Subgroups — C₅×#19447 #11942167

Order 1280.

598 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3079	C₂	1	1	yes	maximal, characteristic
3	C₅×#3076	C₂	1	1	yes	maximal, characteristic
4	C₅×#2989	C₂	1	1	yes	maximal, characteristic
5	C₅×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1703	C₂	1	2	yes	maximal, complemented
7	C₅×#1690	C₂	1	2	yes	maximal, complemented
8	C₅×#1689	C₂	1	2	yes	maximal, complemented
9	C₅×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#494	C₂²	1	2	yes	—
16	C₅×#487	C₂²	1	2	yes	—
17	C₅×#479	—	2	1	no	—
18	C₅×#478	—	2	1	no	—
19	C₅×#477	—	2	1	no	—
20	C₅×#477	C₂²	1	1	yes	characteristic
21	C₅×#476	—	2	1	no	—
22	C₅×#476	C₂²	1	1	yes	characteristic
23	C₅×#475	C₂²	1	1	yes	characteristic
24	C₅×#475	C₂²	1	2	yes	—
25	C₅×#474	C₂²	1	1	yes	characteristic
26	C₅×#474	C₂²	1	2	yes	—
27	C₅×#462	—	2	1	no	—
28	C₅×#462	—	2	1	no	—
29	C₅×#451	—	2	2	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×#436	C₂²	1	2	yes	—
32	C₅×#435	—	2	2	no	—
33	C₅×#432	—	2	1	no	—
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₅×#428	—	2	1	no	—
36	C₅×#427	—	2	1	no	—
37	C₅×#423	—	2	1	no	—
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×#417	—	2	1	no	—
42	C₅×#416	—	2	1	no	—
43	C₅×#334	C₂²	1	2	yes	—
44	C₅×#334	C₂²	1	2	yes	—
45	C₅×#333	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#332	C₂²	1	2	yes	—
49	#19447	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	D₄	1	1	yes	characteristic
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂×C₅×Q₁₆	—	2	2	no	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×#125	—	2	1	no	—
65	C₅×C₂²⋊Q₈	—	2	1	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₄×C₅×Q₈	—	2	1	no	—
68	C₄×C₅×Q₈	—	2	1	no	—
69	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
70	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	D₄	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₅×#117	—	2	1	no	—
76	C₅×#117	—	2	1	no	—
77	C₅×#117	D₄	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₅×#107	—	2	1	no	—
83	C₅×#107	—	2	1	no	—
84	C₅×#107	—	2	2	no	—
85	C₅×#106	—	2	1	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₅×C₄⋊C₈	C₂³	1	2	yes	—
95	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₅×C₄⋊C₈	C₂³	1	2	yes	—
98	C₅×#103	—	2	1	no	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	2	no	—
101	C₅×#103	—	2	2	no	—
102	C₅×#103	—	2	2	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×#102	—	2	2	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	D₄	1	2	yes	—
108	C₅×#97	—	2	2	no	—
109	C₄×C₅×C₈	C₂³	1	2	yes	—
110	#3209	C₂×C₅	1	1	yes	characteristic, complemented
111	#3079	C₂×C₅	1	1	yes	characteristic
112	#3076	C₂×C₅	1	1	yes	characteristic
113	#2989	C₂×C₅	1	1	yes	characteristic
114	#1704	C₂×C₅	1	2	yes	complemented
115	#1703	C₂×C₅	1	2	yes	complemented
116	#1690	C₂×C₅	1	2	yes	complemented
117	#1689	C₂×C₅	1	2	yes	complemented
118	#1570	C₂×C₅	1	1	yes	characteristic, complemented
119	#1550	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
121	C₅×#41	—	2	2	no	—
122	C₅×#41	—	2	2	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	4	1	no	—
127	C₂×C₅×Q₈	—	8	1	no	—
128	C₂×C₅×Q₈	—	8	1	no	—
129	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	4	1	no	—
136	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	#41	1	1	yes	characteristic
139	C₅×Q₁₆	—	8	2	no	—
140	C₅×Q₁₆	—	8	2	no	—
141	C₅×M₁₆	—	4	2	no	—
142	C₅×M₁₆	—	8	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	2	no	—
147	C₂×C₅×C₈	—	4	2	no	—
148	C₂×C₅×C₈	—	8	1	no	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	4	1	no	—
160	C₅×C₄⋊C₄	—	4	1	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
164	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	—	2	1	no	—
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	4	1	no	—
173	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	#41	1	1	yes	characteristic
176	C₄²×C₅	C₂⁴	1	1	yes	characteristic
177	#533	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₄×#41	C₂²×C₅	1	1	yes	characteristic
180	#494	C₂²×C₅	1	2	yes	—
181	#487	C₂²×C₅	1	2	yes	—
182	#479	—	2	1	no	—
183	#478	—	2	1	no	—
184	#477	—	2	1	no	—
185	#477	C₂²×C₅	1	1	yes	characteristic
186	#476	—	2	1	no	—
187	#476	C₂²×C₅	1	1	yes	characteristic
188	#475	C₂²×C₅	1	1	yes	characteristic
189	#475	C₂²×C₅	1	2	yes	—
190	#474	C₂²×C₅	1	1	yes	characteristic
191	#474	C₂²×C₅	1	2	yes	—
192	#462	—	2	1	no	—
193	#462	—	2	1	no	—
194	#451	—	2	2	no	—
195	#446	C₂²×C₅	1	2	yes	—
196	#436	C₂²×C₅	1	2	yes	—
197	#435	—	2	2	no	—
198	#432	—	2	1	no	—
199	#431	C₂²×C₅	1	1	yes	characteristic
200	#428	—	2	1	no	—
201	#427	—	2	1	no	—
202	#423	—	2	1	no	—
203	#423	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	#417	—	2	1	no	—
207	#416	—	2	1	no	—
208	#334	C₂²×C₅	1	2	yes	—
209	#334	C₂²×C₅	1	2	yes	—
210	#333	C₂²×C₅	1	2	yes	—
211	#332	C₂²×C₅	1	2	yes	—
212	#332	C₂²×C₅	1	2	yes	—
213	#332	C₂²×C₅	1	2	yes	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	#121	1	1	yes	characteristic
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	4	1	no	—
219	C₅×Q₈	—	4	2	no	—
220	C₅×Q₈	—	4	1	no	—
221	C₅×Q₈	—	4	2	no	—
222	C₅×Q₈	—	8	1	no	—
223	C₅×Q₈	—	8	2	no	—
224	C₅×D₄	—	2	1	no	—
225	C₅×D₄	—	2	1	no	—
226	C₅×D₄	—	4	2	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	8	1	no	—
240	C₂×C₄×C₅	—	8	2	no	—
241	C₂×C₄×C₅	#121	1	1	yes	characteristic
242	C₂×C₄×C₅	#121	1	1	yes	characteristic
243	C₂×C₄×C₅	#121	1	1	yes	characteristic
244	C₂×C₄×C₅	#137	1	2	yes	—
245	C₂×C₄×C₅	#137	1	2	yes	—
246	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	4	1	no	—
253	C₅×C₈	—	4	2	no	—
254	C₅×C₈	—	4	2	no	—
255	C₂×#41	C₅×D₄	1	1	yes	characteristic
256	C₂²×Q₈	—	2	1	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
269	#125	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
275	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	C₅×D₄	1	1	yes	characteristic
279	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
280	#117	—	2	1	no	—
281	#117	—	2	1	no	—
282	#117	C₅×D₄	1	1	yes	characteristic
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#106	—	2	1	no	—
291	#106	—	2	1	no	—
292	#106	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
298	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₅	1	2	yes	—
300	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₅	1	2	yes	—
303	#103	—	2	1	no	—
304	#103	—	2	1	no	—
305	#103	—	2	2	no	—
306	#103	—	2	2	no	—
307	#103	—	2	2	no	—
308	#102	—	2	1	no	—
309	#102	—	2	1	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	C₅×D₄	1	2	yes	—
313	#97	—	2	2	no	—
314	C₄×C₈	C₂³×C₅	1	2	yes	—
315	C₂²×C₅	—	2	1	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	4	1	no	—
318	C₂²×C₅	—	4	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	#470	1	2	yes	—
321	C₂²×C₅	C₂×#121	1	1	yes	characteristic
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	2	1	no	—
324	C₄×C₅	—	2	1	no	—
325	C₄×C₅	—	4	1	no	—
326	C₄×C₅	—	4	1	no	—
327	C₄×C₅	—	4	1	no	—
328	C₄×C₅	—	8	2	no	—
329	C₄×C₅	—	8	1	no	—
330	C₄×C₅	—	8	1	no	—
331	C₄×C₅	#470	1	2	yes	—
332	C₄×C₅	C₂×#137	1	1	yes	characteristic
333	C₄×C₅	C₂×#137	1	1	yes	characteristic
334	C₄×C₅	#576	1	1	yes	characteristic
335	C₄×C₅	#577	1	1	yes	characteristic
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	8	1	no	—
343	C₂×Q₈	—	8	1	no	—
344	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₅×#41	1	1	yes	characteristic
354	Q₁₆	—	8	2	no	—
355	Q₁₆	—	8	2	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	—	8	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	8	1	no	—
364	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
365	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
389	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
390	C₄²	C₅×#41	1	1	yes	characteristic
391	C₄²	C₂⁴×C₅	1	1	yes	characteristic
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	—	8	1	no	—
394	C₂×C₅	#3045	1	1	yes	characteristic
395	C₂×C₅	C₂×#470	1	1	yes	characteristic
396	C₂×C₅	#3069	1	1	yes	characteristic
397	C₂³	—	2	1	no	—
398	C₂³	C₅×#121	1	1	yes	characteristic
399	Q₈	—	2	1	no	—
400	Q₈	—	2	1	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	8	1	no	—
406	Q₈	—	8	2	no	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	4	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	1	no	—
423	C₂×C₄	—	8	2	no	—
424	C₂×C₄	C₅×#121	1	1	yes	characteristic
425	C₂×C₄	C₅×#121	1	1	yes	characteristic
426	C₂×C₄	C₅×#121	1	1	yes	characteristic
427	C₂×C₄	C₅×#137	1	2	yes	—
428	C₂×C₄	C₅×#137	1	2	yes	—
429	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
431	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₅	#19447	1	1	yes	characteristic, direct product factor, Sylow
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	C₅×#470	1	2	yes	—
445	C₂²	C₂×C₅×#121	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	1	no	—
455	C₄	C₅×#470	1	2	yes	—
456	C₄	C₂×C₅×#137	1	1	yes	characteristic
457	C₄	C₂×C₅×#137	1	1	yes	characteristic
458	C₄	C₅×#576	1	1	yes	characteristic
459	C₄	C₅×#577	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	8	1	no	—
462	C₂	C₅×#3045	1	1	yes	characteristic
463	C₂	C₂×C₅×#470	1	1	yes	characteristic
464	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	D₄
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×#3209	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1703	C₂	semidirect
7. C₅×#1690	C₂	semidirect
8. C₅×#1689	C₂	semidirect
9. C₅×#1570	C₂	semidirect
10. C₅×#1550	C₂	semidirect
11. C₂×C₅×#332	C₂	semidirect
49. #19447	C₅	direct (N × H)
110. #3209	C₂×C₅	semidirect
114. #1704	C₂×C₅	semidirect
115. #1703	C₂×C₅	semidirect
116. #1690	C₂×C₅	semidirect
117. #1689	C₂×C₅	semidirect
118. #1570	C₂×C₅	semidirect
119. #1550	C₂×C₅	semidirect
120. C₂×#332	C₂×C₅	semidirect
438. C₅	#19447	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×#3209	2
C₅×#3079	2
C₅×#3076	2
C₅×#2989	2
C₅×#1704	2
C₅×#1703	2
C₅×#1690	2
C₅×#1689	2
C₅×#1570	2
C₅×#1550	2
C₂×C₅×#332	2
#19447	5

Subgroups — C5×#19447 #11942167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19447 #11942167