Subgroups — C₅×#68712 #14302779

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 440 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	C₅×#5120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5006	C₂	1	1	yes	maximal, characteristic
5	C₅×#5004	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1909	—	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	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₅×#926	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	—	2	2	no	—
21	C₅×#875	C₄	1	2	yes	complemented
22	C₅×#869	C₄	1	2	yes	complemented
23	C₅×#816	—	2	2	no	—
24	C₅×#810	—	2	2	no	—
25	C₅×#806	—	2	2	no	—
26	#68712	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#568	—	3	1	no	—
28	C₅×#536	—	3	1	no	—
29	C₅×#419	—	3	1	no	—
30	C₅×#419	—	3	1	no	—
31	C₅×#410	—	3	1	no	—
32	C₅×H(3,ℤ/4)	—	3	1	no	—
33	C₅×H(3,ℤ/4)	D₃	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	D₄	1	2	yes	—
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	—	2	1	no	—
41	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
43	C₂×C₅×Dic₆	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
49	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
59	C₅×#217	—	2	1	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	4	no	—
62	C₅×C₄⋊Dic₃	—	2	1	no	—
63	C₄×C₅×Dic₃	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₅×#208	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
67	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
68	C₅×D₃×C₈	—	2	4	no	—
69	#5745	C₂×C₅	1	1	yes	characteristic
70	#5526	C₂×C₅	1	1	yes	characteristic
71	#5120	C₂×C₅	1	1	yes	characteristic, complemented
72	#5006	C₂×C₅	1	1	yes	characteristic
73	#5004	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic, complemented
75	#4531	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	—	3	1	no	—
77	C₂²×C₅×Q₈	—	3	1	no	—
78	C₅×#131	—	6	2	no	—
79	C₅×#131	—	6	2	no	—
80	C₂×C₅×M₁₆	—	3	1	no	—
81	C₂×C₅×M₁₆	—	6	2	no	—
82	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	—	3	2	no	—
84	C₅×#124	—	3	2	no	—
85	C₅×#123	—	6	2	no	—
86	C₅×C₂²⋊Q₈	—	6	2	no	—
87	C₅×#117	—	3	1	no	—
88	C₅×#117	C₂×D₃	1	1	yes	characteristic
89	C₅×#117	C₂×D₃	1	1	yes	characteristic
90	C₅×#103	—	6	2	no	—
91	C₅×#103	—	6	2	no	—
92	C₅×#99	—	6	2	no	—
93	#1909	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
104	C₅×#67	—	2	2	no	—
105	C₅×#67	—	2	2	no	—
106	C₂×C₅×Dic₃	—	2	2	no	—
107	C₂×C₅×Dic₃	—	4	1	no	—
108	C₂×C₅×Dic₃	—	4	1	no	—
109	C₂×C₅×Dic₃	—	4	1	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	—	2	2	no	—
118	C₅×Dic₆	—	2	2	no	—
119	C₅×Dic₆	—	4	1	no	—
120	C₅×Dic₆	—	4	1	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₂×#235	C₂²×C₅	1	1	yes	characteristic
124	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
125	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₃×#117	C₂²×C₅	1	1	yes	characteristic
127	C₃×#117	C₂²×C₅	1	1	yes	characteristic
128	#926	C₂²×C₅	1	1	yes	characteristic
129	C₂×#208	C₂²×C₅	1	1	yes	characteristic
130	#907	—	2	2	no	—
131	D₃×M₁₆	—	2	2	no	—
132	#901	—	2	2	no	—
133	#897	—	2	2	no	—
134	#886	—	2	2	no	—
135	#875	C₄×C₅	1	2	yes	complemented
136	#869	C₄×C₅	1	2	yes	complemented
137	#816	—	2	2	no	—
138	#810	—	2	2	no	—
139	#806	—	2	2	no	—
140	C₅×#41	—	6	1	no	—
141	C₅×#41	—	6	1	no	—
142	C₅×#41	—	6	1	no	—
143	C₅×#41	—	6	1	no	—
144	C₂×C₅×Q₈	—	3	1	no	—
145	C₂×C₅×Q₈	—	3	2	no	—
146	C₂×C₅×Q₈	—	6	1	no	—
147	C₂×C₅×Q₈	—	6	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×D₄	—	3	2	no	—
152	C₂×C₅×D₄	—	3	1	no	—
153	C₂²×C₄×C₅	—	3	2	no	—
154	C₂²×C₄×C₅	—	6	1	no	—
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₅×M₁₆	—	2	1	no	—
157	C₅×M₁₆	—	2	1	no	—
158	C₅×M₁₆	—	6	4	no	—
159	C₅×M₁₆	—	6	1	no	—
160	C₅×M₁₆	—	6	1	no	—
161	C₂×C₅×C₈	—	3	2	no	—
162	C₂×C₅×C₈	—	6	4	no	—
163	C₂×C₅×C₈	D₁₂	1	2	yes	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₅×C₄⋊C₄	—	6	1	no	—
168	C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₅×C₂²⋊C₄	—	6	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	6	1	no	—
174	C₄²×C₅	C₄×D₃	1	2	yes	—
175	#568	—	3	1	no	—
176	#536	—	3	1	no	—
177	#419	—	3	1	no	—
178	#419	—	3	1	no	—
179	#410	—	3	1	no	—
180	H(3,ℤ/4)	—	3	1	no	—
181	H(3,ℤ/4)	C₅×D₃	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	—	4	1	no	—
183	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	#121	1	1	yes	characteristic
185	C₂²×C₃×C₅	#121	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	2	no	—
187	C₂×C₅×D₃	—	4	2	no	—
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	8	1	no	—
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	#120	1	1	yes	characteristic
193	C₃×C₄×C₅	#123	1	1	yes	characteristic
194	C₅×Dic₃	—	2	2	no	—
195	C₅×Dic₃	—	4	2	no	—
196	C₅×Dic₃	—	8	1	no	—
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂×#67	C₅×D₄	1	2	yes	—
199	C₂²×Dic₃	—	2	1	no	—
200	#235	—	2	1	no	—
201	#235	—	2	1	no	—
202	#235	—	2	1	no	—
203	#235	—	2	1	no	—
204	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
206	C₂×Dic₆	—	2	1	no	—
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	C₂×C₄×C₅	1	2	yes	—
212	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
213	C₃×M₁₆	—	2	1	no	—
214	C₃×M₁₆	—	2	1	no	—
215	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
216	C₃×C₄⋊C₄	—	2	1	no	—
217	C₃×C₄⋊C₄	—	2	1	no	—
218	C₃×C₂²⋊C₄	—	2	1	no	—
219	C₃×C₂²⋊C₄	—	2	1	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
222	#217	—	2	1	no	—
223	(C₂×D₃)⋊C₄	—	2	4	no	—
224	C₄⋊Dic₃	—	2	4	no	—
225	C₄⋊Dic₃	—	2	1	no	—
226	C₄×Dic₃	—	2	1	no	—
227	#208	—	2	1	no	—
228	#208	—	2	1	no	—
229	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
230	ΓL(1,𝔽₂₅)	—	2	4	no	—
231	D₃×C₈	—	2	4	no	—
232	C₂³×C₅	—	3	2	no	—
233	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
234	C₅×Q₈	—	6	1	no	—
235	C₅×Q₈	—	6	1	no	—
236	C₅×Q₈	—	6	2	no	—
237	C₅×Q₈	—	6	2	no	—
238	C₅×Q₈	—	12	1	no	—
239	C₅×Q₈	—	12	1	no	—
240	C₅×D₄	—	6	2	no	—
241	C₅×D₄	—	6	2	no	—
242	C₅×D₄	—	6	1	no	—
243	C₅×D₄	—	6	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	3	2	no	—
246	C₂×C₄×C₅	—	4	1	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	—	12	1	no	—
251	C₂×C₄×C₅	—	12	1	no	—
252	C₂×C₄×C₅	—	12	1	no	—
253	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
255	C₂×C₄×C₅	#235	1	1	yes	characteristic
256	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	#239	1	1	yes	characteristic
259	C₅×C₈	—	2	2	no	—
260	C₅×C₈	—	6	2	no	—
261	C₂×#41	—	3	1	no	—
262	C₂²×Q₈	—	3	1	no	—
263	#131	—	6	2	no	—
264	#131	—	6	2	no	—
265	C₂×M₁₆	—	3	1	no	—
266	C₂×M₁₆	—	6	2	no	—
267	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
268	C₄⋊Q₈	—	3	2	no	—
269	#124	—	3	2	no	—
270	#123	—	6	2	no	—
271	C₂²⋊Q₈	—	6	2	no	—
272	#117	—	3	1	no	—
273	#117	C₂×C₅×D₃	1	1	yes	characteristic
274	#117	C₂×C₅×D₃	1	1	yes	characteristic
275	#103	—	6	2	no	—
276	#103	—	6	2	no	—
277	#99	—	6	2	no	—
278	C₂×C₃×C₅	—	2	1	no	—
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	2	1	no	—
281	C₂×C₃×C₅	#386	1	1	yes	characteristic
282	C₅×D₃	—	4	2	no	—
283	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	C₅×#41	1	1	yes	characteristic
292	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
293	#67	—	2	2	no	—
294	#67	—	2	2	no	—
295	C₂×Dic₃	—	2	2	no	—
296	C₂×Dic₃	—	4	1	no	—
297	C₂×Dic₃	—	4	1	no	—
298	C₂×Dic₃	—	4	1	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	—	2	2	no	—
307	Dic₆	—	2	2	no	—
308	Dic₆	—	4	1	no	—
309	Dic₆	—	4	1	no	—
310	C₃×C₈	—	2	2	no	—
311	C₃⋊C₈	—	2	2	no	—
312	C₂²×C₅	—	4	1	no	—
313	C₂²×C₅	—	6	2	no	—
314	C₂²×C₅	—	12	2	no	—
315	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₅	#884	1	1	yes	characteristic
317	C₂²×C₅	#895	1	1	yes	characteristic
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	6	2	no	—
320	C₄×C₅	—	8	1	no	—
321	C₄×C₅	—	12	2	no	—
322	C₄×C₅	—	24	1	no	—
323	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
324	C₄×C₅	#882	1	1	yes	characteristic
325	C₄×C₅	#893	1	1	yes	characteristic
326	C₄×C₅	#894	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	—	3	2	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	—	6	1	no	—
342	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	6	4	no	—
346	M₁₆	—	6	1	no	—
347	M₁₆	—	6	1	no	—
348	C₂×C₈	—	3	2	no	—
349	C₂×C₈	—	6	4	no	—
350	C₂×C₈	C₅×D₁₂	1	2	yes	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	6	4	no	—
354	C₄⋊C₄	—	6	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	6	4	no	—
358	C₂²⋊C₄	—	6	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	6	1	no	—
361	C₄²	C₄×C₅×D₃	1	2	yes	—
362	C₃×C₅	#1909	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	C₅×#121	1	1	yes	characteristic
366	C₂²×C₃	C₅×#121	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	—	8	1	no	—
371	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
372	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
373	C₃×C₄	C₅×#120	1	1	yes	characteristic
374	C₃×C₄	C₅×#123	1	1	yes	characteristic
375	Dic₃	—	2	2	no	—
376	Dic₃	—	4	2	no	—
377	Dic₃	—	8	1	no	—
378	C₂×C₅	—	2	1	no	—
379	C₂×C₅	—	2	1	no	—
380	C₂×C₅	—	2	1	no	—
381	C₂×C₅	—	12	2	no	—
382	C₂×C₅	#4665	1	1	yes	characteristic
383	C₂³	—	3	2	no	—
384	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
385	Q₈	—	6	1	no	—
386	Q₈	—	6	1	no	—
387	Q₈	—	6	2	no	—
388	Q₈	—	6	2	no	—
389	Q₈	—	12	1	no	—
390	Q₈	—	12	1	no	—
391	D₄	—	6	2	no	—
392	D₄	—	6	2	no	—
393	D₄	—	6	1	no	—
394	D₄	—	6	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	3	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	6	2	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	—	12	1	no	—
402	C₂×C₄	—	12	1	no	—
403	C₂×C₄	—	12	1	no	—
404	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
405	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
406	C₂×C₄	C₅×#235	1	1	yes	characteristic
407	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
408	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
409	C₂×C₄	C₅×#239	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	6	2	no	—
412	C₂×C₃	—	2	1	no	—
413	C₂×C₃	—	2	1	no	—
414	C₂×C₃	—	2	1	no	—
415	C₂×C₃	C₅×#386	1	1	yes	characteristic
416	D₃	—	4	2	no	—
417	C₅	#68712	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	4	1	no	—
419	C₂²	—	6	2	no	—
420	C₂²	—	12	2	no	—
421	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
422	C₂²	C₅×#884	1	1	yes	characteristic
423	C₂²	C₅×#895	1	1	yes	characteristic
424	C₄	—	4	2	no	—
425	C₄	—	6	2	no	—
426	C₄	—	8	1	no	—
427	C₄	—	12	2	no	—
428	C₄	—	24	1	no	—
429	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
430	C₄	C₅×#882	1	1	yes	characteristic
431	C₄	C₅×#893	1	1	yes	characteristic
432	C₄	C₅×#894	1	1	yes	characteristic
433	C₃	C₅×#1909	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	12	2	no	—
438	C₂	C₅×#4665	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4665
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×H(3,ℤ/4)	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×H(3,ℤ/4)	D₃
hypocenter	C₃	C₅×#1909
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
3. C₅×#5120	C₂	semidirect
5. C₅×#5004	C₂	semidirect
6. C₃×C₅×H(3,ℤ/4)	C₂	semidirect
7. C₅×#4531	C₂	semidirect
21. C₅×#875	C₄	semidirect
22. C₅×#869	C₄	semidirect
26. #68712	C₅	direct (N × H)
33. C₅×H(3,ℤ/4)	D₃	semidirect
71. #5120	C₂×C₅	semidirect
73. #5004	C₂×C₅	semidirect
74. C₃×H(3,ℤ/4)	C₂×C₅	semidirect
75. #4531	C₂×C₅	semidirect
135. #875	C₄×C₅	semidirect
136. #869	C₄×C₅	semidirect
181. H(3,ℤ/4)	C₅×D₃	semidirect
362. C₃×C₅	#1909	semidirect
417. C₅	#68712	direct (N × H)
433. C₃	C₅×#1909	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
C₅×#5120	2
C₅×#5006	2
C₅×#5004	2
C₃×C₅×H(3,ℤ/4)	2
C₅×#4531	2
C₅×#1909	3
#68712	5

Subgroups — C5×#68712 #14302779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68712 #14302779