Subgroups — C₂²×#66258 #13046012

Order 1280.

14590 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊AGL(1,𝔽₅)	C₂	1	4	yes	maximal, complemented
3	C₂×#66258	C₂	1	48	yes	maximal, direct product factor
4	C₂²×D₄×AGL(1,𝔽₅)	C₂	1	8	yes	maximal, complemented
5	C₂²×#4130	C₂	1	2	yes	maximal, complemented
6	C₂⁵×D₅	C₂²	1	2	yes	—
7	C₂⁴×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
8	C₂³×C₅×D₄	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₂²⋊D₅	C₄	1	2	yes	complemented
10	C₂²×D₄×D₅	C₄	1	24	yes	complemented
11	C₂²×D₄×D₅	C₄	1	4	yes	complemented
12	C₂²×D₄×D₅	C₂²	1	4	yes	—
13	C₂²×D₄×D₅	C₂²	1	24	yes	—
14	C₂³×D₂₀	C₄	1	1	yes	characteristic, complemented
15	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
17	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂²	1	96	yes	complemented
18	C₂²×C₂²⋊AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
19	#66258	C₂²	1	256	yes	direct product factor
20	C₂×D₄×AGL(1,𝔽₅)	C₂²	1	192	yes	complemented
21	C₂×#4130	C₂²	1	48	yes	complemented
22	C₂²×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
23	C₂²×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
24	C₂²×#518	—	5	1	no	maximal, Sylow
25	C₂⁵×C₅	C₂×C₄	1	2	yes	complemented
26	C₂⁴×D₅	—	4	16	no	—
27	C₂⁴×D₅	C₂×C₄	1	24	yes	complemented
28	C₂⁴×D₅	C₂×C₄	1	2	yes	complemented
29	C₂⁴×D₅	C₂×C₄	1	4	yes	complemented
30	C₂⁴×D₅	C₂³	1	1	yes	characteristic
31	C₂⁴×D₅	C₂³	1	4	yes	—
32	C₂⁴×D₅	C₂³	1	24	yes	—
33	C₂³×AGL(1,𝔽₅)	—	4	32	no	—
34	C₂³×AGL(1,𝔽₅)	C₂³	1	8	yes	—
35	C₂³×AGL(1,𝔽₅)	C₂³	1	96	yes	complemented
36	C₂²×C₅×D₄	C₂×C₄	1	4	yes	complemented
37	C₂²×C₅×D₄	C₂×C₄	1	24	yes	complemented
38	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₅	C₂×C₄	1	8	yes	complemented
40	C₂²×C₂²⋊D₅	C₂×C₄	1	48	yes	complemented
41	C₂³×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
42	C₂×D₄×D₅	C₂×C₄	1	48	yes	complemented
43	C₂×D₄×D₅	C₂×C₄	1	192	yes	complemented
44	C₂×D₄×D₅	C₂×C₄	1	96	yes	complemented
45	C₂×D₄×D₅	C₂³	1	48	yes	—
46	C₂×D₄×D₅	C₂³	1	64	yes	—
47	C₂²×D₂₀	C₂×C₄	1	4	yes	complemented
48	C₂²×D₂₀	C₂×C₄	1	24	yes	complemented
49	C₂²×C₄×D₅	C₂×C₄	1	12	yes	complemented
50	C₂²×C₄×D₅	C₂×C₄	1	2	yes	complemented
51	C₂²×C₄×D₅	C₂³	1	2	yes	—
52	C₂²×C₄×D₅	C₂³	1	12	yes	—
53	C₂×C₂²⋊AGL(1,𝔽₅)	C₂³	1	48	yes	—
54	C₂×C₂²⋊AGL(1,𝔽₅)	C₂³	1	256	yes	complemented
55	C₂×C₂²⋊AGL(1,𝔽₅)	C₂³	1	96	yes	complemented
56	D₄×AGL(1,𝔽₅)	C₂³	1	512	yes	complemented
57	#4130	C₂³	1	128	yes	complemented
58	C₂×C₄⋊AGL(1,𝔽₅)	C₂³	1	48	yes	complemented
59	C₂×C₄×AGL(1,𝔽₅)	C₂³	1	48	yes	complemented
60	C₂⁴×D₄	—	5	1	no	—
61	C₂×#518	—	5	48	no	—
62	C₂²×C₄×D₄	—	5	8	no	—
63	C₂²×#117	—	5	2	no	—
64	C₂³×C₂²⋊C₄	—	5	4	no	—
65	C₂⁴×C₅	—	4	8	no	—
66	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
67	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
68	C₂⁴×C₅	C₂²×C₄	1	24	yes	complemented
69	C₂³×D₅	—	2	32	no	—
70	C₂³×D₅	—	2	8	no	—
71	C₂³×D₅	—	4	96	no	—
72	C₂³×D₅	—	4	96	no	—
73	C₂³×D₅	—	4	16	no	—
74	C₂³×D₅	—	4	8	no	—
75	C₂³×D₅	C₂²×C₄	1	6	yes	—
76	C₂³×D₅	C₂²×C₄	1	1	yes	characteristic
77	C₂³×D₅	C₂²×C₄	1	4	yes	—
78	C₂³×D₅	C₂²×C₄	1	24	yes	—
79	C₂³×D₅	C₂²×C₄	1	96	yes	complemented
80	C₂³×D₅	C₂²×C₄	1	24	yes	complemented
81	C₂³×D₅	C₂²×C₄	1	48	yes	complemented
82	C₂³×D₅	C₂⁴	1	6	yes	—
83	C₂³×D₅	C₂⁴	1	24	yes	—
84	C₂³×D₅	C₂⁴	1	32	yes	—
85	C₂³×D₅	C₂⁴	1	1	yes	characteristic
86	C₂²×AGL(1,𝔽₅)	—	2	32	no	—
87	C₂²×AGL(1,𝔽₅)	—	4	192	no	—
88	C₂²×AGL(1,𝔽₅)	C₂⁴	1	48	yes	—
89	C₂²×AGL(1,𝔽₅)	C₂⁴	1	128	yes	complemented
90	C₂×C₅×D₄	C₂²×C₄	1	48	yes	complemented
91	C₂×C₅×D₄	C₂²×C₄	1	64	yes	complemented
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	complemented
94	C₂×C₂²⋊D₅	C₂²×C₄	1	96	yes	complemented
95	C₂×C₂²⋊D₅	C₂²×C₄	1	128	yes	complemented
96	C₂²×Dic₅	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₅	C₂²×C₄	1	12	yes	complemented
98	D₄×D₅	C₂²×C₄	1	192	yes	complemented
99	D₄×D₅	C₂²×C₄	1	256	yes	complemented
100	D₄×D₅	C₂⁴	1	64	yes	—
101	C₂×D₂₀	C₂²×C₄	1	48	yes	complemented
102	C₂×D₂₀	C₂²×C₄	1	64	yes	complemented
103	C₂×C₄×D₅	C₂²×C₄	1	12	yes	—
104	C₂×C₄×D₅	C₂²×C₄	1	48	yes	complemented
105	C₂×C₄×D₅	C₂²×C₄	1	24	yes	complemented
106	C₂×C₄×D₅	C₂⁴	1	12	yes	—
107	C₂×C₄×D₅	C₂⁴	1	16	yes	—
108	C₂²⋊AGL(1,𝔽₅)	C₂⁴	1	64	yes	—
109	C₂²⋊AGL(1,𝔽₅)	C₂⁴	1	128	yes	complemented
110	C₄⋊AGL(1,𝔽₅)	C₂⁴	1	64	yes	complemented
111	C₄×AGL(1,𝔽₅)	C₂⁴	1	64	yes	complemented
112	C₂⁶	—	5	2	no	—
113	C₂³×D₄	—	5	2	no	—
114	C₂³×D₄	—	5	4	no	—
115	C₂³×D₄	—	5	24	no	—
116	C₂³×D₄	—	5	4	no	—
117	C₂³×D₄	—	5	24	no	—
118	C₂³×D₄	—	5	1	no	—
119	C₂³×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
120	C₂⁴×C₄	—	5	1	no	—
121	C₂⁴×C₄	—	5	8	no	—
122	#518	—	5	256	no	—
123	C₂×C₄×D₄	—	5	192	no	—
124	C₂×#117	—	5	48	no	—
125	C₂²×C₄⋊C₄	—	5	4	no	—
126	C₂²×C₂²⋊C₄	—	5	4	no	—
127	C₂²×C₂²⋊C₄	—	5	8	no	—
128	C₂²×C₂²⋊C₄	—	5	96	no	—
129	C₂²×C₄²	—	5	4	no	—
130	C₂³×C₅	—	2	4	no	—
131	C₂³×C₅	—	2	16	no	—
132	C₂³×C₅	—	4	48	no	—
133	C₂³×C₅	C₂³×C₄	1	6	yes	—
134	C₂³×C₅	C₂³×C₄	1	24	yes	—
135	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
136	C₂³×C₅	C₂³×C₄	1	32	yes	complemented
137	C₂²×D₅	—	2	4	no	—
138	C₂²×D₅	—	2	16	no	—
139	C₂²×D₅	—	2	24	no	—
140	C₂²×D₅	—	2	96	no	—
141	C₂²×D₅	—	2	96	no	—
142	C₂²×D₅	—	2	24	no	—
143	C₂²×D₅	—	4	192	no	—
144	C₂²×D₅	—	4	64	no	—
145	C₂²×D₅	—	4	96	no	—
146	C₂²×D₅	—	4	48	no	—
147	C₂²×D₅	C₂³×C₄	1	6	yes	—
148	C₂²×D₅	C₂³×C₄	1	12	yes	—
149	C₂²×D₅	C₂³×C₄	1	24	yes	—
150	C₂²×D₅	C₂³×C₄	1	48	yes	—
151	C₂²×D₅	C₂³×C₄	1	3	yes	—
152	C₂²×D₅	C₂³×C₄	1	32	yes	complemented
153	C₂²×D₅	C₂³×C₄	1	64	yes	complemented
154	C₂²×D₅	H(5,𝔽₂)	1	8	yes	—
155	C₂²×D₅	C₂⁵	1	4	yes	—
156	C₂²×D₅	C₂⁵	1	16	yes	—
157	C₂²×D₅	C₂⁵	1	3	yes	—
158	C₂×AGL(1,𝔽₅)	—	2	96	no	—
159	C₂×AGL(1,𝔽₅)	—	4	128	no	—
160	C₂×AGL(1,𝔽₅)	C₂⁵	1	32	yes	—
161	C₅×D₄	C₂³×C₄	1	64	yes	complemented
162	C₂×C₄×C₅	C₂³×C₄	1	12	yes	—
163	C₂×C₄×C₅	C₂³×C₄	1	16	yes	complemented
164	C₂²⋊D₅	C₂³×C₄	1	128	yes	complemented
165	C₂×Dic₅	C₂³×C₄	1	12	yes	—
166	C₂×Dic₅	C₂³×C₄	1	16	yes	complemented
167	D₂₀	C₂³×C₄	1	64	yes	complemented
168	C₄×D₅	C₂³×C₄	1	24	yes	—
169	C₄×D₅	C₂³×C₄	1	32	yes	complemented
170	C₄×D₅	C₂⁵	1	8	yes	—
171	C₂⁵	—	5	1	no	—
172	C₂⁵	—	5	4	no	—
173	C₂⁵	—	5	4	no	—
174	C₂⁵	—	5	2	no	—
175	C₂⁵	—	5	24	no	—
176	C₂⁵	—	5	24	no	—
177	C₂⁵	—	20	16	no	—
178	C₂⁵	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
179	C₂²×D₄	—	5	8	no	—
180	C₂²×D₄	—	5	48	no	—
181	C₂²×D₄	—	5	48	no	—
182	C₂²×D₄	—	5	64	no	—
183	C₂²×D₄	—	5	48	no	—
184	C₂²×D₄	—	5	96	no	—
185	C₂²×D₄	—	5	192	no	—
186	C₂²×D₄	—	5	4	no	—
187	C₂²×D₄	—	5	24	no	—
188	C₂²×D₄	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
189	C₂²×D₄	C₂×AGL(1,𝔽₅)	1	24	yes	complemented
190	C₂³×C₄	—	5	1	no	—
191	C₂³×C₄	—	5	2	no	—
192	C₂³×C₄	—	5	2	no	—
193	C₂³×C₄	—	5	12	no	—
194	C₂³×C₄	—	5	12	no	—
195	C₂³×C₄	—	5	8	no	—
196	C₂³×C₄	—	5	96	no	—
197	C₂³×C₄	—	20	32	no	—
198	C₂³×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
199	C₄×D₄	—	5	512	no	—
200	#117	—	5	128	no	—
201	C₂×C₄⋊C₄	—	5	48	no	—
202	C₂×C₂²⋊C₄	—	5	48	no	—
203	C₂×C₂²⋊C₄	—	5	96	no	—
204	C₂×C₂²⋊C₄	—	5	256	no	—
205	C₂×C₄²	—	5	48	no	—
206	C₂²×C₅	—	2	12	no	—
207	C₂²×C₅	—	2	48	no	—
208	C₂²×C₅	—	4	32	no	—
209	C₂²×C₅	#518	1	4	yes	complemented
210	C₂²×C₅	C₂⁴×C₄	1	4	yes	—
211	C₂²×C₅	C₂⁴×C₄	1	16	yes	—
212	C₂²×C₅	C₂⁴×C₄	1	3	yes	—
213	C₂×D₅	—	2	12	no	—
214	C₂×D₅	—	2	48	no	—
215	C₂×D₅	—	2	32	no	—
216	C₂×D₅	—	2	8	no	—
217	C₂×D₅	—	2	24	no	—
218	C₂×D₅	—	2	96	no	—
219	C₂×D₅	—	4	64	no	—
220	C₂×D₅	—	4	32	no	—
221	C₂×D₅	#518	1	12	yes	complemented
222	C₂×D₅	C₂⁴×C₄	1	4	yes	—
223	C₂×D₅	C₂⁴×C₄	1	16	yes	—
224	C₂×D₅	C₂⁴×C₄	1	3	yes	—
225	C₂×D₅	C₂×H(5,𝔽₂)	1	12	yes	—
226	C₂×D₅	C₂⁶	1	1	yes	characteristic
227	AGL(1,𝔽₅)	—	2	32	no	—
228	C₄×C₅	C₂⁴×C₄	1	8	yes	—
229	Dic₅	C₂⁴×C₄	1	8	yes	—
230	C₂⁴	—	4	8	no	—
231	C₂⁴	—	5	1	no	—
232	C₂⁴	—	5	6	no	—
233	C₂⁴	—	5	24	no	—
234	C₂⁴	—	5	6	no	—
235	C₂⁴	—	5	24	no	—
236	C₂⁴	—	5	1	no	—
237	C₂⁴	—	5	4	no	—
238	C₂⁴	—	5	48	no	—
239	C₂⁴	—	5	24	no	—
240	C₂⁴	—	5	32	no	—
241	C₂⁴	—	5	96	no	—
242	C₂⁴	—	10	32	no	—
243	C₂⁴	—	10	8	no	—
244	C₂⁴	—	20	8	no	—
245	C₂⁴	—	20	16	no	—
246	C₂⁴	—	20	96	no	—
247	C₂⁴	—	20	96	no	—
248	C₂⁴	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
249	C₂⁴	C₂²×AGL(1,𝔽₅)	1	4	yes	—
250	C₂⁴	C₂²×AGL(1,𝔽₅)	1	24	yes	complemented
251	C₂×D₄	—	5	96	no	—
252	C₂×D₄	—	5	128	no	—
253	C₂×D₄	—	5	64	no	—
254	C₂×D₄	—	5	192	no	—
255	C₂×D₄	—	5	256	no	—
256	C₂×D₄	—	5	48	no	—
257	C₂×D₄	—	5	64	no	—
258	C₂×D₄	C₂²×AGL(1,𝔽₅)	1	48	yes	complemented
259	C₂×D₄	C₂²×AGL(1,𝔽₅)	1	64	yes	complemented
260	C₂²×C₄	—	5	12	no	—
261	C₂²×C₄	—	5	2	no	—
262	C₂²×C₄	—	5	12	no	—
263	C₂²×C₄	—	5	12	no	—
264	C₂²×C₄	—	5	24	no	—
265	C₂²×C₄	—	5	16	no	—
266	C₂²×C₄	—	5	48	no	—
267	C₂²×C₄	—	5	48	no	—
268	C₂²×C₄	—	5	128	no	—
269	C₂²×C₄	—	10	32	no	—
270	C₂²×C₄	—	20	192	no	—
271	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
272	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	12	yes	complemented
273	C₄⋊C₄	—	5	64	no	—
274	C₂²⋊C₄	—	5	64	no	—
275	C₂²⋊C₄	—	5	128	no	—
276	C₄²	—	5	64	no	—
277	C₂×C₅	—	2	4	no	—
278	C₂×C₅	—	2	16	no	—
279	C₂×C₅	C₂×#518	1	6	yes	complemented
280	C₂×C₅	C₂⁵×C₄	1	1	yes	characteristic
281	D₅	—	2	4	no	—
282	D₅	—	2	16	no	—
283	D₅	C₂×#518	1	6	yes	complemented
284	D₅	C₂²×H(5,𝔽₂)	1	2	yes	—
285	C₂³	—	2	4	no	—
286	C₂³	—	2	16	no	—
287	C₂³	—	4	48	no	—
288	C₂³	—	5	8	no	—
289	C₂³	—	5	3	no	—
290	C₂³	—	5	3	no	—
291	C₂³	—	5	4	no	—
292	C₂³	—	5	16	no	—
293	C₂³	—	5	12	no	—
294	C₂³	—	5	6	no	—
295	C₂³	—	5	48	no	—
296	C₂³	—	5	24	no	—
297	C₂³	—	5	64	no	—
298	C₂³	—	5	32	no	—
299	C₂³	—	10	96	no	—
300	C₂³	—	10	24	no	—
301	C₂³	—	10	24	no	—
302	C₂³	—	10	96	no	—
303	C₂³	—	10	4	no	—
304	C₂³	—	10	16	no	—
305	C₂³	—	20	48	no	—
306	C₂³	—	20	96	no	—
307	C₂³	—	20	64	no	—
308	C₂³	—	20	192	no	—
309	C₂³	C₂³×AGL(1,𝔽₅)	1	6	yes	—
310	C₂³	C₂³×AGL(1,𝔽₅)	1	24	yes	—
311	C₂³	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
312	C₂³	C₂³×AGL(1,𝔽₅)	1	32	yes	complemented
313	D₄	—	5	128	no	—
314	D₄	—	5	64	no	—
315	D₄	C₂³×AGL(1,𝔽₅)	1	64	yes	complemented
316	C₂×C₄	—	5	12	no	—
317	C₂×C₄	—	5	16	no	—
318	C₂×C₄	—	5	8	no	—
319	C₂×C₄	—	5	24	no	—
320	C₂×C₄	—	5	32	no	—
321	C₂×C₄	—	5	32	no	—
322	C₂×C₄	—	10	96	no	—
323	C₂×C₄	—	20	128	no	—
324	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	12	yes	—
325	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	16	yes	complemented
326	C₅	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
327	C₂²	—	2	12	no	—
328	C₂²	—	2	48	no	—
329	C₂²	—	4	32	no	—
330	C₂²	—	5	12	no	—
331	C₂²	—	5	12	no	—
332	C₂²	—	5	1	no	—
333	C₂²	—	5	3	no	—
334	C₂²	—	5	4	no	—
335	C₂²	—	5	16	no	—
336	C₂²	—	10	32	no	—
337	C₂²	—	10	8	no	—
338	C₂²	—	10	24	no	—
339	C₂²	—	10	96	no	—
340	C₂²	—	10	12	no	—
341	C₂²	—	10	48	no	—
342	C₂²	—	20	32	no	—
343	C₂²	—	20	64	no	—
344	C₂²	#66258	1	4	yes	direct product factor
345	C₂²	C₂⁴×AGL(1,𝔽₅)	1	4	yes	—
346	C₂²	C₂⁴×AGL(1,𝔽₅)	1	16	yes	—
347	C₂²	C₂⁴×AGL(1,𝔽₅)	1	3	yes	—
348	C₄	—	5	8	no	—
349	C₄	—	10	32	no	—
350	C₄	C₂⁴×AGL(1,𝔽₅)	1	8	yes	—
351	C₂	—	2	4	no	—
352	C₂	—	2	16	no	—
353	C₂	—	5	2	no	—
354	C₂	—	5	6	no	—
355	C₂	—	10	4	no	—
356	C₂	—	10	16	no	—
357	C₂	C₂×#66258	1	6	yes	direct product factor
358	C₂	C₂⁵×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂⁵×C₄
Frattini	C₂	C₂⁵×AGL(1,𝔽₅)
Fitting	C₂³×C₅×D₄	C₄
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂³×D₄×D₅	C₂
cosocle	C₂×D₅	C₂⁶
hypercenter	C₂³×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₂²×#518
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₂²⋊AGL(1,𝔽₅)	C₂	semidirect
3. C₂×#66258	C₂	direct (N × H)
4. C₂²×D₄×AGL(1,𝔽₅)	C₂	semidirect
5. C₂²×#4130	C₂	semidirect
7. C₂⁴×AGL(1,𝔽₅)	C₂²	semidirect
8. C₂³×C₅×D₄	C₄	semidirect
9. C₂³×C₂²⋊D₅	C₄	semidirect
10. C₂²×D₄×D₅	C₄	semidirect
11. C₂²×D₄×D₅	C₄	semidirect
14. C₂³×D₂₀	C₄	semidirect
17. C₂²×C₂²⋊AGL(1,𝔽₅)	C₂²	semidirect
18. C₂²×C₂²⋊AGL(1,𝔽₅)	C₂²	semidirect
19. #66258	C₂²	direct (N × H)
20. C₂×D₄×AGL(1,𝔽₅)	C₂²	semidirect
21. C₂×#4130	C₂²	semidirect
22. C₂²×C₄⋊AGL(1,𝔽₅)	C₂²	semidirect
23. C₂²×C₄×AGL(1,𝔽₅)	C₂²	semidirect
25. C₂⁵×C₅	C₂×C₄	semidirect
27. C₂⁴×D₅	C₂×C₄	semidirect
28. C₂⁴×D₅	C₂×C₄	semidirect
29. C₂⁴×D₅	C₂×C₄	semidirect
35. C₂³×AGL(1,𝔽₅)	C₂³	semidirect
36. C₂²×C₅×D₄	C₂×C₄	semidirect
37. C₂²×C₅×D₄	C₂×C₄	semidirect
38. C₂³×C₄×C₅	C₂×C₄	semidirect
39. C₂²×C₂²⋊D₅	C₂×C₄	semidirect
40. C₂²×C₂²⋊D₅	C₂×C₄	semidirect
41. C₂³×Dic₅	C₂×C₄	semidirect
42. C₂×D₄×D₅	C₂×C₄	semidirect
43. C₂×D₄×D₅	C₂×C₄	semidirect
44. C₂×D₄×D₅	C₂×C₄	semidirect
47. C₂²×D₂₀	C₂×C₄	semidirect
48. C₂²×D₂₀	C₂×C₄	semidirect
49. C₂²×C₄×D₅	C₂×C₄	semidirect
50. C₂²×C₄×D₅	C₂×C₄	semidirect
54. C₂×C₂²⋊AGL(1,𝔽₅)	C₂³	semidirect
55. C₂×C₂²⋊AGL(1,𝔽₅)	C₂³	semidirect
56. D₄×AGL(1,𝔽₅)	C₂³	semidirect
57. #4130	C₂³	semidirect
58. C₂×C₄⋊AGL(1,𝔽₅)	C₂³	semidirect
59. C₂×C₄×AGL(1,𝔽₅)	C₂³	semidirect
68. C₂⁴×C₅	C₂²×C₄	semidirect
79. C₂³×D₅	C₂²×C₄	semidirect
80. C₂³×D₅	C₂²×C₄	semidirect
81. C₂³×D₅	C₂²×C₄	semidirect
89. C₂²×AGL(1,𝔽₅)	C₂⁴	semidirect
90. C₂×C₅×D₄	C₂²×C₄	semidirect
91. C₂×C₅×D₄	C₂²×C₄	semidirect
93. C₂²×C₄×C₅	C₂²×C₄	semidirect
94. C₂×C₂²⋊D₅	C₂²×C₄	semidirect
95. C₂×C₂²⋊D₅	C₂²×C₄	semidirect
97. C₂²×Dic₅	C₂²×C₄	semidirect
98. D₄×D₅	C₂²×C₄	semidirect
99. D₄×D₅	C₂²×C₄	semidirect
101. C₂×D₂₀	C₂²×C₄	semidirect
102. C₂×D₂₀	C₂²×C₄	semidirect
104. C₂×C₄×D₅	C₂²×C₄	semidirect
105. C₂×C₄×D₅	C₂²×C₄	semidirect
109. C₂²⋊AGL(1,𝔽₅)	C₂⁴	semidirect
110. C₄⋊AGL(1,𝔽₅)	C₂⁴	semidirect
111. C₄×AGL(1,𝔽₅)	C₂⁴	semidirect
119. C₂³×D₄	AGL(1,𝔽₅)	semidirect
136. C₂³×C₅	C₂³×C₄	semidirect
152. C₂²×D₅	C₂³×C₄	semidirect
153. C₂²×D₅	C₂³×C₄	semidirect
161. C₅×D₄	C₂³×C₄	semidirect
163. C₂×C₄×C₅	C₂³×C₄	semidirect
164. C₂²⋊D₅	C₂³×C₄	semidirect
166. C₂×Dic₅	C₂³×C₄	semidirect
167. D₂₀	C₂³×C₄	semidirect
169. C₄×D₅	C₂³×C₄	semidirect
178. C₂⁵	C₂×AGL(1,𝔽₅)	semidirect
188. C₂²×D₄	C₂×AGL(1,𝔽₅)	semidirect
189. C₂²×D₄	C₂×AGL(1,𝔽₅)	semidirect
198. C₂³×C₄	C₂×AGL(1,𝔽₅)	semidirect
209. C₂²×C₅	#518	semidirect
221. C₂×D₅	#518	semidirect
250. C₂⁴	C₂²×AGL(1,𝔽₅)	semidirect
258. C₂×D₄	C₂²×AGL(1,𝔽₅)	semidirect
259. C₂×D₄	C₂²×AGL(1,𝔽₅)	semidirect
272. C₂²×C₄	C₂²×AGL(1,𝔽₅)	semidirect
279. C₂×C₅	C₂×#518	semidirect
283. D₅	C₂×#518	semidirect
312. C₂³	C₂³×AGL(1,𝔽₅)	semidirect
315. D₄	C₂³×AGL(1,𝔽₅)	semidirect
325. C₂×C₄	C₂³×AGL(1,𝔽₅)	semidirect
326. C₅	C₂²×#518	semidirect
344. C₂²	#66258	direct (N × H)
357. C₂	C₂×#66258	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₅	2
C₂³×C₂²⋊AGL(1,𝔽₅)	2
C₂×#66258	2
C₂²×D₄×AGL(1,𝔽₅)	2
C₂²×#4130	2
C₂²×#518	5

Subgroups — C22×#66258 #13046012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#66258 #13046012