Subgroups — C₅×#33840 #11956560

Order 1280.

748 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#509	C₂	1	2	yes	maximal, complemented
2	C₅×#3287	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2218	C₂	1	2	yes	maximal, complemented
6	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2186	C₂	1	2	yes	maximal, complemented
9	C₅×#2184	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	2	yes	complemented
13	C₂²×C₅×D₈	C₂²	1	2	yes	—
14	C₅×#550	—	2	1	no	—
15	C₅×D₄²	—	2	1	no	—
16	C₅×#509	—	2	8	no	—
17	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
19	C₂×C₅×D₁₆	C₂²	1	2	yes	—
20	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
21	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
22	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
23	C₅×#493	C₂²	1	1	yes	characteristic
24	C₅×#493	C₂²	1	1	yes	characteristic, complemented
25	C₅×#466	C₂²	1	2	yes	—
26	C₅×#466	C₂²	1	2	yes	complemented
27	C₅×#460	—	2	1	no	—
28	C₅×#459	—	2	1	no	—
29	C₅×#449	—	2	2	no	—
30	C₅×#447	—	2	2	no	—
31	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
34	C₅×#367	C₂²	1	1	yes	characteristic, complemented
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₅×#358	C₂²	1	1	yes	characteristic, complemented
37	C₅×#357	C₂²	1	1	yes	characteristic
38	C₅×#357	C₂²	1	2	yes	complemented
39	C₅×#357	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
42	#33840	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	—	2	2	no	—
44	C₂²×C₅×D₄	—	2	2	no	—
45	C₂²×C₅×D₄	—	4	1	no	—
46	C₅×#135	—	2	4	no	—
47	C₅×#135	—	4	2	no	—
48	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₅×SD₁₆	—	2	2	no	—
50	C₂×C₅×D₈	—	2	4	no	—
51	C₂×C₅×D₈	—	2	2	no	—
52	C₂×C₅×D₈	—	2	1	no	—
53	C₂×C₅×D₈	—	2	1	no	—
54	C₂×C₅×D₈	—	4	2	no	—
55	C₂×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₅×D₈	C₂³	1	2	yes	—
57	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	2	yes	—
59	C₅×#127	—	2	1	no	—
60	C₅×#127	—	2	1	no	—
61	C₅×#127	—	4	1	no	—
62	C₅×#121	—	2	2	no	—
63	C₅×#121	—	2	2	no	—
64	C₅×#121	—	4	1	no	—
65	C₅×#121	—	4	2	no	—
66	C₅×#120	—	4	2	no	—
67	C₄×C₅×Q₈	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	4	1	no	—
70	C₄×C₅×D₄	D₄	1	1	yes	characteristic
71	C₅×SD₃₂	—	2	4	no	—
72	C₅×SD₃₂	D₄	1	4	yes	complemented
73	C₅×D₁₆	—	2	4	no	—
74	C₅×D₁₆	—	2	4	no	—
75	C₅×D₁₆	—	4	2	no	—
76	C₅×M₃₂	—	2	4	no	—
77	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₁₆	C₂³	1	2	yes	—
79	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₅×#107	C₂³	1	1	yes	characteristic
81	C₅×#107	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×#103	—	2	1	no	—
84	C₅×#102	—	2	1	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×C₂²⋊C₈	D₄	1	2	yes	—
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂×#509	C₂×C₅	1	2	yes	complemented
90	#3287	C₂×C₅	1	1	yes	characteristic, complemented
91	D₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
92	#2246	C₂×C₅	1	1	yes	characteristic, complemented
93	#2218	C₂×C₅	1	2	yes	complemented
94	#2207	C₂×C₅	1	1	yes	characteristic, complemented
95	#2206	C₂×C₅	1	1	yes	characteristic, complemented
96	#2186	C₂×C₅	1	2	yes	complemented
97	#2184	C₂×C₅	1	2	yes	complemented
98	C₄×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
99	#2169	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂⁴×C₅	—	4	2	no	—
101	C₅×#41	—	4	4	no	—
102	C₅×#41	—	8	2	no	—
103	C₂×C₅×Q₈	—	2	1	no	—
104	C₂×C₅×D₄	—	2	1	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	—	4	4	no	—
108	C₂×C₅×D₄	—	4	2	no	—
109	C₂×C₅×D₄	—	4	2	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂×C₅×D₄	—	8	2	no	—
117	C₂×C₅×D₄	—	8	4	no	—
118	C₂×C₅×D₄	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	4	1	no	—
120	C₂²×C₄×C₅	—	4	2	no	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₅×Q₁₆	—	2	1	no	—
123	C₅×Q₁₆	C₂×D₄	1	2	yes	complemented
124	C₅×SD₁₆	—	4	4	no	—
125	C₅×D₈	—	2	2	no	—
126	C₅×D₈	—	2	2	no	—
127	C₅×D₈	—	2	1	no	—
128	C₅×D₈	—	2	2	no	—
129	C₅×D₈	—	2	2	no	—
130	C₅×D₈	—	4	4	no	—
131	C₅×D₈	—	8	1	no	—
132	C₅×D₈	—	8	1	no	—
133	C₅×D₈	C₂×D₄	1	2	yes	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	4	1	no	—
142	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
143	C₅×C₂²⋊C₄	—	4	1	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	—	4	2	no	—
146	C₅×C₂²⋊C₄	D₈	1	2	yes	—
147	C₄²×C₅	—	4	1	no	—
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₅×C₁₆	—	2	2	no	—
150	C₅×C₁₆	—	2	1	no	—
151	C₅×C₁₆	C₂×D₄	1	2	yes	complemented
152	C₂×#135	C₂²×C₅	1	2	yes	complemented
153	C₂²×D₈	C₂²×C₅	1	2	yes	—
154	#550	—	2	1	no	—
155	D₄²	—	2	1	no	—
156	#509	—	2	8	no	—
157	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
158	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
159	C₂×D₁₆	C₂²×C₅	1	2	yes	—
160	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
161	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
162	C₂×M₃₂	C₂²×C₅	1	2	yes	complemented
163	#493	C₂²×C₅	1	1	yes	characteristic
164	#493	C₂²×C₅	1	1	yes	characteristic, complemented
165	#466	C₂²×C₅	1	2	yes	—
166	#466	C₂²×C₅	1	2	yes	complemented
167	#460	—	2	1	no	—
168	#459	—	2	1	no	—
169	#449	—	2	2	no	—
170	#447	—	2	2	no	—
171	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
173	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
174	#367	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
176	#358	C₂²×C₅	1	1	yes	characteristic, complemented
177	#357	C₂²×C₅	1	1	yes	characteristic
178	#357	C₂²×C₅	1	2	yes	complemented
179	#357	C₂²×C₅	1	2	yes	complemented
180	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
181	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₂³×C₅	—	4	1	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	—	8	4	no	—
186	C₂³×C₅	—	8	4	no	—
187	C₂³×C₅	—	16	2	no	—
188	C₂³×C₅	C₂×D₈	1	2	yes	—
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	4	1	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	8	4	no	—
199	C₅×D₄	—	8	4	no	—
200	C₅×D₄	—	8	4	no	—
201	C₅×D₄	—	8	2	no	—
202	C₅×D₄	—	8	2	no	—
203	C₅×D₄	—	16	1	no	—
204	C₅×D₄	—	16	1	no	—
205	C₅×D₄	—	16	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	8	4	no	—
212	C₂×C₄×C₅	—	8	2	no	—
213	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	2	1	no	—
219	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
220	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×#41	—	2	2	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	4	1	no	—
224	#135	—	2	4	no	—
225	#135	—	4	2	no	—
226	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	4	2	no	—
233	C₂×D₈	C₂³×C₅	1	2	yes	—
234	C₂×D₈	C₂³×C₅	1	2	yes	—
235	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₅	1	2	yes	—
237	#127	—	2	1	no	—
238	#127	—	2	1	no	—
239	#127	—	4	1	no	—
240	#121	—	2	2	no	—
241	#121	—	2	2	no	—
242	#121	—	4	1	no	—
243	#121	—	4	2	no	—
244	#120	—	4	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	4	1	no	—
248	C₄×D₄	C₅×D₄	1	1	yes	characteristic
249	SD₃₂	—	2	4	no	—
250	SD₃₂	C₅×D₄	1	4	yes	complemented
251	D₁₆	—	2	4	no	—
252	D₁₆	—	2	4	no	—
253	D₁₆	—	4	2	no	—
254	M₃₂	—	2	4	no	—
255	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₁₆	C₂³×C₅	1	2	yes	—
257	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
258	#107	C₂³×C₅	1	1	yes	characteristic
259	#107	C₂³×C₅	1	1	yes	characteristic
260	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
261	#103	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	C₅×D₄	1	2	yes	—
266	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₅	—	2	2	no	—
268	C₂²×C₅	—	2	2	no	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	8	1	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	—	8	2	no	—
274	C₂²×C₅	—	8	2	no	—
275	C₂²×C₅	—	8	2	no	—
276	C₂²×C₅	—	8	2	no	—
277	C₂²×C₅	—	8	2	no	—
278	C₂²×C₅	—	8	2	no	—
279	C₂²×C₅	—	16	8	no	—
280	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	8	1	no	—
285	C₄×C₅	—	8	1	no	—
286	C₄×C₅	#509	1	2	yes	complemented
287	C₄×C₅	D₄²	1	1	yes	characteristic
288	C₄×C₅	#576	1	1	yes	characteristic
289	C₂⁴	—	4	2	no	—
290	#41	—	4	4	no	—
291	#41	—	8	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂×D₄	—	8	4	no	—
307	C₂×D₄	C₅×D₈	1	1	yes	characteristic
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
311	Q₁₆	—	2	1	no	—
312	Q₁₆	C₂×C₅×D₄	1	2	yes	complemented
313	SD₁₆	—	4	4	no	—
314	D₈	—	2	2	no	—
315	D₈	—	2	2	no	—
316	D₈	—	2	1	no	—
317	D₈	—	2	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	4	no	—
320	D₈	—	8	1	no	—
321	D₈	—	8	1	no	—
322	D₈	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
327	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	C₅×D₈	1	2	yes	—
336	C₄²	—	4	1	no	—
337	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
338	C₁₆	—	2	2	no	—
339	C₁₆	—	2	1	no	—
340	C₁₆	C₂×C₅×D₄	1	2	yes	complemented
341	C₂×C₅	—	4	2	no	—
342	C₂×C₅	—	8	2	no	—
343	C₂×C₅	—	16	2	no	—
344	C₂×C₅	—	16	2	no	—
345	C₂×C₅	D₄×D₈	1	1	yes	characteristic
346	C₂×C₅	C₂×#509	1	1	yes	characteristic
347	C₂×C₅	#3415	1	1	yes	characteristic
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	8	4	no	—
352	C₂³	—	8	4	no	—
353	C₂³	—	16	2	no	—
354	C₂³	C₂×C₅×D₈	1	2	yes	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	1	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	8	4	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	16	1	no	—
370	D₄	—	16	1	no	—
371	D₄	—	16	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	8	4	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
381	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	1	no	—
385	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
386	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
387	C₅	#33840	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	16	8	no	—
401	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	C₅×#509	1	2	yes	complemented
408	C₄	C₅×D₄²	1	1	yes	characteristic
409	C₄	C₅×#576	1	1	yes	characteristic
410	C₂	—	4	2	no	—
411	C₂	—	8	2	no	—
412	C₂	—	16	2	no	—
413	C₂	—	16	2	no	—
414	C₂	C₅×D₄×D₈	1	1	yes	characteristic
415	C₂	C₂×C₅×#509	1	1	yes	characteristic
416	C₂	C₅×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#509	C₂	semidirect
2. C₅×#3287	C₂	semidirect
3. C₅×D₄×D₈	C₂	semidirect
4. C₅×#2246	C₂	semidirect
5. C₅×#2218	C₂	semidirect
6. C₅×#2207	C₂	semidirect
7. C₅×#2206	C₂	semidirect
8. C₅×#2186	C₂	semidirect
9. C₅×#2184	C₂	semidirect
10. C₄×C₅×SD₃₂	C₂	semidirect
11. C₅×#2169	C₂	semidirect
12. C₂×C₅×#135	C₂²	semidirect
18. C₂×C₅×SD₃₂	C₂²	semidirect
20. C₂×C₅×D₁₆	C₂²	semidirect
21. C₂×C₅×D₁₆	C₂²	semidirect
22. C₂×C₅×M₃₂	C₂²	semidirect
24. C₅×#493	C₂²	semidirect
26. C₅×#466	C₂²	semidirect
31. C₄×C₅×Q₁₆	C₂²	semidirect
34. C₅×#367	C₂²	semidirect
35. C₅×C₄⋊C₁₆	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
38. C₅×#357	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
40. C₅×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₅×C₁₆	C₂²	semidirect
42. #33840	C₅	direct (N × H)
72. C₅×SD₃₂	D₄	semidirect
89. C₂×#509	C₂×C₅	semidirect
90. #3287	C₂×C₅	semidirect
91. D₄×D₈	C₂×C₅	semidirect
92. #2246	C₂×C₅	semidirect
93. #2218	C₂×C₅	semidirect
94. #2207	C₂×C₅	semidirect
95. #2206	C₂×C₅	semidirect
96. #2186	C₂×C₅	semidirect
97. #2184	C₂×C₅	semidirect
98. C₄×SD₃₂	C₂×C₅	semidirect
99. #2169	C₂×C₅	semidirect
123. C₅×Q₁₆	C₂×D₄	semidirect
151. C₅×C₁₆	C₂×D₄	semidirect
152. C₂×#135	C₂²×C₅	semidirect
158. C₂×SD₃₂	C₂²×C₅	semidirect
160. C₂×D₁₆	C₂²×C₅	semidirect
161. C₂×D₁₆	C₂²×C₅	semidirect
162. C₂×M₃₂	C₂²×C₅	semidirect
164. #493	C₂²×C₅	semidirect
166. #466	C₂²×C₅	semidirect
171. C₄×Q₁₆	C₂²×C₅	semidirect
174. #367	C₂²×C₅	semidirect
175. C₄⋊C₁₆	C₂²×C₅	semidirect
176. #358	C₂²×C₅	semidirect
178. #357	C₂²×C₅	semidirect
179. #357	C₂²×C₅	semidirect
180. C₂²⋊C₁₆	C₂²×C₅	semidirect
181. C₄×C₁₆	C₂²×C₅	semidirect
250. SD₃₂	C₅×D₄	semidirect
286. C₄×C₅	#509	semidirect
312. Q₁₆	C₂×C₅×D₄	semidirect
340. C₁₆	C₂×C₅×D₄	semidirect
387. C₅	#33840	direct (N × H)
407. C₄	C₅×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#509	2
C₅×#3287	2
C₅×D₄×D₈	2
C₅×#2246	2
C₅×#2218	2
C₅×#2207	2
C₅×#2206	2
C₅×#2186	2
C₅×#2184	2
C₄×C₅×SD₃₂	2
C₅×#2169	2
#33840	5

Subgroups — C5×#33840 #11956560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33840 #11956560