Subgroups — C₅×#79895 #14458230

Order 1920.

888 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5771	C₂	1	2	yes	maximal, complemented
2	C₅×#5753	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5143	C₂	1	2	yes	maximal, complemented
5	C₅×#4896	C₂	1	2	yes	maximal, complemented
6	C₅×#4826	C₂	1	4	yes	maximal, complemented
7	C₅×#4700	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4699	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3293	—	3	1	no	maximal, Hall
10	C₅×#1010	C₂²	1	4	yes	—
11	C₃×C₅×#135	C₂²	1	1	yes	characteristic
12	C₃×C₅×#131	C₂²	1	2	yes	—
13	C₅×#951	C₂²	1	4	yes	—
14	C₅×D₃×Q₁₆	—	2	2	no	—
15	C₅×#915	—	2	4	no	—
16	C₅×#912	—	2	2	no	—
17	C₅×#909	—	2	4	no	—
18	C₅×#909	C₂²	1	4	yes	—
19	C₂×C₅×Dic₁₂	—	2	2	no	—
20	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
21	C₂×C₅×Dic₁₂	C₂²	1	2	yes	—
22	C₅×#904	—	2	2	no	—
23	C₅×#904	C₂²	1	1	yes	characteristic
24	C₅×#901	C₂²	1	2	yes	—
25	C₅×#869	C₂²	1	2	yes	—
26	C₃×C₅×#108	C₂²	1	1	yes	characteristic
27	C₃×C₅×#104	C₂²	1	2	yes	—
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₅×#824	C₂²	1	4	yes	—
30	C₅×#819	C₂²	1	1	yes	characteristic
31	C₅×#805	C₂²	1	2	yes	—
32	#79895	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#578	—	3	2	no	—
34	C₅×#578	—	3	2	no	—
35	C₅×#494	—	3	1	no	—
36	C₅×#473	—	3	2	no	—
37	C₅×#473	—	3	2	no	—
38	C₅×#456	—	3	4	no	—
39	C₅×#443	—	3	1	no	—
40	C₅×#443	D₃	1	1	yes	characteristic, complemented
41	C₃×C₅×#41	C₂³	1	2	yes	—
42	C₅×D₃×Q₈	—	2	4	no	—
43	C₅×#237	—	2	4	no	—
44	C₅×#237	—	4	4	no	—
45	C₅×#235	—	2	4	no	—
46	C₅×#235	C₂³	1	2	yes	—
47	C₂×C₅×Dic₆	—	2	4	no	—
48	C₂×C₅×Dic₆	C₂³	1	4	yes	—
49	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic
50	C₃×C₅×SD₁₆	D₄	1	2	yes	—
51	C₃×C₅×D₈	D₄	1	1	yes	characteristic
52	C₃×C₅×M₁₆	—	2	2	no	—
53	C₃×C₅×M₁₆	C₂³	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₅×#216	—	2	4	no	—
59	C₅×#214	—	2	4	no	—
60	C₅×C₄⋊Dic₃	—	4	2	no	—
61	C₅×#208	C₂³	1	2	yes	—
62	C₅×Dic₁₂	—	2	4	no	—
63	C₅×Dic₁₂	—	2	2	no	—
64	C₅×Dic₁₂	—	2	2	no	—
65	C₅×Dic₁₂	—	2	2	no	—
66	C₅×Dic₁₂	—	2	2	no	—
67	C₅×Dic₁₂	D₄	1	1	yes	characteristic
68	C₅×D₂₄	D₄	1	1	yes	characteristic
69	C₅×#204	—	2	4	no	—
70	C₅×#204	D₄	1	2	yes	—
71	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
72	C₅×D₃×C₈	—	2	2	no	—
73	#5771	C₂×C₅	1	2	yes	complemented
74	#5753	C₂×C₅	1	2	yes	complemented
75	C₃×#443	C₂×C₅	1	1	yes	characteristic, complemented
76	#5143	C₂×C₅	1	2	yes	complemented
77	#4896	C₂×C₅	1	2	yes	complemented
78	#4826	C₂×C₅	1	4	yes	complemented
79	#4700	C₂×C₅	1	1	yes	characteristic, complemented
80	#4699	C₂×C₅	1	1	yes	characteristic, complemented
81	C₅×2₋¹⁺⁴	—	3	4	no	—
82	C₅×#137	—	3	4	no	—
83	C₅×#137	—	3	4	no	—
84	C₅×#137	—	6	4	no	—
85	C₅×#137	—	6	4	no	—
86	C₅×#135	—	3	1	no	—
87	C₅×#135	—	6	2	no	—
88	C₅×#135	—	6	2	no	—
89	C₅×#135	C₂×D₃	1	1	yes	characteristic
90	C₂×C₅×Q₁₆	—	3	2	no	—
91	C₂×C₅×Q₁₆	—	3	2	no	—
92	C₂×C₅×Q₁₆	—	6	2	no	—
93	C₂×C₅×Q₁₆	—	6	2	no	—
94	C₅×#131	—	3	2	no	—
95	C₅×#131	C₂×D₃	1	2	yes	—
96	C₅×C₄⋊Q₈	—	3	2	no	—
97	C₅×#108	—	3	1	no	—
98	C₅×#108	C₂×D₃	1	1	yes	characteristic
99	C₅×#104	—	3	2	no	—
100	C₅×#104	C₂×D₃	1	2	yes	—
101	C₅×#101	—	3	4	no	—
102	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
103	#3293	—	3	1	no	Sylow
104	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
105	C₃×C₅×D₄	—	2	2	no	—
106	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₅×#67	—	2	2	no	—
111	C₅×#67	—	4	4	no	—
112	C₂×C₅×Dic₃	—	2	4	no	—
113	C₂×C₅×Dic₃	—	4	4	no	—
114	C₅×D₁₂	C₂×D₄	1	2	yes	—
115	C₄×C₅×D₃	—	2	2	no	—
116	C₄×C₅×D₃	—	4	4	no	—
117	C₅×Dic₆	—	2	4	no	—
118	C₅×Dic₆	—	2	4	no	—
119	C₅×Dic₆	—	4	4	no	—
120	C₅×Dic₆	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
123	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
124	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
125	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₅×C₃⋊C₈	—	2	2	no	—
127	#1010	C₂²×C₅	1	4	yes	—
128	C₃×#135	C₂²×C₅	1	1	yes	characteristic
129	C₃×#131	C₂²×C₅	1	2	yes	—
130	#951	C₂²×C₅	1	4	yes	—
131	D₃×Q₁₆	—	2	2	no	—
132	#915	—	2	4	no	—
133	#912	—	2	2	no	—
134	#909	—	2	4	no	—
135	#909	C₂²×C₅	1	4	yes	—
136	C₂×Dic₁₂	—	2	2	no	—
137	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
138	C₂×Dic₁₂	C₂²×C₅	1	2	yes	—
139	#904	—	2	2	no	—
140	#904	C₂²×C₅	1	1	yes	characteristic
141	#901	C₂²×C₅	1	2	yes	—
142	#869	C₂²×C₅	1	2	yes	—
143	C₃×#108	C₂²×C₅	1	1	yes	characteristic
144	C₃×#104	C₂²×C₅	1	2	yes	—
145	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
146	#824	C₂²×C₅	1	4	yes	—
147	#819	C₂²×C₅	1	1	yes	characteristic
148	#805	C₂²×C₅	1	2	yes	—
149	C₅×#41	—	3	2	no	—
150	C₅×#41	—	6	4	no	—
151	C₅×#41	—	6	4	no	—
152	C₅×#41	—	12	4	no	—
153	C₅×#41	C₂²×D₃	1	2	yes	—
154	C₂×C₅×Q₈	—	3	4	no	—
155	C₂×C₅×Q₈	—	6	4	no	—
156	C₂×C₅×Q₈	—	6	4	no	—
157	C₅×Q₁₆	—	3	1	no	—
158	C₅×Q₁₆	—	6	4	no	—
159	C₅×Q₁₆	—	6	4	no	—
160	C₅×Q₁₆	—	6	2	no	—
161	C₅×Q₁₆	—	6	2	no	—
162	C₅×Q₁₆	—	6	2	no	—
163	C₅×Q₁₆	—	6	2	no	—
164	C₅×Q₁₆	D₁₂	1	1	yes	characteristic
165	C₅×SD₁₆	—	3	2	no	—
166	C₅×SD₁₆	—	6	4	no	—
167	C₅×SD₁₆	—	6	4	no	—
168	C₅×SD₁₆	D₁₂	1	2	yes	—
169	C₅×D₈	—	3	1	no	—
170	C₅×D₈	D₁₂	1	1	yes	characteristic
171	C₅×M₁₆	—	2	2	no	—
172	C₅×M₁₆	—	3	2	no	—
173	C₅×M₁₆	—	6	2	no	—
174	C₅×M₁₆	C₂²×D₃	1	2	yes	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	6	2	no	—
177	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
179	C₅×C₄⋊C₄	—	12	2	no	—
180	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
181	#578	—	3	2	no	—
182	#578	—	3	2	no	—
183	#494	—	3	1	no	—
184	#473	—	3	2	no	—
185	#473	—	3	2	no	—
186	#456	—	3	4	no	—
187	#443	—	3	1	no	—
188	#443	C₅×D₃	1	1	yes	characteristic, complemented
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₅×D₃	—	2	2	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	—	2	2	no	—
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₅×Dic₃	—	2	2	no	—
197	C₅×Dic₃	—	4	4	no	—
198	C₃×#41	C₂³×C₅	1	2	yes	—
199	D₃×Q₈	—	2	4	no	—
200	#237	—	2	4	no	—
201	#237	—	4	4	no	—
202	#235	—	2	4	no	—
203	#235	C₂³×C₅	1	2	yes	—
204	C₂×Dic₆	—	2	4	no	—
205	C₂×Dic₆	C₂³×C₅	1	4	yes	—
206	C₃×Q₁₆	C₅×D₄	1	1	yes	characteristic
207	C₃×SD₁₆	C₅×D₄	1	2	yes	—
208	C₃×D₈	C₅×D₄	1	1	yes	characteristic
209	C₃×M₁₆	—	2	2	no	—
210	C₃×M₁₆	C₂³×C₅	1	2	yes	—
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
213	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
214	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
215	#216	—	2	4	no	—
216	#214	—	2	4	no	—
217	C₄⋊Dic₃	—	4	2	no	—
218	#208	C₂³×C₅	1	2	yes	—
219	Dic₁₂	—	2	4	no	—
220	Dic₁₂	—	2	2	no	—
221	Dic₁₂	—	2	2	no	—
222	Dic₁₂	—	2	2	no	—
223	Dic₁₂	—	2	2	no	—
224	Dic₁₂	C₅×D₄	1	1	yes	characteristic
225	D₂₄	C₅×D₄	1	1	yes	characteristic
226	#204	—	2	4	no	—
227	#204	C₅×D₄	1	2	yes	—
228	ΓL(1,𝔽₂₅)	—	2	2	no	—
229	D₃×C₈	—	2	2	no	—
230	C₅×Q₈	—	3	2	no	—
231	C₅×Q₈	—	6	4	no	—
232	C₅×Q₈	—	6	4	no	—
233	C₅×Q₈	—	12	4	no	—
234	C₅×Q₈	C₂×D₁₂	1	2	yes	—
235	C₅×D₄	—	2	2	no	—
236	C₅×D₄	—	3	2	no	—
237	C₅×D₄	—	6	2	no	—
238	C₅×D₄	—	12	4	no	—
239	C₅×D₄	C₂×D₁₂	1	2	yes	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	4	no	—
244	C₂×C₄×C₅	—	12	4	no	—
245	C₂×C₄×C₅	—	12	4	no	—
246	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
247	C₅×C₈	—	2	2	no	—
248	C₅×C₈	—	6	2	no	—
249	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
250	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
251	C₅×C₈	D₃×D₄	1	1	yes	characteristic
252	C₅×C₈	D₃×D₄	1	1	yes	characteristic
253	2₋¹⁺⁴	—	3	4	no	—
254	#137	—	3	4	no	—
255	#137	—	3	4	no	—
256	#137	—	6	4	no	—
257	#137	—	6	4	no	—
258	#135	—	3	1	no	—
259	#135	—	6	2	no	—
260	#135	—	6	2	no	—
261	#135	C₂×C₅×D₃	1	1	yes	characteristic
262	C₂×Q₁₆	—	3	2	no	—
263	C₂×Q₁₆	—	3	2	no	—
264	C₂×Q₁₆	—	6	2	no	—
265	C₂×Q₁₆	—	6	2	no	—
266	#131	—	3	2	no	—
267	#131	C₂×C₅×D₃	1	2	yes	—
268	C₄⋊Q₈	—	3	2	no	—
269	#108	—	3	1	no	—
270	#108	C₂×C₅×D₃	1	1	yes	characteristic
271	#104	—	3	2	no	—
272	#104	C₂×C₅×D₃	1	2	yes	—
273	#101	—	3	4	no	—
274	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂×C₃×C₅	—	2	1	no	—
276	C₂×C₃×C₅	—	4	2	no	—
277	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
278	C₅×D₃	—	4	2	no	—
279	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
285	#67	—	2	2	no	—
286	#67	—	4	4	no	—
287	C₂×Dic₃	—	2	4	no	—
288	C₂×Dic₃	—	4	4	no	—
289	D₁₂	C₂×C₅×D₄	1	2	yes	—
290	C₄×D₃	—	2	2	no	—
291	C₄×D₃	—	4	4	no	—
292	Dic₆	—	2	4	no	—
293	Dic₆	—	2	4	no	—
294	Dic₆	—	4	4	no	—
295	Dic₆	C₂×C₅×D₄	1	2	yes	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
298	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
299	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
300	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
301	C₃⋊C₈	—	2	2	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	6	2	no	—
304	C₂²×C₅	#1009	1	1	yes	characteristic
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	6	2	no	—
308	C₄×C₅	—	12	4	no	—
309	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
310	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
311	#41	—	3	2	no	—
312	#41	—	6	4	no	—
313	#41	—	6	4	no	—
314	#41	—	12	4	no	—
315	#41	C₂²×C₅×D₃	1	2	yes	—
316	C₂×Q₈	—	3	4	no	—
317	C₂×Q₈	—	6	4	no	—
318	C₂×Q₈	—	6	4	no	—
319	Q₁₆	—	3	1	no	—
320	Q₁₆	—	6	4	no	—
321	Q₁₆	—	6	4	no	—
322	Q₁₆	—	6	2	no	—
323	Q₁₆	—	6	2	no	—
324	Q₁₆	—	6	2	no	—
325	Q₁₆	—	6	2	no	—
326	Q₁₆	C₅×D₁₂	1	1	yes	characteristic
327	SD₁₆	—	3	2	no	—
328	SD₁₆	—	6	4	no	—
329	SD₁₆	—	6	4	no	—
330	SD₁₆	C₅×D₁₂	1	2	yes	—
331	D₈	—	3	1	no	—
332	D₈	C₅×D₁₂	1	1	yes	characteristic
333	M₁₆	—	2	2	no	—
334	M₁₆	—	3	2	no	—
335	M₁₆	—	6	2	no	—
336	M₁₆	C₂²×C₅×D₃	1	2	yes	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	6	2	no	—
339	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
340	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
341	C₄⋊C₄	—	12	2	no	—
342	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
343	C₃×C₅	#3293	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×D₃	—	2	2	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
350	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
351	Dic₃	—	2	2	no	—
352	Dic₃	—	4	4	no	—
353	C₂×C₅	—	2	1	no	—
354	C₂×C₅	—	4	2	no	—
355	C₂×C₅	—	12	2	no	—
356	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
357	Q₈	—	3	2	no	—
358	Q₈	—	6	4	no	—
359	Q₈	—	6	4	no	—
360	Q₈	—	12	4	no	—
361	Q₈	C₂×C₅×D₁₂	1	2	yes	—
362	D₄	—	2	2	no	—
363	D₄	—	3	2	no	—
364	D₄	—	6	2	no	—
365	D₄	—	12	4	no	—
366	D₄	C₂×C₅×D₁₂	1	2	yes	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	6	2	no	—
370	C₂×C₄	—	6	4	no	—
371	C₂×C₄	—	12	4	no	—
372	C₂×C₄	—	12	4	no	—
373	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	6	2	no	—
376	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
377	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
378	C₈	C₅×D₃×D₄	1	1	yes	characteristic
379	C₈	C₅×D₃×D₄	1	1	yes	characteristic
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
383	D₃	—	4	2	no	—
384	C₅	#79895	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	2	2	no	—
386	C₂²	—	6	2	no	—
387	C₂²	C₅×#1009	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	6	2	no	—
391	C₄	—	12	4	no	—
392	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
393	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
394	C₃	C₅×#3293	1	1	yes	characteristic, complemented, Sylow
395	C₂	—	2	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	12	2	no	—
398	C₂	C₅×D₄×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₄×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#443	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#443	D₃
hypocenter	C₃	C₅×#3293
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#443

Complements

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

N	H ≅ G/N	type
1. C₅×#5771	C₂	semidirect
2. C₅×#5753	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₅×#5143	C₂	semidirect
5. C₅×#4896	C₂	semidirect
6. C₅×#4826	C₂	semidirect
7. C₅×#4700	C₂	semidirect
8. C₅×#4699	C₂	semidirect
32. #79895	C₅	direct (N × H)
40. C₅×#443	D₃	semidirect
73. #5771	C₂×C₅	semidirect
74. #5753	C₂×C₅	semidirect
75. C₃×#443	C₂×C₅	semidirect
76. #5143	C₂×C₅	semidirect
77. #4896	C₂×C₅	semidirect
78. #4826	C₂×C₅	semidirect
79. #4700	C₂×C₅	semidirect
80. #4699	C₂×C₅	semidirect
188. #443	C₅×D₃	semidirect
343. C₃×C₅	#3293	semidirect
384. C₅	#79895	direct (N × H)
394. C₃	C₅×#3293	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5771	2
C₅×#5753	2
C₃×C₅×#443	2
C₅×#5143	2
C₅×#4896	2
C₅×#4826	2
C₅×#4700	2
C₅×#4699	2
C₅×#3293	3
#79895	5

Subgroups — C5×#79895 #14458230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79895 #14458230