Subgroups — AGL(1,𝔽₅)×#237 #11756844

Order 960.

620 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#237	C₂	1	1	yes	maximal, characteristic
2	D₄×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	#67⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
5	AGL(1,𝔽₅)×#67	C₂	1	2	yes	maximal, complemented
6	#91923	C₂	1	2	yes	maximal, complemented
7	C₂×Dic₃×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
8	C₄×D₃×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
9	ΓL(1,𝔽₁₆)⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#91907	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,𝔽₅)×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
13	C₂²×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
14	C₂²×C₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₂×D₃×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
16	C₂×D₃×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
17	#6819	C₄	1	1	yes	characteristic, complemented
18	C₅×#237	C₄	1	1	yes	characteristic, complemented
19	C₃×D₄×D₅	C₂²	1	1	yes	characteristic
20	D₅×#67	C₂²	1	2	yes	—
21	#6780	C₄	1	2	yes	complemented
22	#6779	C₄	1	2	yes	complemented
23	C₂×D₅×Dic₃	C₂²	1	2	yes	—
24	C₄×D₃×D₅	C₂²	1	1	yes	characteristic
25	#6766	C₄	1	1	yes	characteristic, complemented
26	#6765	C₄	1	1	yes	characteristic, complemented
27	D₅×Dic₆	C₂²	1	1	yes	characteristic
28	#6763	C₂²	1	2	yes	—
29	C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
30	C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
32	C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
33	C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
34	Dic₃⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
35	Dic₃⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
36	(C₂×D₃)⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
37	Dic₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
38	Dic₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
39	Dic₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
40	Dic₃×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
41	Dic₃×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
42	C₄×#237	—	5	1	no	maximal, Hall
43	D₅×#41	—	3	1	no	—
44	Q₈×AGL(1,𝔽₅)	—	3	1	no	—
45	Q₈×AGL(1,𝔽₅)	—	3	1	no	—
46	D₄×AGL(1,𝔽₅)	—	3	2	no	—
47	D₄×AGL(1,𝔽₅)	—	3	1	no	—
48	D₄×AGL(1,𝔽₅)	—	3	2	no	—
49	D₄×AGL(1,𝔽₅)	D₃	1	1	yes	characteristic, complemented
50	#4130	—	3	2	no	—
51	#4130	—	3	1	no	—
52	C₂×C₄×AGL(1,𝔽₅)	—	3	2	no	—
53	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
54	C₂²×C₃×D₅	C₂³	1	2	yes	—
55	C₂×D₃×D₅	C₂³	1	1	yes	characteristic
56	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
57	C₂×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
58	C₂×ΓL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
59	C₂×ΓL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
60	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
61	C₂×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
62	C₂×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
63	C₂×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
64	D₃×AGL(1,𝔽₅)	—	2	2	no	—
65	D₃×AGL(1,𝔽₅)	—	2	2	no	—
66	C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
67	#1220	C₂×C₄	1	2	yes	complemented
68	C₂×Dic₁₅	C₂×C₄	1	2	yes	complemented
69	C₄×D₁₅	C₂×C₄	1	1	yes	characteristic, complemented
70	Dic₃₀	C₂×C₄	1	1	yes	characteristic, complemented
71	C₅×#67	C₂×C₄	1	2	yes	complemented
72	C₂×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
73	C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic, complemented
74	C₅×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
75	C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	complemented
76	C₃×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
77	C₃×C₄×D₅	C₂³	1	1	yes	characteristic
78	#1204	C₂×C₄	1	2	yes	complemented
79	#1202	C₂×C₄	1	2	yes	complemented
80	#1201	C₂×C₄	1	2	yes	complemented
81	#1200	C₂×C₄	1	1	yes	characteristic, complemented
82	D₃×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
83	D₅×Dic₃	C₂×C₄	1	2	yes	complemented
84	D₅×Dic₃	C₂×C₄	1	2	yes	complemented
85	D₅×Dic₃	C₂³	1	1	yes	characteristic
86	D₅×Dic₃	C₂³	1	2	yes	—
87	C₂×#237	—	5	1	no	—
88	C₃×C₄×D₄	—	5	1	no	—
89	D₄×Dic₃	—	5	1	no	—
90	C₄×#67	—	5	2	no	—
91	C₂×C₄×Dic₃	—	5	2	no	—
92	#892	—	5	1	no	—
93	#887	—	5	1	no	—
94	#67⋊C₄	—	5	2	no	—
95	#877	—	5	2	no	—
96	C₄²×D₃	—	5	1	no	—
97	C₄×Dic₆	—	5	1	no	—
98	C₂²×AGL(1,𝔽₅)	—	3	2	no	—
99	C₂²×AGL(1,𝔽₅)	—	3	1	no	—
100	C₂²×AGL(1,𝔽₅)	—	3	1	no	—
101	C₂²×AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
102	C₅×#41	—	3	1	no	—
103	#713	—	3	1	no	—
104	Q₈×D₅	—	3	1	no	—
105	#711	—	3	1	no	—
106	#711	—	3	2	no	—
107	D₄×D₅	—	3	2	no	—
108	D₄×D₅	C₂×D₃	1	1	yes	characteristic
109	#709	—	3	2	no	—
110	#709	—	3	1	no	—
111	C₂×C₄×D₅	—	3	2	no	—
112	C₂×C₄×D₅	—	3	1	no	—
113	C₂²⋊AGL(1,𝔽₅)	—	3	2	no	—
114	C₂²⋊AGL(1,𝔽₅)	—	3	2	no	—
115	C₂²⋊AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
116	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
117	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
118	C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
119	C₄⋊AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
120	C₄×AGL(1,𝔽₅)	—	3	1	no	—
121	C₄×AGL(1,𝔽₅)	—	3	2	no	—
122	C₄×AGL(1,𝔽₅)	—	3	1	no	—
123	C₄×AGL(1,𝔽₅)	—	3	2	no	—
124	C₄×AGL(1,𝔽₅)	—	3	2	no	—
125	C₄×AGL(1,𝔽₅)	—	3	1	no	—
126	C₄×AGL(1,𝔽₅)	C₂×D₃	1	1	yes	characteristic
127	C₄×#41	—	15	1	no	Sylow
128	C₂²×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂×D₁₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×D₅	—	2	2	no	—
132	C₂×C₃×D₅	—	2	2	no	—
133	C₂×C₃×D₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×D₅	C₂⁴	1	1	yes	characteristic
135	D₃×D₅	—	2	1	no	—
136	D₃×D₅	—	2	1	no	—
137	ΓL(1,𝔽₁₆)	—	2	1	no	—
138	ΓL(1,𝔽₁₆)	—	2	2	no	—
139	ΓL(1,𝔽₁₆)	#41	1	2	yes	complemented
140	C₃×AGL(1,𝔽₅)	—	2	1	no	—
141	C₃×AGL(1,𝔽₅)	—	2	2	no	—
142	C₃×AGL(1,𝔽₅)	#41	1	2	yes	complemented
143	C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	Dic₁₅	C₂²×C₄	1	1	yes	characteristic
145	Dic₁₅	C₂²×C₄	1	2	yes	—
146	C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
147	C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
148	C₅×Dic₃	C₂²×C₄	1	2	yes	—
149	C₂×C₃×D₄	—	5	1	no	—
150	C₂²×C₃×C₄	—	5	2	no	—
151	C₂×#67	—	5	2	no	—
152	C₂²×Dic₃	—	5	2	no	—
153	C₂²×Dic₃	—	5	2	no	—
154	#237	—	5	1	no	—
155	#237	—	5	2	no	—
156	#237	—	5	2	no	—
157	#237	—	5	1	no	—
158	#237	—	5	1	no	—
159	#237	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
160	C₂×C₄×D₃	—	5	1	no	—
161	C₂×C₄×D₃	—	5	1	no	—
162	C₂×C₄×D₃	—	5	1	no	—
163	C₂×Dic₆	—	5	1	no	—
164	C₃×C₄⋊C₄	—	5	1	no	—
165	C₃×C₂²⋊C₄	—	5	2	no	—
166	C₃×C₄²	—	5	1	no	—
167	#217	—	5	2	no	—
168	(C₂×D₃)⋊C₄	—	5	2	no	—
169	C₄⋊Dic₃	—	5	1	no	—
170	Dic₃⋊C₄	—	5	2	no	—
171	Dic₃⋊C₄	—	5	2	no	—
172	C₄×Dic₃	—	5	2	no	—
173	C₄×Dic₃	—	5	1	no	—
174	C₄×Dic₃	—	5	1	no	—
175	C₄×Dic₃	—	5	2	no	—
176	C₄×Dic₃	—	5	2	no	—
177	C₄×Dic₃	—	5	1	no	—
178	C₂²×D₅	—	3	1	no	—
179	C₂²×D₅	C₂²×D₃	1	2	yes	—
180	C₂×AGL(1,𝔽₅)	—	2	4	no	—
181	C₂×AGL(1,𝔽₅)	—	3	1	no	—
182	C₂×AGL(1,𝔽₅)	—	3	1	no	—
183	C₂×AGL(1,𝔽₅)	—	3	2	no	—
184	C₂×AGL(1,𝔽₅)	—	6	2	no	—
185	C₂×AGL(1,𝔽₅)	—	6	4	no	—
186	C₂×AGL(1,𝔽₅)	—	6	2	no	—
187	C₂×AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
188	C₂×AGL(1,𝔽₅)	C₂²×D₃	1	1	yes	characteristic
189	C₂×AGL(1,𝔽₅)	C₂²×D₃	1	1	yes	characteristic
190	C₅×Q₈	—	3	1	no	—
191	C₅×D₄	—	3	2	no	—
192	C₅×D₄	C₄×D₃	1	1	yes	characteristic, complemented
193	C₂×C₄×C₅	—	3	2	no	—
194	C₂×C₄×C₅	—	3	1	no	—
195	C₂²⋊D₅	—	3	2	no	—
196	C₂²⋊D₅	—	3	2	no	—
197	C₂²⋊D₅	C₄×D₃	1	2	yes	complemented
198	C₂×Dic₅	—	3	2	no	—
199	C₂×Dic₅	—	3	1	no	—
200	D₂₀	—	3	2	no	—
201	D₂₀	C₄×D₃	1	1	yes	characteristic, complemented
202	C₄×D₅	—	3	2	no	—
203	C₄×D₅	—	3	2	no	—
204	C₄×D₅	—	3	1	no	—
205	C₄×D₅	—	3	2	no	—
206	C₄×D₅	—	3	1	no	—
207	C₄×D₅	—	3	1	no	—
208	C₄×D₅	C₂²×D₃	1	1	yes	characteristic
209	Dic₁₀	—	3	1	no	—
210	Dic₁₀	—	3	2	no	—
211	C₂×#41	—	15	1	no	—
212	C₄×Q₈	—	15	1	no	—
213	C₄×Q₈	—	15	1	no	—
214	C₄×D₄	—	5	1	no	—
215	C₄×D₄	—	15	2	no	—
216	C₄×D₄	—	15	2	no	—
217	C₄×D₄	—	15	1	no	—
218	#117	—	15	2	no	—
219	#117	—	15	1	no	—
220	C₂×C₄²	—	15	1	no	—
221	C₂×C₄²	—	15	2	no	—
222	C₂×C₃×C₅	—	2	2	no	—
223	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	D₁₅	—	2	1	no	—
225	C₃×D₅	—	2	2	no	—
226	C₃×D₅	C₂×#41	1	1	yes	characteristic
227	C₃×D₅	C₂×#41	1	1	yes	characteristic
228	C₅×D₃	—	2	1	no	—
229	C₂³×C₃	—	5	2	no	—
230	C₂²×D₃	—	5	1	no	—
231	C₃×D₄	—	5	2	no	—
232	C₃×D₄	—	5	1	no	—
233	C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
234	C₂×C₃×C₄	—	5	1	no	—
235	C₂×C₃×C₄	—	5	1	no	—
236	C₂×C₃×C₄	—	5	2	no	—
237	C₂×C₃×C₄	—	5	1	no	—
238	C₂×C₃×C₄	—	10	4	no	—
239	#67	—	5	2	no	—
240	#67	—	5	2	no	—
241	#67	—	5	2	no	—
242	#67	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
243	C₂×Dic₃	—	5	1	no	—
244	C₂×Dic₃	—	5	2	no	—
245	C₂×Dic₃	—	5	2	no	—
246	C₂×Dic₃	—	5	2	no	—
247	C₂×Dic₃	—	5	1	no	—
248	C₂×Dic₃	—	5	2	no	—
249	C₂×Dic₃	—	5	1	no	—
250	C₂×Dic₃	—	5	2	no	—
251	C₂×Dic₃	—	10	4	no	—
252	C₂×Dic₃	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
253	C₄×D₃	—	5	1	no	—
254	C₄×D₃	—	5	1	no	—
255	C₄×D₃	—	5	1	no	—
256	C₄×D₃	—	10	2	no	—
257	C₄×D₃	—	10	2	no	—
258	C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
259	Dic₆	—	5	1	no	—
260	Dic₆	—	5	2	no	—
261	Dic₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
262	C₂²×C₅	—	3	1	no	—
263	C₂²×C₅	C₂×C₄×D₃	1	2	yes	—
264	C₂×D₅	—	2	2	no	—
265	C₂×D₅	—	2	2	no	—
266	C₂×D₅	—	3	1	no	—
267	C₂×D₅	—	6	1	no	—
268	C₂×D₅	—	6	1	no	—
269	C₂×D₅	C₂×C₄×D₃	1	2	yes	—
270	C₂×D₅	C₂³×D₃	1	1	yes	characteristic
271	AGL(1,𝔽₅)	—	2	2	no	—
272	AGL(1,𝔽₅)	—	2	1	no	—
273	AGL(1,𝔽₅)	—	3	2	no	—
274	AGL(1,𝔽₅)	—	6	1	no	—
275	AGL(1,𝔽₅)	—	6	2	no	—
276	AGL(1,𝔽₅)	#237	1	2	yes	direct product factor
277	C₄×C₅	—	3	2	no	—
278	C₄×C₅	—	3	1	no	—
279	C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
280	Dic₅	—	3	2	no	—
281	Dic₅	—	3	1	no	—
282	Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
283	#41	—	3	1	no	—
284	#41	—	15	2	no	—
285	#41	—	15	1	no	—
286	#41	—	15	2	no	—
287	#41	—	15	1	no	—
288	#41	—	15	1	no	—
289	C₂×Q₈	—	15	1	no	—
290	C₂×D₄	—	5	1	no	—
291	C₂×D₄	—	15	2	no	—
292	C₂²×C₄	—	5	2	no	—
293	C₂²×C₄	—	15	1	no	—
294	C₂²×C₄	—	15	2	no	—
295	C₂²×C₄	—	15	1	no	—
296	C₂²×C₄	—	15	1	no	—
297	C₂²×C₄	—	15	2	no	—
298	C₄⋊C₄	—	5	1	no	—
299	C₄⋊C₄	—	15	2	no	—
300	C₄⋊C₄	—	15	2	no	—
301	C₄⋊C₄	—	15	1	no	—
302	C₂²⋊C₄	—	5	2	no	—
303	C₂²⋊C₄	—	15	2	no	—
304	C₂²⋊C₄	—	15	2	no	—
305	C₄²	—	5	1	no	—
306	C₄²	—	15	1	no	—
307	C₄²	—	15	1	no	—
308	C₄²	—	15	2	no	—
309	C₄²	—	15	2	no	—
310	C₄²	—	15	1	no	—
311	C₄²	—	15	2	no	—
312	C₃×C₅	C₄×#41	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	—	5	1	no	—
314	C₂²×C₃	—	5	2	no	—
315	C₂²×C₃	—	10	2	no	—
316	C₂²×C₃	—	10	2	no	—
317	C₂²×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
318	C₂×D₃	—	5	1	no	—
319	C₂×D₃	—	10	1	no	—
320	C₂×D₃	—	10	1	no	—
321	C₂×D₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₃×C₄	—	5	2	no	—
323	C₃×C₄	—	5	1	no	—
324	C₃×C₄	—	10	1	no	—
325	C₃×C₄	—	10	2	no	—
326	C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
327	Dic₃	—	5	2	no	—
328	Dic₃	—	5	2	no	—
329	Dic₃	—	5	1	no	—
330	Dic₃	—	10	1	no	—
331	Dic₃	—	10	2	no	—
332	Dic₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
333	Dic₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₂×C₅	—	2	2	no	—
335	C₂×C₅	—	6	1	no	—
336	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
337	D₅	—	2	2	no	—
338	D₅	—	6	1	no	—
339	D₅	C₂×#237	1	1	yes	characteristic
340	D₅	D₃×#41	1	1	yes	characteristic
341	C₂³	—	5	2	no	—
342	C₂³	—	15	1	no	—
343	Q₈	—	3	1	no	—
344	Q₈	—	15	2	no	—
345	Q₈	—	15	1	no	—
346	D₄	—	3	2	no	—
347	D₄	—	5	2	no	—
348	D₄	—	5	1	no	—
349	D₄	—	15	2	no	—
350	D₄	—	15	2	no	—
351	D₄	—	15	2	no	—
352	D₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
353	C₂×C₄	—	3	2	no	—
354	C₂×C₄	—	3	1	no	—
355	C₂×C₄	—	5	1	no	—
356	C₂×C₄	—	5	1	no	—
357	C₂×C₄	—	5	1	no	—
358	C₂×C₄	—	5	2	no	—
359	C₂×C₄	—	10	4	no	—
360	C₂×C₄	—	15	1	no	—
361	C₂×C₄	—	15	1	no	—
362	C₂×C₄	—	15	2	no	—
363	C₂×C₄	—	15	2	no	—
364	C₂×C₄	—	15	2	no	—
365	C₂×C₄	—	15	1	no	—
366	C₂×C₄	—	15	1	no	—
367	C₂×C₄	—	15	2	no	—
368	C₂×C₄	—	15	1	no	—
369	C₂×C₄	—	15	2	no	—
370	C₂×C₄	—	15	1	no	—
371	C₂×C₄	—	30	2	no	—
372	C₂×C₄	—	30	2	no	—
373	C₂×C₄	—	30	4	no	—
374	C₂×C₃	—	2	2	no	—
375	C₂×C₃	—	5	1	no	—
376	C₂×C₃	—	5	1	no	—
377	C₂×C₃	—	10	2	no	—
378	C₂×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
379	D₃	—	2	1	no	—
380	D₃	—	10	1	no	—
381	C₅	C₄×#237	1	1	yes	characteristic, complemented, Sylow
382	C₂²	—	3	1	no	—
383	C₂²	—	5	1	no	—
384	C₂²	—	5	2	no	—
385	C₂²	—	10	2	no	—
386	C₂²	—	10	2	no	—
387	C₂²	—	15	1	no	—
388	C₂²	—	30	1	no	—
389	C₂²	—	30	1	no	—
390	C₂²	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	—
391	C₄	—	3	1	no	—
392	C₄	—	3	2	no	—
393	C₄	—	5	2	no	—
394	C₄	—	5	1	no	—
395	C₄	—	10	2	no	—
396	C₄	—	10	1	no	—
397	C₄	—	15	2	no	—
398	C₄	—	15	1	no	—
399	C₄	—	15	2	no	—
400	C₄	—	30	1	no	—
401	C₄	—	30	2	no	—
402	C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
404	C₂	—	2	2	no	—
405	C₂	—	5	1	no	—
406	C₂	—	5	1	no	—
407	C₂	—	6	1	no	—
408	C₂	—	10	2	no	—
409	C₂	—	30	1	no	—
410	C₂	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×D₄	C₂×C₄
prime radical	D₅×#237	C₂
cosocle	C₂×C₃×D₅	C₂⁴
hypercenter	D₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₄×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
2. D₄×ΓL(1,𝔽₁₆)	C₂	semidirect
3. C₃×D₄×AGL(1,𝔽₅)	C₂	semidirect
4. #67⋊AGL(1,𝔽₅)	C₂	semidirect
5. AGL(1,𝔽₅)×#67	C₂	semidirect
6. #91923	C₂	semidirect
7. C₂×Dic₃×AGL(1,𝔽₅)	C₂	semidirect
8. C₄×D₃×AGL(1,𝔽₅)	C₂	semidirect
9. ΓL(1,𝔽₁₆)⋊Q₈	C₂	semidirect
10. #91907	C₂	semidirect
11. AGL(1,𝔽₅)×Dic₆	C₂	semidirect
17. #6819	C₄	semidirect
18. C₅×#237	C₄	semidirect
21. #6780	C₄	semidirect
22. #6779	C₄	semidirect
25. #6766	C₄	semidirect
26. #6765	C₄	semidirect
49. D₄×AGL(1,𝔽₅)	D₃	semidirect
66. C₃×C₅×D₄	C₂×C₄	semidirect
67. #1220	C₂×C₄	semidirect
68. C₂×Dic₁₅	C₂×C₄	semidirect
69. C₄×D₁₅	C₂×C₄	semidirect
70. Dic₃₀	C₂×C₄	semidirect
71. C₅×#67	C₂×C₄	semidirect
72. C₂×C₅×Dic₃	C₂×C₄	semidirect
73. C₄×C₅×D₃	C₂×C₄	semidirect
74. C₅×Dic₆	C₂×C₄	semidirect
75. C₃×C₂²⋊D₅	C₂×C₄	semidirect
76. C₃×D₂₀	C₂×C₄	semidirect
78. #1204	C₂×C₄	semidirect
79. #1202	C₂×C₄	semidirect
80. #1201	C₂×C₄	semidirect
81. #1200	C₂×C₄	semidirect
82. D₃×Dic₅	C₂×C₄	semidirect
83. D₅×Dic₃	C₂×C₄	semidirect
84. D₅×Dic₃	C₂×C₄	semidirect
139. ΓL(1,𝔽₁₆)	#41	semidirect
142. C₃×AGL(1,𝔽₅)	#41	semidirect
159. #237	AGL(1,𝔽₅)	direct (N × H)
192. C₅×D₄	C₄×D₃	semidirect
197. C₂²⋊D₅	C₄×D₃	semidirect
201. D₂₀	C₄×D₃	semidirect
233. C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
242. #67	C₂×AGL(1,𝔽₅)	semidirect
252. C₂×Dic₃	C₂×AGL(1,𝔽₅)	semidirect
258. C₄×D₃	C₂×AGL(1,𝔽₅)	semidirect
261. Dic₆	C₂×AGL(1,𝔽₅)	semidirect
276. AGL(1,𝔽₅)	#237	direct (N × H)
312. C₃×C₅	C₄×#41	semidirect
352. D₄	D₃×AGL(1,𝔽₅)	semidirect
381. C₅	C₄×#237	semidirect
403. C₃	#41×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
D₅×#237	2
D₄×ΓL(1,𝔽₁₆)	2
C₃×D₄×AGL(1,𝔽₅)	2
#67⋊AGL(1,𝔽₅)	2
AGL(1,𝔽₅)×#67	2
#91923	2
C₂×Dic₃×AGL(1,𝔽₅)	2
C₄×D₃×AGL(1,𝔽₅)	2
ΓL(1,𝔽₁₆)⋊Q₈	2
#91907	2
AGL(1,𝔽₅)×Dic₆	2
#41×AGL(1,𝔽₅)	3
C₄×#237	5

Subgroups — AGL(1,𝔽5)×#237 #11756844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#237 #11756844