Subgroups — #13031512

Order 1280.

616 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617168	C₂	1	2	yes	maximal
2	C₈×#711	C₂	1	1	yes	maximal, characteristic
3	#10604699	C₂	1	1	yes	maximal, characteristic, complemented
4	#10604696	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64883	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604018	C₂	1	2	yes	maximal, complemented
8	#10603902	C₂	1	2	yes	maximal, complemented
9	#10603900	C₂	1	2	yes	maximal, complemented
10	#10603821	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅⋊#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#711	C₂²	1	1	yes	characteristic
13	#65773	—	2	2	no	—
14	#65759	C₂²	1	2	yes	—
15	#65758	C₂²	1	2	yes	—
16	#65748	C₂²	1	2	yes	—
17	C₂×C₄⋊#170	C₂²	1	2	yes	—
18	#65707	—	2	2	no	—
19	#65694	—	2	2	no	—
20	#65692	—	2	2	no	—
21	#65683	C₂²	1	2	yes	—
22	D₅⋊(C₄⋊C₈)	C₂²	1	2	yes	—
23	C₅×C₈×D₄	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
26	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
28	D₄×#168	C₄	1	1	yes	characteristic
29	#65122	C₂²	1	1	yes	characteristic
30	#65119	C₄	1	1	yes	characteristic
31	#65014	C₄	1	1	yes	characteristic
32	#65014	C₄	1	1	yes	characteristic
33	#65007	C₂²	1	1	yes	characteristic
34	#65007	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₀	C₄	1	1	yes	characteristic
37	#64884	C₂²	1	2	yes	—
38	#64884	C₂²	1	2	yes	—
39	#64883	C₂²	1	1	yes	characteristic
40	#64883	C₂²	1	1	yes	characteristic
41	#64883	C₂²	1	1	yes	characteristic
42	#64883	C₂²	1	1	yes	characteristic
43	#64883	C₂²	1	2	yes	—
44	#64882	C₂²	1	2	yes	—
45	#64881	C₂²	1	2	yes	—
46	#64881	C₂²	1	2	yes	—
47	#17834	—	5	1	no	maximal, Sylow
48	C₂×#711	Q₈	1	1	yes	characteristic
49	C₂×#704	—	2	2	no	—
50	C₂²×#170	—	2	2	no	—
51	C₂×D₅⋊C₈	—	2	2	no	—
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
55	D₄×Dic₅	D₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
57	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
60	C₂²×#168	C₂×C₄	1	1	yes	characteristic
61	C₂²×#168	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	#4038	Q₈	1	1	yes	characteristic
65	#4033	D₄	1	1	yes	characteristic
66	#4027	D₄	1	1	yes	characteristic
67	#4027	D₄	1	1	yes	characteristic
68	#4023	Q₈	1	1	yes	characteristic
69	#4023	Q₈	1	1	yes	characteristic
70	C₄²×D₅	C₂³	1	1	yes	characteristic
71	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊#170	—	2	2	no	—
73	C₂²⋊#170	—	2	2	no	—
74	#4004	—	2	2	no	—
75	#4004	—	2	2	no	—
76	#4003	—	2	2	no	—
77	#4002	—	2	2	no	—
78	#4002	—	2	2	no	—
79	C₄⋊#170	—	2	2	no	—
80	C₄⋊#170	C₂³	1	2	yes	—
81	C₄⋊#170	C₂³	1	2	yes	—
82	C₄⋊#170	C₂³	1	2	yes	—
83	C₄⋊#170	C₂³	1	2	yes	—
84	C₄×#170	—	2	2	no	—
85	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
91	#3952	C₂×C₄	1	1	yes	characteristic
92	#3952	C₂×C₄	1	1	yes	characteristic
93	#3946	C₂×C₄	1	1	yes	characteristic
94	#3946	C₂×C₄	1	1	yes	characteristic
95	#3946	C₂×C₄	1	1	yes	characteristic
96	#3946	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₅	C₂³	1	1	yes	characteristic
102	C₈×Dic₅	C₂³	1	1	yes	characteristic
103	C₈×Dic₅	C₂³	1	1	yes	characteristic
104	C₈×Dic₅	C₂³	1	1	yes	characteristic
105	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
106	C₄×#168	C₂×C₄	1	1	yes	characteristic
107	#2990	—	5	2	no	—
108	C₈×#41	—	5	1	no	—
109	#1574	—	5	2	no	—
110	#1573	—	5	2	no	—
111	#1573	—	5	2	no	—
112	#1568	—	5	1	no	—
113	#1568	—	5	1	no	—
114	#1566	—	5	1	no	—
115	#1564	—	5	1	no	—
116	C₂×#334	—	5	1	no	—
117	C₂×#334	—	5	1	no	—
118	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂²×Dic₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×Dic₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×Dic₅	C₂×Q₈	1	1	yes	characteristic
126	C₂²×Dic₅	C₂×Q₈	1	1	yes	characteristic
127	#711	—	2	4	no	—
128	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
131	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
132	#704	—	8	2	no	—
133	C₂×#170	—	2	2	no	—
134	C₂×#170	—	2	2	no	—
135	C₂×#170	—	2	2	no	—
136	C₂×#170	—	2	2	no	—
137	C₂×#170	—	8	2	no	—
138	D₅⋊C₈	—	8	2	no	—
139	C₂×C₅×C₈	—	4	1	no	—
140	C₂×C₅×C₈	—	4	1	no	—
141	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
146	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
150	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
151	#685	C₄⋊C₄	1	1	yes	characteristic
152	#685	C₄⋊C₄	1	1	yes	characteristic
153	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
154	#683	C₄⋊C₄	1	1	yes	characteristic
155	#683	C₄⋊C₄	1	1	yes	characteristic
156	#683	C₄⋊C₄	1	1	yes	characteristic
157	#683	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
161	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
162	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
163	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
164	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
165	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
166	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
167	C₂×#168	—	2	2	no	—
168	C₂×#168	—	2	2	no	—
169	C₂×#168	C₂²×C₄	1	1	yes	characteristic
170	C₂×#168	C₂²×C₄	1	1	yes	characteristic
171	C₂×#168	C₂²×C₄	1	1	yes	characteristic
172	C₂×#168	C₂²×C₄	1	1	yes	characteristic
173	C₈×D₅	—	2	2	no	—
174	C₈×D₅	—	4	1	no	—
175	C₄×#41	—	5	1	no	—
176	#446	—	10	2	no	—
177	C₈×Q₈	—	5	1	no	—
178	C₈×Q₈	—	5	1	no	—
179	#435	—	10	2	no	—
180	#435	—	10	2	no	—
181	C₈×D₄	—	5	1	no	—
182	C₈×D₄	—	5	1	no	—
183	C₈×D₄	—	5	1	no	—
184	C₈×D₄	—	5	1	no	—
185	C₈×D₄	—	5	1	no	—
186	C₈×D₄	—	10	2	no	—
187	C₈×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
188	#432	—	5	2	no	—
189	#432	—	5	2	no	—
190	#431	—	5	1	no	—
191	#431	—	5	1	no	—
192	#431	—	5	1	no	—
193	#431	—	5	2	no	—
194	#423	—	5	2	no	—
195	C₂×C₄⋊C₈	—	5	2	no	—
196	C₂×C₄⋊C₈	—	5	2	no	—
197	C₂×C₄×C₈	—	5	1	no	—
198	C₂×C₄×C₈	—	5	1	no	—
199	C₂×C₄×C₈	—	5	1	no	—
200	#335	—	5	2	no	—
201	#335	—	5	2	no	—
202	#335	—	5	2	no	—
203	#334	—	5	1	no	—
204	#334	—	5	1	no	—
205	#334	—	5	1	no	—
206	#334	—	5	2	no	—
207	#334	—	5	2	no	—
208	#334	—	5	1	no	—
209	#334	—	5	2	no	—
210	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₅×D₄	—	2	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
223	C₂²⋊D₅	—	2	2	no	—
224	C₂²⋊D₅	#108	1	4	yes	—
225	C₂×Dic₅	—	2	2	no	—
226	C₂×Dic₅	—	2	2	no	—
227	C₂×Dic₅	—	2	2	no	—
228	C₂×Dic₅	—	2	2	no	—
229	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×Dic₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×Dic₅	C₂²×Q₈	1	1	yes	characteristic
236	C₄×D₅	—	2	2	no	—
237	C₄×D₅	—	2	1	no	—
238	C₄×D₅	—	2	1	no	—
239	C₄×D₅	—	2	2	no	—
240	Dic₁₀	—	2	2	no	—
241	#170	—	4	2	no	—
242	#170	—	4	2	no	—
243	#170	—	4	2	no	—
244	#170	—	4	2	no	—
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	—	2	1	no	—
247	C₅×C₈	—	2	1	no	—
248	C₅×C₈	—	2	1	no	—
249	#168	—	2	1	no	—
250	#168	—	2	1	no	—
251	#168	—	2	1	no	—
252	#168	#131	1	2	yes	—
253	C₂×#41	—	5	1	no	—
254	C₂×M₁₆	—	10	2	no	—
255	C₂²×C₈	—	5	1	no	—
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₂²×C₈	—	5	1	no	—
259	C₂²×C₈	—	10	2	no	—
260	C₂²×C₈	—	10	2	no	—
261	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
263	C₄×Q₈	—	5	1	no	—
264	C₄×Q₈	—	5	1	no	—
265	C₄×D₄	—	5	1	no	—
266	C₄×D₄	—	5	1	no	—
267	C₄×D₄	—	5	1	no	—
268	C₄×D₄	—	5	1	no	—
269	C₄×D₄	—	5	1	no	—
270	C₄×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
271	#117	—	5	1	no	—
272	#117	—	5	1	no	—
273	#117	—	5	1	no	—
274	C₂×C₄²	—	5	1	no	—
275	C₂×C₄²	—	5	1	no	—
276	C₂×C₄²	—	5	1	no	—
277	C₄⋊C₈	—	5	1	no	—
278	C₄⋊C₈	—	5	1	no	—
279	C₄⋊C₈	—	5	1	no	—
280	C₄⋊C₈	—	5	1	no	—
281	C₄⋊C₈	—	5	2	no	—
282	C₄⋊C₈	—	5	2	no	—
283	C₄⋊C₈	—	5	2	no	—
284	C₄⋊C₈	—	5	2	no	—
285	C₄⋊C₈	—	5	1	no	—
286	C₄⋊C₈	—	10	2	no	—
287	C₄⋊C₈	—	10	2	no	—
288	C₄⋊C₈	—	10	2	no	—
289	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₂²⋊C₈	—	5	1	no	—
291	C₂²⋊C₈	—	5	1	no	—
292	C₂²⋊C₈	—	5	1	no	—
293	C₂²⋊C₈	—	5	1	no	—
294	C₂²⋊C₈	—	10	2	no	—
295	C₂²⋊C₈	—	10	2	no	—
296	C₂²⋊C₈	—	10	2	no	—
297	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₂²⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
299	#97	—	10	2	no	—
300	#97	—	10	2	no	—
301	C₄×C₈	—	5	1	no	—
302	C₄×C₈	—	5	1	no	—
303	C₄×C₈	—	5	1	no	—
304	C₄×C₈	—	5	1	no	—
305	C₄×C₈	—	5	1	no	—
306	C₄×C₈	—	5	1	no	—
307	C₄×C₈	—	5	1	no	—
308	C₄×C₈	—	5	1	no	—
309	C₄×C₈	—	5	1	no	—
310	C₄×C₈	—	10	2	no	—
311	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	2	1	no	—
315	C₂²×C₅	—	2	1	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	C₂×#108	1	2	yes	—
318	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
319	C₂×D₅	—	2	1	no	—
320	C₂×D₅	—	2	1	no	—
321	C₂×D₅	C₂×#108	1	2	yes	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	2	1	no	—
324	C₄×C₅	—	2	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	C₂×#131	1	1	yes	characteristic
327	C₄×C₅	#568	1	1	yes	characteristic
328	Dic₅	—	2	1	no	—
329	Dic₅	—	2	1	no	—
330	Dic₅	—	2	1	no	—
331	Dic₅	—	2	1	no	—
332	Dic₅	—	2	1	no	—
333	Dic₅	C₂×#108	1	2	yes	—
334	Dic₅	#577	1	2	yes	—
335	#41	—	10	4	no	—
336	C₂×Q₈	—	5	1	no	—
337	C₂×D₄	—	5	1	no	—
338	C₂×D₄	—	5	1	no	—
339	C₂×D₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	—	5	1	no	—
344	C₂²×C₄	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
349	M₁₆	—	40	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	5	1	no	—
353	C₂×C₈	—	5	1	no	—
354	C₂×C₈	—	5	1	no	—
355	C₂×C₈	—	5	1	no	—
356	C₂×C₈	—	10	2	no	—
357	C₂×C₈	—	10	2	no	—
358	C₂×C₈	—	10	2	no	—
359	C₂×C₈	—	10	2	no	—
360	C₂×C₈	—	10	2	no	—
361	C₂×C₈	—	10	2	no	—
362	C₂×C₈	—	10	2	no	—
363	C₂×C₈	—	20	1	no	—
364	C₂×C₈	—	40	2	no	—
365	C₂×C₈	—	40	2	no	—
366	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₄⋊C₄	—	5	1	no	—
371	C₄⋊C₄	—	5	1	no	—
372	C₄⋊C₄	—	5	1	no	—
373	C₄⋊C₄	—	5	1	no	—
374	C₄⋊C₄	—	5	1	no	—
375	C₄⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
376	C₂²⋊C₄	—	5	1	no	—
377	C₂²⋊C₄	—	5	1	no	—
378	C₂²⋊C₄	—	5	1	no	—
379	C₂²⋊C₄	—	5	1	no	—
380	C₂²⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₂²⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₄²	—	5	1	no	—
383	C₄²	—	5	1	no	—
384	C₄²	—	5	1	no	—
385	C₄²	—	5	1	no	—
386	C₄²	—	5	1	no	—
387	C₄²	—	5	1	no	—
388	C₄²	—	5	1	no	—
389	C₄²	—	5	1	no	—
390	C₄²	—	5	1	no	—
391	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	—	4	1	no	—
394	C₂×C₅	#2906	1	1	yes	characteristic
395	C₂×C₅	#2912	1	1	yes	characteristic
396	C₂×C₅	C₂²×#108	1	1	yes	characteristic
397	D₅	—	2	2	no	—
398	C₂³	—	5	1	no	—
399	C₂³	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
400	C₂³	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
401	Q₈	—	10	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	5	4	no	—
404	D₄	—	10	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	5	1	no	—
412	C₂×C₄	—	5	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	1	no	—
415	C₂×C₄	—	5	1	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	10	2	no	—
419	C₂×C₄	—	10	2	no	—
420	C₂×C₄	—	10	2	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	1	no	—
423	C₂×C₄	—	10	1	no	—
424	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
427	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
428	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	5	2	no	—
434	C₈	—	10	1	no	—
435	C₈	—	10	1	no	—
436	C₈	—	10	1	no	—
437	C₈	—	20	2	no	—
438	C₈	—	20	2	no	—
439	C₈	—	20	2	no	—
440	C₈	—	20	2	no	—
441	C₅	#17834	1	1	yes	characteristic, complemented, Sylow
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	5	2	no	—
448	C₂²	—	10	1	no	—
449	C₂²	—	10	1	no	—
450	C₂²	D₅⋊#108	1	2	yes	—
451	C₂²	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	5	2	no	—
457	C₄	—	5	2	no	—
458	C₄	—	10	1	no	—
459	C₄	—	10	1	no	—
460	C₄	—	10	1	no	—
461	C₄	—	10	1	no	—
462	C₄	—	10	1	no	—
463	C₄	#66256	1	1	yes	characteristic
464	C₄	D₅⋊#131	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	1	no	—
467	C₂	—	10	2	no	—
468	C₂	#10617138	1	1	yes	characteristic
469	C₂	C₂×D₅⋊#108	1	1	yes	characteristic
470	C₂	#10617416	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×C₈×D₄	C₄
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#711	Q₈
cosocle	C₄×Dic₅	C₂⁴
hypercenter	C₈×D₄	AGL(1,𝔽₅)
hypocenter	C₅	#17834
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
3. #10604699	C₂	semidirect
4. #10604696	C₂	semidirect
5. #10604695	C₂	semidirect
6. C₂×#64883	C₂	semidirect
7. #10604018	C₂	semidirect
8. #10603902	C₂	semidirect
9. #10603900	C₂	semidirect
10. #10603821	C₂	semidirect
11. D₅⋊#334	C₂	semidirect
441. C₅	#17834	semidirect

Maximal subgroups

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

subgroup	index
#10617168	2
C₈×#711	2
#10604699	2
#10604696	2
#10604695	2
C₂×#64883	2
#10604018	2
#10603902	2
#10603900	2
#10603821	2
D₅⋊#334	2
#17834	5