Subgroups — C₅×#19908 #11942628

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3391	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3332	C₂	1	2	yes	maximal, complemented
3	C₅×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1709	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	2	yes	maximal, complemented
6	C₅×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1642	C₂	1	2	yes	maximal, complemented
9	C₅×#1625	C₂	1	2	yes	maximal, complemented
10	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	—	2	1	no	—
13	C₅×#550	C₂²	1	2	yes	—
14	C₅×#547	C₂²	1	2	yes	—
15	C₅×#494	C₂²	1	1	yes	characteristic
16	C₅×#493	—	2	1	no	—
17	C₅×#493	C₂²	1	1	yes	characteristic
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#486	C₂²	1	2	yes	—
20	C₅×#481	—	2	2	no	—
21	C₅×#475	C₂²	1	2	yes	—
22	C₅×#469	—	2	2	no	—
23	C₅×#467	—	2	1	no	—
24	C₅×#461	C₂²	1	2	yes	—
25	C₅×#459	—	2	2	no	—
26	C₅×#459	C₂²	1	2	yes	—
27	C₅×#459	C₂²	1	2	yes	—
28	C₅×#452	—	2	2	no	—
29	C₅×#449	—	2	2	no	—
30	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₈	—	2	1	no	—
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₅×#436	C₂²	1	2	yes	—
35	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
36	C₅×#417	—	2	2	no	—
37	C₅×#335	C₂²	1	1	yes	characteristic
38	C₅×#334	C₂²	1	1	yes	characteristic
39	C₅×#332	C₂²	1	2	yes	—
40	C₅×#331	C₂²	1	2	yes	—
41	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₅×D₄⋊C₈	C₂²	1	2	yes	—
44	C₅×C₈²	C₂²	1	1	yes	characteristic
45	#19908	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	2	no	—
47	C₂×C₅×#41	—	2	2	no	—
48	C₅×#135	—	4	4	no	—
49	C₂×C₅×Q₁₆	—	2	1	no	—
50	C₂×C₅×Q₁₆	—	2	1	no	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
53	C₂×C₅×D₈	—	2	2	no	—
54	C₂×C₅×D₈	—	2	2	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×D₈	D₄	1	1	yes	characteristic
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₅×#127	—	2	2	no	—
62	C₅×#127	C₂³	1	2	yes	—
63	C₅×#123	—	4	2	no	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×#121	—	2	2	no	—
66	C₅×#121	—	2	2	no	—
67	C₅×#121	—	4	2	no	—
68	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₄	—	2	2	no	—
70	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₄	C₂³	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	—	2	2	no	—
73	C₅×#107	D₄	1	1	yes	characteristic
74	C₅×#106	—	2	2	no	—
75	C₅×#106	D₄	1	1	yes	characteristic
76	C₅×C₄⋊C₈	—	2	1	no	—
77	C₅×C₄⋊C₈	C₂³	1	2	yes	—
78	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₅×#103	—	2	2	no	—
81	C₅×#103	—	2	2	no	—
82	C₅×#103	D₄	1	1	yes	characteristic
83	C₅×#102	—	2	2	no	—
84	C₅×#102	—	2	2	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	4	2	no	—
88	C₅×#102	D₄	1	2	yes	—
89	C₅×#102	D₄	1	1	yes	characteristic
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	2	no	—
92	C₄×C₅×C₈	—	2	1	no	—
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
96	#3391	C₂×C₅	1	1	yes	characteristic, complemented
97	#3332	C₂×C₅	1	2	yes	complemented
98	#3283	C₂×C₅	1	1	yes	characteristic, complemented
99	#1709	C₂×C₅	1	1	yes	characteristic, complemented
100	#1701	C₂×C₅	1	2	yes	complemented
101	#1670	C₂×C₅	1	1	yes	characteristic, complemented
102	#1667	C₂×C₅	1	1	yes	characteristic, complemented
103	#1642	C₂×C₅	1	2	yes	complemented
104	#1625	C₂×C₅	1	2	yes	complemented
105	#1589	C₂×C₅	1	1	yes	characteristic, complemented
106	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
107	C₅×#41	—	4	4	no	—
108	C₅×#41	—	4	4	no	—
109	C₅×#41	—	8	2	no	—
110	C₅×#41	—	8	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂×C₅×D₄	—	4	2	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	4	2	no	—
124	C₂²×C₄×C₅	—	4	2	no	—
125	C₅×Q₁₆	—	4	2	no	—
126	C₅×Q₁₆	—	8	1	no	—
127	C₅×SD₁₆	—	2	2	no	—
128	C₅×SD₁₆	—	4	4	no	—
129	C₅×D₈	—	2	2	no	—
130	C₅×D₈	—	4	2	no	—
131	C₅×D₈	—	8	1	no	—
132	C₅×D₈	—	8	2	no	—
133	C₅×D₈	—	8	2	no	—
134	C₅×M₁₆	—	8	2	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	4	2	no	—
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	4	2	no	—
154	C₅×C₂²⋊C₄	—	4	2	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	C₂⁴	1	1	yes	characteristic
157	C₂×#135	—	2	1	no	—
158	#550	C₂²×C₅	1	2	yes	—
159	#547	C₂²×C₅	1	2	yes	—
160	#494	C₂²×C₅	1	1	yes	characteristic
161	#493	—	2	1	no	—
162	#493	C₂²×C₅	1	1	yes	characteristic
163	#486	C₂²×C₅	1	2	yes	—
164	#486	C₂²×C₅	1	2	yes	—
165	#481	—	2	2	no	—
166	#475	C₂²×C₅	1	2	yes	—
167	#469	—	2	2	no	—
168	#467	—	2	1	no	—
169	#461	C₂²×C₅	1	2	yes	—
170	#459	—	2	2	no	—
171	#459	C₂²×C₅	1	2	yes	—
172	#459	C₂²×C₅	1	2	yes	—
173	#452	—	2	2	no	—
174	#449	—	2	2	no	—
175	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
176	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
177	C₄×D₈	—	2	1	no	—
178	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
179	#436	C₂²×C₅	1	2	yes	—
180	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
181	#417	—	2	2	no	—
182	#335	C₂²×C₅	1	1	yes	characteristic
183	#334	C₂²×C₅	1	1	yes	characteristic
184	#332	C₂²×C₅	1	2	yes	—
185	#331	C₂²×C₅	1	2	yes	—
186	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
187	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	D₄⋊C₈	C₂²×C₅	1	2	yes	—
189	C₈²	C₂²×C₅	1	1	yes	characteristic
190	C₂³×C₅	—	2	1	no	—
191	C₂³×C₅	—	2	2	no	—
192	C₂³×C₅	—	4	2	no	—
193	C₅×Q₈	—	2	1	no	—
194	C₅×Q₈	—	4	2	no	—
195	C₅×Q₈	—	4	2	no	—
196	C₅×Q₈	#135	1	2	yes	complemented
197	C₅×D₄	—	2	1	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	2	1	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	4	2	no	—
205	C₅×D₄	—	8	4	no	—
206	C₅×D₄	—	8	2	no	—
207	C₅×D₄	—	8	4	no	—
208	C₅×D₄	—	16	2	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	8	4	no	—
219	C₂×C₄×C₅	—	8	4	no	—
220	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
223	C₅×C₈	—	2	1	no	—
224	C₅×C₈	—	2	1	no	—
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	—	4	1	no	—
227	C₅×C₈	—	4	1	no	—
228	C₅×C₈	—	4	2	no	—
229	C₅×C₈	—	4	1	no	—
230	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	2	no	—
233	#135	—	4	4	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	—	2	1	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	1	no	—
241	C₂×D₈	—	2	1	no	—
242	C₂×D₈	C₅×D₄	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
246	#127	—	2	2	no	—
247	#127	C₂³×C₅	1	2	yes	—
248	#123	—	4	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	#121	—	2	2	no	—
251	#121	—	2	2	no	—
252	#121	—	4	2	no	—
253	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
256	C₄×D₄	C₂³×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	#107	C₅×D₄	1	1	yes	characteristic
259	#106	—	2	2	no	—
260	#106	C₅×D₄	1	1	yes	characteristic
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	C₂³×C₅	1	2	yes	—
263	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
264	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
265	#103	—	2	2	no	—
266	#103	—	2	2	no	—
267	#103	C₅×D₄	1	1	yes	characteristic
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	2	2	no	—
272	#102	—	4	2	no	—
273	#102	C₅×D₄	1	2	yes	—
274	#102	C₅×D₄	1	1	yes	characteristic
275	C₂²⋊C₈	—	2	1	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	—	4	2	no	—
283	C₂²×C₅	—	4	2	no	—
284	C₂²×C₅	—	4	1	no	—
285	C₂²×C₅	—	4	2	no	—
286	C₂²×C₅	—	4	1	no	—
287	C₂²×C₅	—	8	2	no	—
288	C₂²×C₅	—	8	2	no	—
289	C₂²×C₅	—	8	2	no	—
290	C₂²×C₅	D₄²	1	1	yes	characteristic
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	4	1	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	1	no	—
296	C₄×C₅	—	8	2	no	—
297	C₄×C₅	C₂×#135	1	1	yes	characteristic
298	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₄×C₅	#576	1	1	yes	characteristic
300	C₄×C₅	#576	1	1	yes	characteristic
301	#41	—	4	4	no	—
302	#41	—	4	4	no	—
303	#41	—	8	2	no	—
304	#41	—	8	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	Q₁₆	—	4	2	no	—
320	Q₁₆	—	8	1	no	—
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	4	4	no	—
323	D₈	—	2	2	no	—
324	D₈	—	4	2	no	—
325	D₈	—	8	1	no	—
326	D₈	—	8	2	no	—
327	D₈	—	8	2	no	—
328	M₁₆	—	8	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
344	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	C₂⁴×C₅	1	1	yes	characteristic
351	C₂×C₅	—	8	1	no	—
352	C₂×C₅	—	8	2	no	—
353	C₂×C₅	—	16	2	no	—
354	C₂×C₅	#3274	1	1	yes	characteristic
355	C₂×C₅	#3280	1	1	yes	characteristic
356	C₂×C₅	#3290	1	1	yes	characteristic
357	C₂³	—	2	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	4	2	no	—
360	Q₈	—	2	1	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	C₅×#135	1	2	yes	complemented
364	D₄	—	2	1	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	4	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	4	no	—
375	D₄	—	16	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	4	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
389	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	1	no	—
397	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
398	C₅	#19908	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	C₅×D₄²	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	8	2	no	—
415	C₄	C₂×C₅×#135	1	1	yes	characteristic
416	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₄	C₅×#576	1	1	yes	characteristic
418	C₄	C₅×#576	1	1	yes	characteristic
419	C₂	—	8	1	no	—
420	C₂	—	8	2	no	—
421	C₂	—	16	2	no	—
422	C₂	C₅×#3274	1	1	yes	characteristic
423	C₂	C₅×#3280	1	1	yes	characteristic
424	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3391	C₂	semidirect
2. C₅×#3332	C₂	semidirect
3. C₅×#3283	C₂	semidirect
4. C₅×#1709	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1670	C₂	semidirect
7. C₅×#1667	C₂	semidirect
8. C₅×#1642	C₂	semidirect
9. C₅×#1625	C₂	semidirect
10. C₅×#1589	C₂	semidirect
11. C₅×C₈×SD₁₆	C₂	semidirect
45. #19908	C₅	direct (N × H)
96. #3391	C₂×C₅	semidirect
97. #3332	C₂×C₅	semidirect
98. #3283	C₂×C₅	semidirect
99. #1709	C₂×C₅	semidirect
100. #1701	C₂×C₅	semidirect
101. #1670	C₂×C₅	semidirect
102. #1667	C₂×C₅	semidirect
103. #1642	C₂×C₅	semidirect
104. #1625	C₂×C₅	semidirect
105. #1589	C₂×C₅	semidirect
106. C₈×SD₁₆	C₂×C₅	semidirect
196. C₅×Q₈	#135	semidirect
363. Q₈	C₅×#135	semidirect
398. C₅	#19908	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3391	2
C₅×#3332	2
C₅×#3283	2
C₅×#1709	2
C₅×#1701	2
C₅×#1670	2
C₅×#1667	2
C₅×#1642	2
C₅×#1625	2
C₅×#1589	2
C₅×C₈×SD₁₆	2
#19908	5

Subgroups — C5×#19908 #11942628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19908 #11942628