Subgroups — #13031351

Order 1280.

666 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617121	C₂	1	2	yes	maximal
2	#10610280	C₂	1	1	yes	maximal, characteristic
3	#10604740	C₂	1	2	yes	maximal, complemented
4	#10604699	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604697	C₂	1	1	yes	maximal, characteristic, complemented
6	#10603867	C₂	1	2	yes	maximal, complemented
7	#10603865	C₂	1	2	yes	maximal, complemented
8	#10603820	C₂	1	1	yes	maximal, characteristic, complemented
9	#10603818	C₂	1	1	yes	maximal, characteristic, complemented
10	#10603815	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅⋊#335	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#4053	C₄	1	1	yes	characteristic
13	C₂×#4047	C₄	1	1	yes	characteristic
14	#65856	C₂²	1	1	yes	characteristic
15	#65759	C₂²	1	2	yes	—
16	#65758	C₂²	1	2	yes	—
17	#65707	—	2	2	no	—
18	#65704	—	2	2	no	—
19	#65695	—	2	2	no	—
20	#65694	—	2	2	no	—
21	#65683	C₂²	1	2	yes	—
22	#65681	C₂²	1	2	yes	—
23	#65680	C₂²	1	2	yes	—
24	D₅⋊(C₄⋊C₈)	C₂²	1	2	yes	—
25	C₅×#405	C₄	1	1	yes	characteristic
26	M₁₆×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
28	#65286	C₄	1	1	yes	characteristic
29	#64997	C₄	1	1	yes	characteristic
30	#64997	C₄	1	1	yes	characteristic
31	#64996	C₂²	1	1	yes	characteristic
32	#64996	C₂²	1	1	yes	characteristic
33	#64978	C₄	1	1	yes	characteristic
34	#64978	C₄	1	1	yes	characteristic
35	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
37	#64884	C₂²	1	2	yes	—
38	#64884	C₂²	1	2	yes	—
39	#64883	C₂²	1	2	yes	—
40	#64883	C₂²	1	2	yes	—
41	#64882	C₂²	1	1	yes	characteristic
42	#64882	C₂²	1	1	yes	characteristic
43	#64882	C₂²	1	1	yes	characteristic
44	#64882	C₂²	1	1	yes	characteristic
45	#64882	C₂²	1	2	yes	—
46	#64881	C₂²	1	2	yes	—
47	#17799	—	5	1	no	maximal, Sylow
48	C₂×#709	C₂×C₄	1	1	yes	characteristic
49	C₂×#704	—	2	2	no	—
50	C₂×#700	—	2	2	no	—
51	C₂×D₅⋊C₈	—	2	2	no	—
52	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
54	C₅×#117	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
56	C₂×#681	C₂×C₄	1	1	yes	characteristic
57	C₂²×#168	C₂×C₄	1	1	yes	characteristic
58	#4053	—	2	4	no	—
59	#4047	—	2	4	no	—
60	C₂×#676	C₂×C₄	1	1	yes	characteristic
61	C₂×#676	C₂×C₄	1	1	yes	characteristic
62	C₂×#676	C₂×C₄	1	1	yes	characteristic
63	C₂×#676	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
68	#4039	D₄	1	1	yes	characteristic
69	#4039	Q₈	1	1	yes	characteristic
70	#4033	D₄	1	1	yes	characteristic
71	#4033	Q₈	1	1	yes	characteristic
72	#4027	D₄	1	1	yes	characteristic
73	#4027	D₄	1	1	yes	characteristic
74	#4027	Q₈	1	1	yes	characteristic
75	#4027	Q₈	1	1	yes	characteristic
76	#4018	C₂×C₄	1	1	yes	characteristic
77	#4018	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₅	C₂³	1	1	yes	characteristic
79	C₄²×D₅	C₂³	1	1	yes	characteristic
80	C₂²⋊#170	—	2	2	no	—
81	#4004	—	2	2	no	—
82	#4004	—	2	2	no	—
83	#4003	—	2	2	no	—
84	#4003	—	2	2	no	—
85	#4002	—	2	2	no	—
86	#4002	—	2	2	no	—
87	C₄⋊#170	—	2	2	no	—
88	C₄⋊#170	C₂³	1	2	yes	—
89	C₄⋊#170	C₂³	1	2	yes	—
90	C₄⋊#170	C₂³	1	2	yes	—
91	C₄⋊#170	C₂³	1	2	yes	—
92	C₄×#170	—	2	2	no	—
93	C₅×#97	C₂×C₄	1	1	yes	characteristic
94	C₅×#97	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
97	#3947	C₂×C₄	1	1	yes	characteristic
98	#3947	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	#3935	C₂×C₄	1	1	yes	characteristic
106	#3935	C₂×C₄	1	1	yes	characteristic
107	C₄×#168	C₂×C₄	1	1	yes	characteristic
108	C₄×#168	C₂×C₄	1	1	yes	characteristic
109	#2989	—	5	2	no	—
110	C₄×#131	—	5	1	no	—
111	#1569	—	5	2	no	—
112	#1569	—	5	2	no	—
113	#1568	—	5	1	no	—
114	#1568	—	5	1	no	—
115	#1567	—	5	1	no	—
116	#1567	—	5	1	no	—
117	#1565	—	5	2	no	—
118	#1564	—	5	1	no	—
119	C₂×#335	—	5	1	no	—
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×Q₈	1	1	yes	characteristic
125	#709	—	2	2	no	—
126	#709	—	2	2	no	—
127	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
134	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
135	#704	—	8	2	no	—
136	C₂×#170	—	2	2	no	—
137	C₂×#170	—	2	2	no	—
138	C₂×#170	—	2	2	no	—
139	C₂×#170	—	2	2	no	—
140	#700	—	8	2	no	—
141	D₅⋊C₈	—	8	2	no	—
142	C₅×M₁₆	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
150	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
152	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
154	#685	C₄⋊C₄	1	1	yes	characteristic
155	#685	C₄⋊C₄	1	1	yes	characteristic
156	#685	C₄⋊C₄	1	1	yes	characteristic
157	#685	C₄⋊C₄	1	1	yes	characteristic
158	#683	C₄⋊C₄	1	1	yes	characteristic
159	#683	C₄⋊C₄	1	1	yes	characteristic
160	#683	C₄⋊C₄	1	1	yes	characteristic
161	#683	C₄⋊C₄	1	1	yes	characteristic
162	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
164	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
165	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
167	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
168	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
169	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
170	#681	—	2	2	no	—
171	C₂×#168	—	2	2	no	—
172	C₂×#168	C₂²×C₄	1	1	yes	characteristic
173	C₂×#168	C₂²×C₄	1	1	yes	characteristic
174	C₂×#168	C₂²×C₄	1	1	yes	characteristic
175	C₂×#168	C₂²×C₄	1	1	yes	characteristic
176	#676	—	2	2	no	—
177	#676	—	2	2	no	—
178	#676	—	2	2	no	—
179	#676	M₁₆	1	4	yes	complemented
180	C₈×D₅	—	2	2	no	—
181	C₈×D₅	—	2	2	no	—
182	C₈×D₅	—	2	2	no	—
183	C₈×D₅	M₁₆	1	4	yes	complemented
184	C₂×#131	—	5	1	no	—
185	C₂×#131	—	5	1	no	—
186	C₄×#41	—	5	1	no	—
187	#446	—	10	2	no	—
188	#436	—	10	2	no	—
189	#435	—	10	2	no	—
190	#435	—	10	2	no	—
191	#432	—	5	2	no	—
192	#432	—	5	2	no	—
193	#431	—	5	2	no	—
194	#423	—	5	2	no	—
195	#423	—	5	2	no	—
196	C₂×C₄⋊C₈	—	5	2	no	—
197	#405	—	5	1	no	—
198	#405	—	5	1	no	—
199	#405	—	5	1	no	—
200	#405	—	5	1	no	—
201	#405	—	5	1	no	—
202	#405	AGL(1,𝔽₅)	1	1	yes	characteristic
203	C₄×M₁₆	—	5	1	no	—
204	C₄×M₁₆	—	5	1	no	—
205	C₄×M₁₆	—	5	1	no	—
206	C₂×C₄×C₈	—	5	1	no	—
207	C₂×C₄×C₈	—	5	1	no	—
208	C₂×C₄×C₈	—	5	1	no	—
209	#335	—	5	1	no	—
210	#335	—	5	1	no	—
211	#335	—	5	2	no	—
212	#335	—	5	1	no	—
213	#335	—	5	1	no	—
214	#335	—	5	2	no	—
215	#335	—	5	2	no	—
216	#334	—	5	2	no	—
217	#334	—	5	2	no	—
218	#334	—	5	2	no	—
219	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
230	C₂²⋊D₅	—	2	2	no	—
231	C₂²⋊D₅	—	2	2	no	—
232	C₂×Dic₅	—	2	1	no	—
233	C₂×Dic₅	—	2	1	no	—
234	C₂×Dic₅	—	4	1	no	—
235	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂×Dic₅	C₂²×D₄	1	1	yes	characteristic
240	C₂×Dic₅	C₂²×Q₈	1	1	yes	characteristic
241	D₂₀	—	2	2	no	—
242	C₄×D₅	—	2	1	no	—
243	C₄×D₅	—	2	1	no	—
244	C₄×D₅	—	2	1	no	—
245	C₄×D₅	—	2	1	no	—
246	C₄×D₅	—	2	1	no	—
247	C₄×D₅	—	2	1	no	—
248	C₄×D₅	—	4	1	no	—
249	C₄×D₅	—	4	1	no	—
250	C₄×D₅	C₂×M₁₆	1	2	yes	—
251	C₄×D₅	C₂×M₁₆	1	2	yes	—
252	Dic₁₀	—	2	2	no	—
253	#170	—	4	2	no	—
254	#170	—	4	2	no	—
255	#170	—	4	2	no	—
256	#170	—	4	2	no	—
257	C₅×C₈	—	2	1	no	—
258	C₅×C₈	—	2	1	no	—
259	C₅×C₈	C₂×M₁₆	1	2	yes	—
260	C₅×C₈	C₂×M₁₆	1	2	yes	—
261	#168	—	2	1	no	—
262	#168	—	2	1	no	—
263	#168	C₂×M₁₆	1	2	yes	—
264	#168	C₂×M₁₆	1	2	yes	—
265	C₂×#41	—	5	1	no	—
266	#131	—	10	4	no	—
267	#131	—	10	4	no	—
268	C₂×M₁₆	—	5	1	no	—
269	C₂×M₁₆	—	5	1	no	—
270	C₂×M₁₆	—	5	1	no	—
271	C₂×M₁₆	—	5	1	no	—
272	C₂×M₁₆	—	5	1	no	—
273	C₂×M₁₆	—	10	2	no	—
274	C₂×M₁₆	—	10	2	no	—
275	C₂×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
276	C₂²×C₈	—	5	1	no	—
277	C₂²×C₈	—	5	1	no	—
278	C₂²×C₈	—	5	1	no	—
279	C₂²×C₈	—	5	1	no	—
280	C₂²×C₈	—	5	1	no	—
281	C₂²×C₈	—	10	2	no	—
282	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
283	C₄×Q₈	—	5	1	no	—
284	C₄×Q₈	—	5	1	no	—
285	C₄×D₄	—	5	1	no	—
286	C₄×D₄	—	5	1	no	—
287	C₄×D₄	—	5	1	no	—
288	C₄×D₄	—	5	1	no	—
289	C₄×D₄	—	5	1	no	—
290	C₄×D₄	—	5	1	no	—
291	#117	—	5	1	no	—
292	#117	—	5	1	no	—
293	#117	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
294	C₂×C₄²	—	5	1	no	—
295	C₂×C₄²	—	5	1	no	—
296	C₂×C₄²	—	5	1	no	—
297	C₄⋊C₈	—	5	2	no	—
298	C₄⋊C₈	—	5	2	no	—
299	C₄⋊C₈	—	5	2	no	—
300	C₄⋊C₈	—	5	2	no	—
301	C₄⋊C₈	—	10	2	no	—
302	C₄⋊C₈	—	10	2	no	—
303	C₄⋊C₈	—	10	2	no	—
304	C₂²⋊C₈	—	10	2	no	—
305	C₂²⋊C₈	—	10	2	no	—
306	C₂²⋊C₈	—	10	2	no	—
307	#97	—	5	1	no	—
308	#97	—	5	1	no	—
309	#97	—	5	1	no	—
310	#97	—	5	1	no	—
311	#97	—	10	2	no	—
312	#97	—	10	2	no	—
313	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
314	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
315	C₄×C₈	—	5	1	no	—
316	C₄×C₈	—	5	1	no	—
317	C₄×C₈	—	5	1	no	—
318	C₄×C₈	—	5	1	no	—
319	C₄×C₈	—	5	1	no	—
320	C₄×C₈	—	5	1	no	—
321	C₄×C₈	—	5	1	no	—
322	C₄×C₈	—	5	1	no	—
323	C₄×C₈	—	10	2	no	—
324	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
325	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₂²×C₅	—	2	1	no	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
330	C₂×D₅	—	2	1	no	—
331	C₂×D₅	—	2	1	no	—
332	C₂×D₅	—	2	1	no	—
333	C₂×D₅	—	2	1	no	—
334	C₂×D₅	—	2	1	no	—
335	C₂×D₅	#423	1	2	yes	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
342	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
343	Dic₅	—	2	1	no	—
344	Dic₅	—	2	1	no	—
345	Dic₅	—	2	1	no	—
346	Dic₅	—	2	1	no	—
347	Dic₅	#423	1	2	yes	—
348	Dic₅	#576	1	1	yes	characteristic
349	Dic₅	#578	1	1	yes	characteristic
350	#41	—	10	2	no	—
351	#41	—	10	2	no	—
352	C₂×Q₈	—	5	1	no	—
353	C₂×D₄	—	5	1	no	—
354	C₂×D₄	—	5	1	no	—
355	C₂×D₄	—	5	1	no	—
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	5	1	no	—
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	—	5	1	no	—
360	C₂²×C₄	—	5	1	no	—
361	C₂²×C₄	—	5	1	no	—
362	C₂²×C₄	—	5	1	no	—
363	C₂²×C₄	—	5	1	no	—
364	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
365	M₁₆	—	2	2	no	—
366	M₁₆	—	5	4	no	—
367	M₁₆	—	10	2	no	—
368	M₁₆	—	10	2	no	—
369	M₁₆	—	10	2	no	—
370	M₁₆	—	10	2	no	—
371	M₁₆	—	40	2	no	—
372	M₁₆	—	40	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	5	1	no	—
375	C₂×C₈	—	5	1	no	—
376	C₂×C₈	—	5	4	no	—
377	C₂×C₈	—	5	1	no	—
378	C₂×C₈	—	5	1	no	—
379	C₂×C₈	—	10	2	no	—
380	C₂×C₈	—	10	2	no	—
381	C₂×C₈	—	10	2	no	—
382	C₂×C₈	—	10	2	no	—
383	C₂×C₈	—	10	2	no	—
384	C₂×C₈	—	10	2	no	—
385	C₂×C₈	—	10	2	no	—
386	C₂×C₈	—	10	2	no	—
387	C₂×C₈	—	40	2	no	—
388	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
389	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₄⋊C₄	—	5	1	no	—
393	C₄⋊C₄	—	5	1	no	—
394	C₄⋊C₄	—	5	1	no	—
395	C₄⋊C₄	—	5	1	no	—
396	C₄⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
397	C₄⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₂²⋊C₄	—	5	1	no	—
399	C₂²⋊C₄	—	5	1	no	—
400	C₂²⋊C₄	—	5	1	no	—
401	C₂²⋊C₄	—	5	1	no	—
402	C₂²⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₂²⋊C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₄²	—	5	1	no	—
405	C₄²	—	5	1	no	—
406	C₄²	—	5	1	no	—
407	C₄²	—	5	1	no	—
408	C₄²	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	1	no	—
411	C₄²	—	5	1	no	—
412	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₂×C₅	—	4	1	no	—
415	C₂×C₅	C₂×#423	1	1	yes	characteristic
416	C₂×C₅	#2913	1	1	yes	characteristic
417	C₂×C₅	#2916	1	1	yes	characteristic
418	D₅	—	2	2	no	—
419	D₅	—	4	1	no	—
420	C₂³	—	5	1	no	—
421	C₂³	—	5	1	no	—
422	C₂³	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
423	Q₈	—	10	2	no	—
424	D₄	—	10	2	no	—
425	D₄	—	10	2	no	—
426	D₄	—	10	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	5	1	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	5	2	no	—
432	C₂×C₄	—	5	2	no	—
433	C₂×C₄	—	5	1	no	—
434	C₂×C₄	—	5	1	no	—
435	C₂×C₄	—	5	1	no	—
436	C₂×C₄	—	5	1	no	—
437	C₂×C₄	—	10	1	no	—
438	C₂×C₄	—	10	1	no	—
439	C₂×C₄	—	10	1	no	—
440	C₂×C₄	—	10	1	no	—
441	C₂×C₄	—	10	1	no	—
442	C₂×C₄	—	10	1	no	—
443	C₂×C₄	—	10	1	no	—
444	C₂×C₄	—	10	1	no	—
445	C₂×C₄	—	20	1	no	—
446	C₂×C₄	—	20	1	no	—
447	C₂×C₄	—	20	1	no	—
448	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
449	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
453	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	5	2	no	—
457	C₈	—	5	2	no	—
458	C₈	—	10	1	no	—
459	C₈	—	10	1	no	—
460	C₈	—	20	2	no	—
461	C₈	—	20	2	no	—
462	C₈	—	20	2	no	—
463	C₈	—	20	2	no	—
464	C₈	D₅⋊M₁₆	1	2	yes	—
465	C₈	D₅⋊M₁₆	1	2	yes	—
466	C₅	#17799	1	1	yes	characteristic, complemented, Sylow
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	5	2	no	—
471	C₂²	—	10	1	no	—
472	C₂²	—	10	1	no	—
473	C₂²	—	10	1	no	—
474	C₂²	—	10	1	no	—
475	C₂²	—	10	1	no	—
476	C₂²	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	5	1	no	—
483	C₄	—	5	1	no	—
484	C₄	—	5	2	no	—
485	C₄	—	10	1	no	—
486	C₄	—	10	1	no	—
487	C₄	—	10	1	no	—
488	C₄	—	10	1	no	—
489	C₄	C₂×D₅⋊M₁₆	1	1	yes	characteristic
490	C₄	C₂×D₅⋊M₁₆	1	1	yes	characteristic
491	C₂	—	4	1	no	—
492	C₂	—	10	2	no	—
493	C₂	—	20	1	no	—
494	C₂	D₅⋊#423	1	1	yes	characteristic
495	C₂	#10617417	1	1	yes	characteristic
496	C₂	#10617419	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×#405	C₄
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	C₂×C₄
cosocle	C₄×Dic₅	C₂⁴
hypercenter	#405	AGL(1,𝔽₅)
hypocenter	C₅	#17799
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
3. #10604740	C₂	semidirect
4. #10604699	C₂	semidirect
5. #10604697	C₂	semidirect
6. #10603867	C₂	semidirect
7. #10603865	C₂	semidirect
8. #10603820	C₂	semidirect
9. #10603818	C₂	semidirect
10. #10603815	C₂	semidirect
11. D₅⋊#335	C₂	semidirect
179. #676	M₁₆	semidirect
183. C₈×D₅	M₁₆	semidirect
466. C₅	#17799	semidirect

Maximal subgroups

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

subgroup	index
#10617121	2
#10610280	2
#10604740	2
#10604699	2
#10604697	2
#10603867	2
#10603865	2
#10603820	2
#10603818	2
#10603815	2
D₅⋊#335	2
#17799	5