Subgroups — C₅×D₅×#137 #13106930

Order 1600.

576 conjugacy classes of subgroups.

The subgroup lattice has 425 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
2	C₂×C₅×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4097	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4064	C₂	1	2	yes	maximal, complemented
7	C₅×D₅×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#4061	C₂	1	2	yes	maximal, complemented
9	C₅×D₅×SD₁₆	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×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₅×#713	C₂²	1	1	yes	characteristic
15	C₅×Q₈×D₅	—	2	1	no	—
16	C₅×Q₈×D₅	—	2	1	no	—
17	C₅×Q₈×D₅	C₂²	1	2	yes	—
18	C₅×Q₈×D₅	C₂²	1	1	yes	characteristic
19	C₅×Q₈×D₅	C₂²	1	2	yes	complemented
20	C₅×#711	—	2	1	no	—
21	C₅×#711	C₂²	1	1	yes	characteristic
22	C₅×D₄×D₅	—	2	1	no	—
23	C₅×D₄×D₅	C₂²	1	1	yes	characteristic
24	C₅×#709	—	2	1	no	—
25	C₅×#709	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₅	—	2	1	no	—
27	C₂×C₄×C₅×D₅	—	2	1	no	—
28	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₅×Dic₁₀	—	2	1	no	—
30	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
31	C₅²×Q₁₆	C₂²	1	2	yes	complemented
32	C₅²×SD₁₆	C₂²	1	2	yes	complemented
33	C₅²×M₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₅×#689	C₂²	1	2	yes	complemented
35	C₅×#689	C₂²	1	2	yes	complemented
36	C₅×#688	C₂²	1	2	yes	complemented
37	C₅×#687	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	—
43	C₂×C₅×#137	—	5	1	no	maximal
44	D₅×#137	C₅	1	1	yes	maximal, characteristic, direct product factor
45	C₂²×C₅×D₅	—	2	1	no	—
46	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
47	C₅²×Q₈	—	2	1	no	—
48	C₅²×Q₈	C₂³	1	2	yes	—
49	C₅²×Q₈	C₂³	1	1	yes	characteristic
50	C₅²×D₄	—	2	1	no	—
51	C₅²×D₄	C₂³	1	1	yes	characteristic
52	C₂×C₄×C₅²	—	2	1	no	—
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	1	no	—
58	C₂×C₅×Dic₅	—	2	1	no	—
59	C₂×C₅×Dic₅	—	2	1	no	—
60	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
61	C₅×D₂₀	—	2	1	no	—
62	C₅×D₂₀	C₂³	1	1	yes	characteristic
63	C₄×C₅×D₅	—	2	1	no	—
64	C₄×C₅×D₅	—	2	2	no	—
65	C₄×C₅×D₅	—	2	2	no	—
66	C₄×C₅×D₅	—	2	1	no	—
67	C₄×C₅×D₅	—	2	1	no	—
68	C₄×C₅×D₅	D₄	1	1	yes	characteristic
69	C₄×C₅×D₅	D₄	1	1	yes	characteristic
70	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
72	C₅×Dic₁₀	—	2	1	no	—
73	C₅×Dic₁₀	—	2	2	no	—
74	C₅×Dic₁₀	—	2	2	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	C₂²×C₅×Q₈	—	5	1	no	—
82	D₅×#41	C₂×C₅	1	1	yes	characteristic
83	C₂×Q₈×D₅	C₂×C₅	1	1	yes	characteristic, complemented
84	C₅×#137	—	2	2	no	—
85	C₅×#137	—	5	1	no	—
86	C₅×#137	—	5	1	no	—
87	C₅×#137	—	5	2	no	—
88	C₅×#137	—	5	2	no	—
89	C₅×#137	—	5	1	no	—
90	C₅×#137	D₅	1	1	yes	characteristic, direct product factor
91	C₅×#137	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×C₅×Q₁₆	—	5	2	no	—
93	C₂×C₅×SD₁₆	—	5	2	no	—
94	C₂×C₅×M₁₆	—	5	1	no	—
95	#4097	C₂×C₅	1	1	yes	characteristic, complemented
96	#4088	C₂×C₅	1	1	yes	characteristic, complemented
97	#4064	C₂×C₅	1	2	yes	complemented
98	D₅×Q₁₆	C₂×C₅	1	2	yes	complemented
99	#4061	C₂×C₅	1	2	yes	complemented
100	D₅×SD₁₆	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	1	no	—
104	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
105	C₂×C₅×D₅	—	2	2	no	—
106	C₂×C₅×D₅	—	2	1	no	—
107	C₂×C₅×D₅	—	4	2	no	—
108	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
110	C₄×C₅²	—	2	2	no	—
111	C₄×C₅²	—	2	1	no	—
112	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
113	C₄×C₅²	C₂⁴	1	1	yes	characteristic
114	C₅×Dic₅	—	2	2	no	—
115	C₅×Dic₅	—	2	1	no	—
116	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	5	1	no	—
120	C₅×#41	—	5	1	no	—
121	C₅×#41	—	5	1	no	—
122	C₅×#41	—	10	1	no	—
123	C₅×#41	—	10	1	no	—
124	C₅×#41	C₂×D₅	1	1	yes	characteristic
125	C₅×#41	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	5	2	no	—
128	C₂×C₅×Q₈	—	5	1	no	—
129	C₂×C₅×Q₈	—	5	2	no	—
130	C₂×C₅×Q₈	—	5	1	no	—
131	C₂×C₅×Q₈	—	10	1	no	—
132	C₂×C₅×Q₈	—	10	1	no	—
133	C₂×C₅×Q₈	—	10	1	no	—
134	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
135	C₂×C₅×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₂×C₅×D₄	—	5	1	no	—
137	C₂×C₅×D₄	—	10	1	no	—
138	C₂²×C₄×C₅	—	5	1	no	—
139	C₂²×C₄×C₅	—	10	1	no	—
140	C₂²×C₄×C₅	—	10	1	no	—
141	#713	C₂²×C₅	1	1	yes	characteristic
142	Q₈×D₅	—	2	1	no	—
143	Q₈×D₅	—	2	1	no	—
144	Q₈×D₅	C₂²×C₅	1	2	yes	—
145	Q₈×D₅	C₂²×C₅	1	1	yes	characteristic
146	Q₈×D₅	C₂²×C₅	1	2	yes	complemented
147	#711	—	2	1	no	—
148	#711	C₂²×C₅	1	1	yes	characteristic
149	D₄×D₅	—	2	1	no	—
150	D₄×D₅	C₂²×C₅	1	1	yes	characteristic
151	#709	—	2	1	no	—
152	#709	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄×D₅	—	2	1	no	—
154	C₂×C₄×D₅	—	2	1	no	—
155	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic
156	C₂×Dic₁₀	—	2	1	no	—
157	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₅×Q₁₆	—	2	4	no	—
159	C₅×Q₁₆	—	5	2	no	—
160	C₅×Q₁₆	—	5	2	no	—
161	C₅×Q₁₆	—	5	2	no	—
162	C₅×Q₁₆	C₂×D₅	1	2	yes	complemented
163	C₅×Q₁₆	C₂²×C₅	1	2	yes	complemented
164	C₅×SD₁₆	—	2	4	no	—
165	C₅×SD₁₆	—	5	2	no	—
166	C₅×SD₁₆	—	5	2	no	—
167	C₅×SD₁₆	—	5	2	no	—
168	C₅×SD₁₆	C₂×D₅	1	2	yes	complemented
169	C₅×SD₁₆	C₂²×C₅	1	2	yes	complemented
170	C₅×M₁₆	—	2	2	no	—
171	C₅×M₁₆	—	5	1	no	—
172	C₅×M₁₆	—	5	2	no	—
173	C₅×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
174	C₅×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₂×C₅×C₈	—	5	2	no	—
176	#689	C₂²×C₅	1	2	yes	complemented
177	#689	C₂²×C₅	1	2	yes	complemented
178	#688	C₂²×C₅	1	2	yes	complemented
179	#687	C₂²×C₅	1	2	yes	complemented
180	#681	C₂²×C₅	1	1	yes	characteristic, complemented
181	Dic₂₀	C₂²×C₅	1	2	yes	complemented
182	#677	C₂²×C₅	1	2	yes	complemented
183	#676	C₂²×C₅	1	2	yes	complemented
184	C₈×D₅	C₂²×C₅	1	2	yes	—
185	C₂×#137	—	5	1	no	Sylow
186	C₂×C₅²	—	2	1	no	—
187	C₂×C₅²	—	4	1	no	—
188	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
189	C₅×D₅	—	2	1	no	—
190	C₅×D₅	—	4	1	no	—
191	C₅×D₅	#137	1	2	yes	direct product factor
192	C₂³×C₅	—	5	1	no	—
193	C₂³×C₅	—	10	1	no	—
194	C₂²×D₅	—	2	1	no	—
195	C₂²×D₅	C₅×D₄	1	1	yes	characteristic
196	C₅×Q₈	—	2	1	no	—
197	C₅×Q₈	—	2	1	no	—
198	C₅×Q₈	—	2	4	no	—
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	5	2	no	—
202	C₅×Q₈	—	5	1	no	—
203	C₅×Q₈	—	10	2	no	—
204	C₅×Q₈	—	10	2	no	—
205	C₅×Q₈	—	10	1	no	—
206	C₅×Q₈	—	10	1	no	—
207	C₅×Q₈	C₂²×D₅	1	2	yes	—
208	C₅×Q₈	C₂²×D₅	1	1	yes	characteristic
209	C₅×Q₈	C₂³×C₅	1	2	yes	—
210	C₅×Q₈	C₂³×C₅	1	1	yes	characteristic
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	—	2	1	no	—
213	C₅×D₄	—	2	2	no	—
214	C₅×D₄	—	4	2	no	—
215	C₅×D₄	—	5	1	no	—
216	C₅×D₄	—	10	1	no	—
217	C₅×D₄	—	10	1	no	—
218	C₅×D₄	—	10	1	no	—
219	C₅×D₄	—	10	1	no	—
220	C₅×D₄	C₂²×D₅	1	1	yes	characteristic
221	C₅×D₄	C₂³×C₅	1	1	yes	characteristic
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	5	1	no	—
230	C₂×C₄×C₅	—	5	1	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	—	10	1	no	—
235	C₂×C₄×C₅	—	10	1	no	—
236	C₂×C₄×C₅	—	10	2	no	—
237	C₂×C₄×C₅	—	10	2	no	—
238	C₂×C₄×C₅	—	10	1	no	—
239	C₂×C₄×C₅	—	10	1	no	—
240	C₂×C₄×C₅	—	10	1	no	—
241	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
243	C₂²⋊D₅	—	2	1	no	—
244	C₂²⋊D₅	—	2	1	no	—
245	C₂²⋊D₅	—	2	1	no	—
246	C₂×Dic₅	—	2	1	no	—
247	C₂×Dic₅	—	2	1	no	—
248	C₂×Dic₅	C₅×D₄	1	1	yes	characteristic
249	D₂₀	—	2	1	no	—
250	D₂₀	C₂³×C₅	1	1	yes	characteristic
251	C₄×D₅	—	2	1	no	—
252	C₄×D₅	—	2	2	no	—
253	C₄×D₅	—	2	2	no	—
254	C₄×D₅	—	2	1	no	—
255	C₄×D₅	—	2	1	no	—
256	C₄×D₅	C₅×D₄	1	1	yes	characteristic
257	C₄×D₅	C₅×D₄	1	1	yes	characteristic
258	C₄×D₅	C₂³×C₅	1	1	yes	characteristic
259	C₄×D₅	C₂³×C₅	1	1	yes	characteristic
260	Dic₁₀	—	2	1	no	—
261	Dic₁₀	—	2	2	no	—
262	Dic₁₀	—	2	2	no	—
263	Dic₁₀	—	2	1	no	—
264	Dic₁₀	C₂³×C₅	1	2	yes	—
265	Dic₁₀	C₂³×C₅	1	1	yes	characteristic
266	C₅×C₈	—	2	4	no	—
267	C₅×C₈	—	5	2	no	—
268	C₅×C₈	C₂²×D₅	1	2	yes	—
269	C₅×C₈	C₂³×C₅	1	2	yes	—
270	#168	C₂³×C₅	1	2	yes	—
271	C₂×#41	—	5	1	no	—
272	C₂²×Q₈	—	5	1	no	—
273	#137	—	5	1	no	—
274	#137	—	5	1	no	—
275	#137	—	5	2	no	—
276	#137	—	5	2	no	—
277	#137	—	5	1	no	—
278	#137	C₅×D₅	1	1	yes	characteristic, direct product factor
279	C₂×Q₁₆	—	5	2	no	—
280	C₂×SD₁₆	—	5	2	no	—
281	C₂×M₁₆	—	5	1	no	—
282	C₅²	C₂×#137	1	1	yes	characteristic, complemented, Sylow
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	5	1	no	—
288	C₂²×C₅	—	5	1	no	—
289	C₂²×C₅	—	10	2	no	—
290	C₂²×C₅	—	10	1	no	—
291	C₂²×C₅	—	20	2	no	—
292	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
293	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×D₅	—	2	2	no	—
295	C₂×D₅	—	2	1	no	—
296	C₂×D₅	—	4	2	no	—
297	C₂×D₅	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×D₅	C₂×C₅×D₄	1	1	yes	characteristic
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	2	2	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	4	no	—
307	C₄×C₅	—	5	1	no	—
308	C₄×C₅	—	5	1	no	—
309	C₄×C₅	—	10	1	no	—
310	C₄×C₅	—	10	2	no	—
311	C₄×C₅	D₄×D₅	1	1	yes	characteristic
312	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
313	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
314	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
315	Dic₅	—	2	2	no	—
316	Dic₅	—	2	1	no	—
317	Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
318	Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
319	#41	—	5	1	no	—
320	#41	—	5	1	no	—
321	#41	—	5	1	no	—
322	#41	—	10	1	no	—
323	#41	—	10	1	no	—
324	#41	C₂×C₅×D₅	1	1	yes	characteristic
325	C₂×Q₈	—	5	2	no	—
326	C₂×Q₈	—	5	1	no	—
327	C₂×Q₈	—	5	2	no	—
328	C₂×Q₈	—	5	1	no	—
329	C₂×Q₈	—	10	1	no	—
330	C₂×Q₈	—	10	1	no	—
331	C₂×Q₈	—	10	1	no	—
332	C₂×Q₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
333	C₂×D₄	—	5	1	no	—
334	C₂×D₄	—	10	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	10	1	no	—
337	C₂²×C₄	—	10	1	no	—
338	Q₁₆	—	5	2	no	—
339	Q₁₆	—	5	2	no	—
340	Q₁₆	—	5	2	no	—
341	Q₁₆	C₂×C₅×D₅	1	2	yes	complemented
342	SD₁₆	—	5	2	no	—
343	SD₁₆	—	5	2	no	—
344	SD₁₆	—	5	2	no	—
345	SD₁₆	C₂×C₅×D₅	1	2	yes	complemented
346	M₁₆	—	5	1	no	—
347	M₁₆	—	5	2	no	—
348	M₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
349	C₂×C₈	—	5	2	no	—
350	C₂×C₅	—	2	1	no	—
351	C₂×C₅	—	2	1	no	—
352	C₂×C₅	—	2	2	no	—
353	C₂×C₅	—	4	2	no	—
354	C₂×C₅	—	4	1	no	—
355	C₂×C₅	—	4	1	no	—
356	C₂×C₅	—	5	2	no	—
357	C₂×C₅	—	8	2	no	—
358	C₂×C₅	—	10	1	no	—
359	C₂×C₅	—	20	1	no	—
360	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
361	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
362	D₅	—	2	1	no	—
363	D₅	—	4	1	no	—
364	D₅	C₅×#137	1	2	yes	direct product factor
365	C₂³	—	5	1	no	—
366	C₂³	—	10	1	no	—
367	Q₈	—	2	1	no	—
368	Q₈	—	5	2	no	—
369	Q₈	—	5	1	no	—
370	Q₈	—	10	2	no	—
371	Q₈	—	10	2	no	—
372	Q₈	—	10	1	no	—
373	Q₈	—	10	1	no	—
374	Q₈	C₂²×C₅×D₅	1	2	yes	—
375	Q₈	C₂²×C₅×D₅	1	1	yes	characteristic
376	D₄	—	2	1	no	—
377	D₄	—	5	1	no	—
378	D₄	—	10	1	no	—
379	D₄	—	10	1	no	—
380	D₄	—	10	1	no	—
381	D₄	—	10	1	no	—
382	D₄	C₂²×C₅×D₅	1	1	yes	characteristic
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	10	1	no	—
391	C₂×C₄	—	10	1	no	—
392	C₂×C₄	—	10	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	10	1	no	—
395	C₂×C₄	—	10	1	no	—
396	C₂×C₄	—	10	1	no	—
397	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
398	C₈	—	5	2	no	—
399	C₈	C₂²×C₅×D₅	1	2	yes	—
400	C₅	—	2	2	no	—
401	C₅	D₅×#137	1	1	yes	characteristic, direct product factor
402	C₅	C₂×C₅×#137	1	1	yes	characteristic, complemented
403	C₂²	—	2	1	no	—
404	C₂²	—	5	1	no	—
405	C₂²	—	5	1	no	—
406	C₂²	—	10	2	no	—
407	C₂²	—	10	1	no	—
408	C₂²	—	20	2	no	—
409	C₂²	C₅×D₄×D₅	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	5	1	no	—
413	C₄	—	5	1	no	—
414	C₄	—	10	1	no	—
415	C₄	—	10	2	no	—
416	C₄	C₅×D₄×D₅	1	1	yes	characteristic
417	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
418	C₂	—	2	1	no	—
419	C₂	—	4	1	no	—
420	C₂	—	5	2	no	—
421	C₂	—	10	1	no	—
422	C₂	—	20	1	no	—
423	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×#137	C₂
socle	C₂×C₅²	C₂²×D₄
prime radical	C₅×D₅×#41	C₂
hypercenter	C₅×#137	D₅
hypocenter	C₅	C₂×C₅×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#137

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈×D₅	C₂	semidirect
3. C₅²×#137	C₂	semidirect
4. C₅×#4097	C₂	semidirect
5. C₅×#4088	C₂	semidirect
6. C₅×#4064	C₂	semidirect
7. C₅×D₅×Q₁₆	C₂	semidirect
8. C₅×#4061	C₂	semidirect
9. C₅×D₅×SD₁₆	C₂	semidirect
10. C₅×#4055	C₂	semidirect
11. C₅×D₅×M₁₆	C₂	semidirect
13. C₂×C₅²×Q₈	C₂²	semidirect
19. C₅×Q₈×D₅	C₂²	semidirect
30. C₂×C₅×Dic₁₀	C₂²	semidirect
31. C₅²×Q₁₆	C₂²	semidirect
32. C₅²×SD₁₆	C₂²	semidirect
33. C₅²×M₁₆	C₂²	semidirect
34. C₅×#689	C₂²	semidirect
35. C₅×#689	C₂²	semidirect
36. C₅×#688	C₂²	semidirect
37. C₅×#687	C₂²	semidirect
38. C₅×#681	C₂²	semidirect
39. C₅×Dic₂₀	C₂²	semidirect
40. C₅×#677	C₂²	semidirect
41. C₅×#676	C₂²	semidirect
44. D₅×#137	C₅	direct (N × H)
83. C₂×Q₈×D₅	C₂×C₅	semidirect
90. C₅×#137	D₅	direct (N × H)
91. C₅×#137	C₂×C₅	semidirect
95. #4097	C₂×C₅	semidirect
96. #4088	C₂×C₅	semidirect
97. #4064	C₂×C₅	semidirect
98. D₅×Q₁₆	C₂×C₅	semidirect
99. #4061	C₂×C₅	semidirect
100. D₅×SD₁₆	C₂×C₅	semidirect
101. #4055	C₂×C₅	semidirect
102. D₅×M₁₆	C₂×C₅	semidirect
134. C₂×C₅×Q₈	C₂×D₅	semidirect
135. C₂×C₅×Q₈	C₂²×C₅	semidirect
146. Q₈×D₅	C₂²×C₅	semidirect
157. C₂×Dic₁₀	C₂²×C₅	semidirect
162. C₅×Q₁₆	C₂×D₅	semidirect
163. C₅×Q₁₆	C₂²×C₅	semidirect
168. C₅×SD₁₆	C₂×D₅	semidirect
169. C₅×SD₁₆	C₂²×C₅	semidirect
173. C₅×M₁₆	C₂×D₅	semidirect
174. C₅×M₁₆	C₂²×C₅	semidirect
176. #689	C₂²×C₅	semidirect
177. #689	C₂²×C₅	semidirect
178. #688	C₂²×C₅	semidirect
179. #687	C₂²×C₅	semidirect
180. #681	C₂²×C₅	semidirect
181. Dic₂₀	C₂²×C₅	semidirect
182. #677	C₂²×C₅	semidirect
183. #676	C₂²×C₅	semidirect
191. C₅×D₅	#137	direct (N × H)
278. #137	C₅×D₅	direct (N × H)
282. C₅²	C₂×#137	semidirect
332. C₂×Q₈	C₂×C₅×D₅	semidirect
341. Q₁₆	C₂×C₅×D₅	semidirect
345. SD₁₆	C₂×C₅×D₅	semidirect
348. M₁₆	C₂×C₅×D₅	semidirect
364. D₅	C₅×#137	direct (N × H)
401. C₅	D₅×#137	direct (N × H)
402. C₅	C₂×C₅×#137	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×Q₈×D₅	2
C₅²×#137	2
C₅×#4097	2
C₅×#4088	2
C₅×#4064	2
C₅×D₅×Q₁₆	2
C₅×#4061	2
C₅×D₅×SD₁₆	2
C₅×#4055	2
C₅×D₅×M₁₆	2
C₂×C₅×#137	5
D₅×#137	5

Subgroups — C5×D5×#137 #13106930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×#137 #13106930