Subgroups — C₅×D₅×#135 #13106921

Order 1600.

594 conjugacy classes of subgroups.

The subgroup lattice has 366 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	2	yes	maximal, complemented
2	C₅²×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4096	C₂	1	2	yes	maximal, complemented
4	C₅×#4065	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4062	C₂	1	2	yes	maximal, complemented
7	C₅×D₅×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#4058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4050	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅²×#41	C₂²	1	2	yes	complemented
13	C₅×#713	C₂²	1	2	yes	complemented
14	C₅×Q₈×D₅	C₂²	1	2	yes	—
15	C₅×#711	—	2	2	no	—
16	C₅×#711	C₂²	1	2	yes	complemented
17	C₅×D₄×D₅	—	2	2	no	—
18	C₅×D₄×D₅	C₂²	1	2	yes	—
19	C₅×#709	—	2	2	no	—
20	C₅×#709	C₂²	1	2	yes	complemented
21	C₂×C₄×C₅×D₅	—	2	2	no	—
22	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
23	C₅²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₅²×SD₁₆	C₂²	1	2	yes	complemented
25	C₅²×D₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic, complemented
27	C₅×#689	C₂²	1	2	yes	complemented
28	C₅×#688	C₂²	1	2	yes	complemented
29	C₅×#687	C₂²	1	2	yes	complemented
30	C₅×#686	C₂²	1	2	yes	complemented
31	C₂×C₅×#168	C₂²	1	1	yes	characteristic, complemented
32	C₅×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
33	C₅×D₄₀	C₂²	1	1	yes	characteristic, complemented
34	C₅×#677	C₂²	1	2	yes	complemented
35	C₅×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₅×C₈×D₅	C₂²	1	1	yes	characteristic
37	C₅×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
38	C₅×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#135	—	5	1	no	maximal
40	D₅×#135	C₅	1	1	yes	maximal, characteristic, direct product factor
41	C₂²×C₅×D₅	—	2	2	no	—
42	C₂²×C₅×D₅	D₄	1	1	yes	characteristic
43	C₅²×Q₈	C₂³	1	2	yes	—
44	C₅²×D₄	—	2	2	no	—
45	C₅²×D₄	C₂³	1	2	yes	—
46	C₂×C₄×C₅²	—	2	2	no	—
47	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
48	C₅×C₂²⋊D₅	—	2	2	no	—
49	C₅×C₂²⋊D₅	—	2	2	no	—
50	C₅×C₂²⋊D₅	—	2	2	no	—
51	C₂×C₅×Dic₅	—	2	2	no	—
52	C₂×C₅×Dic₅	D₄	1	1	yes	characteristic
53	C₅×D₂₀	—	2	2	no	—
54	C₅×D₂₀	C₂³	1	2	yes	—
55	C₄×C₅×D₅	—	2	2	no	—
56	C₄×C₅×D₅	—	2	2	no	—
57	C₄×C₅×D₅	—	2	2	no	—
58	C₄×C₅×D₅	D₄	1	1	yes	characteristic
59	C₄×C₅×D₅	D₄	1	1	yes	characteristic
60	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
61	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
62	C₅×Dic₁₀	—	2	2	no	—
63	C₅×Dic₁₀	C₂³	1	2	yes	—
64	C₅²×C₈	C₂³	1	1	yes	characteristic
65	C₅²×C₈	C₂³	1	1	yes	characteristic
66	C₅×#168	C₂³	1	1	yes	characteristic
67	C₅×#168	C₂³	1	1	yes	characteristic
68	C₂×C₅×#41	—	5	2	no	—
69	D₅×#41	C₂×C₅	1	2	yes	complemented
70	C₅×#135	—	2	2	no	—
71	C₅×#135	—	5	2	no	—
72	C₅×#135	—	5	1	no	—
73	C₅×#135	—	5	2	no	—
74	C₅×#135	—	5	1	no	—
75	C₅×#135	—	5	1	no	—
76	C₅×#135	D₅	1	1	yes	characteristic, direct product factor
77	C₅×#135	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×C₅×Q₁₆	—	5	1	no	—
79	C₂×C₅×SD₁₆	—	5	2	no	—
80	C₂×C₅×D₈	—	5	1	no	—
81	C₂²×C₅×C₈	—	5	1	no	—
82	#4096	C₂×C₅	1	2	yes	complemented
83	#4065	C₂×C₅	1	1	yes	characteristic, complemented
84	D₅×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
85	#4062	C₂×C₅	1	2	yes	complemented
86	D₅×SD₁₆	C₂×C₅	1	2	yes	complemented
87	#4058	C₂×C₅	1	1	yes	characteristic, complemented
88	D₅×D₈	C₂×C₅	1	1	yes	characteristic, complemented
89	#4050	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×C₈×D₅	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂²×C₅²	—	2	2	no	—
92	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
93	C₂×C₅×D₅	—	2	2	no	—
94	C₂×C₅×D₅	—	2	2	no	—
95	C₂×C₅×D₅	—	4	4	no	—
96	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₅×D₅	C₂×D₄	1	1	yes	characteristic
98	C₄×C₅²	—	2	2	no	—
99	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
100	C₄×C₅²	C₂⁴	1	1	yes	characteristic
101	C₅×Dic₅	—	2	2	no	—
102	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
103	C₅×Dic₅	C₂×D₄	1	1	yes	characteristic
104	C₅×#41	—	2	4	no	—
105	C₅×#41	—	5	2	no	—
106	C₅×#41	—	5	2	no	—
107	C₅×#41	—	5	2	no	—
108	C₅×#41	—	10	2	no	—
109	C₅×#41	—	10	2	no	—
110	C₅×#41	C₂×D₅	1	2	yes	complemented
111	C₅×#41	C₂²×C₅	1	2	yes	complemented
112	C₂×C₅×Q₈	—	5	2	no	—
113	C₂×C₅×D₄	—	5	2	no	—
114	C₂×C₅×D₄	—	10	2	no	—
115	C₂²×C₄×C₅	—	5	1	no	—
116	C₂²×C₄×C₅	—	10	2	no	—
117	#713	C₂²×C₅	1	2	yes	complemented
118	Q₈×D₅	C₂²×C₅	1	2	yes	—
119	#711	—	2	2	no	—
120	#711	C₂²×C₅	1	2	yes	complemented
121	D₄×D₅	—	2	2	no	—
122	D₄×D₅	C₂²×C₅	1	2	yes	—
123	#709	—	2	2	no	—
124	#709	C₂²×C₅	1	2	yes	complemented
125	C₂×C₄×D₅	—	2	2	no	—
126	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic
127	C₅×Q₁₆	—	2	2	no	—
128	C₅×Q₁₆	—	5	2	no	—
129	C₅×Q₁₆	—	5	1	no	—
130	C₅×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
131	C₅×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₅×SD₁₆	—	2	4	no	—
133	C₅×SD₁₆	—	5	2	no	—
134	C₅×SD₁₆	—	5	2	no	—
135	C₅×SD₁₆	—	5	2	no	—
136	C₅×SD₁₆	C₂×D₅	1	2	yes	complemented
137	C₅×SD₁₆	C₂²×C₅	1	2	yes	complemented
138	C₅×D₈	—	2	2	no	—
139	C₅×D₈	—	5	2	no	—
140	C₅×D₈	—	5	1	no	—
141	C₅×D₈	C₂×D₅	1	1	yes	characteristic, complemented
142	C₅×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	5	1	no	—
145	C₂×C₅×C₈	—	5	1	no	—
146	C₂×C₅×C₈	—	5	1	no	—
147	C₂×C₅×C₈	—	5	1	no	—
148	C₂×C₅×C₈	—	5	1	no	—
149	C₂×C₅×C₈	C₂×D₅	1	1	yes	characteristic, complemented
150	C₂×C₅×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
151	#689	C₂²×C₅	1	2	yes	complemented
152	#688	C₂²×C₅	1	2	yes	complemented
153	#687	C₂²×C₅	1	2	yes	complemented
154	#686	C₂²×C₅	1	2	yes	complemented
155	C₂×#168	C₂²×C₅	1	1	yes	characteristic, complemented
156	Dic₂₀	C₂²×C₅	1	1	yes	characteristic, complemented
157	D₄₀	C₂²×C₅	1	1	yes	characteristic, complemented
158	#677	C₂²×C₅	1	2	yes	complemented
159	C₈×D₅	C₂²×C₅	1	1	yes	characteristic
160	C₈×D₅	C₂²×C₅	1	1	yes	characteristic
161	C₈×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
162	C₈×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₂×#135	—	5	1	no	Sylow
164	C₂×C₅²	—	2	1	no	—
165	C₂×C₅²	—	4	2	no	—
166	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
167	C₅×D₅	—	2	1	no	—
168	C₅×D₅	—	4	2	no	—
169	C₅×D₅	#135	1	2	yes	direct product factor
170	C₂³×C₅	—	5	1	no	—
171	C₂³×C₅	—	10	2	no	—
172	C₂²×D₅	—	2	2	no	—
173	C₂²×D₅	C₅×D₄	1	1	yes	characteristic
174	C₅×Q₈	—	2	4	no	—
175	C₅×Q₈	—	5	2	no	—
176	C₅×Q₈	—	10	2	no	—
177	C₅×Q₈	C₂²×D₅	1	2	yes	—
178	C₅×Q₈	C₂³×C₅	1	2	yes	—
179	C₅×D₄	—	2	2	no	—
180	C₅×D₄	—	2	2	no	—
181	C₅×D₄	—	2	4	no	—
182	C₅×D₄	—	4	4	no	—
183	C₅×D₄	—	5	2	no	—
184	C₅×D₄	—	10	2	no	—
185	C₅×D₄	—	10	2	no	—
186	C₅×D₄	—	10	2	no	—
187	C₅×D₄	—	10	2	no	—
188	C₅×D₄	C₂²×D₅	1	2	yes	—
189	C₅×D₄	C₂³×C₅	1	2	yes	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	4	4	no	—
194	C₂×C₄×C₅	—	5	1	no	—
195	C₂×C₄×C₅	—	5	1	no	—
196	C₂×C₄×C₅	—	5	1	no	—
197	C₂×C₄×C₅	—	5	1	no	—
198	C₂×C₄×C₅	—	5	1	no	—
199	C₂×C₄×C₅	—	10	2	no	—
200	C₂×C₄×C₅	—	10	2	no	—
201	C₂×C₄×C₅	—	10	2	no	—
202	C₂×C₄×C₅	—	10	2	no	—
203	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
205	C₂²⋊D₅	—	2	2	no	—
206	C₂²⋊D₅	—	2	2	no	—
207	C₂²⋊D₅	—	2	2	no	—
208	C₂×Dic₅	—	2	2	no	—
209	C₂×Dic₅	C₅×D₄	1	1	yes	characteristic
210	D₂₀	—	2	2	no	—
211	D₂₀	C₂³×C₅	1	2	yes	—
212	C₄×D₅	—	2	2	no	—
213	C₄×D₅	—	2	2	no	—
214	C₄×D₅	—	2	2	no	—
215	C₄×D₅	C₅×D₄	1	1	yes	characteristic
216	C₄×D₅	C₅×D₄	1	1	yes	characteristic
217	C₄×D₅	C₂³×C₅	1	1	yes	characteristic
218	C₄×D₅	C₂³×C₅	1	1	yes	characteristic
219	Dic₁₀	—	2	2	no	—
220	Dic₁₀	C₂³×C₅	1	2	yes	—
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	5	1	no	—
224	C₅×C₈	—	5	1	no	—
225	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
226	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
227	C₅×C₈	C₂³×C₅	1	1	yes	characteristic
228	C₅×C₈	C₂³×C₅	1	1	yes	characteristic
229	#168	C₂³×C₅	1	1	yes	characteristic
230	#168	C₂³×C₅	1	1	yes	characteristic
231	C₂×#41	—	5	2	no	—
232	#135	—	5	2	no	—
233	#135	—	5	1	no	—
234	#135	—	5	2	no	—
235	#135	—	5	1	no	—
236	#135	—	5	1	no	—
237	#135	C₅×D₅	1	1	yes	characteristic, direct product factor
238	C₂×Q₁₆	—	5	1	no	—
239	C₂×SD₁₆	—	5	2	no	—
240	C₂×D₈	—	5	1	no	—
241	C₂²×C₈	—	5	1	no	—
242	C₅²	C₂×#135	1	1	yes	characteristic, complemented, Sylow
243	C₂²×C₅	—	2	2	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	4	4	no	—
247	C₂²×C₅	—	5	1	no	—
248	C₂²×C₅	—	5	1	no	—
249	C₂²×C₅	—	10	2	no	—
250	C₂²×C₅	—	10	2	no	—
251	C₂²×C₅	—	20	4	no	—
252	C₂²×C₅	D₄×D₅	1	1	yes	characteristic
253	C₂²×C₅	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×D₅	—	2	2	no	—
255	C₂×D₅	—	2	2	no	—
256	C₂×D₅	—	4	4	no	—
257	C₂×D₅	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂×D₅	C₂×C₅×D₄	1	1	yes	characteristic
259	C₄×C₅	—	2	2	no	—
260	C₄×C₅	—	2	2	no	—
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	—	5	1	no	—
265	C₄×C₅	—	5	1	no	—
266	C₄×C₅	—	10	2	no	—
267	C₄×C₅	D₄×D₅	1	1	yes	characteristic
268	C₄×C₅	C₂×C₅×D₄	1	1	yes	characteristic
269	C₄×C₅	C₂³×D₅	1	1	yes	characteristic
270	C₄×C₅	C₂⁴×C₅	1	1	yes	characteristic
271	Dic₅	—	2	2	no	—
272	Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
273	Dic₅	C₂×C₅×D₄	1	1	yes	characteristic
274	#41	—	5	2	no	—
275	#41	—	5	2	no	—
276	#41	—	5	2	no	—
277	#41	—	10	2	no	—
278	#41	—	10	2	no	—
279	#41	C₂×C₅×D₅	1	2	yes	complemented
280	C₂×Q₈	—	5	2	no	—
281	C₂×D₄	—	5	2	no	—
282	C₂×D₄	—	10	2	no	—
283	C₂²×C₄	—	5	1	no	—
284	C₂²×C₄	—	10	2	no	—
285	Q₁₆	—	5	2	no	—
286	Q₁₆	—	5	1	no	—
287	Q₁₆	C₂×C₅×D₅	1	1	yes	characteristic, complemented
288	SD₁₆	—	5	2	no	—
289	SD₁₆	—	5	2	no	—
290	SD₁₆	—	5	2	no	—
291	SD₁₆	C₂×C₅×D₅	1	2	yes	complemented
292	D₈	—	5	2	no	—
293	D₈	—	5	1	no	—
294	D₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
295	C₂×C₈	—	5	1	no	—
296	C₂×C₈	—	5	1	no	—
297	C₂×C₈	—	5	1	no	—
298	C₂×C₈	—	5	1	no	—
299	C₂×C₈	—	5	1	no	—
300	C₂×C₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
301	C₂×C₅	—	2	1	no	—
302	C₂×C₅	—	2	1	no	—
303	C₂×C₅	—	2	2	no	—
304	C₂×C₅	—	4	2	no	—
305	C₂×C₅	—	4	2	no	—
306	C₂×C₅	—	4	2	no	—
307	C₂×C₅	—	5	2	no	—
308	C₂×C₅	—	8	4	no	—
309	C₂×C₅	—	10	1	no	—
310	C₂×C₅	—	20	2	no	—
311	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
312	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
313	D₅	—	2	1	no	—
314	D₅	—	4	2	no	—
315	D₅	C₅×#135	1	2	yes	direct product factor
316	C₂³	—	5	1	no	—
317	C₂³	—	10	2	no	—
318	Q₈	—	5	2	no	—
319	Q₈	—	10	2	no	—
320	Q₈	C₂²×C₅×D₅	1	2	yes	—
321	D₄	—	2	2	no	—
322	D₄	—	5	2	no	—
323	D₄	—	10	2	no	—
324	D₄	—	10	2	no	—
325	D₄	—	10	2	no	—
326	D₄	—	10	2	no	—
327	D₄	C₂²×C₅×D₅	1	2	yes	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	5	1	no	—
330	C₂×C₄	—	5	1	no	—
331	C₂×C₄	—	5	1	no	—
332	C₂×C₄	—	5	1	no	—
333	C₂×C₄	—	5	1	no	—
334	C₂×C₄	—	10	2	no	—
335	C₂×C₄	—	10	2	no	—
336	C₂×C₄	—	10	2	no	—
337	C₂×C₄	—	10	2	no	—
338	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
339	C₈	—	5	1	no	—
340	C₈	—	5	1	no	—
341	C₈	C₂²×C₅×D₅	1	1	yes	characteristic
342	C₈	C₂²×C₅×D₅	1	1	yes	characteristic
343	C₅	—	2	2	no	—
344	C₅	D₅×#135	1	1	yes	characteristic, direct product factor
345	C₅	C₂×C₅×#135	1	1	yes	characteristic, complemented
346	C₂²	—	2	2	no	—
347	C₂²	—	5	1	no	—
348	C₂²	—	5	1	no	—
349	C₂²	—	10	2	no	—
350	C₂²	—	10	2	no	—
351	C₂²	—	20	4	no	—
352	C₂²	C₅×D₄×D₅	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	5	1	no	—
355	C₄	—	5	1	no	—
356	C₄	—	10	2	no	—
357	C₄	C₅×D₄×D₅	1	1	yes	characteristic
358	C₄	C₂³×C₅×D₅	1	1	yes	characteristic
359	C₂	—	2	1	no	—
360	C₂	—	4	2	no	—
361	C₂	—	5	2	no	—
362	C₂	—	10	1	no	—
363	C₂	—	20	2	no	—
364	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁴×C₅
Frattini	C₄	C₂³×C₅×D₅
Fitting	C₅²×#135	C₂
socle	C₂×C₅²	C₂²×D₄
hypercenter	C₅×#135	D₅
hypocenter	C₅	C₂×C₅×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₅×D₅×#41	C₂	semidirect
2. C₅²×#135	C₂	semidirect
3. C₅×#4096	C₂	semidirect
4. C₅×#4065	C₂	semidirect
5. C₅×D₅×Q₁₆	C₂	semidirect
6. C₅×#4062	C₂	semidirect
7. C₅×D₅×SD₁₆	C₂	semidirect
8. C₅×#4058	C₂	semidirect
9. C₅×D₅×D₈	C₂	semidirect
10. C₅×#4050	C₂	semidirect
11. C₂×C₅×C₈×D₅	C₂	semidirect
12. C₅²×#41	C₂²	semidirect
13. C₅×#713	C₂²	semidirect
16. C₅×#711	C₂²	semidirect
20. C₅×#709	C₂²	semidirect
23. C₅²×Q₁₆	C₂²	semidirect
24. C₅²×SD₁₆	C₂²	semidirect
25. C₅²×D₈	C₂²	semidirect
26. C₂×C₅²×C₈	C₂²	semidirect
27. C₅×#689	C₂²	semidirect
28. C₅×#688	C₂²	semidirect
29. C₅×#687	C₂²	semidirect
30. C₅×#686	C₂²	semidirect
31. C₂×C₅×#168	C₂²	semidirect
32. C₅×Dic₂₀	C₂²	semidirect
33. C₅×D₄₀	C₂²	semidirect
34. C₅×#677	C₂²	semidirect
37. C₅×C₈×D₅	C₂²	semidirect
38. C₅×C₈×D₅	C₂²	semidirect
40. D₅×#135	C₅	direct (N × H)
69. D₅×#41	C₂×C₅	semidirect
76. C₅×#135	D₅	direct (N × H)
77. C₅×#135	C₂×C₅	semidirect
82. #4096	C₂×C₅	semidirect
83. #4065	C₂×C₅	semidirect
84. D₅×Q₁₆	C₂×C₅	semidirect
85. #4062	C₂×C₅	semidirect
86. D₅×SD₁₆	C₂×C₅	semidirect
87. #4058	C₂×C₅	semidirect
88. D₅×D₈	C₂×C₅	semidirect
89. #4050	C₂×C₅	semidirect
90. C₂×C₈×D₅	C₂×C₅	semidirect
110. C₅×#41	C₂×D₅	semidirect
111. C₅×#41	C₂²×C₅	semidirect
117. #713	C₂²×C₅	semidirect
120. #711	C₂²×C₅	semidirect
124. #709	C₂²×C₅	semidirect
130. C₅×Q₁₆	C₂×D₅	semidirect
131. C₅×Q₁₆	C₂²×C₅	semidirect
136. C₅×SD₁₆	C₂×D₅	semidirect
137. C₅×SD₁₆	C₂²×C₅	semidirect
141. C₅×D₈	C₂×D₅	semidirect
142. C₅×D₈	C₂²×C₅	semidirect
149. C₂×C₅×C₈	C₂×D₅	semidirect
150. C₂×C₅×C₈	C₂²×C₅	semidirect
151. #689	C₂²×C₅	semidirect
152. #688	C₂²×C₅	semidirect
153. #687	C₂²×C₅	semidirect
154. #686	C₂²×C₅	semidirect
155. C₂×#168	C₂²×C₅	semidirect
156. Dic₂₀	C₂²×C₅	semidirect
157. D₄₀	C₂²×C₅	semidirect
158. #677	C₂²×C₅	semidirect
161. C₈×D₅	C₂²×C₅	semidirect
162. C₈×D₅	C₂²×C₅	semidirect
169. C₅×D₅	#135	direct (N × H)
237. #135	C₅×D₅	direct (N × H)
242. C₅²	C₂×#135	semidirect
279. #41	C₂×C₅×D₅	semidirect
287. Q₁₆	C₂×C₅×D₅	semidirect
291. SD₁₆	C₂×C₅×D₅	semidirect
294. D₈	C₂×C₅×D₅	semidirect
300. C₂×C₈	C₂×C₅×D₅	semidirect
315. D₅	C₅×#135	direct (N × H)
344. C₅	D₅×#135	direct (N × H)
345. C₅	C₂×C₅×#135	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
C₅²×#135	2
C₅×#4096	2
C₅×#4065	2
C₅×D₅×Q₁₆	2
C₅×#4062	2
C₅×D₅×SD₁₆	2
C₅×#4058	2
C₅×D₅×D₈	2
C₅×#4050	2
C₂×C₅×C₈×D₅	2
C₂×C₅×#135	5
D₅×#135	5

Subgroups — C5×D5×#135 #13106921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×#135 #13106921