Subgroups — #72242889

Order 5120.

At least 11554 conjugacy classes of subgroups; only the 500 normal subgroups are shown.

The subgroup lattice has 499 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72242878	C₂	1	1	yes	maximal, characteristic, complemented
2	#72242874	C₂	1	1	yes	maximal, characteristic, complemented
3	#72242869	C₂	1	1	yes	maximal, characteristic, complemented
4	#72242866	C₂	1	1	yes	maximal, characteristic, complemented
5	#72242862	C₂	1	1	yes	maximal, characteristic, complemented
6	#72242860	C₂	1	1	yes	maximal, characteristic, complemented
7	#72242858	C₂	1	1	yes	maximal, characteristic, complemented
8	#72242843	C₂	1	1	yes	maximal, characteristic, complemented
9	#72242832	C₂	1	1	yes	maximal, characteristic, complemented
10	#72242827	C₂	1	1	yes	maximal, characteristic, complemented
11	#72242800	C₂	1	1	yes	maximal, characteristic, complemented
12	#72242743	C₂	1	1	yes	maximal, characteristic, complemented
13	#72242710	C₂	1	1	yes	maximal, characteristic, complemented
14	D₅×#33551	C₂	1	1	yes	maximal, characteristic
15	#72221422	C₂	1	1	yes	maximal, characteristic, complemented
16	#13044250	C₂²	1	1	yes	characteristic
17	#13044249	C₂²	1	1	yes	characteristic
18	#13044199	C₂²	1	1	yes	characteristic
19	#13044108	C₂²	1	1	yes	characteristic
20	#13044107	C₂²	1	1	yes	characteristic
21	#13044099	C₂²	1	1	yes	characteristic, complemented
22	C₂×AGL(1,𝔽₅)×#120	C₂²	1	1	yes	characteristic
23	D₅⋊#2127	C₂²	1	1	yes	characteristic
24	D₅⋊#2121	C₂²	1	1	yes	characteristic
25	C₂×D₅⋊AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
26	D₅⋊#1913	C₂²	1	1	yes	characteristic
27	D₅⋊#1911	C₂²	1	1	yes	characteristic
28	C₂×#10604461	C₂²	1	1	yes	characteristic
29	#13034200	C₂²	1	1	yes	characteristic, complemented
30	#13034191	C₂²	1	1	yes	characteristic, complemented
31	C₂×#10605017	C₂²	1	1	yes	characteristic, complemented
32	#13025588	C₂²	1	1	yes	characteristic, complemented
33	#13025588	C₂²	1	1	yes	characteristic, complemented
34	#13025554	C₂²	1	1	yes	characteristic, complemented
35	#13025550	C₂²	1	1	yes	characteristic, complemented
36	C₂×#10598573	C₂²	1	1	yes	characteristic, complemented
37	C₂×#10598567	C₂²	1	1	yes	characteristic, complemented
38	#13021798	C₂²	1	1	yes	characteristic, complemented
39	#13021793	C₂²	1	1	yes	characteristic, complemented
40	#13021793	C₂²	1	1	yes	characteristic, complemented
41	#13021773	C₂²	1	1	yes	characteristic, complemented
42	#13021743	C₂²	1	1	yes	characteristic, complemented
43	#13021725	C₂²	1	1	yes	characteristic, complemented
44	D₅×#3532	C₂²	1	1	yes	characteristic
45	D₅×#3026	C₂²	1	1	yes	characteristic
46	C₂×D₅×B(4,𝔽₂)	C₂²	1	1	yes	characteristic
47	D₅×#3019	C₂²	1	1	yes	characteristic
48	#12253364	C₄	1	1	yes	characteristic, complemented
49	#12253363	C₄	1	1	yes	characteristic, complemented
50	#12253362	C₄	1	1	yes	characteristic, complemented
51	#12253361	C₄	1	1	yes	characteristic, complemented
52	#12253359	C₄	1	1	yes	characteristic, complemented
53	#12253357	C₄	1	1	yes	characteristic, complemented
54	#12253355	C₄	1	1	yes	characteristic, complemented
55	D₅×#2127	C₂²	1	1	yes	characteristic
56	D₅×#2121	C₂²	1	1	yes	characteristic
57	C₂×D₅×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
58	C₅×#33551	C₄	1	1	yes	characteristic, complemented
59	C₂⁵×AGL(1,𝔽₅)	D₄	1	1	yes	characteristic, complemented
60	C₂×D₅×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
61	C₂×#66266	D₄	1	1	yes	characteristic, complemented
62	C₂×#66258	D₄	1	1	yes	characteristic, complemented
63	C₂×#66258	C₂³	1	1	yes	characteristic
64	C₂²×D₄×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
65	C₅×#3532	C₂×C₄	1	1	yes	characteristic
66	#10618991	D₄	1	1	yes	characteristic
67	D₅×H(3,𝔽₄)	D₄	1	1	yes	characteristic
68	#10618981	D₄	1	1	yes	characteristic
69	D₅×#560	D₄	1	1	yes	characteristic
70	#10618719	D₄	1	1	yes	characteristic
71	D₅×#551	D₄	1	1	yes	characteristic
72	#10618523	D₄	1	1	yes	characteristic
73	D₄²×D₅	D₄	1	1	yes	characteristic
74	#10618234	C₂×C₄	1	1	yes	characteristic
75	D₅×#535	C₂³	1	1	yes	characteristic
76	#10618211	C₂×C₄	1	1	yes	characteristic
77	D₅×#534	C₂³	1	1	yes	characteristic
78	#10617822	C₂×C₄	1	1	yes	characteristic
79	C₂×D₅×#120	C₂³	1	1	yes	characteristic
80	C₂×#65800	D₄	1	1	yes	characteristic, complemented
81	#10617555	D₄	1	1	yes	characteristic, complemented
82	#10617507	C₂³	1	1	yes	characteristic
83	#10617506	C₂³	1	1	yes	characteristic
84	C₂×#65779	D₄	1	1	yes	characteristic, complemented
85	C₂×#65779	C₂³	1	1	yes	characteristic
86	C₂×D₅⋊#100	C₂³	1	1	yes	characteristic
87	C₂×D₅⋊#99	C₂³	1	1	yes	characteristic
88	C₂×D₅⋊#99	C₂³	1	1	yes	characteristic
89	#10617370	D₄	1	1	yes	characteristic, complemented
90	#10617369	D₄	1	1	yes	characteristic, complemented
91	#10617328	D₄	1	1	yes	characteristic, complemented
92	#10617327	D₄	1	1	yes	characteristic, complemented
93	#10617308	D₄	1	1	yes	characteristic, complemented
94	#10617307	D₄	1	1	yes	characteristic, complemented
95	#10617224	D₄	1	1	yes	characteristic, complemented
96	#10617224	D₄	1	1	yes	characteristic, complemented
97	#10617224	D₄	1	1	yes	characteristic, complemented
98	#10617223	D₄	1	1	yes	characteristic, complemented
99	#10617223	D₄	1	1	yes	characteristic, complemented
100	#10617223	D₄	1	1	yes	characteristic, complemented
101	#10617128	D₄	1	1	yes	characteristic, complemented
102	#10617127	D₄	1	1	yes	characteristic, complemented
103	C₂×#65699	D₄	1	1	yes	characteristic, complemented
104	C₂×#65699	D₄	1	1	yes	characteristic, complemented
105	#10617067	D₄	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×AGL(1,𝔽₅)	D₄	1	1	yes	characteristic, complemented
107	C₅×#3026	C₂×C₄	1	1	yes	characteristic, complemented
108	C₂×C₅×B(4,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
109	C₅×#3019	C₂×C₄	1	1	yes	characteristic, complemented
110	#10615841	C₂×C₄	1	1	yes	characteristic, complemented
111	C₂×#65533	C₂×C₄	1	1	yes	characteristic, complemented
112	#10615835	C₂×C₄	1	1	yes	characteristic, complemented
113	#10615125	C₂×C₄	1	1	yes	characteristic, complemented
114	#10615106	C₂×C₄	1	1	yes	characteristic, complemented
115	C₂×#65321	C₂×C₄	1	1	yes	characteristic, complemented
116	#10610431	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂×D₅×#100	C₂³	1	1	yes	characteristic
118	C₂×D₅×#99	C₂³	1	1	yes	characteristic
119	C₂×D₅×#99	C₂³	1	1	yes	characteristic
120	#10610417	C₂×C₄	1	1	yes	characteristic, complemented
121	C₂×#65030	C₂×C₄	1	1	yes	characteristic, complemented
122	C₅×#2127	C₂×C₄	1	1	yes	characteristic, complemented
123	C₅×#2121	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂×C₅×AΣL(1,𝔽₁₆)	C₂×C₄	1	1	yes	characteristic, complemented
125	#10602653	C₂×C₄	1	1	yes	characteristic, complemented
126	#10602640	C₂×C₄	1	1	yes	characteristic, complemented
127	C₂×#64756	C₂×C₄	1	1	yes	characteristic, complemented
128	#10600887	C₂×C₄	1	1	yes	characteristic, complemented
129	C₂×#64695	C₂×C₄	1	1	yes	characteristic, complemented
130	#10600812	C₂×C₄	1	1	yes	characteristic, complemented
131	#10600812	C₂×C₄	1	1	yes	characteristic, complemented
132	#10600808	C₂×C₄	1	1	yes	characteristic, complemented
133	C₂×#64691	C₂×C₄	1	1	yes	characteristic, complemented
134	C₂⁵×D₅	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
137	C₂⁴×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic, complemented
139	C₂×D₅×#41	C₂×D₄	1	1	yes	characteristic
140	C₂×#4144	C₂²×C₄	1	1	yes	characteristic, complemented
141	C₂²×D₄×D₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×D₄×D₅	C₂⁴	1	1	yes	characteristic
143	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
148	C₂×#4130	C₂×D₄	1	1	yes	characteristic
149	C₂×#4130	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄⋊AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×AGL(1,𝔽₅)	C₂×D₄	1	1	yes	characteristic
152	C₅×H(3,𝔽₄)	C₂²⋊C₄	1	1	yes	characteristic, complemented
153	C₅×#560	C₂²⋊C₄	1	1	yes	characteristic, complemented
154	C₅×#551	C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₅×D₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	C₅×#535	C₂²×C₄	1	1	yes	characteristic
157	C₅×#534	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₅×#120	C₂²×C₄	1	1	yes	characteristic
159	C₂×#4099	#41	1	1	yes	characteristic
160	#66164	#41	1	1	yes	characteristic
161	#66139	C₂²×C₄	1	1	yes	characteristic
162	#66138	C₂²×C₄	1	1	yes	characteristic
163	#66138	#41	1	1	yes	characteristic
164	C₂×#4083	C₂²×C₄	1	1	yes	characteristic
165	#66054	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	#66051	C₂²⋊C₄	1	1	yes	characteristic, complemented
167	#66049	C₂×D₄	1	1	yes	characteristic
168	#66049	#41	1	1	yes	characteristic
169	D₅×#127	C₂×D₄	1	1	yes	characteristic
170	D₅×#127	C₂×D₄	1	1	yes	characteristic
171	#66017	C₂²⋊C₄	1	1	yes	characteristic, complemented
172	#66013	C₂²⋊C₄	1	1	yes	characteristic, complemented
173	#66008	C₂×D₄	1	1	yes	characteristic
174	#66008	#41	1	1	yes	characteristic
175	D₅×#124	C₂×D₄	1	1	yes	characteristic
176	D₅×#124	C₂×D₄	1	1	yes	characteristic
177	#66000	C₂²⋊C₄	1	1	yes	characteristic, complemented
178	#65993	C₂²⋊C₄	1	1	yes	characteristic, complemented
179	#65987	C₂×D₄	1	1	yes	characteristic
180	#65987	#41	1	1	yes	characteristic
181	D₅×#123	C₂×D₄	1	1	yes	characteristic
182	D₅×#123	C₂×D₄	1	1	yes	characteristic
183	#65929	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	#65928	C₂²⋊C₄	1	1	yes	characteristic, complemented
185	#65928	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	#65924	C₂²⋊C₄	1	1	yes	characteristic, complemented
187	#65924	C₂²⋊C₄	1	1	yes	characteristic, complemented
188	#65923	C₂×D₄	1	1	yes	characteristic
189	#65923	#41	1	1	yes	characteristic
190	D₅×#120	C₂×D₄	1	1	yes	characteristic
191	D₅×#120	C₂×D₄	1	1	yes	characteristic
192	D₅×#120	C₂×D₄	1	1	yes	characteristic
193	D₅×#120	C₂×D₄	1	1	yes	characteristic
194	D₅×#120	C₂×D₄	1	1	yes	characteristic
195	D₅×#120	C₂×D₄	1	1	yes	characteristic
196	D₅×#120	C₂×D₄	1	1	yes	characteristic
197	D₅×#120	C₂×D₄	1	1	yes	characteristic
198	D₅×#120	#41	1	1	yes	characteristic
199	D₅×#120	#41	1	1	yes	characteristic
200	#65921	C₂²⋊C₄	1	1	yes	characteristic, complemented
201	#65859	#41	1	1	yes	characteristic
202	D₅×#117	C₂×D₄	1	1	yes	characteristic
203	#65827	#41	1	1	yes	characteristic
204	C₂×#4028	#41	1	1	yes	characteristic
205	C₂×D₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₂×D₅×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
207	#65780	C₂×D₄	1	1	yes	characteristic
208	#65780	C₂×D₄	1	1	yes	characteristic
209	#65780	C₂×D₄	1	1	yes	characteristic
210	#65780	C₂×D₄	1	1	yes	characteristic
211	#65779	C₂×D₄	1	1	yes	characteristic
212	#65779	C₂×D₄	1	1	yes	characteristic
213	#65779	C₂×D₄	1	1	yes	characteristic
214	#65779	C₂×D₄	1	1	yes	characteristic
215	#65779	C₂×D₄	1	1	yes	characteristic
216	#65779	C₂×D₄	1	1	yes	characteristic
217	#65779	C₂×D₄	1	1	yes	characteristic
218	#65779	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅×#100	C₂²×C₄	1	1	yes	characteristic, complemented
220	C₂×C₅×#99	C₂²×C₄	1	1	yes	characteristic, complemented
221	C₂×C₅×#99	C₂²×C₄	1	1	yes	characteristic, complemented
222	C₂×#3966	C₂²×C₄	1	1	yes	characteristic, complemented
223	C₂×#3966	C₂²×C₄	1	1	yes	characteristic, complemented
224	C₂×#3965	C₂²×C₄	1	1	yes	characteristic, complemented
225	#33551	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
226	C₂⁵×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂⁴×D₅	C₄×D₄	1	1	yes	characteristic
228	C₂⁴×D₅	#120	1	1	yes	characteristic
229	C₂⁴×D₅	#120	1	1	yes	characteristic
230	C₂⁴×D₅	#120	1	1	yes	characteristic
231	C₂⁴×D₅	#121	1	1	yes	characteristic
232	C₂⁴×D₅	#121	1	1	yes	characteristic
233	C₂⁴×D₅	C₂²×D₄	1	1	yes	characteristic
234	C₂⁴×D₅	C₂²×D₄	1	1	yes	characteristic
235	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
236	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
237	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
238	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
239	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
240	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
241	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
242	C₂³×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
243	C₂×C₅×#41	C₄×D₄	1	1	yes	characteristic
244	C₂²×C₅×D₄	C₄×D₄	1	1	yes	characteristic
245	C₂²×C₅×D₄	C₂³×C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊D₅	C₄×D₄	1	1	yes	characteristic
247	C₂²×C₂²⋊D₅	#121	1	1	yes	characteristic
248	C₂²×C₂²⋊D₅	C₂×#41	1	1	yes	characteristic
249	C₂²×C₂²⋊D₅	C₂×#41	1	1	yes	characteristic
250	C₂×#713	#121	1	1	yes	characteristic
251	C₂×Q₈×D₅	#120	1	1	yes	characteristic
252	C₂×#711	#121	1	1	yes	characteristic
253	C₂×D₄×D₅	#120	1	1	yes	characteristic
254	C₂×D₄×D₅	C₂²×D₄	1	1	yes	characteristic
255	C₂×D₄×D₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×D₄×D₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×D₄×D₅	C₂²×D₄	1	1	yes	characteristic
258	C₂×D₄×D₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×D₄×D₅	C₂×#41	1	1	yes	characteristic
260	C₂×D₄×D₅	C₂×#41	1	1	yes	characteristic
261	C₂×D₄×D₅	C₂×#41	1	1	yes	characteristic
262	C₂×#709	C₄×D₄	1	1	yes	characteristic
263	C₂²×D₂₀	#121	1	1	yes	characteristic
264	C₂²×D₂₀	C₂×#41	1	1	yes	characteristic
265	C₂²×C₄×D₅	#120	1	1	yes	characteristic
266	C₂²×C₄×D₅	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₂²⋊AGL(1,𝔽₅)	#120	1	1	yes	characteristic
268	C₂×C₂²⋊AGL(1,𝔽₅)	#120	1	1	yes	characteristic
269	C₂×C₂²⋊AGL(1,𝔽₅)	#120	1	1	yes	characteristic
270	C₂×C₂²⋊AGL(1,𝔽₅)	#120	1	1	yes	characteristic
271	C₂×C₄⋊AGL(1,𝔽₅)	#120	1	1	yes	characteristic
272	C₂×C₄⋊AGL(1,𝔽₅)	#120	1	1	yes	characteristic
273	C₂×C₄×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
274	C₂×C₄×AGL(1,𝔽₅)	#120	1	1	yes	characteristic
275	C₅×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₅×#127	C₄×D₄	1	1	yes	characteristic
277	C₅×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₅×#124	C₄×D₄	1	1	yes	characteristic
279	C₅×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₅×#123	C₄×D₄	1	1	yes	characteristic
281	C₅×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₅×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₅×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₅×#120	C₄×D₄	1	1	yes	characteristic
285	C₅×#120	C₄×D₄	1	1	yes	characteristic
286	C₅×#120	C₄×D₄	1	1	yes	characteristic
287	C₅×#117	C₄×D₄	1	1	yes	characteristic
288	C₂×C₅×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
289	C₂×C₅×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
290	#4099	#121	1	1	yes	characteristic
291	#4099	#121	1	1	yes	characteristic
292	#4099	#121	1	1	yes	characteristic
293	#4099	#123	1	1	yes	characteristic
294	#4099	#123	1	1	yes	characteristic
295	#4099	#123	1	1	yes	characteristic
296	C₂×C₂²⋊Dic₅	C₄×D₄	1	1	yes	characteristic
297	C₂×C₂²⋊Dic₅	C₄×D₄	1	1	yes	characteristic
298	#4093	#121	1	1	yes	characteristic
299	#4093	#123	1	1	yes	characteristic
300	#4086	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	#4086	C₄×D₄	1	1	yes	characteristic
302	#4086	#121	1	1	yes	characteristic
303	#4086	#123	1	1	yes	characteristic
304	#4083	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	#4083	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	#4083	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	#4083	C₄×D₄	1	1	yes	characteristic
308	#4083	C₄×D₄	1	1	yes	characteristic
309	#4083	C₄×D₄	1	1	yes	characteristic
310	#4082	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	#4082	C₄×D₄	1	1	yes	characteristic
312	#4081	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	#4081	C₄×D₄	1	1	yes	characteristic
314	#4075	#121	1	1	yes	characteristic
315	#4075	#123	1	1	yes	characteristic
316	#4072	C₄×D₄	1	1	yes	characteristic
317	#4032	#121	1	1	yes	characteristic
318	#4032	#123	1	1	yes	characteristic
319	#4028	#121	1	1	yes	characteristic
320	#4028	#121	1	1	yes	characteristic
321	#4028	#121	1	1	yes	characteristic
322	#4028	#123	1	1	yes	characteristic
323	#4028	#123	1	1	yes	characteristic
324	#4028	#123	1	1	yes	characteristic
325	D₅×C₂²⋊C₄	#120	1	1	yes	characteristic
326	D₅×C₂²⋊C₄	#120	1	1	yes	characteristic
327	D₅×C₂²⋊C₄	#120	1	1	yes	characteristic
328	D₅×C₂²⋊C₄	#120	1	1	yes	characteristic
329	D₅×C₂²⋊C₄	#121	1	1	yes	characteristic
330	D₅×C₂²⋊C₄	#121	1	1	yes	characteristic
331	D₅×C₂²⋊C₄	#121	1	1	yes	characteristic
332	D₅×C₂²⋊C₄	#121	1	1	yes	characteristic
333	#4021	#121	1	1	yes	characteristic
334	#4021	#123	1	1	yes	characteristic
335	#4020	#121	1	1	yes	characteristic
336	#4020	#123	1	1	yes	characteristic
337	#4018	#121	1	1	yes	characteristic
338	#4018	#121	1	1	yes	characteristic
339	C₄²×D₅	#120	1	1	yes	characteristic
340	C₄²×D₅	#120	1	1	yes	characteristic
341	#3532	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
342	#3026	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
343	C₂×B(4,𝔽₂)	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
344	#3019	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
345	#2127	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
346	#2121	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
347	C₂×AΣL(1,𝔽₁₆)	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
348	C₂⁴×C₅	#386	1	1	yes	characteristic
349	C₂⁴×C₅	#386	1	1	yes	characteristic
350	C₂⁴×C₅	#386	1	1	yes	characteristic, complemented
351	C₂⁴×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₂⁴×C₅	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂³×D₅	#386	1	1	yes	characteristic
354	C₂³×D₅	#386	1	1	yes	characteristic
355	C₂³×D₅	#386	1	1	yes	characteristic, complemented
356	C₂³×D₅	C₂×#120	1	1	yes	characteristic
357	C₂³×D₅	C₂×#120	1	1	yes	characteristic
358	C₂³×D₅	C₂×#120	1	1	yes	characteristic
359	C₂³×D₅	C₂×#120	1	1	yes	characteristic
360	C₂³×D₅	C₂×#120	1	1	yes	characteristic
361	C₂³×D₅	C₂×#121	1	1	yes	characteristic
362	C₂³×D₅	C₂×#121	1	1	yes	characteristic
363	C₂³×D₅	#525	1	1	yes	characteristic
364	C₂³×D₅	#525	1	1	yes	characteristic
365	C₂³×D₅	#525	1	1	yes	characteristic
366	C₂³×D₅	#525	1	1	yes	characteristic
367	C₂²×AGL(1,𝔽₅)	B(4,𝔽₂)	1	2	yes	—
368	C₂×C₅×Q₈	#386	1	1	yes	characteristic, complemented
369	C₂×C₅×D₄	#386	1	1	yes	characteristic, complemented
370	C₂×C₅×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
371	C₂×C₅×D₄	C₂×C₄×D₄	1	1	yes	characteristic
372	C₂×C₅×D₄	C₂×C₄×D₄	1	1	yes	characteristic
373	C₂×C₅×D₄	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₅	#386	1	1	yes	characteristic, complemented
375	C₂²×C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
376	C₂×C₂²⋊D₅	C₂×#121	1	1	yes	characteristic
377	C₂×C₂²⋊D₅	C₂×#121	1	1	yes	characteristic
378	C₂×C₂²⋊D₅	C₂×#123	1	1	yes	characteristic
379	C₂×C₂²⋊D₅	C₂×#123	1	1	yes	characteristic
380	C₂×C₂²⋊D₅	#525	1	1	yes	characteristic
381	C₂×C₂²⋊D₅	#525	1	1	yes	characteristic
382	C₂×C₂²⋊D₅	#525	1	1	yes	characteristic
383	C₂×C₂²⋊D₅	#525	1	1	yes	characteristic
384	C₂²×Dic₅	#386	1	1	yes	characteristic, complemented
385	C₂²×Dic₅	#525	1	1	yes	characteristic
386	C₂×D₂₀	#386	1	1	yes	characteristic, complemented
387	C₂×D₂₀	C₂×#121	1	1	yes	characteristic
388	C₂×D₂₀	C₂×#123	1	1	yes	characteristic
389	C₂×D₂₀	#525	1	1	yes	characteristic
390	C₂×D₂₀	#525	1	1	yes	characteristic
391	C₂×C₄×D₅	C₂×#120	1	1	yes	characteristic
392	C₂×C₄×D₅	C₂×#120	1	1	yes	characteristic
393	C₂×C₄×D₅	C₂×#121	1	1	yes	characteristic
394	C₂×C₄×D₅	#525	1	1	yes	characteristic
395	C₂×Dic₁₀	#386	1	1	yes	characteristic, complemented
396	C₅×C₂²⋊C₄	#386	1	1	yes	characteristic
397	C₅×C₂²⋊C₄	#386	1	1	yes	characteristic
398	C₅×C₂²⋊C₄	#386	1	1	yes	characteristic, complemented
399	C₅×C₂²⋊C₄	#386	1	1	yes	characteristic, complemented
400	C₄²×C₅	#386	1	1	yes	characteristic, complemented
401	C₄²×C₅	#386	1	1	yes	characteristic, complemented
402	C₂²⋊Dic₅	#386	1	1	yes	characteristic
403	C₂²⋊Dic₅	#386	1	1	yes	characteristic
404	C₂²⋊Dic₅	#386	1	1	yes	characteristic, complemented
405	C₂²⋊Dic₅	#386	1	1	yes	characteristic, complemented
406	C₄×Dic₅	#386	1	1	yes	characteristic, complemented
407	C₄×Dic₅	#386	1	1	yes	characteristic, complemented
408	C₂×H(5,𝔽₂)	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
409	H(3,𝔽₄)	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
410	#560	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
411	#551	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
412	D₄²	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
413	#535	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
414	#534	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₂×#120	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
416	C₂×#100	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
417	C₂×#99	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
418	C₂×#99	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
419	C₂³×C₅	C₂×#386	1	1	yes	characteristic
420	C₂³×C₅	C₂×#386	1	1	yes	characteristic
421	C₂³×C₅	C₄×#120	1	1	yes	characteristic
422	C₂³×C₅	C₄×#120	1	1	yes	characteristic
423	C₂³×C₅	C₄×#120	1	1	yes	characteristic
424	C₂²×D₅	#2846	1	1	yes	characteristic
425	C₂²×D₅	#2847	1	1	yes	characteristic
426	C₂²×D₅	#2847	1	1	yes	characteristic
427	C₂²×D₅	#2847	1	1	yes	characteristic
428	C₂²×D₅	#2849	1	1	yes	characteristic
429	C₂²×D₅	#2849	1	1	yes	characteristic
430	C₂²×D₅	C₂×B(4,𝔽₂)	1	1	yes	characteristic
431	C₂²×D₅	#3025	1	1	yes	characteristic
432	C₂²×D₅	#3026	1	1	yes	characteristic
433	C₂²×D₅	#3027	1	1	yes	characteristic
434	C₂×C₄×C₅	C₂×#386	1	1	yes	characteristic
435	C₂×C₄×C₅	C₄×#120	1	1	yes	characteristic
436	C₂×Dic₅	#2847	1	1	yes	characteristic
437	C₂×Dic₅	#2849	1	1	yes	characteristic
438	C₂⁵	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
439	C₂×#41	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₂²×D₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
441	C₂²×D₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
442	#127	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
443	#127	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
444	#124	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
445	#124	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
446	#123	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
447	#123	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
448	#120	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
449	#120	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
450	#120	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
451	#120	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
452	#120	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
453	#120	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
454	#117	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
457	C₂²×C₅	#14694	1	1	yes	characteristic
458	C₂²×C₅	C₄×B(4,𝔽₂)	1	1	yes	characteristic
459	C₂²×C₅	#21482	1	1	yes	characteristic
460	C₂×D₅	#32898	1	1	yes	characteristic
461	C₂×D₅	#32899	1	1	yes	characteristic
462	C₂×D₅	#32926	1	1	yes	characteristic
463	C₂×D₅	#32928	1	1	yes	characteristic
464	C₂⁴	#65779	1	1	yes	characteristic
465	C₂⁴	#65779	1	1	yes	characteristic
466	C₂⁴	#65779	1	1	yes	characteristic, complemented
467	C₂⁴	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
468	C₂⁴	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
469	C₂×Q₈	#65779	1	1	yes	characteristic, complemented
470	C₂×D₄	#65779	1	1	yes	characteristic, complemented
471	C₂×D₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
472	C₂×D₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
473	C₂×D₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
474	C₂×D₄	C₂²×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
475	C₂²×C₄	#65779	1	1	yes	characteristic, complemented
476	C₂²×C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₂²⋊C₄	#65779	1	1	yes	characteristic
478	C₂²⋊C₄	#65779	1	1	yes	characteristic
479	C₂²⋊C₄	#65779	1	1	yes	characteristic, complemented
480	C₂²⋊C₄	#65779	1	1	yes	characteristic, complemented
481	C₄²	#65779	1	1	yes	characteristic, complemented
482	C₄²	#65779	1	1	yes	characteristic, complemented
483	C₂×C₅	#392663	1	1	yes	characteristic
484	D₅	#511790	1	1	yes	characteristic
485	D₅	#511792	1	1	yes	characteristic
486	C₂³	AGL(1,𝔽₅)×#120	1	1	yes	characteristic
487	C₂³	AGL(1,𝔽₅)×#120	1	1	yes	characteristic
488	C₂³	AGL(1,𝔽₅)×#120	1	1	yes	characteristic
489	C₂³	C₂×#65779	1	1	yes	characteristic
490	C₂³	C₂×#65779	1	1	yes	characteristic
491	C₂×C₄	AGL(1,𝔽₅)×#120	1	1	yes	characteristic
492	C₂×C₄	C₂×#65779	1	1	yes	characteristic
493	C₅	#72242789	1	1	yes	characteristic, complemented, Sylow
494	C₂²	#13028921	1	1	yes	characteristic
495	C₂²	AGL(1,𝔽₅)×B(4,𝔽₂)	1	1	yes	characteristic
496	C₂²	#13036209	1	1	yes	characteristic
497	C₂	#72242721	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#72242721
commutator	C₂²×C₅×D₄	C₂³×C₄
Frattini	C₂²×D₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#33551	C₄
socle	C₂×C₅	#392663
prime radical	D₅×#33551	C₂
cosocle	C₂²×D₄×D₅	C₂⁴
hypercenter	#33551	AGL(1,𝔽₅)
hypocenter	C₅	#72242789
LCS	G ▷ C₂²×C₅×D₄ ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×D₄ ◁ #33551

Complements

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

N	H ≅ G/N	type
1. #72242878	C₂	semidirect
2. #72242874	C₂	semidirect
3. #72242869	C₂	semidirect
4. #72242866	C₂	semidirect
5. #72242862	C₂	semidirect
6. #72242860	C₂	semidirect
7. #72242858	C₂	semidirect
8. #72242843	C₂	semidirect
9. #72242832	C₂	semidirect
10. #72242827	C₂	semidirect
11. #72242800	C₂	semidirect
12. #72242743	C₂	semidirect
13. #72242710	C₂	semidirect
15. #72221422	C₂	semidirect
21. #13044099	C₂²	semidirect
29. #13034200	C₂²	semidirect
30. #13034191	C₂²	semidirect
31. C₂×#10605017	C₂²	semidirect
32. #13025588	C₂²	semidirect
33. #13025588	C₂²	semidirect
34. #13025554	C₂²	semidirect
35. #13025550	C₂²	semidirect
36. C₂×#10598573	C₂²	semidirect
37. C₂×#10598567	C₂²	semidirect
38. #13021798	C₂²	semidirect
39. #13021793	C₂²	semidirect
40. #13021793	C₂²	semidirect
41. #13021773	C₂²	semidirect
42. #13021743	C₂²	semidirect
43. #13021725	C₂²	semidirect
48. #12253364	C₄	semidirect
49. #12253363	C₄	semidirect
50. #12253362	C₄	semidirect
51. #12253361	C₄	semidirect
52. #12253359	C₄	semidirect
53. #12253357	C₄	semidirect
54. #12253355	C₄	semidirect
58. C₅×#33551	C₄	semidirect
59. C₂⁵×AGL(1,𝔽₅)	D₄	semidirect
61. C₂×#66266	D₄	semidirect
62. C₂×#66258	D₄	semidirect
80. C₂×#65800	D₄	semidirect
81. #10617555	D₄	semidirect
84. C₂×#65779	D₄	semidirect
89. #10617370	D₄	semidirect
90. #10617369	D₄	semidirect
91. #10617328	D₄	semidirect
92. #10617327	D₄	semidirect
93. #10617308	D₄	semidirect
94. #10617307	D₄	semidirect
95. #10617224	D₄	semidirect
96. #10617224	D₄	semidirect
97. #10617224	D₄	semidirect
98. #10617223	D₄	semidirect
99. #10617223	D₄	semidirect
100. #10617223	D₄	semidirect
101. #10617128	D₄	semidirect
102. #10617127	D₄	semidirect
103. C₂×#65699	D₄	semidirect
104. C₂×#65699	D₄	semidirect
105. #10617067	D₄	semidirect
106. C₂×C₂²⋊C₄×AGL(1,𝔽₅)	D₄	semidirect
107. C₅×#3026	C₂×C₄	semidirect
108. C₂×C₅×B(4,𝔽₂)	C₂×C₄	semidirect
109. C₅×#3019	C₂×C₄	semidirect
110. #10615841	C₂×C₄	semidirect
111. C₂×#65533	C₂×C₄	semidirect
112. #10615835	C₂×C₄	semidirect
113. #10615125	C₂×C₄	semidirect
114. #10615106	C₂×C₄	semidirect
115. C₂×#65321	C₂×C₄	semidirect
116. #10610431	C₂×C₄	semidirect
120. #10610417	C₂×C₄	semidirect
121. C₂×#65030	C₂×C₄	semidirect
122. C₅×#2127	C₂×C₄	semidirect
123. C₅×#2121	C₂×C₄	semidirect
124. C₂×C₅×AΣL(1,𝔽₁₆)	C₂×C₄	semidirect
125. #10602653	C₂×C₄	semidirect
126. #10602640	C₂×C₄	semidirect
127. C₂×#64756	C₂×C₄	semidirect
128. #10600887	C₂×C₄	semidirect
129. C₂×#64695	C₂×C₄	semidirect
130. #10600812	C₂×C₄	semidirect
131. #10600812	C₂×C₄	semidirect
132. #10600808	C₂×C₄	semidirect
133. C₂×#64691	C₂×C₄	semidirect
138. C₂×C₅×H(5,𝔽₂)	C₂²×C₄	semidirect
140. C₂×#4144	C₂²×C₄	semidirect
152. C₅×H(3,𝔽₄)	C₂²⋊C₄	semidirect
153. C₅×#560	C₂²⋊C₄	semidirect
154. C₅×#551	C₂²⋊C₄	semidirect
155. C₅×D₄²	C₂²⋊C₄	semidirect
165. #66054	C₂²⋊C₄	semidirect
166. #66051	C₂²⋊C₄	semidirect
171. #66017	C₂²⋊C₄	semidirect
172. #66013	C₂²⋊C₄	semidirect
177. #66000	C₂²⋊C₄	semidirect
178. #65993	C₂²⋊C₄	semidirect
183. #65929	C₂²⋊C₄	semidirect
184. #65928	C₂²⋊C₄	semidirect
185. #65928	C₂²⋊C₄	semidirect
186. #65924	C₂²⋊C₄	semidirect
187. #65924	C₂²⋊C₄	semidirect
200. #65921	C₂²⋊C₄	semidirect
219. C₂×C₅×#100	C₂²×C₄	semidirect
220. C₂×C₅×#99	C₂²×C₄	semidirect
221. C₂×C₅×#99	C₂²×C₄	semidirect
222. C₂×#3966	C₂²×C₄	semidirect
223. C₂×#3966	C₂²×C₄	semidirect
224. C₂×#3965	C₂²×C₄	semidirect
225. #33551	AGL(1,𝔽₅)	semidirect
342. #3026	C₂×AGL(1,𝔽₅)	semidirect
343. C₂×B(4,𝔽₂)	C₂×AGL(1,𝔽₅)	semidirect
344. #3019	C₂×AGL(1,𝔽₅)	semidirect
345. #2127	C₂×AGL(1,𝔽₅)	semidirect
346. #2121	C₂×AGL(1,𝔽₅)	semidirect
347. C₂×AΣL(1,𝔽₁₆)	C₂×AGL(1,𝔽₅)	semidirect
350. C₂⁴×C₅	#386	semidirect
355. C₂³×D₅	#386	semidirect
368. C₂×C₅×Q₈	#386	semidirect
369. C₂×C₅×D₄	#386	semidirect
374. C₂²×C₄×C₅	#386	semidirect
384. C₂²×Dic₅	#386	semidirect
386. C₂×D₂₀	#386	semidirect
395. C₂×Dic₁₀	#386	semidirect
398. C₅×C₂²⋊C₄	#386	semidirect
399. C₅×C₂²⋊C₄	#386	semidirect
400. C₄²×C₅	#386	semidirect
401. C₄²×C₅	#386	semidirect
404. C₂²⋊Dic₅	#386	semidirect
405. C₂²⋊Dic₅	#386	semidirect
406. C₄×Dic₅	#386	semidirect
407. C₄×Dic₅	#386	semidirect
408. C₂×H(5,𝔽₂)	C₂²×AGL(1,𝔽₅)	semidirect
409. H(3,𝔽₄)	C₂²⋊AGL(1,𝔽₅)	semidirect
410. #560	C₂²⋊AGL(1,𝔽₅)	semidirect
411. #551	C₂²⋊AGL(1,𝔽₅)	semidirect
412. D₄²	C₂²⋊AGL(1,𝔽₅)	semidirect
416. C₂×#100	C₂²×AGL(1,𝔽₅)	semidirect
417. C₂×#99	C₂²×AGL(1,𝔽₅)	semidirect
418. C₂×#99	C₂²×AGL(1,𝔽₅)	semidirect
466. C₂⁴	#65779	semidirect
469. C₂×Q₈	#65779	semidirect
470. C₂×D₄	#65779	semidirect
475. C₂²×C₄	#65779	semidirect
479. C₂²⋊C₄	#65779	semidirect
480. C₂²⋊C₄	#65779	semidirect
481. C₄²	#65779	semidirect
482. C₄²	#65779	semidirect
493. C₅	#72242789	semidirect

Maximal subgroups

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

subgroup	index
#72242878	2
#72242874	2
#72242869	2
#72242866	2
#72242862	2
#72242860	2
#72242858	2
#72242843	2
#72242832	2
#72242827	2
#72242800	2
#72242789	5
#72242743	2
#72242710	2
D₅×#33551	2
#72221422	2