Subgroups — #12252499

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	#10615525	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602797	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602226	C₂	1	2	yes	maximal, complemented
6	#10602223	C₂	1	2	yes	maximal, complemented
7	#10602212	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64727	C₂	1	1	yes	maximal, characteristic, complemented
9	#10602200	C₂	1	2	yes	maximal, complemented
10	C₁₆×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
11	#10602194	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	C₂²	1	1	yes	characteristic
13	#66162	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₅×#504	—	2	4	no	—
16	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₅×M₃₂	C₂²	1	2	yes	complemented
18	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
20	#65523	C₄	1	1	yes	characteristic
21	#65416	C₄	1	2	yes	—
22	#65416	C₄	1	2	yes	—
23	#65415	C₄	1	1	yes	characteristic
24	#65408	C₄	1	1	yes	characteristic
25	C₈×C₂²⋊D₅	C₂²	1	2	yes	—
26	C₈×C₂²⋊D₅	C₂²	1	2	yes	—
27	#65390	C₂²	1	1	yes	characteristic
28	C₂×#3944	C₂²	1	1	yes	characteristic
29	C₂²×#672	C₂²	1	1	yes	characteristic
30	D₅×M₃₂	—	2	4	no	—
31	C₂×#3930	C₂²	1	2	yes	—
32	C₂×D₅×C₁₆	C₂²	1	2	yes	—
33	C₂²⋊#672	C₂²	1	2	yes	complemented
34	C₂²⋊#672	C₂²	1	2	yes	complemented
35	#64727	C₂²	1	1	yes	characteristic
36	#64727	C₂²	1	1	yes	characteristic
37	#64727	C₂²	1	1	yes	characteristic
38	#64727	C₂²	1	1	yes	characteristic
39	#64722	C₂²	1	2	yes	complemented
40	#64721	C₂²	1	2	yes	complemented
41	#64721	C₂²	1	2	yes	complemented
42	C₁₆×Dic₅	C₂²	1	2	yes	complemented
43	#33436	—	5	1	no	maximal, Sylow
44	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
46	C₅×#131	—	2	2	no	—
47	C₅×#131	—	2	2	no	—
48	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	#4092	C₈	1	1	yes	characteristic
53	#4092	C₈	1	1	yes	characteristic
54	#4084	C₈	1	1	yes	characteristic
55	#4084	C₈	1	1	yes	characteristic
56	#4083	C₈	1	2	yes	—
57	#4081	C₈	1	2	yes	—
58	C₄×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₅	C₂×C₄	1	2	yes	—
60	#4072	C₂×C₄	1	1	yes	characteristic
61	C₂×#681	C₂×C₄	1	1	yes	characteristic
62	C₂²×#168	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	—	2	2	no	—
64	C₂×C₈×D₅	—	2	2	no	—
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
69	C₅×M₃₂	—	2	4	no	—
70	C₅×M₃₂	D₄	1	4	yes	complemented
71	C₂×C₅×C₁₆	—	2	2	no	—
72	C₂×C₅×C₁₆	—	2	4	no	—
73	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₁₆	C₂³	1	2	yes	—
76	C₂²⋊#168	C₂×C₄	1	2	yes	—
77	C₂²⋊#168	C₂×C₄	1	2	yes	—
78	#3952	C₂×C₄	1	2	yes	—
79	#3952	C₂×C₄	1	2	yes	—
80	#3947	C₂×C₄	1	2	yes	—
81	#3946	C₂×C₄	1	2	yes	—
82	#3946	C₂×C₄	1	2	yes	—
83	C₈×Dic₅	C₂³	1	2	yes	—
84	#3944	—	2	2	no	—
85	C₂×#672	—	2	2	no	—
86	C₂×#672	C₂³	1	1	yes	characteristic
87	C₂×#672	C₂³	1	1	yes	characteristic
88	C₂×#672	C₂³	1	2	yes	—
89	#3930	—	2	4	no	—
90	D₅×C₁₆	—	2	4	no	—
91	C₂×#504	D₅	1	1	yes	characteristic, complemented
92	C₂²×M₃₂	—	5	1	no	—
93	#2929	—	5	1	no	—
94	#2169	—	5	2	no	—
95	#2168	—	5	2	no	—
96	#2168	—	5	2	no	—
97	D₄×C₁₆	—	5	2	no	—
98	#2151	—	5	1	no	—
99	#2113	—	5	1	no	—
100	C₂×C₂²⋊C₁₆	—	5	1	no	—
101	#2108	—	5	1	no	—
102	C₂³×D₅	C₂×C₈	1	1	yes	characteristic
103	C₅×#41	—	2	2	no	—
104	C₅×#41	—	2	2	no	—
105	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
106	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
107	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₅	C₂×C₈	1	2	yes	—
111	C₂×C₂²⋊D₅	C₂×C₈	1	2	yes	—
112	C₂²×Dic₅	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₅	—	2	2	no	—
114	C₂×C₄×D₅	—	2	2	no	—
115	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
119	C₅×M₁₆	—	2	2	no	—
120	C₅×M₁₆	—	2	4	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
126	C₂×C₅×C₈	#41	1	2	yes	—
127	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
129	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
130	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
131	#685	C₂×C₈	1	2	yes	—
132	#685	C₂×C₈	1	2	yes	—
133	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
134	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
135	#683	C₂×C₈	1	2	yes	—
136	#683	C₂×C₈	1	2	yes	—
137	C₄×Dic₅	C₂²×C₄	1	2	yes	—
138	#681	—	2	2	no	—
139	C₂×#168	—	2	2	no	—
140	C₂×#168	C₂²×C₄	1	2	yes	—
141	C₂×#168	C₂²×C₄	1	1	yes	characteristic
142	C₂×#168	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₅	—	2	2	no	—
144	C₈×D₅	—	2	2	no	—
145	C₈×D₅	—	2	1	no	—
146	C₈×D₅	—	2	1	no	—
147	C₈×D₅	—	2	1	no	—
148	C₈×D₅	—	2	1	no	—
149	C₅×C₁₆	—	2	1	no	—
150	C₅×C₁₆	—	2	1	no	—
151	C₅×C₁₆	C₂×D₄	1	4	yes	—
152	#672	—	2	2	no	—
153	#672	—	2	1	no	—
154	#672	—	2	1	no	—
155	C₂×#131	C₂×D₅	1	1	yes	characteristic
156	C₂³×C₈	—	5	1	no	—
157	#525	—	5	1	no	—
158	#504	—	2	4	no	—
159	C₂×M₃₂	—	5	1	no	—
160	C₂×M₃₂	—	5	2	no	—
161	C₂×M₃₂	—	10	4	no	—
162	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
163	C₂×M₃₂	C₂×D₅	1	2	yes	complemented
164	C₂²×C₁₆	—	5	1	no	—
165	C₂²×C₁₆	—	5	2	no	—
166	C₂²×C₁₆	C₂×D₅	1	1	yes	characteristic
167	C₂²×C₁₆	C₂×D₅	1	2	yes	complemented
168	#435	—	5	2	no	—
169	#435	—	5	2	no	—
170	C₈×D₄	—	5	2	no	—
171	C₈×D₄	—	5	2	no	—
172	#424	—	5	1	no	—
173	#408	—	5	1	no	—
174	#407	—	5	1	no	—
175	#405	—	5	1	no	—
176	C₄⋊C₁₆	—	5	2	no	—
177	C₄⋊C₁₆	—	5	2	no	—
178	C₂²⋊C₁₆	—	5	2	no	—
179	C₂²⋊C₁₆	—	5	2	no	—
180	C₂²⋊C₁₆	—	5	1	no	—
181	C₂²⋊C₁₆	—	5	1	no	—
182	C₂²⋊C₁₆	—	5	1	no	—
183	C₂²⋊C₁₆	—	5	1	no	—
184	#346	—	5	2	no	—
185	C₄×C₁₆	—	5	2	no	—
186	C₂³×C₅	C₂²×C₈	1	2	yes	—
187	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
188	C₂²×D₅	—	2	2	no	—
189	C₂²×D₅	—	2	2	no	—
190	C₂²×D₅	—	4	1	no	—
191	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
192	C₂²×D₅	C₂²×C₈	1	1	yes	characteristic
193	C₅×Q₈	—	2	2	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
200	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
201	C₂×C₄×C₅	#131	1	2	yes	—
202	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₂²⋊D₅	—	2	4	no	—
204	C₂²⋊D₅	—	4	2	no	—
205	C₂×Dic₅	—	2	2	no	—
206	C₂×Dic₅	C₂²×C₈	1	2	yes	—
207	C₂×Dic₅	C₂²×C₈	1	2	yes	—
208	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₅	C₂²×C₈	1	1	yes	characteristic
210	C₄×D₅	—	2	1	no	—
211	C₄×D₅	—	2	1	no	—
212	C₄×D₅	—	2	1	no	—
213	C₄×D₅	—	2	1	no	—
214	C₄×D₅	—	2	2	no	—
215	C₄×D₅	—	2	2	no	—
216	C₅×C₈	—	2	2	no	—
217	C₅×C₈	C₄×D₄	1	2	yes	—
218	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
219	C₅×C₈	C₂×#41	1	1	yes	characteristic
220	#168	—	2	1	no	—
221	#168	—	2	1	no	—
222	#168	—	2	2	no	—
223	C₂×#41	C₄×D₅	1	1	yes	characteristic
224	C₂³×C₄	—	5	1	no	—
225	#131	—	2	2	no	—
226	#131	—	2	2	no	—
227	C₂×M₁₆	—	5	1	no	—
228	C₂×M₁₆	C₄×D₅	1	1	yes	characteristic
229	C₂×M₁₆	C₄×D₅	1	2	yes	—
230	C₂²×C₈	—	5	1	no	—
231	C₂²×C₈	—	5	1	no	—
232	C₂²×C₈	—	5	1	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	5	1	no	—
235	C₂²×C₈	—	10	2	no	—
236	C₂²×C₈	—	10	2	no	—
237	C₂²×C₈	C₂²×D₅	1	2	yes	—
238	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
239	#123	—	5	2	no	—
240	C₂²⋊Q₈	—	5	1	no	—
241	C₂²⋊Q₈	—	5	1	no	—
242	#121	—	5	1	no	—
243	#121	—	5	1	no	—
244	#120	—	5	2	no	—
245	C₄×D₄	—	5	2	no	—
246	C₄×D₄	—	5	2	no	—
247	#117	—	5	1	no	—
248	M₃₂	—	2	4	no	—
249	M₃₂	—	10	2	no	—
250	M₃₂	—	10	4	no	—
251	M₃₂	C₂²⋊D₅	1	4	yes	complemented
252	C₂×C₁₆	—	2	2	no	—
253	C₂×C₁₆	—	2	4	no	—
254	C₂×C₁₆	—	5	1	no	—
255	C₂×C₁₆	—	5	1	no	—
256	C₂×C₁₆	—	5	2	no	—
257	C₂×C₁₆	—	10	2	no	—
258	C₂×C₁₆	—	10	4	no	—
259	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₁₆	C₂²×D₅	1	1	yes	characteristic
261	C₂×C₁₆	C₂²×D₅	1	2	yes	—
262	C₄⋊C₈	—	5	2	no	—
263	C₄⋊C₈	—	5	2	no	—
264	C₂²⋊C₈	—	5	2	no	—
265	C₂²⋊C₈	—	5	2	no	—
266	C₂²⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	5	2	no	—
268	#97	—	5	2	no	—
269	C₄×C₈	—	5	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	C₈×D₄	1	2	yes	—
276	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
277	C₂×D₅	—	2	1	no	—
278	C₂×D₅	—	2	1	no	—
279	C₂×D₅	—	2	1	no	—
280	C₂×D₅	—	2	1	no	—
281	C₂×D₅	—	2	1	no	—
282	C₂×D₅	—	4	4	no	—
283	C₂×D₅	#504	1	2	yes	complemented
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	C₈×D₄	1	2	yes	—
286	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₄×C₅	C₂×#131	1	1	yes	characteristic
288	Dic₅	—	2	2	no	—
289	Dic₅	—	2	2	no	—
290	Dic₅	—	2	1	no	—
291	Dic₅	—	2	1	no	—
292	C₂⁴	—	5	1	no	—
293	#41	—	2	2	no	—
294	#41	—	2	2	no	—
295	C₂×Q₈	C₈×D₅	1	1	yes	characteristic
296	C₂×D₄	—	5	2	no	—
297	C₂×D₄	—	5	2	no	—
298	C₂×D₄	C₈×D₅	1	2	yes	—
299	C₂×D₄	C₈×D₅	1	1	yes	characteristic
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	10	2	no	—
306	C₂²×C₄	—	10	2	no	—
307	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
308	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
309	M₁₆	—	2	2	no	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	10	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	5	2	no	—
315	C₂×C₈	—	5	1	no	—
316	C₂×C₈	—	5	1	no	—
317	C₂×C₈	—	10	2	no	—
318	C₂×C₈	—	10	1	no	—
319	C₂×C₈	—	10	1	no	—
320	C₂×C₈	—	10	1	no	—
321	C₂×C₈	—	10	1	no	—
322	C₂×C₈	—	10	2	no	—
323	C₂×C₈	—	10	2	no	—
324	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
325	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
326	C₂×C₈	#709	1	2	yes	—
327	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
328	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
329	C₄⋊C₄	—	5	1	no	—
330	C₄⋊C₄	—	5	1	no	—
331	C₄⋊C₄	—	5	2	no	—
332	C₄⋊C₄	—	5	2	no	—
333	C₂²⋊C₄	—	5	2	no	—
334	C₂²⋊C₄	—	5	2	no	—
335	C₂²⋊C₄	—	5	2	no	—
336	C₂²⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	2	no	—
338	C₄²	—	5	2	no	—
339	C₁₆	—	2	1	no	—
340	C₁₆	—	2	1	no	—
341	C₁₆	—	10	1	no	—
342	C₁₆	—	10	1	no	—
343	C₁₆	—	10	2	no	—
344	C₁₆	C₂×C₂²⋊D₅	1	4	yes	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	4	2	no	—
347	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
348	C₂×C₅	C₂×#504	1	1	yes	characteristic
349	C₂×C₅	#3407	1	1	yes	characteristic
350	D₅	—	2	2	no	—
351	D₅	—	4	1	no	—
352	C₂³	—	5	1	no	—
353	C₂³	—	5	1	no	—
354	C₂³	—	10	2	no	—
355	C₂³	—	10	2	no	—
356	C₂³	—	20	1	no	—
357	C₂³	C₂×C₈×D₅	1	2	yes	—
358	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	D₄	—	2	4	no	—
361	D₄	—	2	2	no	—
362	D₄	—	10	4	no	—
363	D₄	—	20	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	5	2	no	—
367	C₂×C₄	—	5	2	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	5	1	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	10	1	no	—
372	C₂×C₄	—	10	1	no	—
373	C₂×C₄	—	10	1	no	—
374	C₂×C₄	—	10	1	no	—
375	C₂×C₄	—	10	2	no	—
376	C₂×C₄	—	10	2	no	—
377	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
378	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
379	C₂×C₄	#4047	1	2	yes	—
380	C₂×C₄	C₄×C₂²⋊D₅	1	2	yes	—
381	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	10	2	no	—
384	C₈	—	10	1	no	—
385	C₈	—	10	1	no	—
386	C₈	C₄×C₂²⋊D₅	1	2	yes	—
387	C₈	C₂×#709	1	1	yes	characteristic
388	C₈	C₂²×C₂²⋊D₅	1	1	yes	characteristic
389	C₅	#33436	1	1	yes	characteristic, complemented, Sylow
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	5	2	no	—
396	C₂²	—	10	1	no	—
397	C₂²	—	10	1	no	—
398	C₂²	—	10	1	no	—
399	C₂²	—	10	1	no	—
400	C₂²	—	10	1	no	—
401	C₂²	—	20	4	no	—
402	C₂²	C₈×C₂²⋊D₅	1	2	yes	—
403	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	10	1	no	—
406	C₄	—	10	1	no	—
407	C₄	—	10	2	no	—
408	C₄	—	10	2	no	—
409	C₄	C₈×C₂²⋊D₅	1	2	yes	—
410	C₄	C₂×#4047	1	1	yes	characteristic
411	C₄	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	—	10	2	no	—
415	C₂	—	20	1	no	—
416	C₂	D₅×#504	1	1	yes	characteristic
417	C₂	#10613743	1	1	yes	characteristic
418	C₂	C₂×C₈×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₂×C₅×#504	C₂
prime radical	#66162	C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	C₂×#504	D₅
hypocenter	C₅	#33436
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#504	C₂	semidirect
3. C₂×D₅×M₃₂	C₂	semidirect
4. #10602797	C₂	semidirect
5. #10602226	C₂	semidirect
6. #10602223	C₂	semidirect
7. #10602212	C₂	semidirect
8. C₂×#64727	C₂	semidirect
9. #10602200	C₂	semidirect
10. C₁₆×C₂²⋊D₅	C₂	semidirect
11. #10602194	C₂	semidirect
17. C₂×C₅×M₃₂	C₂²	semidirect
19. C₂²×C₅×C₁₆	C₂²	semidirect
33. C₂²⋊#672	C₂²	semidirect
34. C₂²⋊#672	C₂²	semidirect
39. #64722	C₂²	semidirect
40. #64721	C₂²	semidirect
41. #64721	C₂²	semidirect
42. C₁₆×Dic₅	C₂²	semidirect
70. C₅×M₃₂	D₄	semidirect
91. C₂×#504	D₅	semidirect
163. C₂×M₃₂	C₂×D₅	semidirect
167. C₂²×C₁₆	C₂×D₅	semidirect
251. M₃₂	C₂²⋊D₅	semidirect
283. C₂×D₅	#504	semidirect
389. C₅	#33436	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#504	2
#10615525	2
C₂×D₅×M₃₂	2
#10602797	2
#10602226	2
#10602223	2
#10602212	2
C₂×#64727	2
#10602200	2
C₁₆×C₂²⋊D₅	2
#10602194	2
#33436	5