Subgroups — C₅×#71198 #14289871

Order 1920.

616 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×#5717	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1639	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×D₄	—	2	1	no	—
10	C₂×C₅×D₃×D₄	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₃×C₅×#127	C₂²	1	1	yes	characteristic
13	C₂×C₅×#215	—	2	1	no	—
14	C₅×#938	—	2	1	no	—
15	C₅×#938	—	2	1	no	—
16	C₅×#937	—	2	2	no	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₃×C₅×#102	—	2	2	no	—
20	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
21	C₅×#835	—	2	1	no	—
22	C₅×#809	—	2	1	no	—
23	C₅×#807	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
26	#71198	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄²	—	3	1	no	—
28	C₅×#486	D₃	1	1	yes	characteristic, complemented
29	C₅×#474	—	3	1	no	—
30	C₅×#461	—	3	1	no	—
31	C₅×#331	—	3	1	no	—
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂³×C₅×D₃	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂×C₅×#67	—	2	2	no	—
40	C₂×C₅×#67	—	2	2	no	—
41	C₅×D₃×D₄	—	4	2	no	—
42	C₅×D₃×D₄	—	4	2	no	—
43	C₅×D₃×D₄	—	4	2	no	—
44	C₅×D₃×D₄	—	4	2	no	—
45	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
46	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	—	2	1	no	—
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₅×#217	—	2	2	no	—
54	C₅×#215	—	4	2	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
57	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
58	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	#5717	C₂×C₅	1	1	yes	characteristic
62	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
63	#5087	C₂×C₅	1	1	yes	characteristic, complemented
64	#5083	C₂×C₅	1	1	yes	characteristic, complemented
65	#4544	C₂×C₅	1	1	yes	characteristic, complemented
66	#4459	C₂×C₅	1	1	yes	characteristic, complemented
67	#4459	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×D₄	—	6	1	no	—
69	C₂²×C₅×D₄	—	6	1	no	—
70	C₂×C₅×SD₁₆	—	6	1	no	—
71	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
72	C₅×#127	C₂×D₃	1	1	yes	characteristic
73	C₅×#121	—	6	1	no	—
74	C₅×#121	—	6	1	no	—
75	C₅×#120	—	6	2	no	—
76	C₄×C₅×D₄	—	3	1	no	—
77	C₄×C₅×D₄	—	3	1	no	—
78	C₅×#107	—	6	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×C₄⋊C₈	—	3	1	no	—
81	C₅×#103	—	6	1	no	—
82	C₅×#102	—	2	2	no	—
83	C₅×#102	—	6	1	no	—
84	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
85	#1639	—	3	1	no	Sylow
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₂²×C₅×D₃	—	2	1	no	—
89	C₂²×C₅×D₃	—	4	4	no	—
90	C₂²×C₅×D₃	—	4	4	no	—
91	C₂²×C₅×D₃	—	8	2	no	—
92	C₃×C₅×Q₈	—	4	1	no	—
93	C₃×C₅×Q₈	—	4	1	no	—
94	C₃×C₅×D₄	—	4	2	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₃×C₅×D₄	—	4	1	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₅×#67	—	4	4	no	—
104	C₅×#67	—	4	4	no	—
105	C₂×C₅×Dic₃	—	2	1	no	—
106	C₂×C₅×Dic₃	—	2	1	no	—
107	C₅×D₁₂	—	2	1	no	—
108	C₅×D₁₂	—	2	1	no	—
109	C₅×D₁₂	D₈	1	2	yes	—
110	C₅×D₁₂	SD₁₆	1	2	yes	complemented
111	C₄×C₅×D₃	—	4	1	no	—
112	C₄×C₅×D₃	—	4	1	no	—
113	C₄×C₅×D₃	—	4	1	no	—
114	C₄×C₅×D₃	—	4	1	no	—
115	C₃×C₅×C₈	—	4	1	no	—
116	C₅×C₃⋊C₈	—	4	1	no	—
117	C₅×C₃⋊C₈	—	4	1	no	—
118	C₂×D₃×D₄	—	2	1	no	—
119	C₂×D₃×D₄	—	2	1	no	—
120	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
121	C₃×#127	C₂²×C₅	1	1	yes	characteristic
122	C₂×#215	—	2	1	no	—
123	#938	—	2	1	no	—
124	#938	—	2	1	no	—
125	#937	—	2	2	no	—
126	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
127	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
128	C₃×#102	—	2	2	no	—
129	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
130	#835	—	2	1	no	—
131	#809	—	2	1	no	—
132	#807	—	2	1	no	—
133	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₂⁴×C₅	—	6	2	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	3	1	no	—
140	C₂×C₅×D₄	—	3	1	no	—
141	C₂×C₅×D₄	—	6	2	no	—
142	C₂×C₅×D₄	—	6	2	no	—
143	C₂×C₅×D₄	—	12	2	no	—
144	C₂×C₅×D₄	—	12	2	no	—
145	C₂×C₅×D₄	—	12	2	no	—
146	C₂×C₅×D₄	—	12	2	no	—
147	C₂×C₅×D₄	#67	1	2	yes	—
148	C₂²×C₄×C₅	—	6	1	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₅×SD₁₆	—	12	2	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	6	1	no	—
153	C₂×C₅×C₈	—	6	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	3	1	no	—
157	C₅×C₄⋊C₄	—	3	1	no	—
158	C₅×C₂²⋊C₄	—	6	2	no	—
159	C₅×C₂²⋊C₄	—	6	1	no	—
160	C₅×C₂²⋊C₄	—	6	1	no	—
161	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
162	D₄²	—	3	1	no	—
163	#486	C₅×D₃	1	1	yes	characteristic, complemented
164	#474	—	3	1	no	—
165	#461	—	3	1	no	—
166	#331	—	3	1	no	—
167	D₄⋊C₈	—	3	1	no	—
168	D₄⋊C₈	—	3	1	no	—
169	C₂²×C₃×C₅	—	4	2	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	#120	1	1	yes	characteristic
173	C₂×C₅×D₃	—	2	2	no	—
174	C₂×C₅×D₃	—	2	2	no	—
175	C₂×C₅×D₃	—	4	1	no	—
176	C₂×C₅×D₃	—	4	1	no	—
177	C₂×C₅×D₃	—	4	1	no	—
178	C₂×C₅×D₃	—	4	1	no	—
179	C₂×C₅×D₃	—	8	8	no	—
180	C₃×C₄×C₅	—	2	1	no	—
181	C₃×C₄×C₅	—	8	1	no	—
182	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
183	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
184	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₅×Dic₃	—	4	1	no	—
187	C₅×Dic₃	—	4	1	no	—
188	C₂³×D₃	—	2	2	no	—
189	C₂×C₃×Q₈	—	2	1	no	—
190	C₂×C₃×D₄	—	2	1	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
193	C₂×#67	—	2	2	no	—
194	C₂×#67	—	2	2	no	—
195	D₃×D₄	—	4	2	no	—
196	D₃×D₄	—	4	2	no	—
197	D₃×D₄	—	4	2	no	—
198	D₃×D₄	—	4	2	no	—
199	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
200	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	—	2	1	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₃×C₄⋊C₄	—	2	1	no	—
205	C₃×C₄⋊C₄	—	2	1	no	—
206	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
207	#217	—	2	2	no	—
208	#215	—	4	2	no	—
209	(C₂×D₃)⋊C₄	—	2	1	no	—
210	(C₂×D₃)⋊C₄	—	2	1	no	—
211	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
212	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
213	C₂×C₃⋊C₈	—	2	1	no	—
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	6	1	no	—
217	C₂³×C₅	—	6	1	no	—
218	C₂³×C₅	—	12	4	no	—
219	C₂³×C₅	—	12	4	no	—
220	C₂³×C₅	—	24	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×D₄	—	3	2	no	—
224	C₅×D₄	—	3	2	no	—
225	C₅×D₄	—	4	2	no	—
226	C₅×D₄	—	4	1	no	—
227	C₅×D₄	—	4	1	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	6	1	no	—
231	C₅×D₄	—	6	1	no	—
232	C₅×D₄	—	12	4	no	—
233	C₅×D₄	—	12	4	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	12	1	no	—
238	C₂×C₄×C₅	—	12	1	no	—
239	C₂×C₄×C₅	—	12	1	no	—
240	C₂×C₄×C₅	—	12	1	no	—
241	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	—	12	1	no	—
246	C₅×C₈	—	12	1	no	—
247	C₂²×D₄	—	6	1	no	—
248	C₂²×D₄	—	6	1	no	—
249	C₂×SD₁₆	—	6	1	no	—
250	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
251	#127	C₂×C₅×D₃	1	1	yes	characteristic
252	#121	—	6	1	no	—
253	#121	—	6	1	no	—
254	#120	—	6	2	no	—
255	C₄×D₄	—	3	1	no	—
256	C₄×D₄	—	3	1	no	—
257	#107	—	6	1	no	—
258	C₄⋊C₈	—	3	1	no	—
259	C₄⋊C₈	—	3	1	no	—
260	#103	—	6	1	no	—
261	#102	—	2	2	no	—
262	#102	—	6	1	no	—
263	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
264	C₂×C₃×C₅	—	8	2	no	—
265	C₂×C₃×C₅	#447	1	1	yes	characteristic
266	C₂×C₃×C₅	#450	1	1	yes	characteristic
267	C₂×C₃×C₅	#455	1	1	yes	characteristic
268	C₅×D₃	—	4	2	no	—
269	C₅×D₃	—	4	2	no	—
270	C₂³×C₃	—	2	2	no	—
271	C₂²×D₃	—	2	1	no	—
272	C₂²×D₃	—	2	1	no	—
273	C₂²×D₃	—	4	4	no	—
274	C₂²×D₃	—	4	4	no	—
275	C₂²×D₃	—	8	2	no	—
276	C₃×Q₈	—	4	1	no	—
277	C₃×Q₈	—	4	1	no	—
278	C₃×D₄	—	4	2	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	4	1	no	—
281	C₃×D₄	—	4	1	no	—
282	C₃×D₄	—	4	1	no	—
283	C₂×C₃×C₄	—	4	1	no	—
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	#67	—	4	4	no	—
288	#67	—	4	4	no	—
289	C₂×Dic₃	—	2	1	no	—
290	C₂×Dic₃	—	2	1	no	—
291	D₁₂	—	2	1	no	—
292	D₁₂	—	2	1	no	—
293	D₁₂	C₅×D₈	1	2	yes	—
294	D₁₂	C₅×SD₁₆	1	2	yes	complemented
295	C₄×D₃	—	4	1	no	—
296	C₄×D₃	—	4	1	no	—
297	C₄×D₃	—	4	1	no	—
298	C₄×D₃	—	4	1	no	—
299	C₃×C₈	—	4	1	no	—
300	C₃⋊C₈	—	4	1	no	—
301	C₃⋊C₈	—	4	1	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	—	4	2	no	—
305	C₂²×C₅	—	6	2	no	—
306	C₂²×C₅	—	6	2	no	—
307	C₂²×C₅	—	12	1	no	—
308	C₂²×C₅	—	12	1	no	—
309	C₂²×C₅	—	12	1	no	—
310	C₂²×C₅	—	12	1	no	—
311	C₂²×C₅	—	24	8	no	—
312	C₂²×C₅	#937	1	1	yes	characteristic
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	8	1	no	—
315	C₄×C₅	—	12	1	no	—
316	C₄×C₅	—	12	1	no	—
317	C₄×C₅	D₃×D₈	1	1	yes	characteristic
318	C₄×C₅	#911	1	1	yes	characteristic
319	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
320	C₄×C₅	#914	1	1	yes	characteristic
321	C₂⁴	—	6	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	3	1	no	—
326	C₂×D₄	—	3	1	no	—
327	C₂×D₄	—	6	2	no	—
328	C₂×D₄	—	6	2	no	—
329	C₂×D₄	—	12	2	no	—
330	C₂×D₄	—	12	2	no	—
331	C₂×D₄	—	12	2	no	—
332	C₂×D₄	—	12	2	no	—
333	C₂×D₄	C₅×#67	1	2	yes	—
334	C₂²×C₄	—	6	1	no	—
335	C₂²×C₄	—	6	1	no	—
336	SD₁₆	—	12	2	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	6	1	no	—
339	C₂×C₈	—	6	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	3	1	no	—
343	C₄⋊C₄	—	3	1	no	—
344	C₂²⋊C₄	—	6	2	no	—
345	C₂²⋊C₄	—	6	1	no	—
346	C₂²⋊C₄	—	6	1	no	—
347	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
348	C₃×C₅	#1639	1	1	yes	characteristic, complemented, Hall
349	C₂²×C₃	—	4	2	no	—
350	C₂²×C₃	—	4	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	C₅×#120	1	1	yes	characteristic
353	C₂×D₃	—	2	2	no	—
354	C₂×D₃	—	2	2	no	—
355	C₂×D₃	—	4	1	no	—
356	C₂×D₃	—	4	1	no	—
357	C₂×D₃	—	4	1	no	—
358	C₂×D₃	—	4	1	no	—
359	C₂×D₃	—	8	8	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	8	1	no	—
362	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
363	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
364	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
365	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
366	Dic₃	—	4	1	no	—
367	Dic₃	—	4	1	no	—
368	C₂×C₅	—	8	2	no	—
369	C₂×C₅	—	12	2	no	—
370	C₂×C₅	—	12	2	no	—
371	C₂×C₅	#5061	1	1	yes	characteristic
372	C₂×C₅	#5156	1	1	yes	characteristic
373	C₂×C₅	#5169	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	6	1	no	—
376	C₂³	—	6	1	no	—
377	C₂³	—	12	4	no	—
378	C₂³	—	12	4	no	—
379	C₂³	—	24	2	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	D₄	—	3	2	no	—
383	D₄	—	3	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	6	1	no	—
390	D₄	—	6	1	no	—
391	D₄	—	12	4	no	—
392	D₄	—	12	4	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	6	1	no	—
395	C₂×C₄	—	6	1	no	—
396	C₂×C₄	—	12	1	no	—
397	C₂×C₄	—	12	1	no	—
398	C₂×C₄	—	12	1	no	—
399	C₂×C₄	—	12	1	no	—
400	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
401	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
402	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
403	C₈	—	4	1	no	—
404	C₈	—	12	1	no	—
405	C₈	—	12	1	no	—
406	C₂×C₃	—	8	2	no	—
407	C₂×C₃	C₅×#447	1	1	yes	characteristic
408	C₂×C₃	C₅×#450	1	1	yes	characteristic
409	C₂×C₃	C₅×#455	1	1	yes	characteristic
410	D₃	—	4	2	no	—
411	D₃	—	4	2	no	—
412	C₅	#71198	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	6	2	no	—
417	C₂²	—	6	2	no	—
418	C₂²	—	12	1	no	—
419	C₂²	—	12	1	no	—
420	C₂²	—	12	1	no	—
421	C₂²	—	12	1	no	—
422	C₂²	—	24	8	no	—
423	C₂²	C₅×#937	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	8	1	no	—
426	C₄	—	12	1	no	—
427	C₄	—	12	1	no	—
428	C₄	C₅×D₃×D₈	1	1	yes	characteristic
429	C₄	C₅×#911	1	1	yes	characteristic
430	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
431	C₄	C₅×#914	1	1	yes	characteristic
432	C₃	C₅×#1639	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	8	2	no	—
434	C₂	—	12	2	no	—
435	C₂	—	12	2	no	—
436	C₂	C₅×#5061	1	1	yes	characteristic
437	C₂	C₅×#5156	1	1	yes	characteristic
438	C₂	C₅×#5169	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#486	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5717	C₂
hypercenter	C₅×#486	D₃
hypocenter	C₃	C₅×#1639
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#486

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#486	C₂	semidirect
3. C₅×#5087	C₂	semidirect
4. C₅×#5083	C₂	semidirect
5. C₅×#4544	C₂	semidirect
6. C₅×#4459	C₂	semidirect
7. C₅×#4459	C₂	semidirect
11. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₄×C₅×C₈	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
26. #71198	C₅	direct (N × H)
28. C₅×#486	D₃	semidirect
62. C₃×#486	C₂×C₅	semidirect
63. #5087	C₂×C₅	semidirect
64. #5083	C₂×C₅	semidirect
65. #4544	C₂×C₅	semidirect
66. #4459	C₂×C₅	semidirect
67. #4459	C₂×C₅	semidirect
71. C₅×C₄⋊Q₈	C₂×D₃	semidirect
84. C₄×C₅×C₈	C₂×D₃	semidirect
110. C₅×D₁₂	SD₁₆	semidirect
120. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
129. C₃×C₄×C₈	C₂²×C₅	semidirect
133. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
134. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
163. #486	C₅×D₃	semidirect
250. C₄⋊Q₈	C₂×C₅×D₃	semidirect
263. C₄×C₈	C₂×C₅×D₃	semidirect
294. D₁₂	C₅×SD₁₆	semidirect
348. C₃×C₅	#1639	semidirect
412. C₅	#71198	direct (N × H)
432. C₃	C₅×#1639	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5717	2
C₃×C₅×#486	2
C₅×#5087	2
C₅×#5083	2
C₅×#4544	2
C₅×#4459	2
C₅×#1639	3
#71198	5

Subgroups — C5×#71198 #14289871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71198 #14289871