Subgroups — #12117748

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×#65486	C₂	1	2	yes	maximal
3	#10614243	C₂	1	2	yes	maximal, complemented
4	#10602439	C₂	1	2	yes	maximal, complemented
5	#10601456	C₂	1	2	yes	maximal, complemented
6	#10601085	C₂	1	4	yes	maximal, complemented
7	#10600585	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#135	C₂²	1	1	yes	characteristic
10	C₄×C₅×#41	C₂²	1	2	yes	—
11	C₂×#4094	C₂²	1	4	yes	—
12	C₄×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
13	C₄×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×C₅×SD₁₆	C₄	1	2	yes	complemented
15	C₄×C₅×SD₁₆	C₄	1	2	yes	complemented
16	C₄×C₅×D₈	C₄	1	1	yes	characteristic, complemented
17	C₄×C₅×D₈	C₄	1	1	yes	characteristic, complemented
18	C₅×#427	C₂²	1	1	yes	characteristic
19	C₅×#416	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×#3969	C₂²	1	4	yes	—
22	#65486	—	2	8	no	—
23	C₂×#3951	C₂²	1	2	yes	—
24	C₂×#3951	C₂²	1	2	yes	—
25	C₂×#3947	C₂²	1	2	yes	—
26	#65288	—	2	4	no	—
27	#65288	C₂²	1	4	yes	—
28	C₄×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
29	#65213	—	2	2	no	—
30	#65213	C₂²	1	2	yes	—
31	C₂×C₄⋊#168	—	2	2	no	—
32	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
33	#64770	C₂²	1	2	yes	—
34	#64752	C₂²	1	4	yes	—
35	#22686	—	5	1	no	maximal, Sylow
36	C₂×C₅×#41	C₂³	1	2	yes	—
37	C₅×#135	D₄	1	4	yes	—
38	C₅×#135	Q₈	1	4	yes	—
39	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
40	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
45	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
46	C₄×C₅×D₄	—	2	2	no	—
47	C₄×C₅×D₄	—	2	2	no	—
48	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
49	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₅×#117	—	2	2	no	—
51	C₅×#117	C₂³	1	2	yes	—
52	C₂×C₄²×C₅	—	2	2	no	—
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	#4094	—	2	8	no	—
55	#4094	—	4	4	no	—
56	C₂×C₄⋊Dic₅	—	2	1	no	—
57	C₂×C₄×Dic₅	C₂³	1	2	yes	—
58	C₂×#681	—	2	4	no	—
59	C₂×#681	C₂³	1	4	yes	—
60	C₂²×#168	—	2	4	no	—
61	C₂²×#168	C₂³	1	2	yes	—
62	C₅×#107	C₂×C₄	1	1	yes	characteristic
63	C₅×#107	C₂×C₄	1	1	yes	characteristic
64	C₅×#106	C₂×C₄	1	2	yes	—
65	C₅×#103	C₂×C₄	1	2	yes	—
66	C₅×#103	C₂×C₄	1	2	yes	—
67	C₅×#102	C₂×C₄	1	2	yes	—
68	C₅×#102	C₂×C₄	1	2	yes	—
69	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
71	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
73	#3969	—	2	8	no	—
74	#3963	—	2	1	no	—
75	#3951	—	2	4	no	—
76	#3951	—	4	2	no	—
77	#3947	—	2	4	no	—
78	C₄⋊#168	—	2	2	no	—
79	C₄⋊#168	—	2	2	no	—
80	C₄⋊#168	—	2	4	no	—
81	C₄⋊#168	—	2	4	no	—
82	C₄⋊#168	D₄	1	2	yes	—
83	C₄⋊#168	D₄	1	2	yes	—
84	C₂×#444	—	5	2	no	—
85	C₄×#135	D₅	1	1	yes	characteristic
86	#2906	—	5	2	no	—
87	#1946	—	5	2	no	—
88	#1866	—	5	4	no	—
89	#1848	—	5	1	no	—
90	#1806	—	5	2	no	—
91	#1770	—	5	1	no	—
92	C₅×#41	—	2	2	no	—
93	C₅×#41	—	2	2	no	—
94	C₅×#41	C₂×D₄	1	4	yes	—
95	C₅×#41	C₂×Q₈	1	4	yes	—
96	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
97	C₂×C₅×D₄	—	2	2	no	—
98	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	#41	1	1	yes	characteristic
103	C₂²×C₄×C₅	#41	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₅	—	2	2	no	—
106	C₅×Q₁₆	C₄⋊C₄	1	4	yes	complemented
107	C₅×SD₁₆	C₄⋊C₄	1	8	yes	complemented
108	C₅×D₈	C₄⋊C₄	1	4	yes	complemented
109	C₂×C₅×C₈	—	2	1	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
116	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₄⋊C₄	—	2	2	no	—
119	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
120	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
121	C₅×C₂²⋊C₄	—	2	2	no	—
122	C₅×C₂²⋊C₄	—	2	2	no	—
123	C₅×C₂²⋊C₄	—	2	2	no	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	2	2	no	—
127	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
131	C₄⋊Dic₅	—	4	2	no	—
132	C₄×Dic₅	—	2	2	no	—
133	C₄×Dic₅	—	2	2	no	—
134	#681	—	2	4	no	—
135	#681	—	2	4	no	—
136	#681	—	4	8	no	—
137	C₂×#168	—	2	2	no	—
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	2	4	no	—
140	C₂×#168	—	4	8	no	—
141	C₂×#168	C₂×D₄	1	4	yes	—
142	C₂×#135	C₂×D₅	1	1	yes	characteristic
143	C₂×#131	—	5	4	no	—
144	C₄×#41	C₂×D₅	1	2	yes	—
145	#444	—	10	8	no	—
146	C₄×Q₁₆	Dic₅	1	1	yes	characteristic, complemented
147	C₄×Q₁₆	Dic₅	1	1	yes	characteristic, complemented
148	C₄×SD₁₆	Dic₅	1	2	yes	complemented
149	C₄×SD₁₆	Dic₅	1	2	yes	complemented
150	C₄×D₈	Dic₅	1	1	yes	characteristic, complemented
151	C₄×D₈	Dic₅	1	1	yes	characteristic, complemented
152	C₂×#108	—	5	2	no	—
153	C₂×#108	—	5	2	no	—
154	#427	C₂×D₅	1	1	yes	characteristic
155	#424	—	5	4	no	—
156	#424	—	10	4	no	—
157	#423	—	5	2	no	—
158	#423	—	10	2	no	—
159	C₂×C₄⋊C₈	—	5	1	no	—
160	C₂×C₄⋊C₈	—	10	2	no	—
161	C₂×#104	—	5	4	no	—
162	#416	C₂×D₅	1	2	yes	—
163	C₂×#97	—	5	2	no	—
164	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
165	C₄×C₄⋊C₄	—	5	1	no	—
166	#339	—	5	4	no	—
167	#336	—	5	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	C₂×#41	1	1	yes	characteristic
170	C₅×Q₈	—	2	2	no	—
171	C₅×Q₈	C₂×C₄⋊C₄	1	4	yes	—
172	C₅×D₄	—	2	4	no	—
173	C₅×D₄	—	2	4	no	—
174	C₅×D₄	—	2	2	no	—
175	C₅×D₄	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	2	4	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	4	no	—
184	C₂×C₄×C₅	—	8	2	no	—
185	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
195	C₂×Dic₅	—	4	2	no	—
196	C₂×Dic₅	—	4	2	no	—
197	C₂×Dic₅	—	4	2	no	—
198	C₅×C₈	—	2	1	no	—
199	C₅×C₈	—	2	1	no	—
200	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
201	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
202	#168	—	2	4	no	—
203	#168	—	4	4	no	—
204	C₂×#41	C₂²×D₅	1	2	yes	—
205	#135	Dic₁₀	1	4	yes	—
206	#135	D₂₀	1	4	yes	—
207	C₂×Q₁₆	C₂×Dic₅	1	1	yes	characteristic
208	C₂×SD₁₆	C₂×Dic₅	1	2	yes	—
209	C₂×D₈	C₂×Dic₅	1	1	yes	characteristic
210	#131	—	10	8	no	—
211	#131	—	20	4	no	—
212	C₂×M₁₆	—	5	4	no	—
213	C₂×M₁₆	—	10	4	no	—
214	C₂²×C₈	—	5	2	no	—
215	C₂²×C₈	—	10	4	no	—
216	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
217	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
218	C₄×Q₈	C₂×Dic₅	1	2	yes	—
219	C₄×Q₈	C₂×Dic₅	1	2	yes	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	C₂×Dic₅	1	2	yes	—
223	C₄×D₄	C₂×Dic₅	1	2	yes	—
224	#117	—	2	2	no	—
225	#117	C₂²×D₅	1	2	yes	—
226	C₂×C₄⋊C₄	—	10	1	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	5	2	no	—
229	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
230	#108	—	10	4	no	—
231	#108	—	20	2	no	—
232	#107	C₂×Dic₅	1	1	yes	characteristic
233	#107	C₂×Dic₅	1	1	yes	characteristic
234	#106	C₂×Dic₅	1	2	yes	—
235	C₄⋊C₈	—	5	2	no	—
236	C₄⋊C₈	—	5	2	no	—
237	C₄⋊C₈	—	10	4	no	—
238	C₄⋊C₈	—	10	4	no	—
239	C₄⋊C₈	—	10	2	no	—
240	C₄⋊C₈	—	10	2	no	—
241	#104	—	10	8	no	—
242	#103	C₂×Dic₅	1	2	yes	—
243	#103	C₂×Dic₅	1	2	yes	—
244	#102	C₂×Dic₅	1	2	yes	—
245	#102	C₂×Dic₅	1	2	yes	—
246	#97	—	10	4	no	—
247	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
248	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
249	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
250	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
251	#95	—	10	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	4	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₅	#547	1	1	yes	characteristic
259	C₂²×C₅	#554	1	1	yes	characteristic
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	—	2	1	no	—
264	C₄×C₅	—	4	2	no	—
265	C₄×C₅	—	4	2	no	—
266	C₄×C₅	#444	1	2	yes	complemented
267	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₅	#520	1	1	yes	characteristic
269	C₄×C₅	D₄²	1	1	yes	characteristic
270	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
271	Dic₅	—	8	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	C₂×Dic₁₀	1	4	yes	—
275	#41	C₂×D₂₀	1	4	yes	—
276	C₂×Q₈	C₂²×Dic₅	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	C₂²×Dic₅	1	2	yes	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	10	2	no	—
283	C₂²×C₄	#711	1	1	yes	characteristic
284	C₂²×C₄	#711	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
286	Q₁₆	C₄⋊Dic₅	1	4	yes	complemented
287	SD₁₆	C₄⋊Dic₅	1	8	yes	complemented
288	D₈	C₄⋊Dic₅	1	4	yes	complemented
289	M₁₆	—	10	4	no	—
290	M₁₆	—	10	4	no	—
291	M₁₆	—	20	8	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	5	4	no	—
295	C₂×C₈	—	10	2	no	—
296	C₂×C₈	—	10	2	no	—
297	C₂×C₈	—	10	4	no	—
298	C₂×C₈	—	20	8	no	—
299	C₂×C₈	C₂×Dic₁₀	1	2	yes	—
300	C₂×C₈	C₂×D₂₀	1	2	yes	—
301	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
302	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
303	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	20	2	no	—
308	C₄⋊C₄	C₂²×Dic₅	1	2	yes	—
309	C₄⋊C₄	C₂²×Dic₅	1	2	yes	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	10	2	no	—
317	C₄²	—	10	2	no	—
318	C₄²	D₄×D₅	1	1	yes	characteristic
319	C₄²	D₄×D₅	1	1	yes	characteristic
320	C₄²	C₂²×Dic₅	1	1	yes	characteristic
321	C₄²	C₂²×Dic₅	1	1	yes	characteristic
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	—	4	4	no	—
325	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₅	C₂×#444	1	1	yes	characteristic
327	C₂×C₅	#2957	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	C₂×#711	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	C₂×C₄⋊Dic₅	1	4	yes	—
332	D₄	—	2	4	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	2	no	—
335	D₄	C₂×C₄⋊Dic₅	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	20	2	no	—
346	C₂×C₄	—	20	2	no	—
347	C₂×C₄	—	20	2	no	—
348	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
349	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
350	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
351	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
352	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
355	C₂×C₄	#4149	1	1	yes	characteristic
356	C₂×C₄	#4150	1	1	yes	characteristic
357	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	10	4	no	—
361	C₈	—	20	4	no	—
362	C₈	C₂×C₄⋊Dic₅	1	2	yes	—
363	C₈	C₂×C₄⋊Dic₅	1	2	yes	—
364	C₅	#22686	1	1	yes	characteristic, complemented, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	#65877	1	1	yes	characteristic
371	C₂²	#65889	1	1	yes	characteristic
372	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	40	2	no	—
380	C₄	#65486	1	2	yes	complemented
381	C₄	D₄×Dic₁₀	1	1	yes	characteristic
382	C₄	D₄×D₂₀	1	1	yes	characteristic
383	C₄	C₂²×C₄⋊Dic₅	1	1	yes	characteristic
384	C₄	#66161	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	4	4	no	—
388	C₂	D₄×C₄⋊Dic₅	1	1	yes	characteristic
389	C₂	C₂×#65486	1	1	yes	characteristic
390	C₂	#10615641	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₄×C₅×#135	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#135	C₂²
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	C₄×#135	D₅
hypocenter	C₅	#22686
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
3. #10614243	C₂	semidirect
4. #10602439	C₂	semidirect
5. #10601456	C₂	semidirect
6. #10601085	C₂	semidirect
7. #10600585	C₂	semidirect
8. #10600550	C₂	semidirect
12. C₄×C₅×Q₁₆	C₄	semidirect
13. C₄×C₅×Q₁₆	C₄	semidirect
14. C₄×C₅×SD₁₆	C₄	semidirect
15. C₄×C₅×SD₁₆	C₄	semidirect
16. C₄×C₅×D₈	C₄	semidirect
17. C₄×C₅×D₈	C₄	semidirect
106. C₅×Q₁₆	C₄⋊C₄	semidirect
107. C₅×SD₁₆	C₄⋊C₄	semidirect
108. C₅×D₈	C₄⋊C₄	semidirect
146. C₄×Q₁₆	Dic₅	semidirect
147. C₄×Q₁₆	Dic₅	semidirect
148. C₄×SD₁₆	Dic₅	semidirect
149. C₄×SD₁₆	Dic₅	semidirect
150. C₄×D₈	Dic₅	semidirect
151. C₄×D₈	Dic₅	semidirect
266. C₄×C₅	#444	semidirect
286. Q₁₆	C₄⋊Dic₅	semidirect
287. SD₁₆	C₄⋊Dic₅	semidirect
288. D₈	C₄⋊Dic₅	semidirect
364. C₅	#22686	semidirect
380. C₄	#65486	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#135	2
C₂×#65486	2
#10614243	2
#10602439	2
#10601456	2
#10601085	2
#10600585	2
#10600550	2
#22686	5