Subgroups — #13043658

Order 1280.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611007	C₂	1	1	yes	maximal, characteristic
2	#10604151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#3998	C₂	1	1	yes	maximal, characteristic, complemented
4	#10604026	C₂	1	2	yes	maximal, complemented
5	#10604022	C₂	1	2	yes	maximal, complemented
6	#10603906	C₂	1	2	yes	maximal, complemented
7	#10603905	C₂	1	2	yes	maximal, complemented
8	#10603828	C₂	1	1	yes	maximal, characteristic, complemented
9	#10603828	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#3990	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₅⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#709	C₄	1	1	yes	characteristic
13	C₂×#3998	C₂²	1	2	yes	—
14	C₂×#3990	C₂²	1	2	yes	—
15	C₂×D₅⋊C₁₆	C₂²	1	2	yes	—
16	C₅×#431	C₄	1	1	yes	characteristic
17	C₂×C₄×#168	C₂²	1	1	yes	characteristic
18	#65123	C₄	1	1	yes	characteristic
19	#65123	C₂²	1	1	yes	characteristic
20	#65119	C₄	1	1	yes	characteristic
21	#65119	C₂²	1	1	yes	characteristic
22	#65014	C₄	1	1	yes	characteristic
23	#65014	C₄	1	1	yes	characteristic
24	#65014	C₂²	1	1	yes	characteristic
25	#65014	C₂²	1	1	yes	characteristic
26	#64974	C₄	1	1	yes	characteristic
27	#64974	C₄	1	1	yes	characteristic
28	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
30	C₂²⋊#674	C₂²	1	2	yes	—
31	#64888	C₂²	1	2	yes	—
32	#64888	C₂²	1	2	yes	—
33	#64887	C₂²	1	2	yes	—
34	#64887	C₂²	1	2	yes	—
35	#64886	C₂²	1	2	yes	—
36	#64885	C₂²	1	2	yes	—
37	#64859	C₂²	1	2	yes	—
38	C₄⋊#674	C₂²	1	2	yes	—
39	C₄×#674	C₂²	1	1	yes	characteristic
40	C₄×#674	C₂²	1	1	yes	characteristic
41	C₄×#674	C₂²	1	1	yes	characteristic
42	C₄×#674	C₂²	1	1	yes	characteristic
43	#33479	—	5	1	no	maximal, Sylow
44	C₂×#709	C₈	1	1	yes	characteristic
45	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
47	C₄×C₂²⋊D₅	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
49	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
50	#4072	C₈	1	1	yes	characteristic
51	C₂²×#168	C₂×C₄	1	1	yes	characteristic
52	C₂²×#168	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
57	C₄×D₂₀	C₈	1	1	yes	characteristic
58	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
59	#4018	C₈	1	1	yes	characteristic
60	#4018	C₈	1	1	yes	characteristic
61	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₀	C₈	1	1	yes	characteristic
64	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
65	#3998	—	2	4	no	—
66	C₂×#674	C₂³	1	2	yes	—
67	C₂×#674	C₂³	1	2	yes	—
68	C₂×#674	C₂³	1	2	yes	—
69	C₂×#674	C₂³	1	2	yes	—
70	#3990	—	2	4	no	—
71	D₅⋊C₁₆	—	2	4	no	—
72	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
78	#3952	C₂×C₄	1	1	yes	characteristic
79	#3952	C₂×C₄	1	1	yes	characteristic
80	#3952	C₂×C₄	1	1	yes	characteristic
81	#3952	C₂×C₄	1	1	yes	characteristic
82	#3946	C₂×C₄	1	1	yes	characteristic
83	#3946	C₂×C₄	1	1	yes	characteristic
84	#3946	C₂×C₄	1	1	yes	characteristic
85	#3946	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₅	C₂³	1	1	yes	characteristic
89	C₈×Dic₅	C₂³	1	1	yes	characteristic
90	C₄×#168	C₂×C₄	1	1	yes	characteristic
91	C₄×#168	C₂×C₄	1	1	yes	characteristic
92	C₄×#168	C₂³	1	1	yes	characteristic
93	C₄×#168	C₂³	1	1	yes	characteristic
94	C₈×#41	—	5	1	no	—
95	#2183	—	5	2	no	—
96	#2169	—	5	2	no	—
97	#2168	—	5	2	no	—
98	#2168	—	5	2	no	—
99	#2162	—	5	1	no	—
100	#2162	—	5	1	no	—
101	#2162	—	5	1	no	—
102	C₄×M₃₂	—	5	1	no	—
103	C₄×M₃₂	—	5	1	no	—
104	C₂×C₄×C₁₆	—	5	1	no	—
105	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₅	C₂×C₈	1	1	yes	characteristic
110	#709	—	2	4	no	—
111	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
112	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×Dic₁₀	C₂×C₈	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
124	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
125	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
128	C₂²⋊Dic₅	C₂×C₈	1	1	yes	characteristic
129	#685	C₂×C₈	1	1	yes	characteristic
130	#685	C₂×C₈	1	1	yes	characteristic
131	#685	C₂×C₈	1	1	yes	characteristic
132	#685	C₂×C₈	1	1	yes	characteristic
133	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
134	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
135	#683	C₂×C₈	1	1	yes	characteristic
136	#683	C₂×C₈	1	1	yes	characteristic
137	#683	C₂×C₈	1	1	yes	characteristic
138	#683	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
140	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
141	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
142	C₄×Dic₅	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×#168	—	2	2	no	—
146	C₂×#168	—	2	2	no	—
147	C₂×#168	C₂²×C₄	1	1	yes	characteristic
148	C₂×#168	C₂²×C₄	1	1	yes	characteristic
149	C₂×#168	C₂²×C₄	1	1	yes	characteristic
150	C₂×#168	C₂⁴	1	1	yes	characteristic
151	C₈×D₅	—	2	2	no	—
152	C₈×D₅	—	2	2	no	—
153	C₈×D₅	—	2	2	no	—
154	C₈×D₅	—	2	2	no	—
155	#674	—	2	2	no	—
156	#674	—	2	2	no	—
157	#674	—	2	2	no	—
158	#674	#41	1	4	yes	complemented
159	C₄×#41	—	5	1	no	—
160	C₂×M₃₂	—	5	2	no	—
161	C₂×M₃₂	—	5	2	no	—
162	C₂²×C₁₆	—	5	2	no	—
163	C₈×Q₈	—	5	1	no	—
164	C₈×Q₈	—	5	1	no	—
165	C₈×D₄	—	5	1	no	—
166	C₈×D₄	—	5	1	no	—
167	C₈×D₄	—	5	1	no	—
168	C₈×D₄	—	5	1	no	—
169	C₈×D₄	—	5	1	no	—
170	C₈×D₄	—	5	1	no	—
171	#431	—	5	1	no	—
172	#431	—	5	1	no	—
173	#431	AGL(1,𝔽₅)	1	1	yes	characteristic
174	C₂×C₄×C₈	—	5	1	no	—
175	C₂×C₄×C₈	—	5	1	no	—
176	C₂×C₄×C₈	—	5	1	no	—
177	C₄⋊C₁₆	—	5	2	no	—
178	C₄⋊C₁₆	—	5	2	no	—
179	C₄⋊C₁₆	—	5	2	no	—
180	C₂²⋊C₁₆	—	5	2	no	—
181	C₂²⋊C₁₆	—	5	2	no	—
182	C₂²⋊C₁₆	—	5	2	no	—
183	#346	—	5	2	no	—
184	#346	—	5	2	no	—
185	C₄×C₁₆	—	5	1	no	—
186	C₄×C₁₆	—	5	1	no	—
187	C₄×C₁₆	—	5	2	no	—
188	C₄×C₁₆	—	5	1	no	—
189	C₄×C₁₆	—	5	1	no	—
190	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
191	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
192	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
200	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₂²⋊D₅	—	2	2	no	—
204	C₂²⋊D₅	—	2	2	no	—
205	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
210	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
211	D₂₀	—	2	2	no	—
212	C₄×D₅	—	2	1	no	—
213	C₄×D₅	—	2	1	no	—
214	C₄×D₅	—	2	1	no	—
215	C₄×D₅	—	2	1	no	—
216	C₄×D₅	—	2	2	no	—
217	C₄×D₅	—	2	2	no	—
218	C₄×D₅	—	2	2	no	—
219	C₄×D₅	M₃₂	1	4	yes	complemented
220	Dic₁₀	—	2	2	no	—
221	C₅×C₈	—	2	1	no	—
222	C₅×C₈	—	2	1	no	—
223	C₅×C₈	—	2	1	no	—
224	C₅×C₈	—	2	1	no	—
225	#168	—	2	1	no	—
226	#168	—	2	1	no	—
227	#168	#131	1	2	yes	—
228	#168	C₂×#41	1	2	yes	—
229	C₂×#41	—	5	1	no	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	5	1	no	—
232	C₂²×C₈	—	5	1	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	5	1	no	—
235	C₂²×C₈	—	5	1	no	—
236	C₄×Q₈	—	5	1	no	—
237	C₄×Q₈	—	5	1	no	—
238	C₄×D₄	—	5	1	no	—
239	C₄×D₄	—	5	1	no	—
240	C₄×D₄	—	5	1	no	—
241	C₄×D₄	—	5	1	no	—
242	C₄×D₄	—	5	1	no	—
243	C₄×D₄	—	5	1	no	—
244	#117	—	5	1	no	—
245	#117	—	5	1	no	—
246	#117	—	5	1	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
250	M₃₂	—	10	4	no	—
251	M₃₂	—	10	4	no	—
252	C₂×C₁₆	—	5	2	no	—
253	C₂×C₁₆	—	5	2	no	—
254	C₂×C₁₆	—	5	2	no	—
255	C₂×C₁₆	—	5	2	no	—
256	C₂×C₁₆	—	10	4	no	—
257	C₄⋊C₈	—	5	1	no	—
258	C₄⋊C₈	—	5	1	no	—
259	C₄⋊C₈	—	5	1	no	—
260	C₄⋊C₈	—	5	1	no	—
261	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
263	C₂²⋊C₈	—	5	1	no	—
264	C₂²⋊C₈	—	5	1	no	—
265	C₂²⋊C₈	—	5	1	no	—
266	C₂²⋊C₈	—	5	1	no	—
267	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
268	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
269	C₄×C₈	—	5	1	no	—
270	C₄×C₈	—	5	1	no	—
271	C₄×C₈	—	5	1	no	—
272	C₄×C₈	—	5	1	no	—
273	C₄×C₈	—	5	1	no	—
274	C₄×C₈	—	5	1	no	—
275	C₄×C₈	—	5	1	no	—
276	C₄×C₈	—	5	1	no	—
277	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
278	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
283	C₂×D₅	—	2	1	no	—
284	C₂×D₅	—	2	1	no	—
285	C₂×D₅	—	2	1	no	—
286	C₂×D₅	—	2	1	no	—
287	C₂×D₅	—	2	1	no	—
288	C₂×D₅	C₂×M₃₂	1	2	yes	—
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	C₂×M₃₂	1	2	yes	—
293	C₄×C₅	#504	1	2	yes	—
294	C₄×C₅	C₄×#41	1	1	yes	characteristic
295	C₄×C₅	C₂×#131	1	1	yes	characteristic
296	Dic₅	—	2	1	no	—
297	Dic₅	—	2	1	no	—
298	Dic₅	—	2	1	no	—
299	Dic₅	—	2	1	no	—
300	Dic₅	—	2	1	no	—
301	Dic₅	C₂×M₃₂	1	2	yes	—
302	#41	—	10	4	no	—
303	C₂×Q₈	—	5	1	no	—
304	C₂×D₄	—	5	1	no	—
305	C₂×D₄	—	5	1	no	—
306	C₂×D₄	—	5	1	no	—
307	C₂²×C₄	—	5	1	no	—
308	C₂²×C₄	—	5	1	no	—
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	D₅⋊C₈	1	1	yes	characteristic
314	C₂²×C₄	D₅⋊C₈	1	1	yes	characteristic
315	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₂×C₈	—	5	1	no	—
317	C₂×C₈	—	5	1	no	—
318	C₂×C₈	—	5	1	no	—
319	C₂×C₈	—	5	1	no	—
320	C₂×C₈	—	10	2	no	—
321	C₂×C₈	—	10	2	no	—
322	C₂×C₈	—	10	2	no	—
323	C₂×C₈	—	10	2	no	—
324	C₂×C₈	—	10	2	no	—
325	C₂×C₈	—	10	2	no	—
326	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
329	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
330	C₄⋊C₄	—	5	1	no	—
331	C₄⋊C₄	—	5	1	no	—
332	C₄⋊C₄	—	5	1	no	—
333	C₄⋊C₄	—	5	1	no	—
334	C₄⋊C₄	—	5	1	no	—
335	C₄⋊C₄	—	5	1	no	—
336	C₂²⋊C₄	—	5	1	no	—
337	C₂²⋊C₄	—	5	1	no	—
338	C₂²⋊C₄	—	5	1	no	—
339	C₂²⋊C₄	—	5	1	no	—
340	C₂²⋊C₄	—	5	1	no	—
341	C₂²⋊C₄	—	5	1	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	5	1	no	—
344	C₄²	—	5	1	no	—
345	C₄²	—	5	1	no	—
346	C₄²	—	5	1	no	—
347	C₄²	—	5	1	no	—
348	C₄²	D₅⋊C₈	1	1	yes	characteristic
349	C₄²	D₅⋊C₈	1	1	yes	characteristic
350	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
352	C₁₆	—	5	4	no	—
353	C₁₆	—	10	2	no	—
354	C₁₆	—	10	2	no	—
355	C₁₆	—	10	2	no	—
356	C₂×C₅	—	4	1	no	—
357	C₂×C₅	C₈×#41	1	1	yes	characteristic
358	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
359	C₂×C₅	C₂×#504	1	1	yes	characteristic
360	D₅	—	2	2	no	—
361	D₅	—	4	1	no	—
362	C₂³	—	5	1	no	—
363	C₂³	—	5	1	no	—
364	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
365	Q₈	—	10	2	no	—
366	D₄	—	10	2	no	—
367	D₄	—	10	2	no	—
368	D₄	—	10	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	5	1	no	—
374	C₂×C₄	—	5	4	no	—
375	C₂×C₄	—	5	1	no	—
376	C₂×C₄	—	5	1	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	—	10	2	no	—
382	C₂×C₄	—	10	2	no	—
383	C₂×C₄	—	10	1	no	—
384	C₂×C₄	—	10	1	no	—
385	C₂×C₄	—	10	1	no	—
386	C₂×C₄	—	10	1	no	—
387	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
388	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
389	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
390	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
391	C₂×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
392	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	5	2	no	—
398	C₈	—	5	2	no	—
399	C₈	—	10	1	no	—
400	C₈	—	10	1	no	—
401	C₅	#33479	1	1	yes	characteristic, complemented, Sylow
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	5	2	no	—
406	C₂²	—	10	1	no	—
407	C₂²	—	10	1	no	—
408	C₂²	—	10	1	no	—
409	C₂²	—	10	1	no	—
410	C₂²	—	10	1	no	—
411	C₂²	C₂²×D₅⋊C₈	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	5	2	no	—
416	C₄	—	10	1	no	—
417	C₄	—	10	1	no	—
418	C₄	—	10	1	no	—
419	C₄	—	10	1	no	—
420	C₄	—	10	1	no	—
421	C₄	D₅⋊M₃₂	1	2	yes	—
422	C₄	#65725	1	2	yes	—
423	C₄	D₅⋊#131	1	1	yes	characteristic
424	C₄	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	10	2	no	—
427	C₂	—	20	1	no	—
428	C₂	#10617114	1	1	yes	characteristic
429	C₂	C₂×D₅⋊M₃₂	1	1	yes	characteristic
430	C₂	C₂×#65725	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#431	C₄
prime radical	C₂×#709	C₈
cosocle	C₂×#168	C₂⁴
hypercenter	#431	AGL(1,𝔽₅)
hypocenter	C₅	#33479
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
2. #10604151	C₂	semidirect
3. C₄×#3998	C₂	semidirect
4. #10604026	C₂	semidirect
5. #10604022	C₂	semidirect
6. #10603906	C₂	semidirect
7. #10603905	C₂	semidirect
8. #10603828	C₂	semidirect
9. #10603828	C₂	semidirect
10. C₄×#3990	C₂	semidirect
11. C₄×D₅⋊C₁₆	C₂	semidirect
158. #674	#41	semidirect
219. C₄×D₅	M₃₂	semidirect
401. C₅	#33479	semidirect

Maximal subgroups

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

subgroup	index
#10611007	2
#10604151	2
C₄×#3998	2
#10604026	2
#10604022	2
#10603906	2
#10603905	2
#10603828	2
C₄×#3990	2
C₄×D₅⋊C₁₆	2
#33479	5