Subgroups — #72317073

Order 2048.

At least 8101 conjugacy classes of subgroups; only the 372 normal subgroups are shown.

The subgroup lattice has 340 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317071	C₂	1	2	yes	maximal, complemented
2	#72317070	C₂	1	2	yes	maximal, complemented
3	#72317066	C₂	1	2	yes	maximal, complemented
4	#72259002	C₂	1	1	yes	maximal, characteristic, complemented
5	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
6	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
7	#72237608	C₂	1	1	yes	maximal, characteristic, complemented
8	#72234681	C₂	1	1	yes	maximal, characteristic
9	#72232808	C₂	1	2	yes	maximal, complemented
10	#72232723	C₂	1	1	yes	maximal, characteristic, complemented
11	#72232723	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#46996	C₄	1	1	yes	characteristic, complemented
13	C₂×#34981	C₂²	1	1	yes	characteristic
14	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
15	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
16	#4932982	C₄	1	1	yes	characteristic, complemented
17	#4932982	C₂²	1	1	yes	characteristic
18	#4599104	C₄	1	1	yes	characteristic, complemented
19	#4599104	C₂²	1	1	yes	characteristic
20	#4321066	C₄	1	1	yes	characteristic, complemented
21	#4321066	C₄	1	1	yes	characteristic, complemented
22	#2805719	C₄	1	1	yes	characteristic, complemented
23	#2805719	C₂²	1	1	yes	characteristic
24	#1465620	C₄	1	1	yes	characteristic, complemented
25	#1465620	C₂²	1	1	yes	characteristic
26	#616961	C₂²	1	1	yes	characteristic
27	#616961	C₂²	1	1	yes	characteristic
28	#576189	C₄	1	1	yes	characteristic, complemented
29	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
30	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
31	#139720	C₂²	1	2	yes	complemented
32	#139720	C₂²	1	2	yes	complemented
33	#139718	C₂²	1	2	yes	—
34	#139718	C₂²	1	2	yes	—
35	#139504	C₂²	1	2	yes	—
36	#139504	C₂²	1	2	yes	—
37	#139486	C₂²	1	2	yes	complemented
38	#139486	C₂²	1	2	yes	complemented
39	#133895	C₂²	1	2	yes	complemented
40	#133893	C₂²	1	2	yes	—
41	#115164	C₂²	1	2	yes	complemented
42	#115163	C₂²	1	2	yes	—
43	C₂²×#535	D₄	1	1	yes	characteristic
44	C₂²×#535	D₄	1	1	yes	characteristic
45	C₂²×#534	D₄	1	1	yes	characteristic
46	C₂³×#120	D₄	1	1	yes	characteristic
47	C₂³×#120	C₂³	1	1	yes	characteristic
48	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
49	C₂×#2760	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#2760	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#2840	C₂×C₄	1	1	yes	characteristic, complemented
52	C₂×#2404	C₂×C₄	1	1	yes	characteristic
53	C₂×#2404	C₂×C₄	1	1	yes	characteristic
54	C₂×#2404	D₄	1	1	yes	characteristic
55	C₂×#2404	D₄	1	1	yes	characteristic
56	C₂×#2412	C₂×C₄	1	1	yes	characteristic
57	C₂×#2412	D₄	1	1	yes	characteristic
58	C₂×#2412	D₄	1	1	yes	characteristic
59	C₂×#2412	C₂³	1	1	yes	characteristic
60	C₂×#2410	C₂×C₄	1	1	yes	characteristic
61	C₂×#2410	D₄	1	1	yes	characteristic
62	C₂×#2410	D₄	1	1	yes	characteristic
63	C₂×#2410	C₂³	1	1	yes	characteristic
64	C₂×#2403	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×#2315	C₂×C₄	1	1	yes	characteristic
66	C₂×#2308	C₂×C₄	1	1	yes	characteristic
67	C₂×#2308	D₄	1	1	yes	characteristic
68	#21746	C₂³	1	2	yes	—
69	#21746	C₂³	1	2	yes	—
70	#15635	C₂×C₄	1	1	yes	characteristic, complemented
71	#15635	C₂×C₄	1	1	yes	characteristic, complemented
72	#15622	C₂×C₄	1	1	yes	characteristic, complemented
73	#15622	C₂×C₄	1	1	yes	characteristic, complemented
74	#15568	C₂×C₄	1	1	yes	characteristic, complemented
75	#15568	C₂×C₄	1	1	yes	characteristic, complemented
76	#15420	C₂×C₄	1	1	yes	characteristic, complemented
77	#15420	C₂×C₄	1	1	yes	characteristic, complemented
78	#15259	C₂×C₄	1	1	yes	characteristic
79	#15259	C₂×C₄	1	1	yes	characteristic
80	#15259	D₄	1	1	yes	characteristic
81	#15259	D₄	1	1	yes	characteristic
82	#15259	D₄	1	1	yes	characteristic
83	#15259	D₄	1	1	yes	characteristic
84	#15259	C₂³	1	1	yes	characteristic
85	#15259	C₂³	1	1	yes	characteristic
86	#15258	C₂×C₄	1	1	yes	characteristic
87	#15258	C₂×C₄	1	1	yes	characteristic
88	#15258	D₄	1	1	yes	characteristic
89	#15258	D₄	1	1	yes	characteristic
90	#15258	D₄	1	1	yes	characteristic
91	#15258	D₄	1	1	yes	characteristic
92	#15258	C₂³	1	1	yes	characteristic
93	#15258	C₂³	1	1	yes	characteristic
94	#14365	C₂×C₄	1	1	yes	characteristic, complemented
95	#14365	C₂×C₄	1	1	yes	characteristic, complemented
96	#14335	D₄	1	1	yes	characteristic
97	#14335	D₄	1	1	yes	characteristic
98	#13868	C₂×C₄	1	1	yes	characteristic
99	#13868	C₂×C₄	1	1	yes	characteristic
100	#13868	D₄	1	1	yes	characteristic
101	#13868	D₄	1	1	yes	characteristic
102	#13828	C₂×C₄	1	1	yes	characteristic, complemented
103	#13807	C₂×C₄	1	1	yes	characteristic, complemented
104	#8547	C₂³	1	2	yes	—
105	#8541	C₂³	1	2	yes	—
106	C₂⁷	C₂×D₄	1	1	yes	characteristic
107	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#127	C₂×D₄	1	1	yes	characteristic
118	C₂²×#127	C₂×D₄	1	1	yes	characteristic
119	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×#124	C₂×D₄	1	1	yes	characteristic
122	C₂²×#124	C₂×D₄	1	1	yes	characteristic
123	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#123	C₂×D₄	1	1	yes	characteristic
125	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
127	C₂²×#120	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂×D₄	1	1	yes	characteristic
129	C₂²×#120	C₂×D₄	1	1	yes	characteristic
130	C₂²×#120	C₂×D₄	1	1	yes	characteristic
131	C₂²×#120	C₂×D₄	1	1	yes	characteristic
132	C₂²×#120	C₂×D₄	1	1	yes	characteristic
133	C₂²×#120	C₂×D₄	1	1	yes	characteristic
134	C₂²×#120	C₂⁴	1	1	yes	characteristic
135	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
141	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#393	C₂²×C₄	1	1	yes	characteristic
154	C₂×#393	C₂²×C₄	1	1	yes	characteristic
155	C₂×#393	C₂×D₄	1	1	yes	characteristic
156	C₂×#393	C₂×D₄	1	1	yes	characteristic
157	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#392	C₂²×C₄	1	1	yes	characteristic
162	C₂×#392	C₂²×C₄	1	1	yes	characteristic
163	C₂×#392	C₂×D₄	1	1	yes	characteristic
164	C₂×#392	C₂×D₄	1	1	yes	characteristic
165	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#386	C₂×D₄	1	1	yes	characteristic
168	C₂×#386	C₂×D₄	1	1	yes	characteristic
169	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#385	C₂²×C₄	1	1	yes	characteristic
172	C₂×#385	C₂²×C₄	1	1	yes	characteristic
173	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
175	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
176	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×#381	C₂²×C₄	1	1	yes	characteristic
179	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#379	C₂²×C₄	1	1	yes	characteristic
181	#1438	C₂²⋊C₄	1	1	yes	characteristic
182	#1438	C₂²⋊C₄	1	1	yes	characteristic
183	#1438	C₂²⋊C₄	1	1	yes	characteristic
184	#1438	C₂²⋊C₄	1	1	yes	characteristic
185	#1438	C₂×D₄	1	1	yes	characteristic
186	#1438	C₂×D₄	1	1	yes	characteristic
187	#1438	C₂×D₄	1	1	yes	characteristic
188	#1438	C₂×D₄	1	1	yes	characteristic
189	#1437	C₂²⋊C₄	1	1	yes	characteristic
190	#1437	C₂²⋊C₄	1	1	yes	characteristic
191	#1437	C₂²⋊C₄	1	1	yes	characteristic
192	#1437	C₂²⋊C₄	1	1	yes	characteristic
193	#1437	C₂²⋊C₄	1	1	yes	characteristic
194	#1437	C₂²⋊C₄	1	1	yes	characteristic
195	#1437	C₂²⋊C₄	1	1	yes	characteristic
196	#1437	C₂²⋊C₄	1	1	yes	characteristic
197	#1437	C₂²×C₄	1	1	yes	characteristic
198	#1437	C₂²×C₄	1	1	yes	characteristic
199	#1437	C₂²×C₄	1	1	yes	characteristic
200	#1437	C₂²×C₄	1	1	yes	characteristic
201	#1437	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂×D₄	1	1	yes	characteristic
203	#1437	C₂×D₄	1	1	yes	characteristic
204	#1437	C₂×D₄	1	1	yes	characteristic
205	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂⁶	#120	1	1	yes	characteristic
209	C₂⁶	#120	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂⁶	#120	1	1	yes	characteristic
213	C₂⁶	C₂²×D₄	1	1	yes	characteristic
214	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×D₄	#99	1	2	yes	—
217	C₂³×D₄	#99	1	2	yes	—
218	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×D₄	#120	1	1	yes	characteristic
224	C₂³×D₄	#120	1	1	yes	characteristic
225	C₂³×D₄	#120	1	1	yes	characteristic
226	C₂³×D₄	#120	1	1	yes	characteristic
227	C₂³×D₄	#120	1	1	yes	characteristic
228	C₂³×D₄	#120	1	1	yes	characteristic
229	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
231	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
232	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂⁴×C₄	#120	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	#99	1	2	yes	—
239	C₂²×C₂²⋊C₄	#99	1	2	yes	—
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
256	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁵	#379	1	1	yes	characteristic
269	C₂⁵	#379	1	1	yes	characteristic
270	C₂⁵	#379	1	1	yes	characteristic
271	C₂⁵	#379	1	1	yes	characteristic
272	C₂⁵	#379	1	1	yes	characteristic
273	C₂⁵	C₂×#99	1	1	yes	characteristic
274	C₂⁵	C₂×#99	1	1	yes	characteristic
275	C₂⁵	C₂×#99	1	1	yes	characteristic
276	C₂⁵	C₂×#99	1	1	yes	characteristic
277	C₂⁵	C₂×#99	1	2	yes	—
278	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
279	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
280	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
281	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
282	C₂⁵	#458	1	1	yes	characteristic
283	C₂⁵	#458	1	1	yes	characteristic
284	C₂⁵	#458	1	1	yes	characteristic
285	C₂⁵	#458	1	1	yes	characteristic
286	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
287	C₂⁵	C₂×#120	1	1	yes	characteristic
288	C₂⁵	C₂×#120	1	1	yes	characteristic
289	C₂⁵	C₂×#120	1	1	yes	characteristic
290	C₂³×C₄	#379	1	1	yes	characteristic
291	C₂³×C₄	#379	1	1	yes	characteristic
292	C₂³×C₄	#379	1	1	yes	characteristic
293	C₂³×C₄	C₂×#99	1	2	yes	—
294	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂³×C₄	C₂×#120	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
299	C₂⁴	#1781	1	1	yes	characteristic
300	C₂⁴	#1781	1	1	yes	characteristic
301	C₂⁴	#1781	1	1	yes	characteristic
302	C₂⁴	#1781	1	1	yes	characteristic
303	C₂⁴	#1790	1	1	yes	characteristic
304	C₂⁴	#1790	1	1	yes	characteristic
305	C₂⁴	#1790	1	1	yes	characteristic
306	C₂⁴	#1790	1	1	yes	characteristic
307	C₂⁴	#1790	1	1	yes	characteristic
308	C₂⁴	#1790	1	1	yes	characteristic
309	C₂⁴	#1790	1	1	yes	characteristic
310	C₂⁴	#1790	1	1	yes	characteristic
311	C₂⁴	C₂×#379	1	1	yes	characteristic
312	C₂⁴	C₂²×#99	1	1	yes	characteristic
313	C₂⁴	C₂²×#99	1	1	yes	characteristic
314	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
315	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
316	C₂⁴	C₂×#458	1	1	yes	characteristic
317	C₂⁴	C₂×#458	1	1	yes	characteristic
318	C₂³	#8534	1	1	yes	characteristic
319	C₂³	#8534	1	1	yes	characteristic
320	C₂³	#8534	1	1	yes	characteristic
321	C₂³	#8534	1	1	yes	characteristic
322	C₂³	#12707	1	2	yes	—
323	C₂³	#12753	1	2	yes	—
324	C₂³	C₂×#1781	1	1	yes	characteristic
325	C₂³	C₂×#1790	1	1	yes	characteristic
326	C₂³	C₂×#1790	1	1	yes	characteristic
327	C₂³	#33358	1	2	yes	—
328	C₂³	#33551	1	2	yes	—
329	C₂²	C₂×#8534	1	1	yes	characteristic
330	C₂²	#493371	1	1	yes	characteristic
331	C₂²	C₂×#12707	1	1	yes	characteristic
332	C₂²	C₂×#12753	1	1	yes	characteristic
333	C₂²	#493562	1	1	yes	characteristic
334	C₂²	#493582	1	1	yes	characteristic
335	C₂²	#493594	1	1	yes	characteristic
336	C₂	#72258234	1	1	yes	characteristic
337	C₂	#72258238	1	1	yes	characteristic
338	C₂	#72266241	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#8534
commutator	C₂²×C₂²⋊C₄	C₂³×C₄
Frattini, cosocle	C₂²×#120	C₂⁴
prime radical	#72234681	C₂
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72317071	C₂	semidirect
2. #72317070	C₂	semidirect
3. #72317066	C₂	semidirect
4. #72259002	C₂	semidirect
5. #72240132	C₂	semidirect
6. #72240132	C₂	semidirect
7. #72237608	C₂	semidirect
9. #72232808	C₂	semidirect
10. #72232723	C₂	semidirect
11. #72232723	C₂	semidirect
12. C₂×#46996	C₄	semidirect
14. C₂×#21746	C₂²	semidirect
15. C₂×#21746	C₂²	semidirect
16. #4932982	C₄	semidirect
18. #4599104	C₄	semidirect
20. #4321066	C₄	semidirect
21. #4321066	C₄	semidirect
22. #2805719	C₄	semidirect
24. #1465620	C₄	semidirect
28. #576189	C₄	semidirect
29. C₂×#8547	C₂²	semidirect
30. C₂×#8541	C₂²	semidirect
31. #139720	C₂²	semidirect
32. #139720	C₂²	semidirect
37. #139486	C₂²	semidirect
38. #139486	C₂²	semidirect
39. #133895	C₂²	semidirect
41. #115164	C₂²	semidirect
49. C₂×#2760	C₂×C₄	semidirect
50. C₂×#2760	C₂×C₄	semidirect
51. C₂×#2840	C₂×C₄	semidirect
64. C₂×#2403	C₂×C₄	semidirect
70. #15635	C₂×C₄	semidirect
71. #15635	C₂×C₄	semidirect
72. #15622	C₂×C₄	semidirect
73. #15622	C₂×C₄	semidirect
74. #15568	C₂×C₄	semidirect
75. #15568	C₂×C₄	semidirect
76. #15420	C₂×C₄	semidirect
77. #15420	C₂×C₄	semidirect
94. #14365	C₂×C₄	semidirect
95. #14365	C₂×C₄	semidirect
102. #13828	C₂×C₄	semidirect
103. #13807	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72317071	2
#72317070	2
#72317066	2
#72259002	2
#72240132	2
#72237608	2
#72234681	2
#72232808	2
#72232723	2