Subgroups — C₅×#19416 #11942136

Order 1280.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3035	C₂	1	1	yes	maximal, characteristic
4	C₅×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1682	C₂	1	2	yes	maximal, complemented
6	C₅×#1681	C₂	1	2	yes	maximal, complemented
7	C₅×#1674	C₂	1	2	yes	maximal, complemented
8	C₅×#1673	C₂	1	2	yes	maximal, complemented
9	C₅×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	2	1	no	—
13	C₂×C₅×#135	—	2	1	no	—
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₅×#500	C₂²	1	2	yes	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#480	—	2	2	no	—
20	C₅×#474	—	2	1	no	—
21	C₅×#474	—	2	1	no	—
22	C₅×#464	—	2	1	no	—
23	C₅×#463	—	2	1	no	—
24	C₅×#462	—	2	1	no	—
25	C₅×#462	C₂²	1	1	yes	characteristic
26	C₅×#462	C₂²	1	2	yes	—
27	C₅×#461	—	2	1	no	—
28	C₅×#461	C₂²	1	1	yes	characteristic
29	C₅×#461	C₂²	1	2	yes	—
30	C₅×#460	C₂²	1	1	yes	characteristic
31	C₅×#459	C₂²	1	1	yes	characteristic
32	C₅×C₈×Q₈	C₂²	1	2	yes	—
33	C₅×C₈×D₄	—	2	2	no	—
34	C₅×C₈×D₄	C₂²	1	2	yes	—
35	C₅×#431	—	2	1	no	—
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#423	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	—	2	1	no	—
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×#419	—	2	1	no	—
42	C₅×#416	—	2	1	no	—
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#335	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19416	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	D₄	1	1	yes	characteristic
52	C₂²×C₅×Q₈	—	2	1	no	—
53	C₅×#137	—	4	4	no	—
54	C₅×#135	—	4	4	no	—
55	C₂×C₅×Q₁₆	—	2	2	no	—
56	C₂×C₅×Q₁₆	—	2	1	no	—
57	C₂×C₅×SD₁₆	—	2	1	no	—
58	C₂×C₅×SD₁₆	—	2	2	no	—
59	C₂×C₅×SD₁₆	—	2	1	no	—
60	C₂×C₅×D₈	—	2	1	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₅×C₄⋊Q₈	—	2	1	no	—
66	C₅×C₄⋊Q₈	—	2	1	no	—
67	C₅×C₄⋊Q₈	—	2	1	no	—
68	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₅×#127	C₂³	1	1	yes	characteristic
71	C₅×#124	—	2	1	no	—
72	C₅×#121	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
75	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	—	2	1	no	—
80	C₄×C₅×D₄	D₄	1	1	yes	characteristic
81	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₅×#117	—	2	1	no	—
83	C₅×#117	D₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₅×#107	—	2	2	no	—
89	C₅×#107	—	2	2	no	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	—	2	1	no	—
94	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
95	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
96	C₅×C₄⋊C₈	C₂³	1	2	yes	—
97	C₅×C₄⋊C₈	C₂³	1	2	yes	—
98	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₅×#103	—	2	1	no	—
101	C₅×#103	—	2	1	no	—
102	C₅×#103	—	2	2	no	—
103	C₅×#103	—	2	2	no	—
104	C₅×#102	—	2	2	no	—
105	C₅×#102	—	2	2	no	—
106	C₅×#102	—	2	1	no	—
107	C₅×#102	—	2	1	no	—
108	C₅×C₂²⋊C₈	—	2	2	no	—
109	C₅×C₂²⋊C₈	D₄	1	2	yes	—
110	C₄×C₅×C₈	—	2	2	no	—
111	C₄×C₅×C₈	C₂³	1	2	yes	—
112	#3226	C₂×C₅	1	1	yes	characteristic, complemented
113	#3039	C₂×C₅	1	1	yes	characteristic, complemented
114	#3035	C₂×C₅	1	1	yes	characteristic
115	#2988	C₂×C₅	1	1	yes	characteristic, complemented
116	#1682	C₂×C₅	1	2	yes	complemented
117	#1681	C₂×C₅	1	2	yes	complemented
118	#1674	C₂×C₅	1	2	yes	complemented
119	#1673	C₂×C₅	1	2	yes	complemented
120	#1571	C₂×C₅	1	1	yes	characteristic, complemented
121	#1547	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	4	2	no	—
125	C₅×#41	—	4	2	no	—
126	C₅×#41	D₈	1	4	yes	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	—	4	1	no	—
130	C₂×C₅×Q₈	—	4	2	no	—
131	C₂×C₅×Q₈	—	4	2	no	—
132	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	4	1	no	—
138	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	4	1	no	—
143	C₂²×C₄×C₅	—	4	1	no	—
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	#41	1	1	yes	characteristic
147	C₅×Q₁₆	—	4	2	no	—
148	C₅×Q₁₆	—	4	4	no	—
149	C₅×SD₁₆	—	4	2	no	—
150	C₅×SD₁₆	—	4	2	no	—
151	C₅×SD₁₆	—	4	4	no	—
152	C₅×D₈	—	4	2	no	—
153	C₅×M₁₆	—	4	2	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	2	1	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	4	2	no	—
159	C₂×C₅×C₈	—	8	2	no	—
160	C₂×C₅×C₈	—	8	1	no	—
161	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
162	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	4	1	no	—
170	C₅×C₄⋊C₄	—	4	1	no	—
171	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
172	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₅×C₂²⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	2	1	no	—
176	C₅×C₂²⋊C₄	—	4	1	no	—
177	C₅×C₂²⋊C₄	—	4	1	no	—
178	C₄²×C₅	—	2	1	no	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₅	#41	1	1	yes	characteristic
184	C₄²×C₅	C₂⁴	1	1	yes	characteristic
185	C₂×#137	—	2	1	no	—
186	C₂×#135	—	2	1	no	—
187	#532	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₄×#41	C₂²×C₅	1	1	yes	characteristic
190	#500	C₂²×C₅	1	2	yes	—
191	#486	C₂²×C₅	1	2	yes	—
192	#480	—	2	2	no	—
193	#474	—	2	1	no	—
194	#474	—	2	1	no	—
195	#464	—	2	1	no	—
196	#463	—	2	1	no	—
197	#462	—	2	1	no	—
198	#462	C₂²×C₅	1	1	yes	characteristic
199	#462	C₂²×C₅	1	2	yes	—
200	#461	—	2	1	no	—
201	#461	C₂²×C₅	1	1	yes	characteristic
202	#461	C₂²×C₅	1	2	yes	—
203	#460	C₂²×C₅	1	1	yes	characteristic
204	#459	C₂²×C₅	1	1	yes	characteristic
205	C₈×Q₈	C₂²×C₅	1	2	yes	—
206	C₈×D₄	—	2	2	no	—
207	C₈×D₄	C₂²×C₅	1	2	yes	—
208	#431	—	2	1	no	—
209	#431	C₂²×C₅	1	1	yes	characteristic
210	#423	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
214	#419	—	2	1	no	—
215	#416	—	2	1	no	—
216	#335	C₂²×C₅	1	2	yes	—
217	#335	C₂²×C₅	1	2	yes	—
218	#332	C₂²×C₅	1	2	yes	—
219	#332	C₂²×C₅	1	2	yes	—
220	#332	C₂²×C₅	1	2	yes	—
221	#331	C₂²×C₅	1	2	yes	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	—	4	1	no	—
224	C₂³×C₅	#121	1	1	yes	characteristic
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	4	2	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×Q₈	—	8	2	no	—
231	C₅×Q₈	C₂×D₈	1	2	yes	—
232	C₅×D₄	—	2	4	no	—
233	C₅×D₄	—	2	1	no	—
234	C₅×D₄	—	4	1	no	—
235	C₅×D₄	—	4	1	no	—
236	C₅×D₄	—	4	1	no	—
237	C₅×D₄	—	4	1	no	—
238	C₅×D₄	—	8	1	no	—
239	C₅×D₄	—	8	2	no	—
240	C₅×D₄	C₂×D₈	1	2	yes	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	8	1	no	—
253	C₂×C₄×C₅	—	8	2	no	—
254	C₂×C₄×C₅	—	8	2	no	—
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	#121	1	1	yes	characteristic
257	C₂×C₄×C₅	#121	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
259	C₂×C₄×C₅	#135	1	2	yes	—
260	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	4	1	no	—
266	C₅×C₈	—	4	1	no	—
267	C₅×C₈	—	4	2	no	—
268	C₅×C₈	—	4	2	no	—
269	C₂×#41	—	2	1	no	—
270	C₂×#41	C₅×D₄	1	1	yes	characteristic
271	C₂²×Q₈	—	2	1	no	—
272	#137	—	4	4	no	—
273	#135	—	4	4	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	1	no	—
277	C₂×SD₁₆	—	2	1	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
289	#127	C₂³×C₅	1	1	yes	characteristic
290	#124	—	2	1	no	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
294	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	C₅×D₄	1	1	yes	characteristic
300	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
301	#117	—	2	1	no	—
302	#117	C₅×D₄	1	1	yes	characteristic
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
314	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₅	1	2	yes	—
316	C₄⋊C₈	C₂³×C₅	1	2	yes	—
317	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
318	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
319	#103	—	2	1	no	—
320	#103	—	2	1	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	1	no	—
326	#102	—	2	1	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	C₅×D₄	1	2	yes	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	C₂³×C₅	1	2	yes	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	—	4	1	no	—
336	C₂²×C₅	—	8	1	no	—
337	C₂²×C₅	—	8	1	no	—
338	C₂²×C₅	—	8	1	no	—
339	C₂²×C₅	#466	1	2	yes	—
340	C₂²×C₅	C₂×#121	1	1	yes	characteristic
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	—	4	1	no	—
346	C₄×C₅	—	4	1	no	—
347	C₄×C₅	—	8	1	no	—
348	C₄×C₅	—	8	2	no	—
349	C₄×C₅	#466	1	2	yes	—
350	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
351	C₄×C₅	C₂×#135	1	1	yes	characteristic
352	C₄×C₅	#577	1	1	yes	characteristic
353	C₄×C₅	#578	1	1	yes	characteristic
354	#41	—	2	2	no	—
355	#41	—	4	2	no	—
356	#41	—	4	2	no	—
357	#41	C₅×D₈	1	4	yes	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₅×#41	1	1	yes	characteristic
378	Q₁₆	—	4	2	no	—
379	Q₁₆	—	4	4	no	—
380	SD₁₆	—	4	2	no	—
381	SD₁₆	—	4	2	no	—
382	SD₁₆	—	4	4	no	—
383	D₈	—	4	2	no	—
384	M₁₆	—	4	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	8	2	no	—
391	C₂×C₈	—	8	1	no	—
392	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
393	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
403	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
413	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
414	C₄²	C₅×#41	1	1	yes	characteristic
415	C₄²	C₂⁴×C₅	1	1	yes	characteristic
416	C₂×C₅	—	2	2	no	—
417	C₂×C₅	—	4	2	no	—
418	C₂×C₅	—	16	1	no	—
419	C₂×C₅	#3046	1	1	yes	characteristic
420	C₂×C₅	C₂×#466	1	1	yes	characteristic
421	C₂×C₅	#3069	1	1	yes	characteristic
422	C₂³	—	2	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	C₅×#121	1	1	yes	characteristic
425	Q₈	—	2	1	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	2	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	8	2	no	—
431	Q₈	C₂×C₅×D₈	1	2	yes	—
432	D₄	—	2	4	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	8	1	no	—
439	D₄	—	8	2	no	—
440	D₄	C₂×C₅×D₈	1	2	yes	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	C₅×#121	1	1	yes	characteristic
456	C₂×C₄	C₅×#121	1	1	yes	characteristic
457	C₂×C₄	C₅×#121	1	1	yes	characteristic
458	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
459	C₂×C₄	C₅×#135	1	2	yes	—
460	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
461	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₅	#19416	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	C₅×#466	1	2	yes	—
479	C₂²	C₂×C₅×#121	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	2	no	—
488	C₄	C₅×#466	1	2	yes	—
489	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
490	C₄	C₂×C₅×#135	1	1	yes	characteristic
491	C₄	C₅×#577	1	1	yes	characteristic
492	C₄	C₅×#578	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	16	1	no	—
496	C₂	C₅×#3046	1	1	yes	characteristic
497	C₂	C₂×C₅×#466	1	1	yes	characteristic
498	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3035	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3226	C₂	semidirect
2. C₅×#3039	C₂	semidirect
4. C₅×#2988	C₂	semidirect
5. C₅×#1682	C₂	semidirect
6. C₅×#1681	C₂	semidirect
7. C₅×#1674	C₂	semidirect
8. C₅×#1673	C₂	semidirect
9. C₅×#1571	C₂	semidirect
10. C₅×#1547	C₂	semidirect
11. C₂×C₅×#332	C₂	semidirect
49. #19416	C₅	direct (N × H)
112. #3226	C₂×C₅	semidirect
113. #3039	C₂×C₅	semidirect
115. #2988	C₂×C₅	semidirect
116. #1682	C₂×C₅	semidirect
117. #1681	C₂×C₅	semidirect
118. #1674	C₂×C₅	semidirect
119. #1673	C₂×C₅	semidirect
120. #1571	C₂×C₅	semidirect
121. #1547	C₂×C₅	semidirect
122. C₂×#332	C₂×C₅	semidirect
469. C₅	#19416	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3226	2
C₅×#3039	2
C₅×#3035	2
C₅×#2988	2
C₅×#1682	2
C₅×#1681	2
C₅×#1674	2
C₅×#1673	2
C₅×#1571	2
C₅×#1547	2
C₂×C₅×#332	2
#19416	5

Subgroups — C5×#19416 #11942136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19416 #11942136