Subgroups — C₅×#66107 #13106927

Order 1600.

592 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4062	C₂	1	2	yes	maximal, complemented
7	C₅×#4061	C₂	1	2	yes	maximal, complemented
8	C₅×#4058	C₂	1	2	yes	maximal, complemented
9	C₅×#4057	C₂	1	2	yes	maximal, complemented
10	C₅×#4055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅²×#41	C₂²	1	1	yes	characteristic
13	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₅×C₂²⋊D₅	—	2	1	no	—
15	C₂²×C₅×Dic₅	—	2	1	no	—
16	C₅×#713	C₂²	1	1	yes	characteristic, complemented
17	C₅×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
18	C₅×#711	—	2	1	no	—
19	C₅×#711	—	2	1	no	—
20	C₅×#711	—	2	1	no	—
21	C₅×#711	C₂²	1	2	yes	—
22	C₅×#711	C₂²	1	1	yes	characteristic, complemented
23	C₅×#711	C₂²	1	2	yes	complemented
24	C₅×D₄×D₅	—	2	1	no	—
25	C₅×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
26	C₅×#709	—	2	1	no	—
27	C₅×#709	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₅	—	2	1	no	—
29	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
30	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
31	C₅²×SD₁₆	C₂²	1	2	yes	complemented
32	C₅²×D₈	C₂²	1	2	yes	complemented
33	C₅²×M₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₅×#689	C₂²	1	2	yes	complemented
35	C₅×#687	C₂²	1	2	yes	complemented
36	C₅×#687	C₂²	1	2	yes	complemented
37	C₅×#686	C₂²	1	2	yes	complemented
38	C₅×#681	C₂²	1	1	yes	characteristic, complemented
39	C₅×Dic₂₀	C₂²	1	2	yes	complemented
40	C₅×#677	C₂²	1	2	yes	complemented
41	C₅×#676	C₂²	1	2	yes	complemented
42	C₅×C₈×D₅	C₂²	1	2	yes	complemented
43	C₅×#575	—	5	1	no	maximal
44	#66107	C₅	1	1	yes	maximal, characteristic, direct product factor
45	C₂³×C₅²	—	2	1	no	—
46	C₂²×C₅×D₅	—	2	1	no	—
47	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
48	C₅²×Q₈	C₂³	1	1	yes	characteristic
49	C₅²×D₄	—	2	1	no	—
50	C₅²×D₄	—	2	1	no	—
51	C₅²×D₄	C₂³	1	1	yes	characteristic
52	C₅²×D₄	C₂³	1	2	yes	—
53	C₂×C₄×C₅²	—	2	1	no	—
54	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
55	C₅×C₂²⋊D₅	—	2	1	no	—
56	C₅×C₂²⋊D₅	—	2	1	no	—
57	C₅×C₂²⋊D₅	—	2	2	no	—
58	C₅×C₂²⋊D₅	—	2	2	no	—
59	C₅×C₂²⋊D₅	—	2	1	no	—
60	C₂×C₅×Dic₅	—	2	1	no	—
61	C₂×C₅×Dic₅	—	2	1	no	—
62	C₂×C₅×Dic₅	—	2	2	no	—
63	C₂×C₅×Dic₅	—	2	2	no	—
64	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
65	C₅×D₂₀	—	2	1	no	—
66	C₅×D₂₀	C₂³	1	1	yes	characteristic
67	C₄×C₅×D₅	—	2	1	no	—
68	C₄×C₅×D₅	—	2	1	no	—
69	C₄×C₅×D₅	—	2	1	no	—
70	C₄×C₅×D₅	D₄	1	1	yes	characteristic
71	C₄×C₅×D₅	D₄	1	1	yes	characteristic
72	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
74	C₅×Dic₁₀	—	2	1	no	—
75	C₅×Dic₁₀	—	2	1	no	—
76	C₅×Dic₁₀	C₂³	1	2	yes	—
77	C₅×Dic₁₀	C₂³	1	1	yes	characteristic
78	C₅²×C₈	C₂³	1	2	yes	—
79	C₅×#168	C₂³	1	2	yes	—
80	C₂×C₅×#41	—	5	1	no	—
81	C₂×C₅×#41	—	5	1	no	—
82	D₅×#41	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×#711	C₂×C₅	1	1	yes	characteristic, complemented
84	C₅×#137	—	5	1	no	—
85	C₅×#137	—	5	2	no	—
86	C₅×#137	—	5	1	no	—
87	C₅×AGL(1,ℤ/8)	—	2	2	no	—
88	C₅×AGL(1,ℤ/8)	—	5	1	no	—
89	C₅×AGL(1,ℤ/8)	—	5	2	no	—
90	C₅×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
91	C₅×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
92	C₅×#135	—	5	2	no	—
93	C₅×#135	—	5	2	no	—
94	C₂×C₅×M₁₆	—	5	1	no	—
95	#4097	C₂×C₅	1	1	yes	characteristic, complemented
96	#4078	C₂×C₅	1	1	yes	characteristic, complemented
97	#4062	C₂×C₅	1	2	yes	complemented
98	#4061	C₂×C₅	1	2	yes	complemented
99	#4058	C₂×C₅	1	2	yes	complemented
100	#4057	C₂×C₅	1	2	yes	complemented
101	#4055	C₂×C₅	1	1	yes	characteristic, complemented
102	D₅×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂²×C₅²	—	2	2	no	—
104	C₂²×C₅²	—	2	1	no	—
105	C₂²×C₅²	—	4	2	no	—
106	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
107	C₂×C₅×D₅	—	2	1	no	—
108	C₂×C₅×D₅	—	4	1	no	—
109	C₂×C₅×D₅	—	4	2	no	—
110	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
112	C₄×C₅²	—	2	1	no	—
113	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
114	C₄×C₅²	C₂⁴	1	1	yes	characteristic
115	C₅×Dic₅	—	2	1	no	—
116	C₅×Dic₅	—	2	2	no	—
117	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
118	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	5	1	no	—
121	C₅×#41	—	5	2	no	—
122	C₅×#41	—	5	1	no	—
123	C₅×#41	—	5	2	no	—
124	C₅×#41	—	5	1	no	—
125	C₅×#41	—	10	1	no	—
126	C₅×#41	—	10	1	no	—
127	C₅×#41	—	10	1	no	—
128	C₅×#41	—	10	1	no	—
129	C₅×#41	C₂×D₅	1	1	yes	characteristic
130	C₅×#41	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₅×Q₈	—	5	1	no	—
132	C₂×C₅×Q₈	—	5	1	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	5	1	no	—
135	C₂×C₅×D₄	—	10	1	no	—
136	C₂×C₅×D₄	—	10	1	no	—
137	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
138	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₂²×C₄×C₅	—	5	1	no	—
140	C₂²×C₄×C₅	—	10	1	no	—
141	C₂²×C₄×C₅	—	10	1	no	—
142	C₂×C₂²⋊D₅	—	2	1	no	—
143	C₂²×Dic₅	—	2	1	no	—
144	#713	C₂²×C₅	1	1	yes	characteristic, complemented
145	Q₈×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
146	#711	—	2	1	no	—
147	#711	—	2	1	no	—
148	#711	—	2	1	no	—
149	#711	C₂²×C₅	1	2	yes	—
150	#711	C₂²×C₅	1	2	yes	complemented
151	#711	C₂²×C₅	1	1	yes	characteristic, complemented
152	D₄×D₅	—	2	1	no	—
153	D₄×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
154	#709	—	2	1	no	—
155	#709	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄×D₅	—	2	1	no	—
157	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic
158	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₅×Q₁₆	—	5	2	no	—
160	C₅×Q₁₆	—	5	2	no	—
161	C₅×SD₁₆	—	2	4	no	—
162	C₅×SD₁₆	—	5	2	no	—
163	C₅×SD₁₆	—	5	2	no	—
164	C₅×SD₁₆	—	5	2	no	—
165	C₅×SD₁₆	C₂×D₅	1	2	yes	complemented
166	C₅×SD₁₆	C₂²×C₅	1	2	yes	complemented
167	C₅×D₈	—	2	4	no	—
168	C₅×D₈	—	5	2	no	—
169	C₅×D₈	C₂×D₅	1	2	yes	complemented
170	C₅×D₈	C₂²×C₅	1	2	yes	complemented
171	C₅×M₁₆	—	2	2	no	—
172	C₅×M₁₆	—	5	1	no	—
173	C₅×M₁₆	—	5	2	no	—
174	C₅×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
175	C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
176	C₂×C₅×C₈	—	5	2	no	—
177	#689	C₂²×C₅	1	2	yes	complemented
178	#687	C₂²×C₅	1	2	yes	complemented
179	#687	C₂²×C₅	1	2	yes	complemented
180	#686	C₂²×C₅	1	2	yes	complemented
181	#681	C₂²×C₅	1	1	yes	characteristic, complemented
182	Dic₂₀	C₂²×C₅	1	2	yes	complemented
183	#677	C₂²×C₅	1	2	yes	complemented
184	#676	C₂²×C₅	1	2	yes	complemented
185	C₈×D₅	C₂²×C₅	1	2	yes	complemented
186	#575	—	5	1	no	Sylow
187	C₂×C₅²	—	2	1	no	—
188	C₂×C₅²	—	4	1	no	—
189	C₂×C₅²	—	4	2	no	—
190	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
191	C₅×D₅	—	2	1	no	—
192	C₅×D₅	—	2	1	no	—
193	C₅×D₅	—	4	1	no	—
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	—	2	1	no	—
196	C₂³×C₅	—	4	2	no	—
197	C₂³×C₅	—	5	1	no	—
198	C₂³×C₅	—	10	1	no	—
199	C₂²×D₅	—	2	1	no	—
200	C₂²×D₅	C₅×D₄	1	1	yes	characteristic
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	5	2	no	—
203	C₅×Q₈	—	5	1	no	—
204	C₅×Q₈	—	10	1	no	—
205	C₅×Q₈	—	10	1	no	—
206	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
207	C₅×Q₈	C₂³×C₅	1	1	yes	characteristic
208	C₅×D₄	—	2	1	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	—	2	1	no	—
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	—	2	2	no	—
213	C₅×D₄	—	2	4	no	—
214	C₅×D₄	—	4	2	no	—
215	C₅×D₄	—	4	2	no	—
216	C₅×D₄	—	5	1	no	—
217	C₅×D₄	—	10	1	no	—
218	C₅×D₄	—	10	1	no	—
219	C₅×D₄	—	10	1	no	—
220	C₅×D₄	—	10	2	no	—
221	C₅×D₄	—	10	2	no	—
222	C₅×D₄	—	10	1	no	—
223	C₅×D₄	C₂²×D₅	1	2	yes	—
224	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
225	C₅×D₄	C₂³×C₅	1	2	yes	—
226	C₅×D₄	C₂³×C₅	1	1	yes	characteristic
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	4	2	no	—
231	C₂×C₄×C₅	—	5	1	no	—
232	C₂×C₄×C₅	—	5	1	no	—
233	C₂×C₄×C₅	—	5	1	no	—
234	C₂×C₄×C₅	—	5	1	no	—
235	C₂×C₄×C₅	—	5	1	no	—
236	C₂×C₄×C₅	—	10	1	no	—
237	C₂×C₄×C₅	—	10	1	no	—
238	C₂×C₄×C₅	—	10	1	no	—
239	C₂×C₄×C₅	—	10	2	no	—
240	C₂×C₄×C₅	—	10	2	no	—
241	C₂×C₄×C₅	—	10	1	no	—
242	C₂×C₄×C₅	—	10	1	no	—
243	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
245	C₂²⋊D₅	—	2	1	no	—
246	C₂²⋊D₅	—	2	1	no	—
247	C₂²⋊D₅	—	2	2	no	—
248	C₂²⋊D₅	—	2	2	no	—
249	C₂²⋊D₅	—	2	1	no	—
250	C₂×Dic₅	—	2	1	no	—
251	C₂×Dic₅	—	2	1	no	—
252	C₂×Dic₅	—	2	2	no	—
253	C₂×Dic₅	—	2	2	no	—
254	C₂×Dic₅	C₅×D₄	1	1	yes	characteristic
255	D₂₀	—	2	1	no	—
256	D₂₀	C₂³×C₅	1	1	yes	characteristic
257	C₄×D₅	—	2	1	no	—
258	C₄×D₅	—	2	1	no	—
259	C₄×D₅	—	2	1	no	—
260	C₄×D₅	C₅×D₄	1	1	yes	characteristic
261	C₄×D₅	C₅×D₄	1	1	yes	characteristic
262	C₄×D₅	C₂³×C₅	1	1	yes	characteristic
263	C₄×D₅	C₂³×C₅	1	1	yes	characteristic
264	Dic₁₀	—	2	1	no	—
265	Dic₁₀	—	2	1	no	—
266	Dic₁₀	C₂³×C₅	1	2	yes	—
267	Dic₁₀	C₂³×C₅	1	1	yes	characteristic
268	C₅×C₈	—	2	4	no	—
269	C₅×C₈	—	5	2	no	—
270	C₅×C₈	C₂²×D₅	1	2	yes	—
271	C₅×C₈	C₂³×C₅	1	2	yes	—
272	#168	C₂³×C₅	1	2	yes	—
273	C₂×#41	—	5	1	no	—
274	C₂×#41	—	5	1	no	—
275	#137	—	5	1	no	—
276	#137	—	5	2	no	—
277	#137	—	5	1	no	—
278	AGL(1,ℤ/8)	—	5	1	no	—
279	AGL(1,ℤ/8)	—	5	2	no	—
280	AGL(1,ℤ/8)	C₅×D₅	1	1	yes	characteristic, complemented
281	#135	—	5	2	no	—
282	#135	—	5	2	no	—
283	C₂×M₁₆	—	5	1	no	—
284	C₅²	#575	1	1	yes	characteristic, complemented, Sylow
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	2	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	—	4	4	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	5	1	no	—
295	C₂²×C₅	—	5	1	no	—
296	C₂²×C₅	—	8	4	no	—
297	C₂²×C₅	—	10	1	no	—
298	C₂²×C₅	—	20	1	no	—
299	C₂²×C₅	—	20	2	no	—
300	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
301	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×D₅	—	2	1	no	—
303	C₂×D₅	—	4	1	no	—
304	C₂×D₅	—	4	2	no	—
305	C₂×D₅	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×D₅	C₂×C₅×D₄	1	1	yes	characteristic
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	5	1	no	—
313	C₄×C₅	—	5	1	no	—
314	C₄×C₅	—	10	1	no	—
315	C₄×C₅	—	10	2	no	—
316	C₄×C₅	D₄×D₅	1	1	yes	characteristic
317	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
318	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
319	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
320	Dic₅	—	2	1	no	—
321	Dic₅	—	2	2	no	—
322	Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
323	Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
324	#41	—	5	1	no	—
325	#41	—	5	2	no	—
326	#41	—	5	1	no	—
327	#41	—	5	2	no	—
328	#41	—	5	1	no	—
329	#41	—	10	1	no	—
330	#41	—	10	1	no	—
331	#41	—	10	1	no	—
332	#41	—	10	1	no	—
333	#41	C₂×C₅×D₅	1	1	yes	characteristic
334	C₂×Q₈	—	5	1	no	—
335	C₂×Q₈	—	5	1	no	—
336	C₂×D₄	—	5	1	no	—
337	C₂×D₄	—	10	1	no	—
338	C₂×D₄	—	10	1	no	—
339	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	10	1	no	—
342	C₂²×C₄	—	10	1	no	—
343	Q₁₆	—	5	2	no	—
344	Q₁₆	—	5	2	no	—
345	SD₁₆	—	5	2	no	—
346	SD₁₆	—	5	2	no	—
347	SD₁₆	—	5	2	no	—
348	SD₁₆	C₂×C₅×D₅	1	2	yes	complemented
349	D₈	—	5	2	no	—
350	D₈	C₂×C₅×D₅	1	2	yes	complemented
351	M₁₆	—	5	1	no	—
352	M₁₆	—	5	2	no	—
353	M₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
354	C₂×C₈	—	5	2	no	—
355	C₂×C₅	—	2	1	no	—
356	C₂×C₅	—	2	1	no	—
357	C₂×C₅	—	2	2	no	—
358	C₂×C₅	—	4	2	no	—
359	C₂×C₅	—	4	2	no	—
360	C₂×C₅	—	4	1	no	—
361	C₂×C₅	—	4	1	no	—
362	C₂×C₅	—	4	2	no	—
363	C₂×C₅	—	8	2	no	—
364	C₂×C₅	—	8	4	no	—
365	C₂×C₅	—	10	1	no	—
366	C₂×C₅	—	10	1	no	—
367	C₂×C₅	—	20	1	no	—
368	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
369	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
370	D₅	—	2	1	no	—
371	D₅	—	2	1	no	—
372	D₅	—	4	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	5	1	no	—
375	C₂³	—	10	1	no	—
376	Q₈	—	5	1	no	—
377	Q₈	—	5	2	no	—
378	Q₈	—	10	1	no	—
379	Q₈	—	10	1	no	—
380	Q₈	C₂²×C₅×D₅	1	1	yes	characteristic
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	5	1	no	—
384	D₄	—	10	1	no	—
385	D₄	—	10	1	no	—
386	D₄	—	10	1	no	—
387	D₄	—	10	2	no	—
388	D₄	—	10	2	no	—
389	D₄	—	10	1	no	—
390	D₄	C₂²×C₅×D₅	1	2	yes	—
391	D₄	C₂²×C₅×D₅	1	1	yes	characteristic
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	10	1	no	—
399	C₂×C₄	—	10	1	no	—
400	C₂×C₄	—	10	1	no	—
401	C₂×C₄	—	10	2	no	—
402	C₂×C₄	—	10	2	no	—
403	C₂×C₄	—	10	1	no	—
404	C₂×C₄	—	10	1	no	—
405	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
406	C₈	—	5	2	no	—
407	C₈	C₂²×C₅×D₅	1	2	yes	—
408	C₅	—	2	2	no	—
409	C₅	#66107	1	1	yes	characteristic, direct product factor
410	C₅	C₅×#575	1	1	yes	characteristic, complemented
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	5	1	no	—
415	C₂²	—	5	1	no	—
416	C₂²	—	10	1	no	—
417	C₂²	—	20	1	no	—
418	C₂²	—	20	2	no	—
419	C₂²	C₅×D₄×D₅	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	5	1	no	—
422	C₄	—	5	1	no	—
423	C₄	—	10	1	no	—
424	C₄	—	10	2	no	—
425	C₄	C₅×D₄×D₅	1	1	yes	characteristic
426	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	—	4	1	no	—
430	C₂	—	10	1	no	—
431	C₂	—	10	1	no	—
432	C₂	—	20	1	no	—
433	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₅
Fitting	C₅²×AGL(1,ℤ/8)	C₂
socle	C₂×C₅²	C₂²×D₄
hypercenter	C₅×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₅×#575
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×#41	C₂	semidirect
2. C₂×C₅×#711	C₂	semidirect
3. C₅²×AGL(1,ℤ/8)	C₂	semidirect
4. C₅×#4097	C₂	semidirect
5. C₅×#4078	C₂	semidirect
6. C₅×#4062	C₂	semidirect
7. C₅×#4061	C₂	semidirect
8. C₅×#4058	C₂	semidirect
9. C₅×#4057	C₂	semidirect
10. C₅×#4055	C₂	semidirect
11. C₅×D₅×M₁₆	C₂	semidirect
13. C₂×C₅²×D₄	C₂²	semidirect
16. C₅×#713	C₂²	semidirect
17. C₅×Q₈×D₅	C₂²	semidirect
22. C₅×#711	C₂²	semidirect
23. C₅×#711	C₂²	semidirect
25. C₅×D₄×D₅	C₂²	semidirect
30. C₂×C₅×Dic₁₀	C₂²	semidirect
31. C₅²×SD₁₆	C₂²	semidirect
32. C₅²×D₈	C₂²	semidirect
33. C₅²×M₁₆	C₂²	semidirect
34. C₅×#689	C₂²	semidirect
35. C₅×#687	C₂²	semidirect
36. C₅×#687	C₂²	semidirect
37. C₅×#686	C₂²	semidirect
38. C₅×#681	C₂²	semidirect
39. C₅×Dic₂₀	C₂²	semidirect
40. C₅×#677	C₂²	semidirect
41. C₅×#676	C₂²	semidirect
42. C₅×C₈×D₅	C₂²	semidirect
44. #66107	C₅	direct (N × H)
82. D₅×#41	C₂×C₅	semidirect
83. C₂×#711	C₂×C₅	semidirect
90. C₅×AGL(1,ℤ/8)	D₅	semidirect
91. C₅×AGL(1,ℤ/8)	C₂×C₅	semidirect
95. #4097	C₂×C₅	semidirect
96. #4078	C₂×C₅	semidirect
97. #4062	C₂×C₅	semidirect
98. #4061	C₂×C₅	semidirect
99. #4058	C₂×C₅	semidirect
100. #4057	C₂×C₅	semidirect
101. #4055	C₂×C₅	semidirect
102. D₅×M₁₆	C₂×C₅	semidirect
137. C₂×C₅×D₄	C₂×D₅	semidirect
138. C₂×C₅×D₄	C₂²×C₅	semidirect
144. #713	C₂²×C₅	semidirect
145. Q₈×D₅	C₂²×C₅	semidirect
150. #711	C₂²×C₅	semidirect
151. #711	C₂²×C₅	semidirect
153. D₄×D₅	C₂²×C₅	semidirect
158. C₂×Dic₁₀	C₂²×C₅	semidirect
165. C₅×SD₁₆	C₂×D₅	semidirect
166. C₅×SD₁₆	C₂²×C₅	semidirect
169. C₅×D₈	C₂×D₅	semidirect
170. C₅×D₈	C₂²×C₅	semidirect
174. C₅×M₁₆	C₂×D₅	semidirect
175. C₅×M₁₆	C₂²×C₅	semidirect
177. #689	C₂²×C₅	semidirect
178. #687	C₂²×C₅	semidirect
179. #687	C₂²×C₅	semidirect
180. #686	C₂²×C₅	semidirect
181. #681	C₂²×C₅	semidirect
182. Dic₂₀	C₂²×C₅	semidirect
183. #677	C₂²×C₅	semidirect
184. #676	C₂²×C₅	semidirect
185. C₈×D₅	C₂²×C₅	semidirect
280. AGL(1,ℤ/8)	C₅×D₅	semidirect
284. C₅²	#575	semidirect
339. C₂×D₄	C₂×C₅×D₅	semidirect
348. SD₁₆	C₂×C₅×D₅	semidirect
350. D₈	C₂×C₅×D₅	semidirect
353. M₁₆	C₂×C₅×D₅	semidirect
409. C₅	#66107	direct (N × H)
410. C₅	C₅×#575	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₅×#41	2
C₂×C₅×#711	2
C₅²×AGL(1,ℤ/8)	2
C₅×#4097	2
C₅×#4078	2
C₅×#4062	2
C₅×#4061	2
C₅×#4058	2
C₅×#4057	2
C₅×#4055	2
C₅×D₅×M₁₆	2
C₅×#575	5
#66107	5

Subgroups — C5×#66107 #13106927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66107 #13106927