Subgroups — #12117767

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 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×#65485	C₂	1	2	yes	maximal
3	#10614243	C₂	1	2	yes	maximal, complemented
4	#10602439	C₂	1	2	yes	maximal, complemented
5	#10601455	C₂	1	2	yes	maximal, complemented
6	#10601085	C₂	1	4	yes	maximal, complemented
7	#10600585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₄⋊Dic₅	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	#65485	—	2	8	no	—
23	C₂×#3951	C₂²	1	2	yes	—
24	C₂×#3951	C₂²	1	2	yes	—
25	C₂×C₈×Dic₅	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	#22688	—	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	C₈×Dic₅	—	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	1	yes	characteristic
84	C₄⋊#168	D₄	1	1	yes	characteristic
85	C₂×#443	—	5	2	no	—
86	C₄×#135	D₅	1	1	yes	characteristic
87	#2906	—	5	2	no	—
88	#1945	—	5	2	no	—
89	#1866	—	5	4	no	—
90	#1848	—	5	1	no	—
91	#1806	—	5	2	no	—
92	C₈×C₄⋊C₄	—	5	1	no	—
93	C₅×#41	—	2	2	no	—
94	C₅×#41	—	2	2	no	—
95	C₅×#41	C₂×D₄	1	4	yes	—
96	C₅×#41	C₂×Q₈	1	4	yes	—
97	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
98	C₂×C₅×D₄	—	2	2	no	—
99	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	—	2	2	no	—
101	C₂²×C₄×C₅	—	2	2	no	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	#41	1	1	yes	characteristic
104	C₂²×C₄×C₅	#41	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₅	—	2	2	no	—
107	C₅×Q₁₆	C₄⋊C₄	1	4	yes	complemented
108	C₅×SD₁₆	C₄⋊C₄	1	8	yes	complemented
109	C₅×D₈	C₄⋊C₄	1	4	yes	complemented
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
118	C₅×C₄⋊C₄	—	2	2	no	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
121	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
122	C₅×C₂²⋊C₄	—	2	2	no	—
123	C₅×C₂²⋊C₄	—	2	2	no	—
124	C₅×C₂²⋊C₄	—	2	2	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	2	2	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
132	C₄⋊Dic₅	—	2	4	no	—
133	C₄×Dic₅	—	2	2	no	—
134	C₄×Dic₅	—	2	2	no	—
135	#681	—	2	4	no	—
136	#681	—	2	4	no	—
137	#681	—	4	8	no	—
138	C₂×#168	—	2	2	no	—
139	C₂×#168	—	2	2	no	—
140	C₂×#168	—	2	4	no	—
141	C₂×#168	—	4	8	no	—
142	C₂×#168	C₂×D₄	1	2	yes	—
143	C₂×#168	C₂×D₄	1	2	yes	—
144	C₂×#135	C₂×D₅	1	1	yes	characteristic
145	C₂×#131	—	5	4	no	—
146	C₄×#41	C₂×D₅	1	2	yes	—
147	#443	—	10	8	no	—
148	C₄×Q₁₆	Dic₅	1	1	yes	characteristic, complemented
149	C₄×Q₁₆	Dic₅	1	1	yes	characteristic, complemented
150	C₄×SD₁₆	Dic₅	1	2	yes	complemented
151	C₄×SD₁₆	Dic₅	1	2	yes	complemented
152	C₄×D₈	Dic₅	1	1	yes	characteristic, complemented
153	C₄×D₈	Dic₅	1	1	yes	characteristic, complemented
154	C₂×#108	—	5	2	no	—
155	C₂×#108	—	5	2	no	—
156	#427	C₂×D₅	1	1	yes	characteristic
157	#424	—	5	4	no	—
158	#424	—	10	4	no	—
159	#423	—	5	2	no	—
160	#423	—	10	2	no	—
161	C₂×C₄⋊C₈	—	5	1	no	—
162	C₂×C₄⋊C₈	—	10	2	no	—
163	C₂×#104	—	5	4	no	—
164	#416	C₂×D₅	1	2	yes	—
165	C₂×C₄×C₈	—	5	2	no	—
166	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
167	C₄×C₄⋊C₄	—	5	1	no	—
168	#339	—	5	4	no	—
169	#336	—	5	2	no	—
170	C₂³×C₅	—	2	2	no	—
171	C₂³×C₅	C₂×#41	1	1	yes	characteristic
172	C₅×Q₈	—	2	2	no	—
173	C₅×Q₈	C₂×C₄⋊C₄	1	4	yes	—
174	C₅×D₄	—	2	4	no	—
175	C₅×D₄	—	2	4	no	—
176	C₅×D₄	—	2	2	no	—
177	C₅×D₄	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	4	no	—
180	C₂×C₄×C₅	—	2	4	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	4	1	no	—
185	C₂×C₄×C₅	—	4	4	no	—
186	C₂×C₄×C₅	—	8	2	no	—
187	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×Dic₅	—	2	4	no	—
198	C₂×Dic₅	—	4	2	no	—
199	C₂×Dic₅	—	4	2	no	—
200	C₅×C₈	—	2	1	no	—
201	C₅×C₈	—	2	1	no	—
202	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
203	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
204	#168	—	2	2	no	—
205	#168	—	2	2	no	—
206	#168	—	4	4	no	—
207	C₂×#41	C₂²×D₅	1	2	yes	—
208	#135	Dic₁₀	1	4	yes	—
209	#135	D₂₀	1	4	yes	—
210	C₂×Q₁₆	C₂×Dic₅	1	1	yes	characteristic
211	C₂×SD₁₆	C₂×Dic₅	1	2	yes	—
212	C₂×D₈	C₂×Dic₅	1	1	yes	characteristic
213	#131	—	10	8	no	—
214	#131	—	20	4	no	—
215	C₂×M₁₆	—	5	4	no	—
216	C₂×M₁₆	—	10	4	no	—
217	C₂²×C₈	—	5	2	no	—
218	C₂²×C₈	—	10	4	no	—
219	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
220	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
221	C₄×Q₈	C₂×Dic₅	1	2	yes	—
222	C₄×Q₈	C₂×Dic₅	1	2	yes	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	C₂×Dic₅	1	2	yes	—
226	C₄×D₄	C₂×Dic₅	1	2	yes	—
227	#117	—	2	2	no	—
228	#117	C₂²×D₅	1	2	yes	—
229	C₂×C₄⋊C₄	—	10	1	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	5	2	no	—
232	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
233	#108	—	10	4	no	—
234	#108	—	20	2	no	—
235	#107	C₂×Dic₅	1	1	yes	characteristic
236	#107	C₂×Dic₅	1	1	yes	characteristic
237	#106	C₂×Dic₅	1	2	yes	—
238	C₄⋊C₈	—	5	1	no	—
239	C₄⋊C₈	—	5	1	no	—
240	C₄⋊C₈	—	5	2	no	—
241	C₄⋊C₈	—	10	4	no	—
242	C₄⋊C₈	—	10	4	no	—
243	C₄⋊C₈	—	10	2	no	—
244	C₄⋊C₈	—	10	2	no	—
245	#104	—	10	8	no	—
246	#103	C₂×Dic₅	1	2	yes	—
247	#103	C₂×Dic₅	1	2	yes	—
248	#102	C₂×Dic₅	1	2	yes	—
249	#102	C₂×Dic₅	1	2	yes	—
250	C₄×C₈	—	10	4	no	—
251	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
252	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
253	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
254	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
255	#95	—	10	1	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	4	no	—
259	C₂²×C₅	—	4	2	no	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₅	#547	1	1	yes	characteristic
263	C₂²×C₅	#554	1	1	yes	characteristic
264	C₄×C₅	—	2	4	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	#443	1	2	yes	complemented
271	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
272	C₄×C₅	#520	1	1	yes	characteristic
273	C₄×C₅	D₄²	1	1	yes	characteristic
274	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
275	Dic₅	—	4	4	no	—
276	#41	—	2	2	no	—
277	#41	—	2	2	no	—
278	#41	C₂×Dic₁₀	1	4	yes	—
279	#41	C₂×D₂₀	1	4	yes	—
280	C₂×Q₈	C₂²×Dic₅	1	2	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂²×Dic₅	1	2	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	10	2	no	—
287	C₂²×C₄	#711	1	1	yes	characteristic
288	C₂²×C₄	#711	1	1	yes	characteristic
289	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
290	Q₁₆	C₄⋊Dic₅	1	4	yes	complemented
291	SD₁₆	C₄⋊Dic₅	1	8	yes	complemented
292	D₈	C₄⋊Dic₅	1	4	yes	complemented
293	M₁₆	—	10	4	no	—
294	M₁₆	—	10	4	no	—
295	M₁₆	—	20	8	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	5	2	no	—
299	C₂×C₈	—	5	2	no	—
300	C₂×C₈	—	10	2	no	—
301	C₂×C₈	—	10	2	no	—
302	C₂×C₈	—	10	4	no	—
303	C₂×C₈	—	20	8	no	—
304	C₂×C₈	C₂×Dic₁₀	1	2	yes	—
305	C₂×C₈	C₂×D₂₀	1	2	yes	—
306	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
307	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
308	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
309	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	10	4	no	—
313	C₄⋊C₄	C₂²×Dic₅	1	2	yes	—
314	C₄⋊C₄	C₂²×Dic₅	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	10	2	no	—
322	C₄²	—	10	2	no	—
323	C₄²	D₄×D₅	1	1	yes	characteristic
324	C₄²	D₄×D₅	1	1	yes	characteristic
325	C₄²	C₂²×Dic₅	1	1	yes	characteristic
326	C₄²	C₂²×Dic₅	1	1	yes	characteristic
327	C₂×C₅	—	2	1	no	—
328	C₂×C₅	—	2	1	no	—
329	C₂×C₅	—	4	4	no	—
330	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₅	C₂×#443	1	1	yes	characteristic
332	C₂×C₅	#2957	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	C₂×#711	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	C₂×C₄⋊Dic₅	1	4	yes	—
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	C₂×C₄⋊Dic₅	1	4	yes	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	10	4	no	—
351	C₂×C₄	—	20	2	no	—
352	C₂×C₄	—	20	2	no	—
353	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
354	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
355	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
356	C₂×C₄	D₄×Dic₅	1	1	yes	characteristic
357	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
360	C₂×C₄	#4149	1	1	yes	characteristic
361	C₂×C₄	#4150	1	1	yes	characteristic
362	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	10	2	no	—
366	C₈	—	10	2	no	—
367	C₈	—	20	4	no	—
368	C₈	C₂×C₄⋊Dic₅	1	2	yes	—
369	C₈	C₂×C₄⋊Dic₅	1	2	yes	—
370	C₅	#22688	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	#65877	1	1	yes	characteristic
377	C₂²	#65889	1	1	yes	characteristic
378	C₂²	C₂×D₄×Dic₅	1	1	yes	characteristic
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	20	4	no	—
386	C₄	#65485	1	2	yes	complemented
387	C₄	D₄×Dic₁₀	1	1	yes	characteristic
388	C₄	D₄×D₂₀	1	1	yes	characteristic
389	C₄	C₂²×C₄⋊Dic₅	1	1	yes	characteristic
390	C₄	#66161	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	4	no	—
394	C₂	D₄×C₄⋊Dic₅	1	1	yes	characteristic
395	C₂	C₂×#65485	1	1	yes	characteristic
396	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	#22688
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. #10601455	C₂	semidirect
6. #10601085	C₂	semidirect
7. #10600585	C₂	semidirect
8. C₈×C₄⋊Dic₅	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
107. C₅×Q₁₆	C₄⋊C₄	semidirect
108. C₅×SD₁₆	C₄⋊C₄	semidirect
109. C₅×D₈	C₄⋊C₄	semidirect
148. C₄×Q₁₆	Dic₅	semidirect
149. C₄×Q₁₆	Dic₅	semidirect
150. C₄×SD₁₆	Dic₅	semidirect
151. C₄×SD₁₆	Dic₅	semidirect
152. C₄×D₈	Dic₅	semidirect
153. C₄×D₈	Dic₅	semidirect
270. C₄×C₅	#443	semidirect
290. Q₁₆	C₄⋊Dic₅	semidirect
291. SD₁₆	C₄⋊Dic₅	semidirect
292. D₈	C₄⋊Dic₅	semidirect
370. C₅	#22688	semidirect
386. C₄	#65485	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×#65485	2
#10614243	2
#10602439	2
#10601455	2
#10601085	2
#10600585	2
C₈×C₄⋊Dic₅	2
#22688	5