Subgroups — C₂×#11751654 #14413395

Order 1920.

1072 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×#91907	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
4	C₂×#91222	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#91160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91159	C₂	1	1	yes	maximal, characteristic, complemented
8	#11751654	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65727	—	3	1	no	maximal, Hall
10	C₂²×D₃×AGL(1,𝔽₅)	—	2	1	no	—
11	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
16	C₂×Dic₃⋊AGL(1,𝔽₅)	—	2	1	no	—
17	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)	—	2	1	no	—
18	C₂×Dic₃×AGL(1,𝔽₅)	—	2	1	no	—
19	D₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
20	D₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
21	#91907	—	2	2	no	—
22	#91907	C₂²	1	4	yes	—
23	C₂×#6705	C₄	1	1	yes	characteristic, complemented
24	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic, complemented
25	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×#6651	C₄	1	1	yes	characteristic, complemented
27	C₂×#6650	C₄	1	1	yes	characteristic, complemented
28	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	D₅×ΓL(1,𝔽₂₅)	C₄	1	4	yes	complemented
30	D₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
31	#91222	C₂²	1	4	yes	complemented
32	C₃×#3994	C₂²	1	4	yes	complemented
33	#91160	C₂²	1	4	yes	complemented
34	#91159	C₂²	1	4	yes	complemented
35	C₂×#4881	—	5	1	no	maximal, Hall
36	C₂×#4130	—	3	1	no	—
37	C₂²×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
38	C₂×D₅×M₁₆	—	3	1	no	—
39	#65727	—	3	8	no	—
40	C₂×#3994	—	3	1	no	—
41	C₂×#3994	D₃	1	1	yes	characteristic, complemented
42	C₂×#3993	—	3	1	no	—
43	C₂×#3993	—	3	1	no	—
44	C₂²×D₃×D₅	D₄	1	1	yes	characteristic
45	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
46	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
47	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
48	C₂²×C₃×AGL(1,𝔽₅)	—	2	1	no	—
49	C₂×D₃×AGL(1,𝔽₅)	—	2	4	no	—
50	C₂×D₃×AGL(1,𝔽₅)	—	4	4	no	—
51	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
54	C₂×#1200	Q₈	1	1	yes	characteristic
55	C₂×D₃×Dic₅	Q₈	1	1	yes	characteristic
56	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
57	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
58	C₄×D₃×D₅	D₄	1	2	yes	—
59	C₄×D₃×D₅	Q₈	1	2	yes	—
60	C₄×D₃×D₅	C₂³	1	2	yes	—
61	C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
62	C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
63	C₄⋊ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
64	C₄⋊ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
65	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
66	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
67	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
68	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
69	Dic₃⋊AGL(1,𝔽₅)	—	2	4	no	—
70	(C₂×D₃)⋊AGL(1,𝔽₅)	—	2	4	no	—
71	Dic₃×AGL(1,𝔽₅)	—	2	4	no	—
72	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic, complemented
74	#6705	C₂×C₄	1	4	yes	complemented
75	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
76	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	4	yes	complemented
77	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic, complemented
78	C₃×C₈×D₅	C₂×C₄	1	2	yes	complemented
79	C₃×C₈×D₅	C₂³	1	2	yes	—
80	#6651	C₂×C₄	1	4	yes	complemented
81	#6650	C₂×C₄	1	4	yes	complemented
82	D₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
83	D₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
85	C₂×#892	—	5	1	no	—
86	C₂×D₃×C₄⋊C₄	—	5	1	no	—
87	C₂×C₃×#107	—	5	1	no	—
88	C₂×#817	—	5	1	no	—
89	C₂×#808	—	5	1	no	—
90	C₂×#807	—	5	1	no	—
91	#4881	—	5	8	no	—
92	C₂³×AGL(1,𝔽₅)	—	6	1	no	—
93	C₂²×C₄×D₅	—	3	1	no	—
94	C₂×C₂²⋊AGL(1,𝔽₅)	—	6	1	no	—
95	#4130	—	3	4	no	—
96	#4130	—	6	2	no	—
97	C₂×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
98	C₂×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
99	C₂×C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
100	C₂×C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
101	C₂×C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
102	C₂×C₄⋊AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
103	C₂×C₄⋊AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
104	C₂×C₄×AGL(1,𝔽₅)	—	6	1	no	—
105	C₂×C₅×M₁₆	—	3	1	no	—
106	C₂×#681	—	3	1	no	—
107	D₅×M₁₆	—	3	4	no	—
108	D₅×M₁₆	—	3	4	no	—
109	C₂×#676	—	3	1	no	—
110	C₂×#676	—	3	1	no	—
111	C₂×C₈×D₅	—	3	1	no	—
112	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
113	#3994	—	3	4	no	—
114	#3994	C₂×D₃	1	4	yes	complemented
115	#3993	—	3	4	no	—
116	#3993	—	3	4	no	—
117	C₂×#428	—	15	1	no	Sylow
118	C₂²×D₁₅	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
121	C₂×D₃×D₅	—	2	2	no	—
122	C₂×D₃×D₅	—	2	2	no	—
123	C₂×D₃×D₅	C₄⋊C₄	1	2	yes	—
124	C₂×D₃×D₅	C₂×D₄	1	2	yes	—
125	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
126	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
127	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
128	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
129	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
130	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
131	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
132	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
133	D₃×AGL(1,𝔽₅)	—	4	8	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₅	C₄⋊C₄	1	1	yes	characteristic
136	C₄×D₁₅	C₄⋊C₄	1	2	yes	—
137	C₄×D₁₅	C₂²×C₄	1	2	yes	—
138	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
139	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
140	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
141	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
142	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
143	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
144	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
145	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
146	#1200	C₄⋊C₄	1	2	yes	—
147	#1200	C₂×Q₈	1	2	yes	—
148	D₃×Dic₅	C₄⋊C₄	1	2	yes	—
149	D₃×Dic₅	C₂×Q₈	1	2	yes	—
150	D₅×Dic₃	C₄⋊C₄	1	2	yes	—
151	D₅×Dic₃	C₂×D₄	1	2	yes	—
152	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
153	C₃⋊#168	C₂²×C₄	1	2	yes	complemented
154	C₃×#168	C₂²×C₄	1	2	yes	complemented
155	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
156	C₂²×C₄×D₃	—	5	1	no	—
157	C₂²×C₄×D₃	—	10	1	no	—
158	C₂²×C₃×C₈	—	5	1	no	—
159	C₂×C₃×C₄⋊C₄	—	5	1	no	—
160	C₂×C₃×C₄⋊C₄	—	5	1	no	—
161	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
162	C₂×C₄⋊Dic₃	—	5	1	no	—
163	C₂×C₄⋊Dic₃	—	5	1	no	—
164	C₂×Dic₃⋊C₄	—	10	1	no	—
165	C₂×C₄×Dic₃	—	10	1	no	—
166	C₂²×C₃⋊C₈	—	5	1	no	—
167	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
168	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
169	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
170	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
171	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
172	C₂×ΓL(1,𝔽₂₅)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
173	#892	—	5	4	no	—
174	#892	—	10	2	no	—
175	D₃×C₄⋊C₄	—	5	4	no	—
176	D₃×C₄⋊C₄	—	10	2	no	—
177	C₃×#107	—	5	4	no	—
178	#817	—	5	4	no	—
179	#808	—	5	4	no	—
180	#807	—	5	4	no	—
181	C₂³×D₅	—	3	1	no	—
182	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
183	C₂²×AGL(1,𝔽₅)	—	2	1	no	—
184	C₂²×AGL(1,𝔽₅)	—	6	4	no	—
185	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
186	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
187	C₂²×AGL(1,𝔽₅)	—	12	4	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂²×Dic₅	—	3	1	no	—
190	C₂×C₄×D₅	—	3	1	no	—
191	C₂×C₄×D₅	—	3	1	no	—
192	C₂×C₄×D₅	—	3	1	no	—
193	C₂×C₄×D₅	—	3	2	no	—
194	C₂×C₄×D₅	—	3	2	no	—
195	C₂×C₄×D₅	—	3	2	no	—
196	C₂×C₄×D₅	—	3	2	no	—
197	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
198	C₂²⋊AGL(1,𝔽₅)	—	6	4	no	—
199	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
200	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
201	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
202	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
203	C₄⋊AGL(1,𝔽₅)	—	6	4	no	—
204	C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
205	C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
206	C₄⋊AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
207	C₄⋊AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
208	C₄×AGL(1,𝔽₅)	—	6	4	no	—
209	C₅×M₁₆	—	3	4	no	—
210	C₂×C₅×C₈	—	3	1	no	—
211	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic, complemented
212	#681	—	3	4	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	C₄×D₃	1	1	yes	characteristic, complemented
215	#676	—	3	4	no	—
216	#676	—	3	4	no	—
217	C₈×D₅	—	3	2	no	—
218	C₈×D₅	—	3	2	no	—
219	C₈×D₅	C₄×D₃	1	2	yes	complemented
220	C₈×D₅	C₂²×D₃	1	2	yes	—
221	C₂²×M₁₆	—	15	1	no	—
222	C₂×#117	—	15	1	no	—
223	C₂²×C₄⋊C₄	—	15	1	no	—
224	#428	—	15	8	no	—
225	C₂×#107	—	5	1	no	—
226	C₂×#107	—	15	1	no	—
227	C₂×#106	—	15	1	no	—
228	C₂×#106	—	15	1	no	—
229	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×D₁₅	—	2	2	no	—
231	C₂×D₁₅	C₂×C₄⋊C₄	1	2	yes	—
232	C₂×C₅×D₃	—	2	2	no	—
233	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
234	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₃×D₅	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₃×D₅	#137	1	2	yes	—
237	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
238	D₃×D₅	—	2	2	no	—
239	D₃×D₅	—	2	2	no	—
240	D₃×D₅	—	2	4	no	—
241	ΓL(1,𝔽₁₆)	—	4	2	no	—
242	ΓL(1,𝔽₁₆)	—	4	2	no	—
243	C₃×AGL(1,𝔽₅)	—	4	2	no	—
244	C₃×AGL(1,𝔽₅)	—	4	2	no	—
245	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
247	Dic₁₅	C₂×C₄⋊C₄	1	2	yes	—
248	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
250	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
251	C₂³×D₃	—	5	1	no	—
252	C₂²×C₃×C₄	—	5	1	no	—
253	C₂²×C₃×C₄	—	10	1	no	—
254	C₂²×C₃×C₄	—	10	1	no	—
255	C₂²×Dic₃	—	5	1	no	—
256	C₂²×Dic₃	—	10	1	no	—
257	C₂²×Dic₃	—	10	1	no	—
258	C₂×C₄×D₃	—	5	1	no	—
259	C₂×C₄×D₃	—	5	1	no	—
260	C₂×C₄×D₃	—	5	1	no	—
261	C₂×C₄×D₃	—	5	2	no	—
262	C₂×C₄×D₃	—	5	2	no	—
263	C₂×C₄×D₃	—	5	2	no	—
264	C₂×C₄×D₃	—	5	2	no	—
265	C₂×C₄×D₃	—	10	4	no	—
266	C₂×C₄×D₃	—	20	4	no	—
267	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
268	C₂×C₃×C₈	—	5	1	no	—
269	C₂×C₃×C₈	—	5	2	no	—
270	C₂×C₃×C₈	—	5	2	no	—
271	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
272	C₃×C₄⋊C₄	—	5	2	no	—
273	C₃×C₄⋊C₄	—	5	2	no	—
274	C₃×C₄⋊C₄	—	10	1	no	—
275	C₃×C₄⋊C₄	—	10	1	no	—
276	(C₂×D₃)⋊C₄	—	10	4	no	—
277	C₄⋊Dic₃	—	5	2	no	—
278	C₄⋊Dic₃	—	5	2	no	—
279	C₄⋊Dic₃	—	10	1	no	—
280	C₄⋊Dic₃	—	10	1	no	—
281	Dic₃⋊C₄	—	10	4	no	—
282	C₄×Dic₃	—	10	4	no	—
283	C₂×C₃⋊C₈	—	5	1	no	—
284	C₂×C₃⋊C₈	—	5	2	no	—
285	C₂×C₃⋊C₈	—	5	2	no	—
286	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
287	ΓL(1,𝔽₂₅)	—	5	4	no	—
288	ΓL(1,𝔽₂₅)	—	5	4	no	—
289	ΓL(1,𝔽₂₅)	—	5	4	no	—
290	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
291	C₂³×C₅	—	3	1	no	—
292	C₂²×D₅	—	3	1	no	—
293	C₂²×D₅	—	3	2	no	—
294	C₂²×D₅	—	3	2	no	—
295	C₂²×D₅	—	6	2	no	—
296	C₂²×D₅	—	6	2	no	—
297	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
298	C₂×AGL(1,𝔽₅)	—	2	2	no	—
299	C₂×AGL(1,𝔽₅)	—	2	2	no	—
300	C₂×AGL(1,𝔽₅)	—	4	2	no	—
301	C₂×AGL(1,𝔽₅)	—	4	2	no	—
302	C₂×AGL(1,𝔽₅)	—	6	2	no	—
303	C₂×AGL(1,𝔽₅)	—	6	2	no	—
304	C₂×AGL(1,𝔽₅)	—	12	8	no	—
305	C₂×AGL(1,𝔽₅)	—	12	2	no	—
306	C₂×AGL(1,𝔽₅)	—	12	2	no	—
307	C₂×C₄×C₅	—	3	1	no	—
308	C₂×C₄×C₅	—	3	2	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
311	C₂×Dic₅	—	3	1	no	—
312	C₂×Dic₅	—	3	2	no	—
313	C₂×Dic₅	—	3	2	no	—
314	C₂×Dic₅	D₃×Q₈	1	1	yes	characteristic
315	C₄×D₅	—	3	2	no	—
316	C₄×D₅	—	3	2	no	—
317	C₄×D₅	—	3	2	no	—
318	C₄×D₅	—	3	2	no	—
319	C₄×D₅	—	3	2	no	—
320	C₄×D₅	—	3	2	no	—
321	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
322	C₄×D₅	D₃×D₄	1	1	yes	characteristic
323	C₄×D₅	D₃×Q₈	1	1	yes	characteristic
324	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×C₈	—	3	2	no	—
326	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
327	#168	—	3	2	no	—
328	#168	C₂×C₄×D₃	1	2	yes	complemented
329	C₂³×C₄	—	15	1	no	—
330	C₂³×C₄	—	30	1	no	—
331	C₂×M₁₆	—	3	1	no	—
332	C₂×M₁₆	—	15	1	no	—
333	C₂×M₁₆	—	15	4	no	—
334	C₂×M₁₆	—	15	4	no	—
335	C₂×M₁₆	—	15	1	no	—
336	C₂×M₁₆	—	15	1	no	—
337	C₂²×C₈	—	5	1	no	—
338	C₂²×C₈	—	15	1	no	—
339	#117	—	15	4	no	—
340	#117	—	30	2	no	—
341	C₂×C₄⋊C₄	—	5	1	no	—
342	C₂×C₄⋊C₄	—	5	1	no	—
343	C₂×C₄⋊C₄	—	15	4	no	—
344	C₂×C₄⋊C₄	—	15	1	no	—
345	C₂×C₄⋊C₄	—	15	1	no	—
346	C₂×C₄⋊C₄	—	30	2	no	—
347	C₂×C₄⋊C₄	—	30	1	no	—
348	C₂×C₂²⋊C₄	—	30	1	no	—
349	C₂×C₄²	—	30	1	no	—
350	#107	—	5	4	no	—
351	#107	—	15	4	no	—
352	#106	—	15	4	no	—
353	#106	—	15	4	no	—
354	C₂×C₃×C₅	#428	1	2	yes	complemented
355	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
356	D₁₅	—	2	2	no	—
357	C₃×D₅	#428	1	2	yes	complemented
358	C₃×D₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
359	C₃×D₅	C₂×#137	1	1	yes	characteristic
360	C₅×D₃	—	2	2	no	—
361	C₂³×C₃	—	5	1	no	—
362	C₂²×D₃	—	5	1	no	—
363	C₂²×D₃	—	5	2	no	—
364	C₂²×D₃	—	5	2	no	—
365	C₂²×D₃	—	10	2	no	—
366	C₂²×D₃	—	10	2	no	—
367	C₂²×D₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₂×C₃×C₄	—	5	1	no	—
369	C₂×C₃×C₄	—	5	1	no	—
370	C₂×C₃×C₄	—	5	1	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	5	1	no	—
373	C₂×C₃×C₄	—	10	2	no	—
374	C₂×C₃×C₄	—	10	2	no	—
375	C₂×C₃×C₄	—	20	2	no	—
376	C₂×C₃×C₄	—	20	2	no	—
377	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₂×Dic₃	—	5	1	no	—
379	C₂×Dic₃	—	5	2	no	—
380	C₂×Dic₃	—	5	2	no	—
381	C₂×Dic₃	—	10	2	no	—
382	C₂×Dic₃	—	10	2	no	—
383	C₂×Dic₃	—	20	2	no	—
384	C₂×Dic₃	—	20	2	no	—
385	C₂×Dic₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₄×D₃	—	5	2	no	—
387	C₄×D₃	—	5	2	no	—
388	C₄×D₃	—	5	2	no	—
389	C₄×D₃	—	5	2	no	—
390	C₄×D₃	—	5	2	no	—
391	C₄×D₃	—	5	2	no	—
392	C₄×D₃	—	20	8	no	—
393	C₄×D₃	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
394	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
395	C₃×C₈	—	5	2	no	—
396	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
397	C₃⋊C₈	—	5	2	no	—
398	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
399	C₂²×C₅	—	3	2	no	—
400	C₂²×C₅	—	6	2	no	—
401	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
402	C₂×D₅	—	3	2	no	—
403	C₂×D₅	—	6	2	no	—
404	C₂×D₅	—	6	4	no	—
405	C₂×D₅	—	6	2	no	—
406	C₂×D₅	—	6	2	no	—
407	C₂×D₅	D₃×C₄⋊C₄	1	1	yes	characteristic
408	C₂×D₅	#911	1	2	yes	—
409	C₂×D₅	#918	1	2	yes	—
410	C₂×D₅	C₂×D₃×D₄	1	1	yes	characteristic
411	AGL(1,𝔽₅)	—	4	2	no	—
412	AGL(1,𝔽₅)	—	4	2	no	—
413	AGL(1,𝔽₅)	—	12	2	no	—
414	AGL(1,𝔽₅)	—	12	2	no	—
415	C₄×C₅	—	3	2	no	—
416	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
417	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
418	Dic₅	—	3	2	no	—
419	Dic₅	D₃×C₄⋊C₄	1	1	yes	characteristic
420	Dic₅	C₂×D₃×Q₈	1	1	yes	characteristic
421	C₂⁴	—	15	1	no	—
422	C₂²×C₄	—	3	1	no	—
423	C₂²×C₄	—	5	1	no	—
424	C₂²×C₄	—	10	1	no	—
425	C₂²×C₄	—	10	1	no	—
426	C₂²×C₄	—	15	2	no	—
427	C₂²×C₄	—	15	2	no	—
428	C₂²×C₄	—	15	2	no	—
429	C₂²×C₄	—	15	1	no	—
430	C₂²×C₄	—	15	2	no	—
431	C₂²×C₄	—	15	1	no	—
432	C₂²×C₄	—	15	1	no	—
433	C₂²×C₄	—	15	1	no	—
434	C₂²×C₄	—	30	4	no	—
435	C₂²×C₄	—	30	1	no	—
436	C₂²×C₄	—	30	1	no	—
437	C₂²×C₄	—	60	4	no	—
438	M₁₆	—	3	4	no	—
439	M₁₆	—	15	4	no	—
440	M₁₆	—	15	4	no	—
441	M₁₆	—	15	4	no	—
442	C₂×C₈	—	3	1	no	—
443	C₂×C₈	—	5	1	no	—
444	C₂×C₈	—	5	2	no	—
445	C₂×C₈	—	5	2	no	—
446	C₂×C₈	—	15	2	no	—
447	C₂×C₈	—	15	2	no	—
448	C₂×C₈	—	15	1	no	—
449	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
450	C₄⋊C₄	—	5	2	no	—
451	C₄⋊C₄	—	5	2	no	—
452	C₄⋊C₄	—	10	1	no	—
453	C₄⋊C₄	—	10	1	no	—
454	C₄⋊C₄	—	15	2	no	—
455	C₄⋊C₄	—	15	2	no	—
456	C₄⋊C₄	—	30	1	no	—
457	C₄⋊C₄	—	30	1	no	—
458	C₄⋊C₄	—	30	4	no	—
459	C₂²⋊C₄	—	30	4	no	—
460	C₄²	—	30	4	no	—
461	C₃×C₅	C₂×#428	1	1	yes	characteristic, complemented, Hall
462	C₂²×C₃	—	5	2	no	—
463	C₂²×C₃	—	5	2	no	—
464	C₂²×C₃	—	5	1	no	—
465	C₂²×C₃	—	5	1	no	—
466	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	5	2	no	—
469	C₂×D₃	—	10	2	no	—
470	C₂×D₃	—	10	2	no	—
471	C₂×D₃	—	10	4	no	—
472	C₂×D₃	—	10	2	no	—
473	C₂×D₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
474	C₃×C₄	—	5	1	no	—
475	C₃×C₄	—	5	1	no	—
476	C₃×C₄	—	20	2	no	—
477	C₃×C₄	—	20	2	no	—
478	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
480	Dic₃	—	5	2	no	—
481	Dic₃	—	20	2	no	—
482	Dic₃	—	20	2	no	—
483	Dic₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
484	C₂×C₅	—	6	2	no	—
485	C₂×C₅	#4881	1	2	yes	complemented
486	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
487	D₅	—	6	2	no	—
488	D₅	#4881	1	2	yes	complemented
489	D₅	C₂×#911	1	1	yes	characteristic
490	D₅	C₂×#918	1	1	yes	characteristic
491	C₂³	—	3	1	no	—
492	C₂³	—	5	1	no	—
493	C₂³	—	15	2	no	—
494	C₂³	—	15	2	no	—
495	C₂³	—	15	1	no	—
496	C₂³	—	30	2	no	—
497	C₂³	—	30	2	no	—
498	C₂×C₄	—	3	1	no	—
499	C₂×C₄	—	3	2	no	—
500	C₂×C₄	—	3	2	no	—
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	10	2	no	—
507	C₂×C₄	—	10	2	no	—
508	C₂×C₄	—	15	2	no	—
509	C₂×C₄	—	15	2	no	—
510	C₂×C₄	—	15	2	no	—
511	C₂×C₄	—	15	2	no	—
512	C₂×C₄	—	15	2	no	—
513	C₂×C₄	—	15	2	no	—
514	C₂×C₄	—	15	1	no	—
515	C₂×C₄	—	15	2	no	—
516	C₂×C₄	—	15	2	no	—
517	C₂×C₄	—	20	2	no	—
518	C₂×C₄	—	20	2	no	—
519	C₂×C₄	—	30	2	no	—
520	C₂×C₄	—	30	2	no	—
521	C₂×C₄	—	60	8	no	—
522	C₂×C₄	—	60	2	no	—
523	C₂×C₄	—	60	2	no	—
524	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
525	C₈	—	3	2	no	—
526	C₈	—	5	2	no	—
527	C₈	—	15	2	no	—
528	C₈	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	complemented
529	C₂×C₃	—	5	1	no	—
530	C₂×C₃	—	5	1	no	—
531	C₂×C₃	—	5	2	no	—
532	C₂×C₃	#65727	1	2	yes	complemented
533	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
534	D₃	—	2	2	no	—
535	D₃	—	10	2	no	—
536	C₅	C₂×#4881	1	1	yes	characteristic, complemented, Sylow
537	C₂²	—	3	2	no	—
538	C₂²	—	5	1	no	—
539	C₂²	—	5	1	no	—
540	C₂²	—	5	2	no	—
541	C₂²	—	5	2	no	—
542	C₂²	—	6	2	no	—
543	C₂²	—	15	2	no	—
544	C₂²	—	30	2	no	—
545	C₂²	—	30	2	no	—
546	C₂²	—	30	4	no	—
547	C₂²	—	30	2	no	—
548	C₂²	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
549	C₄	—	3	2	no	—
550	C₄	—	5	1	no	—
551	C₄	—	5	1	no	—
552	C₄	—	15	2	no	—
553	C₄	—	20	2	no	—
554	C₄	—	20	2	no	—
555	C₄	—	60	2	no	—
556	C₄	—	60	2	no	—
557	C₄	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
558	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
559	C₃	C₂×#65727	1	1	yes	characteristic, complemented, Sylow
560	C₂	—	5	1	no	—
561	C₂	—	5	1	no	—
562	C₂	—	5	2	no	—
563	C₂	—	6	2	no	—
564	C₂	—	30	2	no	—
565	C₂	#11751654	1	2	yes	direct product factor
566	C₂	C₂×D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×C₄⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂²×D₃×D₅	D₄
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#428
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×#91222	C₂	semidirect
5. C₂×C₃×#3994	C₂	semidirect
6. C₂×#91160	C₂	semidirect
7. C₂×#91159	C₂	semidirect
8. #11751654	C₂	direct (N × H)
23. C₂×#6705	C₄	semidirect
24. C₂×C₅×ΓL(1,𝔽₂₅)	C₄	semidirect
26. C₂×#6651	C₄	semidirect
27. C₂×#6650	C₄	semidirect
29. D₅×ΓL(1,𝔽₂₅)	C₄	semidirect
31. #91222	C₂²	semidirect
32. C₃×#3994	C₂²	semidirect
33. #91160	C₂²	semidirect
34. #91159	C₂²	semidirect
41. C₂×#3994	D₃	semidirect
72. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
73. C₂×C₃⋊#168	C₂×C₄	semidirect
74. #6705	C₂×C₄	semidirect
75. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
76. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
77. C₂×C₃×#168	C₂×C₄	semidirect
78. C₃×C₈×D₅	C₂×C₄	semidirect
80. #6651	C₂×C₄	semidirect
81. #6650	C₂×C₄	semidirect
82. D₅×C₃⋊C₈	C₂×C₄	semidirect
114. #3994	C₂×D₃	semidirect
152. C₃×C₅×C₈	C₂²×C₄	semidirect
153. C₃⋊#168	C₂²×C₄	semidirect
154. C₃×#168	C₂²×C₄	semidirect
155. C₅×C₃⋊C₈	C₂²×C₄	semidirect
172. C₂×ΓL(1,𝔽₂₅)	AGL(1,𝔽₅)	semidirect
211. C₂×C₅×C₈	C₄×D₃	semidirect
214. C₂×#168	C₄×D₃	semidirect
219. C₈×D₅	C₄×D₃	semidirect
271. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
286. C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	semidirect
290. ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	semidirect
326. C₅×C₈	C₂×C₄×D₃	semidirect
328. #168	C₂×C₄×D₃	semidirect
354. C₂×C₃×C₅	#428	semidirect
357. C₃×D₅	#428	semidirect
396. C₃×C₈	C₂²×AGL(1,𝔽₅)	semidirect
398. C₃⋊C₈	C₂²×AGL(1,𝔽₅)	semidirect
449. C₂×C₈	D₃×AGL(1,𝔽₅)	semidirect
461. C₃×C₅	C₂×#428	semidirect
485. C₂×C₅	#4881	semidirect
488. D₅	#4881	semidirect
528. C₈	C₂×D₃×AGL(1,𝔽₅)	semidirect
532. C₂×C₃	#65727	semidirect
536. C₅	C₂×#4881	semidirect
559. C₃	C₂×#65727	semidirect
565. C₂	#11751654	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₃×C₄⋊AGL(1,𝔽₅)	2
C₂×#91907	2
C₂×D₅×ΓL(1,𝔽₂₅)	2
C₂×#91222	2
C₂×C₃×#3994	2
C₂×#91160	2
C₂×#91159	2
#11751654	2
C₂×#65727	3
C₂×#4881	5

Subgroups — C2×#11751654 #14413395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751654 #14413395