂²×D₃	—	2	4	no	—
446	C₂²×D₃	—	2	4	no	—
447	C₂²×D₃	—	2	4	no	—
448	C₂²×D₃	—	2	16	no	—
449	C₂²×D₃	—	4	16	no	—
450	C₂²×D₃	—	4	4	no	—
451	C₂²×D₃	—	4	4	no	—
452	C₂²×D₃	—	4	8	no	—
453	C₂²×D₃	—	4	8	no	—
454	C₂²×D₃	—	4	32	no	—
455	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
456	C₂²×D₃	C₂×C₅×D₄	1	16	yes	complemented
457	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
458	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
459	C₃×D₄	—	2	16	no	—
460	C₃×D₄	—	4	4	no	—
461	C₂×C₃×C₄	—	2	4	no	—
462	C₂×C₃×C₄	—	2	2	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	4	4	no	—
465	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
466	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
467	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
468	#67	—	2	16	no	—
469	#67	—	2	16	no	—
470	#67	—	4	8	no	—
471	C₂×Dic₃	—	2	4	no	—
472	C₂×Dic₃	—	2	4	no	—
473	C₂×Dic₃	—	4	4	no	—
474	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
475	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
476	D₁₂	—	2	16	no	—
477	D₁₂	—	4	4	no	—
478	C₄×D₃	—	2	16	no	—
479	C₂²×C₅	—	2	2	no	—
480	C₂²×C₅	—	2	2	no	—
481	C₂²×C₅	—	2	8	no	—
482	C₂²×C₅	—	2	4	no	—
483	C₂²×C₅	—	2	4	no	—
484	C₂²×C₅	—	2	4	no	—
485	C₂²×C₅	—	3	8	no	—
486	C₂²×C₅	—	4	8	no	—
487	C₂²×C₅	—	6	4	no	—
488	C₂²×C₅	—	6	4	no	—
489	C₂²×C₅	—	6	16	no	—
490	C₂²×C₅	—	6	4	no	—
491	C₂²×C₅	—	6	4	no	—
492	C₂²×C₅	—	6	4	no	—
493	C₂²×C₅	—	12	16	no	—
494	C₂²×C₅	—	12	32	no	—
495	C₂²×C₅	—	12	8	no	—
496	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
497	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
498	C₂²×C₅	#1004	1	2	yes	—
499	C₂²×C₅	#1009	1	2	yes	—
500	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
501	C₄×C₅	—	2	4	no	—
502	C₄×C₅	—	2	2	no	—
503	C₄×C₅	—	2	2	no	—
504	C₄×C₅	—	6	4	no	—
505	C₄×C₅	—	6	4	no	—
506	C₂⁴	—	3	2	no	—
507	C₂⁴	—	3	8	no	—
508	C₂⁴	—	3	4	no	—
509	C₂⁴	—	3	2	no	—
510	C₂⁴	—	3	8	no	—
511	C₂⁴	—	6	8	no	—
512	C₂⁴	—	12	2	no	—
513	C₂⁴	—	12	2	no	—
514	C₂⁴	—	12	4	no	—
515	C₂⁴	—	12	4	no	—
516	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
517	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
518	C₂×D₄	—	2	8	no	—
519	C₂×D₄	—	3	8	no	—
520	C₂×D₄	—	3	8	no	—
521	C₂×D₄	—	3	8	no	—
522	C₂×D₄	—	3	8	no	—
523	C₂×D₄	—	3	4	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	—	6	8	no	—
526	C₂×D₄	—	6	64	no	—
527	C₂×D₄	—	6	8	no	—
528	C₂×D₄	—	6	8	no	—
529	C₂×D₄	—	12	2	no	—
530	C₂×D₄	—	12	4	no	—
531	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
532	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
533	C₂²×C₄	—	3	2	no	—
534	C₂²×C₄	—	3	2	no	—
535	C₂²×C₄	—	3	4	no	—
536	C₂²×C₄	—	3	8	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	6	8	no	—
539	C₂²×C₄	—	12	2	no	—
540	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
543	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
544	C₄⋊C₄	—	3	8	no	—
545	C₄⋊C₄	—	3	4	no	—
546	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
547	C₂²⋊C₄	—	3	8	no	—
548	C₂²⋊C₄	—	3	8	no	—
549	C₂²⋊C₄	—	3	8	no	—
550	C₂²⋊C₄	—	3	8	no	—
551	C₂²⋊C₄	—	3	8	no	—
552	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	complemented
553	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
554	C₂²×C₃	—	2	8	no	—
555	C₂²×C₃	—	2	2	no	—
556	C₂²×C₃	—	2	2	no	—
557	C₂²×C₃	—	2	4	no	—
558	C₂²×C₃	—	2	4	no	—
559	C₂²×C₃	—	2	4	no	—
560	C₂²×C₃	—	4	8	no	—
561	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
562	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
563	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
564	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
565	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
566	C₂×D₃	—	2	16	no	—
567	C₂×D₃	—	2	4	no	—
568	C₂×D₃	—	2	4	no	—
569	C₂×D₃	—	2	4	no	—
570	C₂×D₃	—	2	4	no	—
571	C₂×D₃	—	2	4	no	—
572	C₂×D₃	—	4	16	no	—
573	C₂×D₃	—	4	32	no	—
574	C₂×D₃	—	4	8	no	—
575	C₂×D₃	C₂²×C₅×D₄	1	8	yes	—
576	C₃×C₄	—	2	4	no	—
577	C₃×C₄	—	2	2	no	—
578	C₃×C₄	—	2	2	no	—
579	Dic₃	—	2	4	no	—
580	Dic₃	—	2	4	no	—
581	C₂×C₅	—	2	4	no	—
582	C₂×C₅	—	4	4	no	—
583	C₂×C₅	—	6	8	no	—
584	C₂×C₅	—	12	4	no	—
585	C₂×C₅	#5605	1	4	yes	direct product factor
586	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
587	C₂×C₅	C₂×#1004	1	1	yes	characteristic
588	C₂×C₅	C₂×#1009	1	1	yes	characteristic
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	3	8	no	—
595	C₂³	—	3	4	no	—
596	C₂³	—	3	16	no	—
597	C₂³	—	3	4	no	—
598	C₂³	—	6	16	no	—
599	C₂³	—	6	4	no	—
600	C₂³	—	6	4	no	—
601	C₂³	—	6	4	no	—
602	C₂³	—	6	4	no	—
603	C₂³	—	6	4	no	—
604	C₂³	—	12	4	no	—
605	C₂³	—	12	4	no	—
606	C₂³	—	12	16	no	—
607	C₂³	—	12	8	no	—
608	C₂³	—	12	8	no	—
609	C₂³	—	12	32	no	—
610	C₂³	C₅×D₃×D₄	1	4	yes	—
611	C₂³	C₂³×C₅×D₃	1	4	yes	—
612	C₂³	C₂³×C₅×D₃	1	2	yes	—
613	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
614	D₄	—	2	16	no	—
615	D₄	—	4	4	no	—
616	D₄	—	6	16	no	—
617	D₄	—	6	16	no	—
618	D₄	—	6	16	no	—
619	D₄	—	12	4	no	—
620	D₄	—	12	8	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	3	4	no	—
625	C₂×C₄	—	3	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	6	16	no	—
628	C₂×C₄	—	6	4	no	—
629	C₂×C₄	—	6	4	no	—
630	C₂×C₄	—	12	4	no	—
631	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
632	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
633	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
634	C₂×C₃	—	2	4	no	—
635	C₂×C₃	—	4	4	no	—
636	C₂×C₃	C₅×#534	1	4	yes	complemented
637	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
638	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
640	D₃	—	2	8	no	—
641	D₃	—	4	4	no	—
642	C₅	C₂×#5605	1	1	yes	characteristic, direct product factor, Sylow
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	3	8	no	—
650	C₂²	—	4	8	no	—
651	C₂²	—	6	4	no	—
652	C₂²	—	6	4	no	—
653	C₂²	—	6	16	no	—
654	C₂²	—	6	4	no	—
655	C₂²	—	6	4	no	—
656	C₂²	—	6	4	no	—
657	C₂²	—	12	16	no	—
658	C₂²	—	12	32	no	—
659	C₂²	—	12	8	no	—
660	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
661	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
662	C₂²	C₅×#1004	1	2	yes	—
663	C₂²	C₅×#1009	1	2	yes	—
664	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	6	4	no	—
669	C₄	—	6	4	no	—
670	C₃	C₂×C₅×#534	1	1	yes	characteristic, complemented, Sylow
671	C₂	—	2	4	no	—
672	C₂	—	4	4	no	—
673	C₂	—	6	8	no	—
674	C₂	—	12	4	no	—
675	C₂	C₅×#5605	1	4	yes	direct product factor
676	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
677	C₂	C₂×C₅×#1004	1	1	yes	characteristic
678	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×#534
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. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₅×#939	C₂	semidirect
4. C₂×C₅×#937	C₂	semidirect
5. C₂×C₅×#930	C₂	semidirect
6. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₅×#5605	C₂	direct (N × H)
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×#883	C₂	semidirect
10. C₂×C₅×#882	C₂	semidirect
13. C₂⁴×C₅×D₃	C₂²	semidirect
14. C₂²×C₃×C₅×D₄	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂³×C₃×C₄×C₅	C₂²	semidirect
18. C₂²×C₅×#67	C₂²	semidirect
19. C₂²×C₅×#67	C₂²	semidirect
20. C₂³×C₅×Dic₃	C₂²	semidirect
22. C₂×C₅×D₃×D₄	C₂²	semidirect
24. C₂²×C₅×D₁₂	C₂²	semidirect
25. C₂²×C₄×C₅×D₃	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
27. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₅×#217	C₂²	semidirect
30. C₅×#939	C₂²	semidirect
31. C₅×#937	C₂²	semidirect
32. C₅×#930	C₂²	semidirect
33. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
38. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
39. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
40. C₅×#894	C₂²	semidirect
41. C₅×#883	C₂²	semidirect
42. C₅×#882	C₂²	semidirect
43. C₂×#5605	C₅	direct (N × H)
50. C₂×C₅×#121	D₃	semidirect
61. C₂³×C₅×D₃	D₄	semidirect
65. C₂³×C₅×D₃	C₂³	semidirect
68. C₂×C₃×C₅×D₄	C₂³	semidirect
69. C₂×C₃×C₅×D₄	C₂³	semidirect
74. C₂²×C₃×C₄×C₅	C₂³	semidirect
79. C₂×C₅×#67	C₂³	semidirect
80. C₂×C₅×#67	C₂³	semidirect
84. C₂²×C₅×Dic₃	C₂³	semidirect
89. C₂×C₅×D₁₂	C₂³	semidirect
91. C₂×C₄×C₅×D₃	C₂³	semidirect
92. C₃×C₅×C₄⋊C₄	C₂³	semidirect
93. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
94. C₅×#217	C₂³	semidirect
95. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
96. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
97. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
98. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
99. C₅×C₄⋊Dic₃	C₂³	semidirect
100. C₅×Dic₃⋊C₄	C₂³	semidirect
101. C₂²×D₃×D₄	C₂×C₅	semidirect
102. C₂×C₃×#121	C₂×C₅	semidirect
103. C₂×#939	C₂×C₅	semidirect
104. C₂×#937	C₂×C₅	semidirect
105. C₂×#930	C₂×C₅	semidirect
106. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
107. #5605	C₂×C₅	direct (N × H)
108. C₂×#894	C₂×C₅	semidirect
109. C₂×#883	C₂×C₅	semidirect
110. C₂×#882	C₂×C₅	semidirect
120. C₂²×C₅×D₄	C₂×D₃	semidirect
121. C₂²×C₅×D₄	C₂×D₃	semidirect
124. C₂³×C₄×C₅	C₂×D₃	semidirect
129. C₅×#121	C₂×D₃	semidirect
134. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
141. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
165. C₂²×C₅×D₃	C₂×D₄	semidirect
189. C₂⁴×D₃	C₂²×C₅	semidirect
190. C₂²×C₃×D₄	C₂²×C₅	semidirect
191. C₂²×C₃×D₄	C₂²×C₅	semidirect
192. C₂³×C₃×C₄	C₂²×C₅	semidirect
194. C₂²×#67	C₂²×C₅	semidirect
195. C₂²×#67	C₂²×C₅	semidirect
196. C₂³×Dic₃	C₂²×C₅	semidirect
198. C₂×D₃×D₄	C₂²×C₅	semidirect
200. C₂²×D₁₂	C₂²×C₅	semidirect
201. C₂²×C₄×D₃	C₂²×C₅	semidirect
202. C₃×#121	C₂²×C₅	semidirect
203. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
204. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
205. C₂×#217	C₂²×C₅	semidirect
206. #939	C₂²×C₅	semidirect
207. #937	C₂²×C₅	semidirect
208. #930	C₂²×C₅	semidirect
209. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
210. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
211. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
212. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
213. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
214. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
215. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
216. #894	C₂²×C₅	semidirect
217. #883	C₂²×C₅	semidirect
218. #882	C₂²×C₅	semidirect
244. C₂×C₅×D₄	C₂²×D₃	semidirect
245. C₂×C₅×D₄	C₂²×D₃	semidirect
256. C₂²×C₄×C₅	C₂²×D₃	semidirect
259. C₅×C₄⋊C₄	C₂²×D₃	semidirect
265. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
272. C₂×#121	C₅×D₃	semidirect
310. C₂³×D₃	C₅×D₄	semidirect
314. C₂³×D₃	C₂³×C₅	semidirect
317. C₂×C₃×D₄	C₂³×C₅	semidirect
318. C₂×C₃×D₄	C₂³×C₅	semidirect
323. C₂²×C₃×C₄	C₂³×C₅	semidirect
328. C₂×#67	C₂³×C₅	semidirect
329. C₂×#67	C₂³×C₅	semidirect
333. C₂²×Dic₃	C₂³×C₅	semidirect
338. C₂×D₁₂	C₂³×C₅	semidirect
340. C₂×C₄×D₃	C₂³×C₅	semidirect
341. C₃×C₄⋊C₄	C₂³×C₅	semidirect
342. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
343. #217	C₂³×C₅	semidirect
344. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
345. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
346. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
347. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
348. C₄⋊Dic₃	C₂³×C₅	semidirect
349. Dic₃⋊C₄	C₂³×C₅	semidirect
404. C₂²×D₄	C₂×C₅×D₃	semidirect
405. C₂²×D₄	C₂×C₅×D₃	semidirect
408. C₂³×C₄	C₂×C₅×D₃	semidirect
413. #121	C₂×C₅×D₃	semidirect
418. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
425. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
428. C₂×C₃×C₅	#534	semidirect
456. C₂²×D₃	C₂×C₅×D₄	semidirect
531. C₂×D₄	C₂²×C₅×D₃	semidirect
532. C₂×D₄	C₂²×C₅×D₃	semidirect
543. C₂²×C₄	C₂²×C₅×D₃	semidirect
546. C₄⋊C₄	C₂²×C₅×D₃	semidirect
552. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
553. C₃×C₅	C₂×#534	semidirect
585. C₂×C₅	#5605	direct (N × H)
636. C₂×C₃	C₅×#534	semidirect
642. C₅	C₂×#5605	direct (N × H)
670. C₃	C₂×C₅×#534	semidirect
675. C₂	C₅×#5605	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
C₂×C₃×C₅×#121	2
C₂×C₅×#939	2
C₂×C₅×#937	2
C₂×C₅×#930	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₅×#5605	2
C₂×C₅×#894	2
C₂×C₅×#883	2
C₂×C₅×#882	2
C₂×C₅×#534	3
C₂×#5605	5

Subgroups — C2×C5×#5605 #14480290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5605 #14480290