Subgroups — C₅×#33817 #11956537

Order 1280.

534 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2228	C₂	1	2	yes	maximal, complemented
4	C₅×#2225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2220	C₂	1	2	yes	maximal, complemented
7	C₅×#2218	C₂	1	2	yes	maximal, complemented
8	C₅×#2210	C₂	1	2	yes	maximal, complemented
9	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2150	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#532	—	2	1	no	—
13	C₅×#529	—	2	1	no	—
14	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
15	C₂×C₅×D₁₆	C₂²	1	2	yes	—
16	C₂×C₅×M₃₂	C₂²	1	2	yes	—
17	C₅×#500	C₂²	1	1	yes	characteristic
18	C₅×#499	C₂²	1	1	yes	characteristic
19	C₅×#495	C₂²	1	1	yes	characteristic
20	C₅×#493	C₂²	1	1	yes	characteristic
21	C₅×#488	—	2	1	no	—
22	C₅×#486	—	2	1	no	—
23	C₅×#467	C₂²	1	1	yes	characteristic
24	C₅×#466	—	2	1	no	—
25	C₅×#466	C₂²	1	1	yes	characteristic
26	C₅×#466	C₂²	1	2	yes	—
27	C₅×#465	—	2	1	no	—
28	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×SD₁₆	—	2	1	no	—
30	C₄×C₅×D₈	—	2	1	no	—
31	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₈	C₂²	1	2	yes	—
33	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₅×#367	C₂²	1	2	yes	—
35	C₅×#366	C₂²	1	2	yes	—
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
39	C₅×#358	C₂²	1	2	yes	—
40	C₅×#357	C₂²	1	2	yes	—
41	C₅×#357	C₂²	1	2	yes	—
42	C₅×#357	C₂²	1	2	yes	—
43	#33817	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	4	1	no	—
45	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
46	C₂×C₅×SD₁₆	—	2	1	no	—
47	C₂×C₅×D₈	—	2	1	no	—
48	C₂×C₅×D₈	C₂³	1	2	yes	—
49	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×#127	—	2	1	no	—
54	C₅×#126	—	4	1	no	—
55	C₅×#125	—	2	1	no	—
56	C₅×#124	—	2	1	no	—
57	C₅×#124	—	4	1	no	—
58	C₅×#123	—	4	1	no	—
59	C₅×C₂²⋊Q₈	—	2	1	no	—
60	C₅×#121	—	2	1	no	—
61	C₅×#121	—	2	2	no	—
62	C₅×#121	—	4	1	no	—
63	C₄×C₅×Q₈	—	2	1	no	—
64	C₄×C₅×D₄	—	2	2	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	—	4	1	no	—
67	C₄×C₅×D₄	—	4	1	no	—
68	C₅×#117	—	4	1	no	—
69	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
70	C₅×SD₃₂	—	4	2	no	—
71	C₅×D₁₆	—	4	2	no	—
72	C₅×M₃₂	—	4	2	no	—
73	C₂×C₅×C₁₆	C₂³	1	2	yes	—
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₅×#107	—	2	1	no	—
76	C₅×#107	C₂³	1	1	yes	characteristic
77	C₅×#107	C₂³	1	1	yes	characteristic
78	C₅×#107	C₂³	1	2	yes	—
79	C₅×#106	—	2	1	no	—
80	C₅×#103	—	2	1	no	—
81	C₅×#103	—	2	1	no	—
82	C₅×#102	—	2	2	no	—
83	C₅×#102	—	2	1	no	—
84	C₅×#102	—	2	2	no	—
85	C₅×#102	—	2	1	no	—
86	C₄×C₅×C₈	D₄	1	1	yes	characteristic
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	#3169	C₂×C₅	1	1	yes	characteristic, complemented
91	#3168	C₂×C₅	1	1	yes	characteristic, complemented
92	#2228	C₂×C₅	1	2	yes	complemented
93	#2225	C₂×C₅	1	1	yes	characteristic, complemented
94	#2224	C₂×C₅	1	1	yes	characteristic, complemented
95	#2220	C₂×C₅	1	2	yes	complemented
96	#2218	C₂×C₅	1	2	yes	complemented
97	#2210	C₂×C₅	1	2	yes	complemented
98	#2207	C₂×C₅	1	1	yes	characteristic, complemented
99	#2206	C₂×C₅	1	1	yes	characteristic, complemented
100	#2150	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×#41	—	8	4	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	4	1	no	—
104	C₂×C₅×D₄	—	2	1	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	4	1	no	—
107	C₂×C₅×D₄	—	4	2	no	—
108	C₂×C₅×D₄	—	4	1	no	—
109	C₂×C₅×D₄	—	4	1	no	—
110	C₂²×C₄×C₅	—	4	1	no	—
111	C₂²×C₄×C₅	—	4	2	no	—
112	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₅×Q₁₆	—	2	1	no	—
116	C₅×Q₁₆	—	2	1	no	—
117	C₅×SD₁₆	—	4	2	no	—
118	C₅×D₈	—	2	1	no	—
119	C₅×D₈	—	2	2	no	—
120	C₅×D₈	—	2	2	no	—
121	C₅×D₈	—	2	1	no	—
122	C₅×D₈	—	4	2	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	4	1	no	—
126	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	4	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₄⋊C₄	—	4	1	no	—
138	C₅×C₂²⋊C₄	—	4	1	no	—
139	C₅×C₂²⋊C₄	—	4	1	no	—
140	C₅×C₂²⋊C₄	—	4	1	no	—
141	C₅×C₂²⋊C₄	—	4	2	no	—
142	C₅×C₂²⋊C₄	—	4	1	no	—
143	C₅×C₂²⋊C₄	—	4	2	no	—
144	C₅×C₂²⋊C₄	—	4	1	no	—
145	C₄²×C₅	—	4	1	no	—
146	C₄²×C₅	D₈	1	1	yes	characteristic
147	C₄²×C₅	D₈	1	1	yes	characteristic
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
150	C₅×C₁₆	—	2	2	no	—
151	C₅×C₁₆	—	2	2	no	—
152	#532	—	2	1	no	—
153	#529	—	2	1	no	—
154	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
155	C₂×D₁₆	C₂²×C₅	1	2	yes	—
156	C₂×M₃₂	C₂²×C₅	1	2	yes	—
157	#500	C₂²×C₅	1	1	yes	characteristic
158	#499	C₂²×C₅	1	1	yes	characteristic
159	#495	C₂²×C₅	1	1	yes	characteristic
160	#493	C₂²×C₅	1	1	yes	characteristic
161	#488	—	2	1	no	—
162	#486	—	2	1	no	—
163	#467	C₂²×C₅	1	1	yes	characteristic
164	#466	—	2	1	no	—
165	#466	C₂²×C₅	1	1	yes	characteristic
166	#466	C₂²×C₅	1	2	yes	—
167	#465	—	2	1	no	—
168	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
169	C₄×SD₁₆	—	2	1	no	—
170	C₄×D₈	—	2	1	no	—
171	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
172	C₄×D₈	C₂²×C₅	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
174	#367	C₂²×C₅	1	2	yes	—
175	#366	C₂²×C₅	1	2	yes	—
176	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
177	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
178	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
179	#358	C₂²×C₅	1	2	yes	—
180	#357	C₂²×C₅	1	2	yes	—
181	#357	C₂²×C₅	1	2	yes	—
182	#357	C₂²×C₅	1	2	yes	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
186	C₅×Q₈	—	4	1	no	—
187	C₅×Q₈	—	4	1	no	—
188	C₅×Q₈	—	8	2	no	—
189	C₅×D₄	—	4	1	no	—
190	C₅×D₄	—	4	2	no	—
191	C₅×D₄	—	4	2	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	8	2	no	—
194	C₅×D₄	—	8	2	no	—
195	C₅×D₄	—	8	4	no	—
196	C₅×D₄	—	8	2	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	8	4	no	—
206	C₂×C₄×C₅	—	8	2	no	—
207	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	—	2	1	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
217	C₅×C₈	2₋¹⁺⁴	1	1	yes	characteristic
218	C₂×#41	—	4	1	no	—
219	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
220	C₂×SD₁₆	—	2	1	no	—
221	C₂×D₈	—	2	1	no	—
222	C₂×D₈	C₂³×C₅	1	2	yes	—
223	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
226	C₄⋊Q₈	—	2	1	no	—
227	#127	—	2	1	no	—
228	#126	—	4	1	no	—
229	#125	—	2	1	no	—
230	#124	—	2	1	no	—
231	#124	—	4	1	no	—
232	#123	—	4	1	no	—
233	C₂²⋊Q₈	—	2	1	no	—
234	#121	—	2	1	no	—
235	#121	—	2	2	no	—
236	#121	—	4	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	4	1	no	—
241	C₄×D₄	—	4	1	no	—
242	#117	—	4	1	no	—
243	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
244	SD₃₂	—	4	2	no	—
245	D₁₆	—	4	2	no	—
246	M₃₂	—	4	2	no	—
247	C₂×C₁₆	C₂³×C₅	1	2	yes	—
248	C₂×C₁₆	C₂³×C₅	1	2	yes	—
249	#107	—	2	1	no	—
250	#107	C₂³×C₅	1	1	yes	characteristic
251	#107	C₂³×C₅	1	1	yes	characteristic
252	#107	C₂³×C₅	1	2	yes	—
253	#106	—	2	1	no	—
254	#103	—	2	1	no	—
255	#103	—	2	1	no	—
256	#102	—	2	2	no	—
257	#102	—	2	1	no	—
258	#102	—	2	2	no	—
259	#102	—	2	1	no	—
260	C₄×C₈	C₅×D₄	1	1	yes	characteristic
261	C₄×C₈	C₅×D₄	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₅	—	2	1	no	—
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	8	2	no	—
268	C₂²×C₅	—	8	1	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	1	no	—
271	C₂²×C₅	—	8	2	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
274	C₄×C₅	—	2	1	no	—
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	8	1	no	—
279	C₄×C₅	—	8	2	no	—
280	C₄×C₅	—	8	1	no	—
281	C₄×C₅	—	8	1	no	—
282	C₄×C₅	#509	1	2	yes	—
283	C₄×C₅	#537	1	1	yes	characteristic
284	C₄×C₅	#575	1	1	yes	characteristic
285	#41	—	8	4	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
297	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	Q₁₆	—	2	1	no	—
300	Q₁₆	—	2	1	no	—
301	SD₁₆	—	4	2	no	—
302	D₈	—	2	1	no	—
303	D₈	—	2	2	no	—
304	D₈	—	2	2	no	—
305	D₈	—	2	1	no	—
306	D₈	—	4	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₅×D₈	1	1	yes	characteristic
331	C₄²	C₅×D₈	1	1	yes	characteristic
332	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
333	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₂×C₅	—	4	1	no	—
337	C₂×C₅	—	16	2	no	—
338	C₂×C₅	—	16	1	no	—
339	C₂×C₅	#3245	1	1	yes	characteristic
340	C₂×C₅	C₂×#509	1	1	yes	characteristic
341	C₂×C₅	#3414	1	1	yes	characteristic
342	C₂³	—	4	1	no	—
343	C₂³	—	4	2	no	—
344	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	8	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	1	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	4	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	4	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
368	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
369	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
370	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
376	C₈	C₅×2₋¹⁺⁴	1	1	yes	characteristic
377	C₅	#33817	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	1	no	—
387	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	C₅×#509	1	2	yes	—
397	C₄	C₅×#537	1	1	yes	characteristic
398	C₄	C₅×#575	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	16	2	no	—
401	C₂	—	16	1	no	—
402	C₂	C₅×#3245	1	1	yes	characteristic
403	C₂	C₂×C₅×#509	1	1	yes	characteristic
404	C₂	C₅×#3414	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 ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3169	C₂	semidirect
2. C₅×#3168	C₂	semidirect
3. C₅×#2228	C₂	semidirect
4. C₅×#2225	C₂	semidirect
5. C₅×#2224	C₂	semidirect
6. C₅×#2220	C₂	semidirect
7. C₅×#2218	C₂	semidirect
8. C₅×#2210	C₂	semidirect
9. C₅×#2207	C₂	semidirect
10. C₅×#2206	C₂	semidirect
11. C₅×#2150	C₂	semidirect
43. #33817	C₅	direct (N × H)
90. #3169	C₂×C₅	semidirect
91. #3168	C₂×C₅	semidirect
92. #2228	C₂×C₅	semidirect
93. #2225	C₂×C₅	semidirect
94. #2224	C₂×C₅	semidirect
95. #2220	C₂×C₅	semidirect
96. #2218	C₂×C₅	semidirect
97. #2210	C₂×C₅	semidirect
98. #2207	C₂×C₅	semidirect
99. #2206	C₂×C₅	semidirect
100. #2150	C₂×C₅	semidirect
377. C₅	#33817	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×#3169	2
C₅×#3168	2
C₅×#2228	2
C₅×#2225	2
C₅×#2224	2
C₅×#2220	2
C₅×#2218	2
C₅×#2210	2
C₅×#2207	2
C₅×#2206	2
C₅×#2150	2
#33817	5

Subgroups — C5×#33817 #11956537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33817 #11956537