Subgroups — C₅×#79894 #14458176

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5769	C₂	1	2	yes	maximal, complemented
2	C₅×#5752	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5142	C₂	1	2	yes	maximal, complemented
5	C₅×#4897	C₂	1	2	yes	maximal, complemented
6	C₅×#4822	C₂	1	4	yes	maximal, complemented
7	C₅×#4700	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4695	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3292	—	3	1	no	maximal, Hall
10	C₅×#1009	C₂²	1	4	yes	complemented
11	C₃×C₅×#135	C₂²	1	1	yes	characteristic
12	C₃×C₅×#131	C₂²	1	2	yes	complemented
13	C₅×#949	C₂²	1	4	yes	complemented
14	C₅×#919	—	2	2	no	—
15	C₅×#914	—	2	4	no	—
16	C₅×D₃×D₈	—	2	2	no	—
17	C₅×#908	—	2	4	no	—
18	C₅×#908	C₂²	1	4	yes	complemented
19	C₅×#904	—	2	2	no	—
20	C₅×#904	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₂₄	—	2	2	no	—
22	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
23	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
24	C₅×#901	C₂²	1	2	yes	complemented
25	C₅×#874	C₂²	1	2	yes	complemented
26	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#104	C₂²	1	2	yes	complemented
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
29	C₅×#823	C₂²	1	4	yes	complemented
30	C₅×#819	C₂²	1	1	yes	characteristic, complemented
31	C₅×#805	C₂²	1	2	yes	complemented
32	#79894	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#576	—	3	2	no	—
34	C₅×#576	—	3	2	no	—
35	C₅×#493	—	3	1	no	—
36	C₅×#472	—	3	2	no	—
37	C₅×#472	—	3	2	no	—
38	C₅×#453	—	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×#239	—	2	4	no	—
43	C₅×D₃×D₄	—	2	4	no	—
44	C₅×D₃×D₄	—	4	4	no	—
45	C₅×#235	—	2	4	no	—
46	C₅×#235	C₂³	1	2	yes	—
47	C₂×C₅×D₁₂	—	2	4	no	—
48	C₂×C₅×D₁₂	—	4	2	no	—
49	C₂×C₅×D₁₂	C₂³	1	4	yes	—
50	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic, complemented
51	C₃×C₅×SD₁₆	D₄	1	2	yes	complemented
52	C₃×C₅×D₈	D₄	1	1	yes	characteristic, complemented
53	C₃×C₅×M₁₆	—	2	2	no	—
54	C₃×C₅×M₁₆	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₅×#215	—	2	4	no	—
60	C₅×#213	—	2	4	no	—
61	C₅×#208	C₂³	1	2	yes	—
62	C₅×Dic₁₂	D₄	1	1	yes	characteristic, complemented
63	C₅×D₂₄	—	2	4	no	—
64	C₅×D₂₄	—	2	2	no	—
65	C₅×D₂₄	—	2	2	no	—
66	C₅×D₂₄	—	2	2	no	—
67	C₅×D₂₄	—	2	2	no	—
68	C₅×D₂₄	D₄	1	1	yes	characteristic, complemented
69	C₅×#204	—	2	4	no	—
70	C₅×#204	D₄	1	2	yes	complemented
71	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
72	C₅×D₃×C₈	—	2	2	no	—
73	#5769	C₂×C₅	1	2	yes	complemented
74	#5752	C₂×C₅	1	2	yes	complemented
75	C₃×#443	C₂×C₅	1	1	yes	characteristic, complemented
76	#5142	C₂×C₅	1	2	yes	complemented
77	#4897	C₂×C₅	1	2	yes	complemented
78	#4822	C₂×C₅	1	4	yes	complemented
79	#4700	C₂×C₅	1	1	yes	characteristic, complemented
80	#4695	C₂×C₅	1	1	yes	characteristic, complemented
81	C₅×H(5,𝔽₂)	—	3	4	no	—
82	C₅×AGL(1,ℤ/8)	—	3	4	no	—
83	C₅×AGL(1,ℤ/8)	—	3	4	no	—
84	C₅×AGL(1,ℤ/8)	—	6	4	no	—
85	C₅×AGL(1,ℤ/8)	—	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×D₈	—	3	2	no	—
91	C₂×C₅×D₈	—	3	2	no	—
92	C₂×C₅×D₈	—	6	2	no	—
93	C₂×C₅×D₈	—	6	2	no	—
94	C₅×#131	—	3	2	no	—
95	C₅×#131	C₂×D₃	1	2	yes	complemented
96	C₅×#127	—	3	2	no	—
97	C₅×#108	—	3	1	no	—
98	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
99	C₅×#104	—	3	2	no	—
100	C₅×#104	C₂×D₃	1	2	yes	complemented
101	C₅×#100	—	3	4	no	—
102	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
103	#3292	—	3	1	no	Sylow
104	C₂²×C₅×D₃	—	2	4	no	—
105	C₂²×C₅×D₃	—	4	4	no	—
106	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	—	2	1	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	—	2	2	no	—
113	C₅×#67	—	4	4	no	—
114	C₅×D₁₂	—	2	4	no	—
115	C₅×D₁₂	—	2	4	no	—
116	C₅×D₁₂	—	4	4	no	—
117	C₅×D₁₂	—	8	4	no	—
118	C₅×D₁₂	C₂×D₄	1	2	yes	—
119	C₄×C₅×D₃	—	2	2	no	—
120	C₄×C₅×D₃	—	4	4	no	—
121	C₅×Dic₆	C₂×D₄	1	2	yes	—
122	C₃×C₅×C₈	—	2	2	no	—
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	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₅×C₃⋊C₈	—	2	2	no	—
128	#1009	C₂²×C₅	1	4	yes	complemented
129	C₃×#135	C₂²×C₅	1	1	yes	characteristic
130	C₃×#131	C₂²×C₅	1	2	yes	complemented
131	#949	C₂²×C₅	1	4	yes	complemented
132	#919	—	2	2	no	—
133	#914	—	2	4	no	—
134	D₃×D₈	—	2	2	no	—
135	#908	—	2	4	no	—
136	#908	C₂²×C₅	1	4	yes	complemented
137	#904	—	2	2	no	—
138	#904	C₂²×C₅	1	1	yes	characteristic
139	C₂×D₂₄	—	2	2	no	—
140	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
141	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
142	#901	C₂²×C₅	1	2	yes	complemented
143	#874	C₂²×C₅	1	2	yes	complemented
144	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₃×#104	C₂²×C₅	1	2	yes	complemented
146	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
147	#823	C₂²×C₅	1	4	yes	complemented
148	#819	C₂²×C₅	1	1	yes	characteristic, complemented
149	#805	C₂²×C₅	1	2	yes	complemented
150	C₅×#41	—	3	2	no	—
151	C₅×#41	—	6	4	no	—
152	C₅×#41	—	6	4	no	—
153	C₅×#41	C₂²×D₃	1	2	yes	—
154	C₂×C₅×D₄	—	3	4	no	—
155	C₂×C₅×D₄	—	6	4	no	—
156	C₂×C₅×D₄	—	6	4	no	—
157	C₂×C₅×D₄	—	12	2	no	—
158	C₂×C₅×D₄	—	12	4	no	—
159	C₅×Q₁₆	—	3	1	no	—
160	C₅×Q₁₆	D₁₂	1	1	yes	characteristic, complemented
161	C₅×SD₁₆	—	3	2	no	—
162	C₅×SD₁₆	—	6	4	no	—
163	C₅×SD₁₆	—	6	4	no	—
164	C₅×SD₁₆	D₁₂	1	2	yes	complemented
165	C₅×D₈	—	3	1	no	—
166	C₅×D₈	—	6	4	no	—
167	C₅×D₈	—	6	4	no	—
168	C₅×D₈	—	6	2	no	—
169	C₅×D₈	—	6	2	no	—
170	C₅×D₈	—	6	2	no	—
171	C₅×D₈	—	6	2	no	—
172	C₅×D₈	D₁₂	1	1	yes	characteristic, complemented
173	C₅×M₁₆	—	2	2	no	—
174	C₅×M₁₆	—	3	2	no	—
175	C₅×M₁₆	—	6	2	no	—
176	C₅×M₁₆	C₂²×D₃	1	2	yes	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	6	2	no	—
179	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
181	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
182	#576	—	3	2	no	—
183	#576	—	3	2	no	—
184	#493	—	3	1	no	—
185	#472	—	3	2	no	—
186	#472	—	3	2	no	—
187	#453	—	3	4	no	—
188	#443	—	3	1	no	—
189	#443	C₅×D₃	1	1	yes	characteristic, complemented
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₅×D₃	—	2	2	no	—
193	C₂×C₅×D₃	—	4	4	no	—
194	C₂×C₅×D₃	—	8	4	no	—
195	C₂×C₅×D₃	—	16	4	no	—
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₅×Dic₃	—	2	2	no	—
201	C₃×#41	C₂³×C₅	1	2	yes	—
202	#239	—	2	4	no	—
203	D₃×D₄	—	2	4	no	—
204	D₃×D₄	—	4	4	no	—
205	#235	—	2	4	no	—
206	#235	C₂³×C₅	1	2	yes	—
207	C₂×D₁₂	—	2	4	no	—
208	C₂×D₁₂	—	4	2	no	—
209	C₂×D₁₂	C₂³×C₅	1	4	yes	—
210	C₃×Q₁₆	C₅×D₄	1	1	yes	characteristic, complemented
211	C₃×SD₁₆	C₅×D₄	1	2	yes	complemented
212	C₃×D₈	C₅×D₄	1	1	yes	characteristic, complemented
213	C₃×M₁₆	—	2	2	no	—
214	C₃×M₁₆	C₂³×C₅	1	2	yes	—
215	C₂×C₃×C₈	—	2	2	no	—
216	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
219	#215	—	2	4	no	—
220	#213	—	2	4	no	—
221	#208	C₂³×C₅	1	2	yes	—
222	Dic₁₂	C₅×D₄	1	1	yes	characteristic, complemented
223	D₂₄	—	2	4	no	—
224	D₂₄	—	2	2	no	—
225	D₂₄	—	2	2	no	—
226	D₂₄	—	2	2	no	—
227	D₂₄	—	2	2	no	—
228	D₂₄	C₅×D₄	1	1	yes	characteristic, complemented
229	#204	—	2	4	no	—
230	#204	C₅×D₄	1	2	yes	complemented
231	ΓL(1,𝔽₂₅)	—	2	2	no	—
232	D₃×C₈	—	2	2	no	—
233	C₂³×C₅	—	6	4	no	—
234	C₂³×C₅	—	12	4	no	—
235	C₅×Q₈	—	3	2	no	—
236	C₅×Q₈	C₂×D₁₂	1	2	yes	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	3	2	no	—
239	C₅×D₄	—	6	2	no	—
240	C₅×D₄	—	6	4	no	—
241	C₅×D₄	—	6	4	no	—
242	C₅×D₄	—	12	4	no	—
243	C₅×D₄	—	12	4	no	—
244	C₅×D₄	—	24	4	no	—
245	C₅×D₄	C₂×D₁₂	1	2	yes	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	12	4	no	—
250	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	6	2	no	—
253	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
254	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
255	C₅×C₈	D₃×D₄	1	1	yes	characteristic
256	C₅×C₈	D₃×D₄	1	1	yes	characteristic
257	H(5,𝔽₂)	—	3	4	no	—
258	AGL(1,ℤ/8)	—	3	4	no	—
259	AGL(1,ℤ/8)	—	3	4	no	—
260	AGL(1,ℤ/8)	—	6	4	no	—
261	AGL(1,ℤ/8)	—	6	4	no	—
262	#135	—	3	1	no	—
263	#135	—	6	2	no	—
264	#135	—	6	2	no	—
265	#135	C₂×C₅×D₃	1	1	yes	characteristic
266	C₂×D₈	—	3	2	no	—
267	C₂×D₈	—	3	2	no	—
268	C₂×D₈	—	6	2	no	—
269	C₂×D₈	—	6	2	no	—
270	#131	—	3	2	no	—
271	#131	C₂×C₅×D₃	1	2	yes	complemented
272	#127	—	3	2	no	—
273	#108	—	3	1	no	—
274	#108	C₂×C₅×D₃	1	1	yes	characteristic, complemented
275	#104	—	3	2	no	—
276	#104	C₂×C₅×D₃	1	2	yes	complemented
277	#100	—	3	4	no	—
278	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
279	C₂×C₃×C₅	—	2	1	no	—
280	C₂×C₃×C₅	—	4	2	no	—
281	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
282	C₅×D₃	—	4	2	no	—
283	C₅×D₃	—	8	4	no	—
284	C₂²×D₃	—	2	4	no	—
285	C₂²×D₃	—	4	4	no	—
286	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
292	#67	—	2	2	no	—
293	#67	—	4	4	no	—
294	D₁₂	—	2	4	no	—
295	D₁₂	—	2	4	no	—
296	D₁₂	—	4	4	no	—
297	D₁₂	—	8	4	no	—
298	D₁₂	C₂×C₅×D₄	1	2	yes	—
299	C₄×D₃	—	2	2	no	—
300	C₄×D₃	—	4	4	no	—
301	Dic₆	C₂×C₅×D₄	1	2	yes	—
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
304	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
305	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
306	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
307	C₃⋊C₈	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	6	2	no	—
310	C₂²×C₅	—	12	4	no	—
311	C₂²×C₅	—	24	4	no	—
312	C₂²×C₅	—	48	4	no	—
313	C₂²×C₅	#1009	1	1	yes	characteristic
314	C₄×C₅	—	2	2	no	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	6	2	no	—
317	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
318	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
319	#41	—	3	2	no	—
320	#41	—	6	4	no	—
321	#41	—	6	4	no	—
322	#41	C₂²×C₅×D₃	1	2	yes	—
323	C₂×D₄	—	3	4	no	—
324	C₂×D₄	—	6	4	no	—
325	C₂×D₄	—	6	4	no	—
326	C₂×D₄	—	12	2	no	—
327	C₂×D₄	—	12	4	no	—
328	Q₁₆	—	3	1	no	—
329	Q₁₆	C₅×D₁₂	1	1	yes	characteristic, complemented
330	SD₁₆	—	3	2	no	—
331	SD₁₆	—	6	4	no	—
332	SD₁₆	—	6	4	no	—
333	SD₁₆	C₅×D₁₂	1	2	yes	complemented
334	D₈	—	3	1	no	—
335	D₈	—	6	4	no	—
336	D₈	—	6	4	no	—
337	D₈	—	6	2	no	—
338	D₈	—	6	2	no	—
339	D₈	—	6	2	no	—
340	D₈	—	6	2	no	—
341	D₈	C₅×D₁₂	1	1	yes	characteristic, complemented
342	M₁₆	—	2	2	no	—
343	M₁₆	—	3	2	no	—
344	M₁₆	—	6	2	no	—
345	M₁₆	C₂²×C₅×D₃	1	2	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	6	2	no	—
348	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
349	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
350	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
351	C₃×C₅	#3292	1	1	yes	characteristic, complemented, Hall
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×D₃	—	2	2	no	—
355	C₂×D₃	—	4	4	no	—
356	C₂×D₃	—	8	4	no	—
357	C₂×D₃	—	16	4	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
361	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
362	Dic₃	—	2	2	no	—
363	C₂×C₅	—	2	1	no	—
364	C₂×C₅	—	4	2	no	—
365	C₂×C₅	—	12	2	no	—
366	C₂×C₅	—	24	4	no	—
367	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
368	C₂³	—	6	4	no	—
369	C₂³	—	12	4	no	—
370	Q₈	—	3	2	no	—
371	Q₈	C₂×C₅×D₁₂	1	2	yes	—
372	D₄	—	2	2	no	—
373	D₄	—	3	2	no	—
374	D₄	—	6	2	no	—
375	D₄	—	6	4	no	—
376	D₄	—	6	4	no	—
377	D₄	—	12	4	no	—
378	D₄	—	12	4	no	—
379	D₄	—	24	4	no	—
380	D₄	C₂×C₅×D₁₂	1	2	yes	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	12	4	no	—
385	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	6	2	no	—
388	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
389	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
390	C₈	C₅×D₃×D₄	1	1	yes	characteristic
391	C₈	C₅×D₃×D₄	1	1	yes	characteristic
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
395	D₃	—	4	2	no	—
396	D₃	—	8	4	no	—
397	C₅	#79894	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	2	no	—
399	C₂²	—	6	2	no	—
400	C₂²	—	12	4	no	—
401	C₂²	—	24	4	no	—
402	C₂²	—	48	4	no	—
403	C₂²	C₅×#1009	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	6	2	no	—
407	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
408	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
409	C₃	C₅×#3292	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	4	2	no	—
412	C₂	—	12	2	no	—
413	C₂	—	24	4	no	—
414	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×#3292
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×#5769	C₂	semidirect
2. C₅×#5752	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₅×#5142	C₂	semidirect
5. C₅×#4897	C₂	semidirect
6. C₅×#4822	C₂	semidirect
7. C₅×#4700	C₂	semidirect
8. C₅×#4695	C₂	semidirect
10. C₅×#1009	C₂²	semidirect
12. C₃×C₅×#131	C₂²	semidirect
13. C₅×#949	C₂²	semidirect
18. C₅×#908	C₂²	semidirect
22. C₂×C₅×D₂₄	C₂²	semidirect
23. C₂×C₅×D₂₄	C₂²	semidirect
24. C₅×#901	C₂²	semidirect
25. C₅×#874	C₂²	semidirect
26. C₃×C₅×#108	C₂²	semidirect
27. C₃×C₅×#104	C₂²	semidirect
28. C₃×C₄×C₅×C₈	C₂²	semidirect
29. C₅×#823	C₂²	semidirect
30. C₅×#819	C₂²	semidirect
31. C₅×#805	C₂²	semidirect
32. #79894	C₅	direct (N × H)
40. C₅×#443	D₃	semidirect
50. C₃×C₅×Q₁₆	D₄	semidirect
51. C₃×C₅×SD₁₆	D₄	semidirect
52. C₃×C₅×D₈	D₄	semidirect
62. C₅×Dic₁₂	D₄	semidirect
68. C₅×D₂₄	D₄	semidirect
70. C₅×#204	D₄	semidirect
73. #5769	C₂×C₅	semidirect
74. #5752	C₂×C₅	semidirect
75. C₃×#443	C₂×C₅	semidirect
76. #5142	C₂×C₅	semidirect
77. #4897	C₂×C₅	semidirect
78. #4822	C₂×C₅	semidirect
79. #4700	C₂×C₅	semidirect
80. #4695	C₂×C₅	semidirect
95. C₅×#131	C₂×D₃	semidirect
98. C₅×#108	C₂×D₃	semidirect
100. C₅×#104	C₂×D₃	semidirect
102. C₄×C₅×C₈	C₂×D₃	semidirect
128. #1009	C₂²×C₅	semidirect
130. C₃×#131	C₂²×C₅	semidirect
131. #949	C₂²×C₅	semidirect
136. #908	C₂²×C₅	semidirect
140. C₂×D₂₄	C₂²×C₅	semidirect
141. C₂×D₂₄	C₂²×C₅	semidirect
142. #901	C₂²×C₅	semidirect
143. #874	C₂²×C₅	semidirect
144. C₃×#108	C₂²×C₅	semidirect
145. C₃×#104	C₂²×C₅	semidirect
146. C₃×C₄×C₈	C₂²×C₅	semidirect
147. #823	C₂²×C₅	semidirect
148. #819	C₂²×C₅	semidirect
149. #805	C₂²×C₅	semidirect
160. C₅×Q₁₆	D₁₂	semidirect
164. C₅×SD₁₆	D₁₂	semidirect
172. C₅×D₈	D₁₂	semidirect
189. #443	C₅×D₃	semidirect
210. C₃×Q₁₆	C₅×D₄	semidirect
211. C₃×SD₁₆	C₅×D₄	semidirect
212. C₃×D₈	C₅×D₄	semidirect
222. Dic₁₂	C₅×D₄	semidirect
228. D₂₄	C₅×D₄	semidirect
230. #204	C₅×D₄	semidirect
271. #131	C₂×C₅×D₃	semidirect
274. #108	C₂×C₅×D₃	semidirect
276. #104	C₂×C₅×D₃	semidirect
278. C₄×C₈	C₂×C₅×D₃	semidirect
329. Q₁₆	C₅×D₁₂	semidirect
333. SD₁₆	C₅×D₁₂	semidirect
341. D₈	C₅×D₁₂	semidirect
351. C₃×C₅	#3292	semidirect
397. C₅	#79894	direct (N × H)
409. C₃	C₅×#3292	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5769	2
C₅×#5752	2
C₃×C₅×#443	2
C₅×#5142	2
C₅×#4897	2
C₅×#4822	2
C₅×#4700	2
C₅×#4695	2
C₅×#3292	3
#79894	5

Subgroups — C5×#79894 #14458176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79894 #14458176