Subgroups — #72318510

Order 2048.

At least 11336 conjugacy classes of subgroups; only the 856 normal subgroups are shown.

The subgroup lattice has 536 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72318321	C₂	1	2	yes	maximal, complemented
2	#72318296	C₂	1	2	yes	maximal, complemented
3	#72318273	C₂	1	2	yes	maximal, complemented
4	#72318233	C₂	1	2	yes	maximal, complemented
5	#72318192	C₂	1	2	yes	maximal, complemented
6	#72318189	C₂	1	2	yes	maximal, complemented
7	#72317906	C₂	1	1	yes	maximal, characteristic, complemented
8	#72317828	C₂	1	1	yes	maximal, characteristic, complemented
9	#72317804	C₂	1	1	yes	maximal, characteristic, complemented
10	#72317796	C₂	1	1	yes	maximal, characteristic, complemented
11	#72317715	C₂	1	1	yes	maximal, characteristic, complemented
12	#72317709	C₂	1	1	yes	maximal, characteristic, complemented
13	#72317705	C₂	1	1	yes	maximal, characteristic, complemented
14	#72317692	C₂	1	1	yes	maximal, characteristic, complemented
15	#72317688	C₂	1	1	yes	maximal, characteristic, complemented
16	#72284453	C₂	1	2	yes	maximal, complemented
17	#72284336	C₂	1	2	yes	maximal, complemented
18	#72279284	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#6591500	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#13348	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#508087	C₂	1	1	yes	maximal, characteristic, complemented
22	#72225750	C₂	1	1	yes	maximal, characteristic, complemented
23	#72225691	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂³×B(4,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂³×#455	C₂²	1	1	yes	characteristic
27	C₂²×#2684	C₂²	1	1	yes	characteristic, complemented
28	C₂×#36212	C₂²	1	1	yes	characteristic
29	C₂³×#354	C₂²	1	1	yes	characteristic, complemented
30	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
31	C₂×#32975	C₂²	1	1	yes	characteristic, complemented
32	C₂×#32898	C₂²	1	1	yes	characteristic
33	C₂×#32898	C₂²	1	2	yes	—
34	C₂×#32898	C₂²	1	1	yes	characteristic, complemented
35	C₂×#32891	C₂²	1	2	yes	complemented
36	C₂×#25899	C₂²	1	1	yes	characteristic, complemented
37	C₂×#24260	C₂²	1	1	yes	characteristic, complemented
38	C₂×#24056	C₂²	1	1	yes	characteristic
39	C₂×#24056	C₂²	1	1	yes	characteristic, complemented
40	C₂×#24404	C₂²	1	1	yes	characteristic
41	C₂×#24404	C₂²	1	1	yes	characteristic, complemented
42	C₂×#23900	C₂²	1	1	yes	characteristic
43	C₂×#23907	C₂²	1	1	yes	characteristic
44	C₂×D₄×#99	C₂²	1	1	yes	characteristic
45	C₂×C₄×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#1790	C₂²	1	1	yes	characteristic
47	C₂²×#1790	C₂²	1	1	yes	characteristic, complemented
48	#4932609	C₂²	1	2	yes	complemented
49	#4932464	C₂²	1	2	yes	complemented
50	#899160	C₂²	1	2	yes	complemented
51	#875301	C₂²	1	2	yes	complemented
52	#848801	C₂²	1	1	yes	characteristic, complemented
53	#845297	C₂²	1	1	yes	characteristic, complemented
54	#649042	C₂²	1	1	yes	characteristic
55	#647656	C₂²	1	1	yes	characteristic
56	#559943	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13424	C₂²	1	2	yes	complemented
58	C₂×#13424	C₂²	1	2	yes	complemented
59	C₂×#13348	C₂²	1	2	yes	—
60	C₂×#13348	C₂²	1	2	yes	—
61	C₂×#13348	C₂²	1	2	yes	complemented
62	C₂×#13348	C₂²	1	2	yes	complemented
63	C₂×#13348	C₂²	1	2	yes	complemented
64	C₂×#13348	C₂²	1	2	yes	complemented
65	C₂×#13348	C₂²	1	2	yes	complemented
66	C₂×#13348	C₂²	1	2	yes	complemented
67	C₂×#13348	C₂²	1	2	yes	complemented
68	C₂×#13343	C₂²	1	2	yes	—
69	C₂×#13343	C₂²	1	2	yes	complemented
70	C₂×#13343	C₂²	1	2	yes	complemented
71	C₂×#13090	C₂²	1	2	yes	complemented
72	C₂×#13086	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13086	C₂²	1	2	yes	complemented
74	C₂×#13082	C₂²	1	1	yes	characteristic, complemented
75	C₂×#12852	C₂²	1	1	yes	characteristic, complemented
76	C₂×#12694	C₂²	1	1	yes	characteristic, complemented
77	C₂×#12687	C₂²	1	1	yes	characteristic, complemented
78	C₂²×#1390	C₂²	1	1	yes	characteristic, complemented
79	#394066	C₂²	1	2	yes	—
80	#393971	C₂²	1	2	yes	complemented
81	#393934	C₂²	1	2	yes	—
82	#393895	C₂²	1	2	yes	complemented
83	#392663	C₂²	1	2	yes	—
84	#392654	C₂²	1	2	yes	complemented
85	#392128	C₂²	1	1	yes	characteristic
86	#392125	C₂²	1	1	yes	characteristic
87	#359583	C₂²	1	1	yes	characteristic
88	#359579	C₂²	1	1	yes	characteristic
89	#359539	C₂²	1	1	yes	characteristic
90	#359531	C₂²	1	1	yes	characteristic
91	#149425	C₂²	1	2	yes	complemented
92	#148816	C₂²	1	2	yes	complemented
93	#148238	C₂²	1	2	yes	complemented
94	#148234	C₂²	1	2	yes	complemented
95	#148167	C₂²	1	2	yes	complemented
96	#148167	C₂²	1	2	yes	complemented
97	#148167	C₂²	1	2	yes	complemented
98	#148000	C₂²	1	2	yes	complemented
99	#147995	C₂²	1	2	yes	complemented
100	#147826	C₂²	1	2	yes	complemented
101	#147779	C₂²	1	2	yes	complemented
102	#147771	C₂²	1	2	yes	complemented
103	#147771	C₂²	1	2	yes	complemented
104	#147771	C₂²	1	2	yes	complemented
105	#147749	C₂²	1	2	yes	—
106	#147749	C₂²	1	2	yes	complemented
107	#147749	C₂²	1	2	yes	complemented
108	#147561	C₂²	1	2	yes	complemented
109	#147555	C₂²	1	2	yes	complemented
110	#147555	C₂²	1	2	yes	complemented
111	#147508	C₂²	1	2	yes	complemented
112	#147500	C₂²	1	2	yes	complemented
113	#147489	C₂²	1	2	yes	complemented
114	#147489	C₂²	1	2	yes	complemented
115	#147489	C₂²	1	2	yes	complemented
116	#147330	C₂²	1	2	yes	complemented
117	#146661	C₂²	1	2	yes	complemented
118	#146569	C₂²	1	1	yes	characteristic, complemented
119	#146569	C₂²	1	1	yes	characteristic, complemented
120	#146566	C₂²	1	1	yes	characteristic, complemented
121	#146564	C₂²	1	1	yes	characteristic, complemented
122	#146457	C₂²	1	2	yes	complemented
123	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
124	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
125	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
126	C₂×#3496	C₂³	1	1	yes	characteristic
127	C₂×#3484	C₂³	1	1	yes	characteristic
128	C₂×#3484	C₂³	1	1	yes	characteristic
129	C₂²×D₄²	C₂³	1	1	yes	characteristic
130	C₂³×#124	C₂³	1	1	yes	characteristic
131	C₂³×#120	D₄	1	1	yes	characteristic, complemented
132	C₂³×#120	C₂³	1	1	yes	characteristic
133	C₂×C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
134	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
135	C₂²×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
136	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
137	C₂²×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
138	C₂²×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
139	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
140	C₂²×#455	C₂³	1	2	yes	—
141	C₂²×#455	C₂³	1	2	yes	—
142	C₂²×#455	C₂³	1	2	yes	—
143	C₂³×#100	C₂³	1	1	yes	characteristic
144	C₂³×#99	C₂³	1	1	yes	characteristic
145	C₂³×#99	C₂³	1	1	yes	characteristic
146	C₂³×#99	C₂³	1	1	yes	characteristic
147	C₂×#2684	C₂³	1	2	yes	—
148	C₂×#2684	C₂³	1	2	yes	—
149	C₂×#2684	C₂³	1	2	yes	—
150	C₂×#2679	C₂³	1	2	yes	—
151	C₂×#2849	D₄	1	1	yes	characteristic, complemented
152	C₂×#2849	D₄	1	1	yes	characteristic, complemented
153	C₂×#2847	D₄	1	1	yes	characteristic, complemented
154	C₂×#2846	D₄	1	1	yes	characteristic, complemented
155	C₂×#2436	D₄	1	1	yes	characteristic, complemented
156	C₂×#2436	D₄	1	1	yes	characteristic, complemented
157	C₂×#2435	C₂³	1	2	yes	—
158	C₂×#2409	D₄	1	1	yes	characteristic, complemented
159	C₂×#2409	C₂³	1	1	yes	characteristic
160	C₂×#2410	D₄	1	1	yes	characteristic, complemented
161	C₂×#2410	D₄	1	1	yes	characteristic, complemented
162	C₂×#2403	C₂³	1	1	yes	characteristic
163	C₂×#2403	C₂³	1	2	yes	—
164	C₂×#2403	C₂³	1	1	yes	characteristic
165	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
166	C₂×C₄×#120	C₂³	1	1	yes	characteristic
167	C₂²×#386	C₂³	1	1	yes	characteristic
168	C₂²×#386	C₂³	1	1	yes	characteristic
169	C₂²×#354	C₂³	1	2	yes	—
170	C₂²×#354	C₂³	1	2	yes	—
171	C₂²×#354	C₂³	1	2	yes	—
172	C₂²×#354	C₂³	1	2	yes	—
173	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
174	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
175	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
176	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
177	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
178	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	2	yes	—
179	#24056	D₄	1	8	yes	complemented
180	C₂×#1889	C₂³	1	1	yes	characteristic
181	C₂×#1889	C₂³	1	2	yes	—
182	C₂×#1885	C₂³	1	2	yes	—
183	C₂×#1867	C₂³	1	1	yes	characteristic
184	C₂×#1867	C₂³	1	1	yes	characteristic
185	C₂×#1867	C₂³	1	1	yes	characteristic
186	C₂×#1799	C₂³	1	1	yes	characteristic
187	C₂×#1792	C₂³	1	2	yes	—
188	C₂×#1792	C₂³	1	2	yes	—
189	C₂×#1792	C₂³	1	2	yes	—
190	C₂×#1790	D₄	1	8	yes	complemented
191	C₂×#1790	C₂³	1	1	yes	characteristic
192	C₂×#1790	C₂³	1	1	yes	characteristic
193	C₂×#1790	C₂³	1	1	yes	characteristic
194	C₂×#1790	C₂³	1	2	yes	—
195	C₂×#1790	C₂³	1	2	yes	—
196	C₂×#1790	C₂³	1	1	yes	characteristic
197	C₂×#1790	C₂³	1	1	yes	characteristic
198	C₂×#1790	C₂³	1	1	yes	characteristic
199	C₂×#1790	C₂³	1	1	yes	characteristic
200	C₂×#1790	C₂³	1	1	yes	characteristic
201	C₂×#1790	C₂³	1	1	yes	characteristic
202	C₂×#1790	C₂³	1	2	yes	—
203	C₂×#1783	C₂³	1	1	yes	characteristic
204	C₂×#1783	C₂³	1	2	yes	—
205	C₂×#1781	C₂³	1	1	yes	characteristic
206	C₂×#1781	C₂³	1	1	yes	characteristic
207	C₂×#1781	C₂³	1	2	yes	—
208	C₂×#1781	C₂³	1	1	yes	characteristic
209	C₂×C₄×#99	C₂³	1	1	yes	characteristic
210	#15227	D₄	1	2	yes	complemented
211	#15215	D₄	1	2	yes	complemented
212	#14716	D₄	1	2	yes	complemented
213	#14715	D₄	1	2	yes	complemented
214	#14698	D₄	1	1	yes	characteristic, complemented
215	#14513	C₂³	1	2	yes	—
216	#14473	C₂³	1	2	yes	—
217	#14357	C₂³	1	2	yes	—
218	#14134	D₄	1	1	yes	characteristic, complemented
219	#14027	C₂³	1	2	yes	—
220	#13967	C₂³	1	2	yes	—
221	#13902	C₂³	1	1	yes	characteristic
222	#13867	D₄	1	1	yes	characteristic, complemented
223	#13867	C₂³	1	1	yes	characteristic
224	#13832	C₂³	1	2	yes	—
225	C₄×#386	D₄	1	1	yes	characteristic, complemented
226	C₂×#1393	C₂³	1	2	yes	—
227	C₂×#1393	C₂³	1	2	yes	—
228	C₂×#1393	C₂³	1	2	yes	—
229	C₂×#1393	C₂³	1	2	yes	—
230	C₂×#1390	C₂³	1	2	yes	—
231	C₂×#1390	C₂³	1	2	yes	—
232	C₂×#1390	C₂³	1	2	yes	—
233	C₂×#1390	C₂³	1	2	yes	—
234	C₂×#1390	C₂³	1	2	yes	—
235	C₂×#1390	C₂³	1	2	yes	—
236	C₂×#1390	C₂³	1	2	yes	—
237	C₂×#1390	C₂³	1	2	yes	—
238	C₂×#1390	C₂³	1	2	yes	—
239	C₂×#1390	C₂³	1	2	yes	—
240	#10762	C₂³	1	2	yes	—
241	#10761	C₂³	1	2	yes	—
242	#10749	C₂³	1	2	yes	—
243	#10745	C₂³	1	2	yes	—
244	C₂⁷	C₂×D₄	1	1	yes	characteristic
245	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
246	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
247	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
248	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
249	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
250	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
251	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
252	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
253	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
254	C₂⁴×D₄	C₂×D₄	1	2	yes	—
255	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
256	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
257	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
258	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
259	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
261	#3484	C₂×D₄	1	4	yes	—
262	C₂²×#127	C₂×D₄	1	1	yes	characteristic
263	C₂²×#124	C₂×D₄	1	2	yes	—
264	C₂²×#124	C₂×D₄	1	2	yes	complemented
265	C₂²×#124	C₂⁴	1	2	yes	—
266	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
267	C₂²×#121	C₂×D₄	1	1	yes	characteristic
268	C₂²×#121	C₂×D₄	1	1	yes	characteristic
269	C₂²×#121	C₂×D₄	1	1	yes	characteristic
270	C₂²×#121	C₂×D₄	1	1	yes	characteristic
271	C₂²×#120	C₂×D₄	1	2	yes	—
272	C₂²×#120	C₂×D₄	1	1	yes	characteristic
273	C₂²×#120	C₂×D₄	1	2	yes	—
274	C₂²×#120	C₂×D₄	1	1	yes	characteristic
275	C₂²×#120	C₂×D₄	1	1	yes	characteristic
276	C₂²×#120	C₂×D₄	1	1	yes	characteristic
277	C₂²×#120	C₂×D₄	1	1	yes	characteristic
278	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
279	C₂²×#120	C₂⁴	1	2	yes	—
280	C₂²×#120	C₂⁴	1	1	yes	characteristic
281	C₂×#518	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
284	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
285	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
288	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
290	C₂²×#100	C₂⁴	1	2	yes	—
291	C₂²×#100	C₂⁴	1	2	yes	—
292	C₂²×#99	C₂×D₄	1	4	yes	—
293	C₂²×#99	C₂⁴	1	2	yes	—
294	C₂²×#99	C₂⁴	1	1	yes	characteristic
295	C₂²×#99	C₂⁴	1	1	yes	characteristic
296	C₂²×#99	C₂⁴	1	1	yes	characteristic
297	C₂²×#99	C₂⁴	1	1	yes	characteristic
298	C₂²×#99	C₂⁴	1	2	yes	—
299	C₂×#391	C₂×D₄	1	2	yes	complemented
300	C₂×#391	C₂×D₄	1	2	yes	complemented
301	C₂×#390	C₂×D₄	1	2	yes	—
302	C₂×#390	C₂×D₄	1	2	yes	complemented
303	C₂×#390	C₂⁴	1	2	yes	—
304	C₂×#386	C₂×D₄	1	4	yes	—
305	C₂×#386	C₂×D₄	1	4	yes	—
306	C₂×#386	C₂×D₄	1	1	yes	characteristic
307	C₂×#386	C₂×D₄	1	1	yes	characteristic
308	C₂×#386	C₂×D₄	1	1	yes	characteristic
309	C₂×#386	C₂×D₄	1	2	yes	—
310	C₂×#386	C₂×D₄	1	2	yes	—
311	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
312	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
314	C₂×#386	C₂⁴	1	2	yes	—
315	C₂×#386	C₂⁴	1	1	yes	characteristic
316	C₂×#386	C₂⁴	1	1	yes	characteristic
317	C₂×#386	C₂⁴	1	1	yes	characteristic
318	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
319	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
320	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
321	C₂×#380	C₂×D₄	1	1	yes	characteristic
322	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
323	C₂×#379	C₂×D₄	1	1	yes	characteristic
324	C₂×#379	C₂×D₄	1	1	yes	characteristic
325	C₂×#379	C₂×D₄	1	2	yes	—
326	C₂×#379	C₂×D₄	1	2	yes	—
327	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
328	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
329	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
331	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
332	#1867	C₂×D₄	1	4	yes	complemented
333	#1867	C₂×D₄	1	4	yes	complemented
334	#1790	C₂×D₄	1	4	yes	—
335	#1790	C₂×D₄	1	4	yes	—
336	#1790	C₂×D₄	1	4	yes	—
337	#1790	C₂×D₄	1	4	yes	—
338	#1790	C₂×D₄	1	4	yes	complemented
339	#1790	C₂×D₄	1	4	yes	complemented
340	#1781	C₂×D₄	1	4	yes	—
341	C₄⋊#95	C₂×D₄	1	2	yes	complemented
342	C₂²⋊#95	C₂×D₄	1	2	yes	—
343	C₂²⋊#95	C₂×D₄	1	2	yes	—
344	C₄×#95	C₂×D₄	1	2	yes	complemented
345	C₂⁶	C₂²×D₄	1	1	yes	characteristic
346	C₂⁶	C₂²×D₄	1	1	yes	characteristic
347	C₂⁶	C₂²×D₄	1	1	yes	characteristic
348	C₂⁶	C₂²×D₄	1	1	yes	characteristic
349	C₂⁶	C₂²×D₄	1	1	yes	characteristic
350	C₂⁶	C₂²×D₄	1	2	yes	—
351	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
352	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
353	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
354	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
355	C₂³×Q₈	C₂²×D₄	1	2	yes	—
356	C₂³×D₄	#120	1	1	yes	characteristic
357	C₂³×D₄	#120	1	1	yes	characteristic
358	C₂³×D₄	#120	1	1	yes	characteristic
359	C₂³×D₄	#120	1	1	yes	characteristic
360	C₂³×D₄	#120	1	1	yes	characteristic
361	C₂³×D₄	#120	1	1	yes	characteristic
362	C₂³×D₄	#120	1	1	yes	characteristic
363	C₂³×D₄	#120	1	1	yes	characteristic
364	C₂³×D₄	#120	1	1	yes	characteristic
365	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
366	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
367	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
368	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
369	C₂³×D₄	C₂²×D₄	1	2	yes	—
370	C₂³×D₄	C₂²×D₄	1	2	yes	—
371	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
372	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
373	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
374	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
375	C₂³×D₄	C₂⁵	1	1	yes	characteristic
376	C₂⁴×C₄	#120	1	4	yes	complemented
377	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
378	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
382	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
383	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
384	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
385	#518	C₂²×D₄	1	2	yes	—
386	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
389	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
396	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
398	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
400	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×D₄	1	2	yes	—
405	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
406	C₂²×C₄²	C₂²×D₄	1	2	yes	—
407	C₂×#100	H(5,𝔽₂)	1	4	yes	—
408	C₂×#99	C₂²×D₄	1	2	yes	—
409	C₂×#99	C₂²×D₄	1	2	yes	—
410	C₂×#99	C₂²×D₄	1	2	yes	—
411	C₂×#99	C₂²×D₄	1	2	yes	—
412	C₂×#99	H(5,𝔽₂)	1	4	yes	—
413	#386	#120	1	4	yes	complemented
414	#386	#120	1	4	yes	complemented
415	#386	C₂²×D₄	1	2	yes	—
416	#386	C₂²×D₄	1	2	yes	—
417	#386	C₂²×D₄	1	2	yes	—
418	#386	C₂²×D₄	1	2	yes	—
419	C₂⁵	C₂×#120	1	1	yes	characteristic
420	C₂⁵	C₂×#120	1	1	yes	characteristic
421	C₂⁵	C₂×#120	1	1	yes	characteristic
422	C₂⁵	C₂×#120	1	1	yes	characteristic
423	C₂⁵	C₂×#120	1	1	yes	characteristic
424	C₂⁵	C₂×#120	1	1	yes	characteristic
425	C₂⁵	C₂×#120	1	2	yes	—
426	C₂⁵	#534	1	2	yes	—
427	C₂⁵	D₄²	1	2	yes	—
428	C₂⁵	D₄²	1	2	yes	—
429	C₂⁵	C₂³×D₄	1	1	yes	characteristic
430	C₂⁵	C₂³×D₄	1	1	yes	characteristic
431	H(5,𝔽₂)	#535	1	4	yes	—
432	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
433	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
434	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
435	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
436	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
437	C₂²×D₄	C₂×#120	1	2	yes	—
438	C₂²×D₄	#534	1	2	yes	—
439	C₂²×D₄	D₄²	1	2	yes	—
440	C₂²×D₄	D₄²	1	2	yes	—
441	C₂²×D₄	D₄²	1	2	yes	—
442	C₂²×D₄	D₄²	1	2	yes	—
443	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
444	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
445	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
448	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
450	C₂²×D₄	#585	1	2	yes	—
451	C₂³×C₄	C₂×#120	1	1	yes	characteristic
452	C₂³×C₄	C₂×#120	1	1	yes	characteristic
453	C₂³×C₄	C₂×#120	1	1	yes	characteristic
454	C₂³×C₄	C₂×#120	1	1	yes	characteristic
455	C₂³×C₄	C₂×#120	1	1	yes	characteristic
456	C₂³×C₄	C₂×#120	1	1	yes	characteristic
457	C₂³×C₄	C₂×#120	1	2	yes	—
458	C₂³×C₄	C₂×#120	1	2	yes	—
459	C₂³×C₄	D₄²	1	2	yes	—
460	C₂³×C₄	D₄²	1	2	yes	—
461	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
464	C₂⁴	#2403	1	2	yes	—
465	C₂⁴	#2403	1	2	yes	—
466	C₂⁴	#2403	1	2	yes	—
467	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
468	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
469	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
470	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
471	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
472	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
473	C₂⁴	C₂²×#120	1	1	yes	characteristic
474	C₂⁴	C₂²×#120	1	1	yes	characteristic
475	C₂⁴	C₂×#534	1	1	yes	characteristic
476	C₂⁴	C₂×D₄²	1	1	yes	characteristic
477	C₂⁴	C₂×D₄²	1	1	yes	characteristic
478	C₂⁴	#3484	1	2	yes	—
479	C₂⁴	#3488	1	2	yes	—
480	C₂⁴	#3496	1	2	yes	—
481	C₂⁴	#3498	1	2	yes	—
482	C₂×D₄	#2199	1	4	yes	—
483	C₂×D₄	C₂×#535	1	1	yes	characteristic
484	C₂×D₄	#3449	1	1	yes	characteristic
485	C₂×D₄	#3484	1	1	yes	characteristic
486	C₂×D₄	#3484	1	1	yes	characteristic
487	C₂×D₄	#3488	1	2	yes	—
488	C₂×D₄	#3498	1	2	yes	—
489	C₂×D₄	#3532	1	2	yes	—
490	C₂×D₄	#3532	1	2	yes	—
491	C₂×D₄	#3542	1	2	yes	—
492	C₂×D₄	#3542	1	2	yes	—
493	C₂²×C₄	#2403	1	2	yes	—
494	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
495	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
496	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
497	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
499	C₂²×C₄	#3484	1	2	yes	—
500	C₂²×C₄	#3496	1	2	yes	—
501	C₂³	#23900	1	2	yes	—
502	C₂³	#23900	1	2	yes	—
503	C₂³	C₂×#2199	1	2	yes	—
504	C₂³	C₂×#2199	1	2	yes	—
505	C₂³	#33551	1	2	yes	—
506	C₂³	C₂×#2403	1	1	yes	characteristic
507	C₂³	#35250	1	1	yes	characteristic
508	C₂³	#35527	1	1	yes	characteristic
509	C₂³	#35680	1	2	yes	—
510	C₂³	#37645	1	1	yes	characteristic
511	C₂³	#39332	1	1	yes	characteristic
512	C₂³	#41932	1	2	yes	—
513	C₂³	#43886	1	2	yes	—
514	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
515	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
516	C₂³	#60399	1	2	yes	—
517	C₂×C₄	C₂×#2199	1	2	yes	—
518	C₂×C₄	#37645	1	1	yes	characteristic
519	C₂×C₄	#39332	1	1	yes	characteristic
520	C₂×C₄	#43886	1	2	yes	—
521	C₂²	#499795	1	4	yes	—
522	C₂²	#686202	1	1	yes	characteristic
523	C₂²	C₂×#23900	1	1	yes	characteristic
524	C₂²	#6437632	1	1	yes	characteristic
525	C₂²	#6533135	1	2	yes	—
526	C₂²	#6533135	1	2	yes	—
527	C₂²	C₂²×#2199	1	1	yes	characteristic
528	C₂²	C₂×#33551	1	1	yes	characteristic
529	C₂²	#7622881	1	2	yes	—
530	C₂	C₂×#499795	1	1	yes	characteristic
531	C₂	#72311330	1	2	yes	—
532	C₂	#72317485	1	2	yes	—
533	C₂	#72317593	1	1	yes	characteristic
534	C₂	#72317603	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72318321	C₂	semidirect
2. #72318296	C₂	semidirect
3. #72318273	C₂	semidirect
4. #72318233	C₂	semidirect
5. #72318192	C₂	semidirect
6. #72318189	C₂	semidirect
7. #72317906	C₂	semidirect
8. #72317828	C₂	semidirect
9. #72317804	C₂	semidirect
10. #72317796	C₂	semidirect
11. #72317715	C₂	semidirect
12. #72317709	C₂	semidirect
13. #72317705	C₂	semidirect
14. #72317692	C₂	semidirect
15. #72317688	C₂	semidirect
16. #72284453	C₂	semidirect
17. #72284336	C₂	semidirect
18. #72279284	C₂	semidirect
19. C₂×#6591500	C₂	semidirect
20. C₂²×#13348	C₂	semidirect
21. C₂×#508087	C₂	semidirect
22. #72225750	C₂	semidirect
23. #72225691	C₂	semidirect
27. C₂²×#2684	C₂²	semidirect
29. C₂³×#354	C₂²	semidirect
30. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
31. C₂×#32975	C₂²	semidirect
34. C₂×#32898	C₂²	semidirect
35. C₂×#32891	C₂²	semidirect
36. C₂×#25899	C₂²	semidirect
37. C₂×#24260	C₂²	semidirect
39. C₂×#24056	C₂²	semidirect
41. C₂×#24404	C₂²	semidirect
45. C₂×C₄×B(4,𝔽₂)	C₂²	semidirect
47. C₂²×#1790	C₂²	semidirect
48. #4932609	C₂²	semidirect
49. #4932464	C₂²	semidirect
50. #899160	C₂²	semidirect
51. #875301	C₂²	semidirect
52. #848801	C₂²	semidirect
53. #845297	C₂²	semidirect
56. #559943	C₂²	semidirect
57. C₂×#13424	C₂²	semidirect
58. C₂×#13424	C₂²	semidirect
61. C₂×#13348	C₂²	semidirect
62. C₂×#13348	C₂²	semidirect
63. C₂×#13348	C₂²	semidirect
64. C₂×#13348	C₂²	semidirect
65. C₂×#13348	C₂²	semidirect
66. C₂×#13348	C₂²	semidirect
67. C₂×#13348	C₂²	semidirect
69. C₂×#13343	C₂²	semidirect
70. C₂×#13343	C₂²	semidirect
71. C₂×#13090	C₂²	semidirect
72. C₂×#13086	C₂²	semidirect
73. C₂×#13086	C₂²	semidirect
74. C₂×#13082	C₂²	semidirect
75. C₂×#12852	C₂²	semidirect
76. C₂×#12694	C₂²	semidirect
77. C₂×#12687	C₂²	semidirect
78. C₂²×#1390	C₂²	semidirect
80. #393971	C₂²	semidirect
82. #393895	C₂²	semidirect
84. #392654	C₂²	semidirect
91. #149425	C₂²	semidirect
92. #148816	C₂²	semidirect
93. #148238	C₂²	semidirect
94. #148234	C₂²	semidirect
95. #148167	C₂²	semidirect
96. #148167	C₂²	semidirect
97. #148167	C₂²	semidirect
98. #148000	C₂²	semidirect
99. #147995	C₂²	semidirect
100. #147826	C₂²	semidirect
101. #147779	C₂²	semidirect
102. #147771	C₂²	semidirect
103. #147771	C₂²	semidirect
104. #147771	C₂²	semidirect
106. #147749	C₂²	semidirect
107. #147749	C₂²	semidirect
108. #147561	C₂²	semidirect
109. #147555	C₂²	semidirect
110. #147555	C₂²	semidirect
111. #147508	C₂²	semidirect
112. #147500	C₂²	semidirect
113. #147489	C₂²	semidirect
114. #147489	C₂²	semidirect
115. #147489	C₂²	semidirect
116. #147330	C₂²	semidirect
117. #146661	C₂²	semidirect
118. #146569	C₂²	semidirect
119. #146569	C₂²	semidirect
120. #146566	C₂²	semidirect
121. #146564	C₂²	semidirect
122. #146457	C₂²	semidirect
125. C₂⁴×#41	D₄	semidirect
131. C₂³×#120	D₄	semidirect
151. C₂×#2849	D₄	semidirect
152. C₂×#2849	D₄	semidirect
153. C₂×#2847	D₄	semidirect
154. C₂×#2846	D₄	semidirect
155. C₂×#2436	D₄	semidirect
156. C₂×#2436	D₄	semidirect
158. C₂×#2409	D₄	semidirect
160. C₂×#2410	D₄	semidirect
161. C₂×#2410	D₄	semidirect
165. C₂×D₄×C₂²⋊C₄	D₄	semidirect
179. #24056	D₄	semidirect
190. C₂×#1790	D₄	semidirect
210. #15227	D₄	semidirect
211. #15215	D₄	semidirect
212. #14716	D₄	semidirect
213. #14715	D₄	semidirect
214. #14698	D₄	semidirect
218. #14134	D₄	semidirect
222. #13867	D₄	semidirect
225. C₄×#386	D₄	semidirect
250. C₂⁴×Q₈	C₂×D₄	semidirect
255. C₂⁴×D₄	C₂×D₄	semidirect
259. C₂⁵×C₄	C₂×D₄	semidirect
260. C₂⁵×C₄	C₂×D₄	semidirect
264. C₂²×#124	C₂×D₄	semidirect
266. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
278. C₂²×#120	C₂×D₄	semidirect
288. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
299. C₂×#391	C₂×D₄	semidirect
300. C₂×#391	C₂×D₄	semidirect
302. C₂×#390	C₂×D₄	semidirect
311. C₂×#386	C₂×D₄	semidirect
312. C₂×#386	C₂×D₄	semidirect
313. C₂×#386	C₂×D₄	semidirect
318. C₂×#385	C₂×D₄	semidirect
319. C₂×#385	C₂×D₄	semidirect
320. C₂×#385	C₂×D₄	semidirect
322. C₂×#380	C₂×D₄	semidirect
327. C₂×#379	C₂×D₄	semidirect
328. C₂×#379	C₂×D₄	semidirect
330. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
331. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
332. #1867	C₂×D₄	semidirect
333. #1867	C₂×D₄	semidirect
338. #1790	C₂×D₄	semidirect
339. #1790	C₂×D₄	semidirect
341. C₄⋊#95	C₂×D₄	semidirect
344. C₄×#95	C₂×D₄	semidirect
376. C₂⁴×C₄	#120	semidirect
395. C₂²×C₂²⋊C₄	#120	semidirect
413. #386	#120	semidirect
414. #386	#120	semidirect

Maximal subgroups

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

subgroup	index
#72318321	2
#72318296	2
#72318273	2
#72318233	2
#72318192	2
#72318189	2
#72317906	2
#72317828	2
#72317804	2
#72317796	2
#72317715	2
#72317709	2
#72317705	2
#72317692	2
#72317688	2
#72284453	2
#72284336	2
#72279284	2
C₂×#6591500	2
C₂²×#13348	2
C₂×#508087	2
#72225750	2
#72225691	2