Subgroups — #72243373

Order 5120.

At least 6680 conjugacy classes of subgroups; only the 508 normal subgroups are shown.

The subgroup lattice has 284 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72243023	C₂	1	1	yes	maximal, characteristic, complemented
2	#72243003	C₂	1	1	yes	maximal, characteristic, complemented
3	#72242981	C₂	1	1	yes	maximal, characteristic, complemented
4	#72242951	C₂	1	1	yes	maximal, characteristic, complemented
5	#72242948	C₂	1	1	yes	maximal, characteristic, complemented
6	#72242878	C₂	1	4	yes	maximal, complemented
7	#72242842	C₂	1	4	yes	maximal, complemented
8	#72242730	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅×#23900	C₂	1	1	yes	maximal, characteristic
10	#13044199	C₂²	1	4	yes	—
11	#13044014	C₂²	1	1	yes	characteristic
12	#13044014	C₂²	1	1	yes	characteristic
13	C₂×D₅⋊AΣL(1,𝔽₁₆)	C₂²	1	4	yes	—
14	#13034200	C₂²	1	2	yes	complemented
15	#13034191	C₂²	1	2	yes	complemented
16	D₅⋊#1783	C₂²	1	1	yes	characteristic
17	D₅⋊#1781	C₂²	1	1	yes	characteristic
18	#13025588	C₂²	1	4	yes	complemented
19	#13025550	C₂²	1	4	yes	complemented
20	#13021772	C₂²	1	2	yes	complemented
21	#13021724	C₂²	1	2	yes	complemented
22	D₅×#3484	C₂²	1	1	yes	characteristic
23	C₂²×D₅×#120	C₂²	1	1	yes	characteristic
24	C₂×D₅×B(4,𝔽₂)	C₂²	1	2	yes	—
25	#12130882	C₄	1	1	yes	characteristic, complemented
26	#12130881	C₄	1	1	yes	characteristic, complemented
27	#12130880	C₄	1	2	yes	complemented
28	#12130878	C₄	1	2	yes	complemented
29	#12130877	C₄	1	1	yes	characteristic, complemented
30	D₅×#1889	C₂²	1	2	yes	—
31	D₅×#1781	C₂²	1	1	yes	characteristic
32	C₅×#23900	C₄	1	1	yes	characteristic, complemented
33	C₂⁶×D₅	D₄	1	1	yes	characteristic
34	C₂×D₅×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
35	C₂³×D₄×D₅	C₂³	1	1	yes	characteristic
36	C₂×#66258	D₄	1	1	yes	characteristic, complemented
37	C₂×#66258	D₄	1	1	yes	characteristic, complemented
38	C₂×#66258	D₄	1	1	yes	characteristic, complemented
39	C₂×#66258	D₄	1	1	yes	characteristic, complemented
40	C₅×#3484	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂²×C₅×#120	C₂×C₄	1	1	yes	characteristic
42	C₂²×#4099	D₄	1	1	yes	characteristic
43	#10619185	C₂×C₄	1	1	yes	characteristic, complemented
44	#10619140	C₂×C₄	1	1	yes	characteristic, complemented
45	C₂²×#4083	C₂×C₄	1	1	yes	characteristic
46	C₂×D₅×#120	C₂×C₄	1	2	yes	—
47	C₂×D₅×#120	D₄	1	2	yes	—
48	C₂×D₅×#120	D₄	1	2	yes	—
49	C₂×D₅×#120	C₂³	1	2	yes	—
50	#10617768	C₂×C₄	1	1	yes	characteristic, complemented
51	D₅×#518	C₂³	1	1	yes	characteristic
52	C₂²×#4028	D₄	1	1	yes	characteristic
53	C₂²×D₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
54	C₂×#65800	D₄	1	2	yes	complemented
55	#10617507	C₂³	1	2	yes	—
56	#10617506	C₂³	1	2	yes	—
57	C₂×D₅⋊#100	C₂³	1	2	yes	—
58	C₂×D₅⋊#99	C₂³	1	2	yes	—
59	#10617480	D₄	1	2	yes	complemented
60	#10617224	D₄	1	8	yes	complemented
61	#10617223	D₄	1	8	yes	complemented
62	C₂×C₅×B(4,𝔽₂)	C₂×C₄	1	2	yes	complemented
63	C₂×#65533	C₂×C₄	1	2	yes	complemented
64	C₂×#65321	C₂×C₄	1	2	yes	complemented
65	C₂×D₅×#99	C₂³	1	2	yes	—
66	C₂×#65030	C₂×C₄	1	2	yes	complemented
67	C₅×#1889	C₂×C₄	1	2	yes	complemented
68	C₅×#1781	C₂×C₄	1	1	yes	characteristic, complemented
69	#10602923	C₂×C₄	1	1	yes	characteristic, complemented
70	#10602462	C₂×C₄	1	2	yes	complemented
71	#10602447	C₂×C₄	1	2	yes	complemented
72	#10600828	C₂×C₄	1	2	yes	complemented
73	#10600815	C₂×C₄	1	2	yes	complemented
74	C₂⁶×C₅	C₂²⋊C₄	1	1	yes	characteristic, complemented
75	C₂⁵×D₅	C₂²⋊C₄	1	2	yes	complemented
76	C₂⁵×D₅	C₂²⋊C₄	1	1	yes	characteristic, complemented
77	C₂⁵×D₅	C₂×D₄	1	1	yes	characteristic
78	C₂⁵×D₅	C₂×D₄	1	2	yes	—
79	C₂⁵×D₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₅×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic, complemented
81	C₂³×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
82	C₂³×C₂²⋊D₅	C₂×D₄	1	1	yes	characteristic
83	C₂³×C₂²⋊D₅	#41	1	1	yes	characteristic
84	C₂×#4144	C₂²×C₄	1	1	yes	characteristic, complemented
85	C₂²×D₄×D₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×D₄×D₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×D₄×D₅	C₂×D₄	1	1	yes	characteristic
88	C₂²×D₄×D₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×D₄×D₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×D₄×D₅	#41	1	1	yes	characteristic
91	C₂²×D₄×D₅	#41	1	1	yes	characteristic
92	C₂²×D₄×D₅	C₂⁴	1	1	yes	characteristic
93	C₂³×D₂₀	#41	1	1	yes	characteristic
94	C₂³×C₄×D₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
96	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
97	C₂×#4130	C₂×D₄	1	2	yes	—
98	C₂×#4130	C₂×D₄	1	2	yes	—
99	C₂×C₅×#120	C₂²⋊C₄	1	2	yes	complemented
100	C₂×C₅×#120	C₂²×C₄	1	2	yes	—
101	C₅×#518	C₂²×C₄	1	1	yes	characteristic, complemented
102	C₂²×C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
103	C₂×#4099	C₂²⋊C₄	1	2	yes	complemented
104	C₂×#4099	C₂×D₄	1	2	yes	—
105	C₂²×C₂²⋊Dic₅	C₂²⋊C₄	1	1	yes	characteristic, complemented
106	C₂×#4083	C₂²⋊C₄	1	2	yes	complemented
107	C₂×#4083	C₂²×C₄	1	2	yes	—
108	#66132	C₂²×C₄	1	1	yes	characteristic, complemented
109	D₅×#120	C₂×D₄	1	4	yes	—
110	D₅×#120	C₂×D₄	1	4	yes	—
111	D₅×#120	#41	1	4	yes	—
112	D₅×#120	#41	1	4	yes	—
113	C₂×#4028	C₂²⋊C₄	1	2	yes	complemented
114	C₂×#4028	C₂×D₄	1	2	yes	—
115	C₂×D₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
116	C₂×D₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
117	#65780	C₂×D₄	1	8	yes	—
118	#65779	C₂×D₄	1	8	yes	—
119	C₂×C₅×#99	C₂²×C₄	1	2	yes	complemented
120	C₂×#3966	C₂²×C₄	1	2	yes	complemented
121	#23900	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
122	C₂⁵×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂⁵×C₅	C₂×C₂²⋊C₄	1	2	yes	—
124	C₂⁵×C₅	C₄×D₄	1	1	yes	characteristic
125	C₂⁴×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂⁴×D₅	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂⁴×D₅	C₄×D₄	1	1	yes	characteristic
128	C₂⁴×D₅	#120	1	1	yes	characteristic
129	C₂⁴×D₅	#120	1	1	yes	characteristic
130	C₂⁴×D₅	#120	1	1	yes	characteristic
131	C₂⁴×D₅	#120	1	2	yes	—
132	C₂⁴×D₅	#120	1	2	yes	—
133	C₂⁴×D₅	#121	1	1	yes	characteristic
134	C₂⁴×D₅	#121	1	1	yes	characteristic
135	C₂⁴×D₅	#123	1	1	yes	characteristic
136	C₂⁴×D₅	#123	1	1	yes	characteristic
137	C₂⁴×D₅	#123	1	2	yes	—
138	C₂⁴×D₅	#123	1	2	yes	—
139	C₂⁴×D₅	C₂²×D₄	1	1	yes	characteristic
140	C₂⁴×D₅	C₂²×D₄	1	1	yes	characteristic
141	C₂³×AGL(1,𝔽₅)	#120	1	4	yes	complemented
142	C₂²×C₅×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₅×D₄	C₄×D₄	1	1	yes	characteristic
144	C₂²×C₅×D₄	C₄×D₄	1	1	yes	characteristic
145	C₂²×C₅×D₄	C₂³×C₄	1	1	yes	characteristic
146	C₂³×C₄×C₅	C₄×D₄	1	1	yes	characteristic
147	C₂²×C₂²⋊D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₂²⋊D₅	C₄×D₄	1	1	yes	characteristic
149	C₂²×C₂²⋊D₅	#121	1	1	yes	characteristic
150	C₂²×C₂²⋊D₅	#121	1	1	yes	characteristic
151	C₂²×C₂²⋊D₅	#121	1	1	yes	characteristic
152	C₂²×C₂²⋊D₅	#123	1	1	yes	characteristic
153	C₂²×C₂²⋊D₅	C₂²×D₄	1	1	yes	characteristic
154	C₂²×C₂²⋊D₅	C₂×#41	1	1	yes	characteristic
155	C₂³×Dic₅	#121	1	1	yes	characteristic
156	C₂×D₄×D₅	C₂²×D₄	1	4	yes	—
157	C₂×D₄×D₅	C₂×#41	1	4	yes	—
158	C₂²×D₂₀	C₄×D₄	1	1	yes	characteristic
159	C₂²×D₂₀	#121	1	1	yes	characteristic
160	C₂²×D₂₀	#123	1	1	yes	characteristic
161	C₂²×D₂₀	C₂×#41	1	1	yes	characteristic
162	C₂²×C₄×D₅	C₄×D₄	1	1	yes	characteristic
163	C₂²×C₄×D₅	#120	1	1	yes	characteristic
164	C₂²×C₄×D₅	#121	1	1	yes	characteristic
165	C₂²×C₄×D₅	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₂²⋊AGL(1,𝔽₅)	#120	1	4	yes	complemented
167	C₂×C₄⋊AGL(1,𝔽₅)	#120	1	4	yes	complemented
168	C₂×C₄×AGL(1,𝔽₅)	#120	1	4	yes	complemented
169	C₅×#120	C₄×D₄	1	4	yes	—
170	C₅×#120	C₄×D₄	1	4	yes	—
171	C₂×C₅×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
172	#4099	#121	1	4	yes	—
173	#4099	#121	1	4	yes	—
174	C₂×C₂²⋊Dic₅	C₂×C₂²⋊C₄	1	2	yes	—
175	#4083	C₄×D₄	1	4	yes	—
176	#4083	C₄×D₄	1	4	yes	—
177	#4028	#121	1	4	yes	—
178	#4028	#121	1	4	yes	—
179	D₅×C₂²⋊C₄	#120	1	4	yes	—
180	D₅×C₂²⋊C₄	#123	1	4	yes	—
181	#3484	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
182	C₂²×#120	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
183	C₂×B(4,𝔽₂)	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
184	#1889	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
185	#1781	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
186	C₂⁴×C₅	#386	1	1	yes	characteristic
187	C₂⁴×C₅	#386	1	1	yes	characteristic
188	C₂⁴×C₅	#386	1	1	yes	characteristic
189	C₂⁴×C₅	#386	1	2	yes	—
190	C₂⁴×C₅	#386	1	2	yes	—
191	C₂⁴×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂⁴×C₅	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂³×D₅	#386	1	1	yes	characteristic
194	C₂³×D₅	#386	1	1	yes	characteristic
195	C₂³×D₅	#386	1	1	yes	characteristic
196	C₂³×D₅	#386	1	2	yes	—
197	C₂³×D₅	#386	1	2	yes	—
198	C₂³×D₅	B(4,𝔽₂)	1	2	yes	—
199	C₂³×D₅	B(4,𝔽₂)	1	2	yes	—
200	C₂³×D₅	C₂×#120	1	2	yes	—
201	C₂³×D₅	C₂×#120	1	2	yes	—
202	C₂³×D₅	C₂×#120	1	1	yes	characteristic
203	C₂³×D₅	C₂×#121	1	1	yes	characteristic
204	C₂³×D₅	C₂×#123	1	1	yes	characteristic
205	C₂³×D₅	C₂×#123	1	2	yes	—
206	C₂³×D₅	#525	1	2	yes	—
207	C₂×C₅×D₄	C₂×C₄×D₄	1	4	yes	—
208	C₂²×C₄×C₅	#386	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂×C₂²⋊D₅	C₂×#121	1	4	yes	—
211	C₂×C₂²⋊D₅	#525	1	4	yes	—
212	C₂²×Dic₅	#386	1	1	yes	characteristic
213	C₂²×Dic₅	C₂×#121	1	1	yes	characteristic
214	C₂×D₂₀	#525	1	4	yes	—
215	C₂×C₄×D₅	C₂×#120	1	2	yes	—
216	C₂×C₄×D₅	#525	1	2	yes	—
217	C₅×C₂²⋊C₄	#386	1	4	yes	—
218	C₂²⋊Dic₅	#386	1	4	yes	—
219	C₂⁶	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
220	C₂×H(5,𝔽₂)	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
221	C₂³×D₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
222	C₂×#120	C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
223	C₂×#120	C₂²×AGL(1,𝔽₅)	1	2	yes	—
224	#518	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
225	C₂²×C₂²⋊C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
226	C₂×#99	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
227	C₂³×C₅	#1889	1	2	yes	—
228	C₂³×C₅	C₂×#386	1	2	yes	—
229	C₂³×C₅	C₂×#386	1	1	yes	characteristic
230	C₂³×C₅	C₄×#120	1	2	yes	—
231	C₂²×D₅	#1889	1	2	yes	—
232	C₂²×D₅	#2846	1	1	yes	characteristic
233	C₂²×D₅	#2847	1	2	yes	—
234	C₂²×D₅	#2849	1	2	yes	—
235	C₂²×D₅	#2849	1	1	yes	characteristic
236	C₂²×D₅	C₂×B(4,𝔽₂)	1	1	yes	characteristic
237	C₂²×D₅	C₂×B(4,𝔽₂)	1	1	yes	characteristic
238	C₂²×D₅	#3026	1	1	yes	characteristic
239	C₂²×D₅	#3026	1	1	yes	characteristic
240	C₂×C₄×C₅	C₄×#120	1	2	yes	—
241	C₂×Dic₅	#2847	1	2	yes	—
242	C₂⁵	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
243	C₂⁵	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₂⁵	C₂×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
245	C₂²×D₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
246	C₂²×D₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
247	C₂²×D₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
248	C₂²×D₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
249	C₂³×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
250	#120	D₄×AGL(1,𝔽₅)	1	4	yes	—
251	#120	D₄×AGL(1,𝔽₅)	1	4	yes	—
252	C₂×C₂²⋊C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
253	C₂²×C₅	#14694	1	1	yes	characteristic
254	C₂²×C₅	C₂×#1889	1	1	yes	characteristic
255	C₂²×C₅	#20960	1	1	yes	characteristic
256	C₂×D₅	#32898	1	1	yes	characteristic
257	C₂×D₅	#32898	1	1	yes	characteristic
258	C₂×D₅	#33020	1	1	yes	characteristic
259	C₂×D₅	#33020	1	1	yes	characteristic
260	C₂⁴	#65779	1	1	yes	characteristic
261	C₂⁴	#65779	1	1	yes	characteristic
262	C₂⁴	#65779	1	1	yes	characteristic
263	C₂⁴	#65779	1	2	yes	—
264	C₂⁴	#65779	1	2	yes	—
265	C₂⁴	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
266	C₂⁴	C₂²×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₂×D₄	C₂×D₄×AGL(1,𝔽₅)	1	4	yes	—
268	C₂²×C₄	#65779	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
270	C₂²⋊C₄	#65779	1	4	yes	—
271	C₂×C₅	#392658	1	1	yes	characteristic
272	D₅	#511790	1	2	yes	—
273	C₂³	#10604461	1	2	yes	—
274	C₂³	AGL(1,𝔽₅)×#120	1	2	yes	—
275	C₂³	C₂×#65779	1	2	yes	—
276	C₂³	C₂×#65779	1	1	yes	characteristic
277	C₂×C₄	AGL(1,𝔽₅)×#120	1	2	yes	—
278	C₅	#72218104	1	1	yes	characteristic, complemented, Sylow
279	C₂²	#13028921	1	1	yes	characteristic
280	C₂²	C₂×#10604461	1	1	yes	characteristic
281	C₂²	#13034964	1	1	yes	characteristic
282	C₂	#72242760	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#72242760
commutator	C₂²×C₅×D₄	C₂³×C₄
Frattini	C₂²×D₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#23900	C₄
socle	C₂×C₅	#392658
prime radical	D₅×#23900	C₂
cosocle	C₂²×D₄×D₅	C₂⁴
hypercenter	#23900	AGL(1,𝔽₅)
hypocenter	C₅	#72218104
LCS	G ▷ C₂²×C₅×D₄ ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×D₄ ◁ #23900

Complements

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

N	H ≅ G/N	type
1. #72243023	C₂	semidirect
2. #72243003	C₂	semidirect
3. #72242981	C₂	semidirect
4. #72242951	C₂	semidirect
5. #72242948	C₂	semidirect
6. #72242878	C₂	semidirect
7. #72242842	C₂	semidirect
8. #72242730	C₂	semidirect
14. #13034200	C₂²	semidirect
15. #13034191	C₂²	semidirect
18. #13025588	C₂²	semidirect
19. #13025550	C₂²	semidirect
20. #13021772	C₂²	semidirect
21. #13021724	C₂²	semidirect
25. #12130882	C₄	semidirect
26. #12130881	C₄	semidirect
27. #12130880	C₄	semidirect
28. #12130878	C₄	semidirect
29. #12130877	C₄	semidirect
32. C₅×#23900	C₄	semidirect
36. C₂×#66258	D₄	semidirect
37. C₂×#66258	D₄	semidirect
38. C₂×#66258	D₄	semidirect
39. C₂×#66258	D₄	semidirect
40. C₅×#3484	C₂×C₄	semidirect
43. #10619185	C₂×C₄	semidirect
44. #10619140	C₂×C₄	semidirect
50. #10617768	C₂×C₄	semidirect
54. C₂×#65800	D₄	semidirect
59. #10617480	D₄	semidirect
60. #10617224	D₄	semidirect
61. #10617223	D₄	semidirect
62. C₂×C₅×B(4,𝔽₂)	C₂×C₄	semidirect
63. C₂×#65533	C₂×C₄	semidirect
64. C₂×#65321	C₂×C₄	semidirect
66. C₂×#65030	C₂×C₄	semidirect
67. C₅×#1889	C₂×C₄	semidirect
68. C₅×#1781	C₂×C₄	semidirect
69. #10602923	C₂×C₄	semidirect
70. #10602462	C₂×C₄	semidirect
71. #10602447	C₂×C₄	semidirect
72. #10600828	C₂×C₄	semidirect
73. #10600815	C₂×C₄	semidirect
74. C₂⁶×C₅	C₂²⋊C₄	semidirect
75. C₂⁵×D₅	C₂²⋊C₄	semidirect
76. C₂⁵×D₅	C₂²⋊C₄	semidirect
80. C₂×C₅×H(5,𝔽₂)	C₂²×C₄	semidirect
84. C₂×#4144	C₂²×C₄	semidirect
99. C₂×C₅×#120	C₂²⋊C₄	semidirect
101. C₅×#518	C₂²×C₄	semidirect
102. C₂²×C₅×C₂²⋊C₄	C₂²⋊C₄	semidirect
103. C₂×#4099	C₂²⋊C₄	semidirect
105. C₂²×C₂²⋊Dic₅	C₂²⋊C₄	semidirect
106. C₂×#4083	C₂²⋊C₄	semidirect
108. #66132	C₂²×C₄	semidirect
113. C₂×#4028	C₂²⋊C₄	semidirect
115. C₂×D₅×C₂²⋊C₄	C₂²⋊C₄	semidirect
119. C₂×C₅×#99	C₂²×C₄	semidirect
120. C₂×#3966	C₂²×C₄	semidirect
121. #23900	AGL(1,𝔽₅)	semidirect
141. C₂³×AGL(1,𝔽₅)	#120	semidirect
166. C₂×C₂²⋊AGL(1,𝔽₅)	#120	semidirect
167. C₂×C₄⋊AGL(1,𝔽₅)	#120	semidirect
168. C₂×C₄×AGL(1,𝔽₅)	#120	semidirect
181. #3484	C₂×AGL(1,𝔽₅)	semidirect
183. C₂×B(4,𝔽₂)	C₂×AGL(1,𝔽₅)	semidirect
184. #1889	C₂×AGL(1,𝔽₅)	semidirect
185. #1781	C₂×AGL(1,𝔽₅)	semidirect
219. C₂⁶	C₂²⋊AGL(1,𝔽₅)	semidirect
220. C₂×H(5,𝔽₂)	C₂²×AGL(1,𝔽₅)	semidirect
222. C₂×#120	C₂²⋊AGL(1,𝔽₅)	semidirect
224. #518	C₂²×AGL(1,𝔽₅)	semidirect
225. C₂²×C₂²⋊C₄	C₂²⋊AGL(1,𝔽₅)	semidirect
226. C₂×#99	C₂²×AGL(1,𝔽₅)	semidirect
278. C₅	#72218104	semidirect

Maximal subgroups

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

subgroup	index
#72243023	2
#72243003	2
#72242981	2
#72242951	2
#72242948	2
#72242878	2
#72242842	2
#72242730	2
D₅×#23900	2
#72218104	5