Subgroups — C₅×#69041 #14303079

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5745	C₂	1	1	yes	maximal, characteristic
2	C₅×#5526	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#824	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#824	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5132	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1915	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#907	—	2	2	no	—
17	C₅×D₃×M₁₆	—	2	2	no	—
18	C₅×#901	—	2	2	no	—
19	C₅×#897	—	2	2	no	—
20	C₅×#886	C₄	1	4	yes	—
21	C₅×#875	—	2	1	no	—
22	C₅×#869	—	2	1	no	—
23	C₅×#824	—	2	1	no	—
24	C₅×#824	—	2	2	no	—
25	C₅×#824	—	2	2	no	—
26	C₅×#823	—	2	1	no	—
27	#69041	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₅×#568	—	3	1	no	—
29	C₅×#536	—	3	1	no	—
30	C₅×#413	—	3	1	no	—
31	C₂×C₅×#101	—	3	1	no	—
32	C₂×C₅×#101	—	3	1	no	—
33	C₅×#344	—	3	1	no	—
34	C₅×#344	D₃	1	1	yes	characteristic, complemented
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₅×#67	C₂×C₄	1	2	yes	—
37	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	—	2	1	no	—
41	C₅×#235	—	2	1	no	—
42	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
43	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
44	C₂×C₅×Dic₆	—	2	1	no	—
45	C₂×C₅×Dic₆	—	2	1	no	—
46	C₂×C₅×Dic₆	—	2	1	no	—
47	C₂×C₅×Dic₆	—	2	1	no	—
48	C₂×C₅×Dic₆	—	2	1	no	—
49	C₂×C₅×Dic₆	—	2	1	no	—
50	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₃×C₅×M₁₆	D₄	1	2	yes	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	4	no	—
62	C₅×#208	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₅×#208	D₄	1	2	yes	—
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
69	C₅×D₃×C₈	—	2	4	no	—
70	#5745	C₂×C₅	1	1	yes	characteristic
71	#5526	C₂×C₅	1	1	yes	characteristic
72	C₂×#824	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#824	C₂×C₅	1	1	yes	characteristic, complemented
74	#5132	C₂×C₅	1	1	yes	characteristic
75	C₃×#344	C₂×C₅	1	1	yes	characteristic, complemented
76	#4533	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	—	3	1	no	—
78	C₂²×C₅×Q₈	—	3	1	no	—
79	C₅×#131	—	6	2	no	—
80	C₅×#131	—	6	2	no	—
81	C₂×C₅×M₁₆	—	3	1	no	—
82	C₂×C₅×M₁₆	—	3	1	no	—
83	C₂×C₅×M₁₆	—	6	2	no	—
84	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
85	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	—	6	1	no	—
87	C₅×#124	—	6	1	no	—
88	C₅×#123	—	3	4	no	—
89	C₅×C₂²⋊Q₈	—	6	2	no	—
90	C₅×#117	C₂×D₃	1	1	yes	characteristic
91	C₅×#101	—	6	2	no	—
92	C₅×#101	—	6	1	no	—
93	C₅×#101	—	6	2	no	—
94	C₅×#100	—	6	1	no	—
95	#1915	—	3	1	no	Sylow
96	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₅×#67	—	2	2	no	—
106	C₅×#67	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	2	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	2	no	—
110	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
111	C₅×D₁₂	—	2	1	no	—
112	C₅×D₁₂	—	2	1	no	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₄×C₅×D₃	—	2	2	no	—
115	C₅×Dic₆	—	2	1	no	—
116	C₅×Dic₆	—	2	1	no	—
117	C₅×Dic₆	—	4	1	no	—
118	C₅×Dic₆	—	4	1	no	—
119	C₅×Dic₆	—	4	1	no	—
120	C₅×Dic₆	—	4	1	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	—	4	1	no	—
123	C₅×C₃⋊C₈	—	2	2	no	—
124	C₅×C₃⋊C₈	—	4	1	no	—
125	C₂×#235	C₂²×C₅	1	1	yes	characteristic
126	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
129	C₃×#117	C₂²×C₅	1	1	yes	characteristic
130	C₂×#208	C₂²×C₅	1	1	yes	characteristic
131	C₂×#208	C₂²×C₅	1	1	yes	characteristic
132	#907	—	2	2	no	—
133	D₃×M₁₆	—	2	2	no	—
134	#901	—	2	2	no	—
135	#897	—	2	2	no	—
136	#886	C₄×C₅	1	4	yes	—
137	#875	—	2	1	no	—
138	#869	—	2	1	no	—
139	#824	—	2	1	no	—
140	#824	—	2	2	no	—
141	#824	—	2	2	no	—
142	#823	—	2	1	no	—
143	C₅×#41	—	6	1	no	—
144	C₅×#41	—	6	1	no	—
145	C₅×#41	—	6	1	no	—
146	C₅×#41	—	6	1	no	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×Q₈	—	6	1	no	—
149	C₂×C₅×Q₈	—	6	1	no	—
150	C₂×C₅×Q₈	—	6	1	no	—
151	C₂×C₅×Q₈	—	6	1	no	—
152	C₂×C₅×Q₈	—	6	1	no	—
153	C₂×C₅×Q₈	—	6	1	no	—
154	C₂×C₅×D₄	—	3	2	no	—
155	C₂×C₅×D₄	—	3	1	no	—
156	C₂²×C₄×C₅	—	3	2	no	—
157	C₂²×C₄×C₅	—	3	2	no	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₅×M₁₆	—	2	1	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	3	2	no	—
163	C₅×M₁₆	—	6	4	no	—
164	C₅×M₁₆	—	6	1	no	—
165	C₅×M₁₆	—	6	1	no	—
166	C₅×M₁₆	—	6	1	no	—
167	C₅×M₁₆	D₁₂	1	2	yes	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	6	4	no	—
171	C₂×C₅×C₈	—	6	1	no	—
172	C₂×C₅×C₈	—	6	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	6	4	no	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
177	C₄²×C₅	—	2	1	no	—
178	#568	—	3	1	no	—
179	#536	—	3	1	no	—
180	#413	—	3	1	no	—
181	C₂×#101	—	3	1	no	—
182	C₂×#101	—	3	1	no	—
183	#344	—	3	1	no	—
184	#344	C₅×D₃	1	1	yes	characteristic, complemented
185	C₂²×C₃×C₅	—	4	1	no	—
186	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
189	C₂×C₅×D₃	—	2	2	no	—
190	C₂×C₅×D₃	—	4	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	#120	1	1	yes	characteristic
193	C₃×C₄×C₅	#121	1	1	yes	characteristic
194	C₃×C₄×C₅	#121	1	1	yes	characteristic
195	C₃×C₄×C₅	#123	1	1	yes	characteristic
196	C₅×Dic₃	—	2	2	no	—
197	C₅×Dic₃	—	4	2	no	—
198	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
199	C₂×#67	C₂×C₄×C₅	1	2	yes	—
200	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
201	#235	—	2	1	no	—
202	#235	—	2	1	no	—
203	#235	—	2	1	no	—
204	#235	—	2	1	no	—
205	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
206	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
207	C₂×Dic₆	—	2	1	no	—
208	C₂×Dic₆	—	2	1	no	—
209	C₂×Dic₆	—	2	1	no	—
210	C₂×Dic₆	—	2	1	no	—
211	C₂×Dic₆	—	2	1	no	—
212	C₂×Dic₆	—	2	1	no	—
213	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
214	C₃×M₁₆	—	2	1	no	—
215	C₃×M₁₆	—	2	1	no	—
216	C₃×M₁₆	—	2	1	no	—
217	C₃×M₁₆	C₅×D₄	1	2	yes	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
222	C₃×C₄²	—	2	1	no	—
223	(C₂×D₃)⋊C₄	—	2	4	no	—
224	C₄⋊Dic₃	—	2	4	no	—
225	#208	—	2	1	no	—
226	#208	—	2	1	no	—
227	#208	—	2	1	no	—
228	#208	C₅×D₄	1	2	yes	—
229	C₂×C₃⋊C₈	—	2	1	no	—
230	C₂×C₃⋊C₈	—	2	1	no	—
231	ΓL(1,𝔽₂₅)	—	2	4	no	—
232	D₃×C₈	—	2	4	no	—
233	C₂³×C₅	—	3	2	no	—
234	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
235	C₅×Q₈	—	6	1	no	—
236	C₅×Q₈	—	6	1	no	—
237	C₅×Q₈	—	12	1	no	—
238	C₅×Q₈	—	12	1	no	—
239	C₅×Q₈	—	12	1	no	—
240	C₅×Q₈	—	12	1	no	—
241	C₅×D₄	—	6	2	no	—
242	C₅×D₄	—	6	2	no	—
243	C₅×D₄	—	6	1	no	—
244	C₅×D₄	—	6	1	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	3	2	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	6	2	no	—
252	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
253	C₂×C₄×C₅	#235	1	1	yes	characteristic
254	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	#239	1	1	yes	characteristic
258	C₅×C₈	—	2	2	no	—
259	C₅×C₈	—	4	1	no	—
260	C₅×C₈	—	6	2	no	—
261	C₅×C₈	—	12	1	no	—
262	C₂×#41	—	3	1	no	—
263	C₂²×Q₈	—	3	1	no	—
264	#131	—	6	2	no	—
265	#131	—	6	2	no	—
266	C₂×M₁₆	—	3	1	no	—
267	C₂×M₁₆	—	3	1	no	—
268	C₂×M₁₆	—	6	2	no	—
269	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
270	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	6	1	no	—
272	#124	—	6	1	no	—
273	#123	—	3	4	no	—
274	C₂²⋊Q₈	—	6	2	no	—
275	#117	C₂×C₅×D₃	1	1	yes	characteristic
276	#101	—	6	2	no	—
277	#101	—	6	1	no	—
278	#101	—	6	2	no	—
279	#100	—	6	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	—	2	1	no	—
283	C₂×C₃×C₅	#386	1	1	yes	characteristic
284	C₅×D₃	—	4	2	no	—
285	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
293	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
294	#67	—	2	2	no	—
295	#67	—	2	2	no	—
296	C₂×Dic₃	—	2	2	no	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	—	2	2	no	—
299	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
300	D₁₂	—	2	1	no	—
301	D₁₂	—	2	1	no	—
302	C₄×D₃	—	2	2	no	—
303	C₄×D₃	—	2	2	no	—
304	Dic₆	—	2	1	no	—
305	Dic₆	—	2	1	no	—
306	Dic₆	—	4	1	no	—
307	Dic₆	—	4	1	no	—
308	Dic₆	—	4	1	no	—
309	Dic₆	—	4	1	no	—
310	C₃×C₈	—	2	2	no	—
311	C₃×C₈	—	4	1	no	—
312	C₃⋊C₈	—	2	2	no	—
313	C₃⋊C₈	—	4	1	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	—	6	2	no	—
316	C₂²×C₅	—	12	2	no	—
317	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
318	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₅	#893	1	1	yes	characteristic
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	6	2	no	—
322	C₄×C₅	—	12	2	no	—
323	C₄×C₅	#882	1	1	yes	characteristic
324	C₄×C₅	#884	1	1	yes	characteristic
325	C₄×C₅	#894	1	1	yes	characteristic
326	C₄×C₅	#895	1	1	yes	characteristic
327	#41	—	6	1	no	—
328	#41	—	6	1	no	—
329	#41	—	6	1	no	—
330	#41	—	6	1	no	—
331	C₂×Q₈	—	3	1	no	—
332	C₂×Q₈	—	6	1	no	—
333	C₂×Q₈	—	6	1	no	—
334	C₂×Q₈	—	6	1	no	—
335	C₂×Q₈	—	6	1	no	—
336	C₂×Q₈	—	6	1	no	—
337	C₂×Q₈	—	6	1	no	—
338	C₂×D₄	—	3	2	no	—
339	C₂×D₄	—	3	1	no	—
340	C₂²×C₄	—	3	2	no	—
341	C₂²×C₄	—	3	2	no	—
342	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	3	2	no	—
347	M₁₆	—	6	4	no	—
348	M₁₆	—	6	1	no	—
349	M₁₆	—	6	1	no	—
350	M₁₆	—	6	1	no	—
351	M₁₆	C₅×D₁₂	1	2	yes	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	6	4	no	—
355	C₂×C₈	—	6	1	no	—
356	C₂×C₈	—	6	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	6	4	no	—
359	C₂²⋊C₄	—	6	4	no	—
360	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
361	C₄²	—	2	1	no	—
362	C₃×C₅	#1915	1	1	yes	characteristic, complemented, Hall
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
366	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
367	C₂×D₃	—	2	2	no	—
368	C₂×D₃	—	4	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	C₅×#120	1	1	yes	characteristic
371	C₃×C₄	C₅×#121	1	1	yes	characteristic
372	C₃×C₄	C₅×#121	1	1	yes	characteristic
373	C₃×C₄	C₅×#123	1	1	yes	characteristic
374	Dic₃	—	2	2	no	—
375	Dic₃	—	4	2	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	2	1	no	—
378	C₂×C₅	—	2	1	no	—
379	C₂×C₅	—	12	2	no	—
380	C₂×C₅	#4665	1	1	yes	characteristic
381	C₂³	—	3	2	no	—
382	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
383	Q₈	—	6	1	no	—
384	Q₈	—	6	1	no	—
385	Q₈	—	12	1	no	—
386	Q₈	—	12	1	no	—
387	Q₈	—	12	1	no	—
388	Q₈	—	12	1	no	—
389	D₄	—	6	2	no	—
390	D₄	—	6	2	no	—
391	D₄	—	6	1	no	—
392	D₄	—	6	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	3	2	no	—
395	C₂×C₄	—	6	2	no	—
396	C₂×C₄	—	6	2	no	—
397	C₂×C₄	—	6	2	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
401	C₂×C₄	C₅×#235	1	1	yes	characteristic
402	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
403	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
404	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
405	C₂×C₄	C₅×#239	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	6	2	no	—
409	C₈	—	12	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	2	1	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	C₅×#386	1	1	yes	characteristic
414	D₃	—	4	2	no	—
415	C₅	#69041	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	4	1	no	—
417	C₂²	—	6	2	no	—
418	C₂²	—	12	2	no	—
419	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
420	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
421	C₂²	C₅×#893	1	1	yes	characteristic
422	C₄	—	4	2	no	—
423	C₄	—	6	2	no	—
424	C₄	—	12	2	no	—
425	C₄	C₅×#882	1	1	yes	characteristic
426	C₄	C₅×#884	1	1	yes	characteristic
427	C₄	C₅×#894	1	1	yes	characteristic
428	C₄	C₅×#895	1	1	yes	characteristic
429	C₃	C₅×#1915	1	1	yes	characteristic, complemented, Sylow
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	12	2	no	—
434	C₂	C₅×#4665	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4665
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#344	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#344	D₃
hypocenter	C₃	C₅×#1915
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#344

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#824	C₂	semidirect
4. C₂×C₅×#824	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₅×#4533	C₂	semidirect
27. #69041	C₅	direct (N × H)
34. C₅×#344	D₃	semidirect
72. C₂×#824	C₂×C₅	semidirect
73. C₂×#824	C₂×C₅	semidirect
75. C₃×#344	C₂×C₅	semidirect
76. #4533	C₂×C₅	semidirect
184. #344	C₅×D₃	semidirect
362. C₃×C₅	#1915	semidirect
415. C₅	#69041	direct (N × H)
429. C₃	C₅×#1915	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5745	2
C₅×#5526	2
C₂×C₅×#824	2
C₅×#5132	2
C₃×C₅×#344	2
C₅×#4533	2
C₅×#1915	3
#69041	5

Subgroups — C5×#69041 #14303079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69041 #14303079