Subgroups — #72315009

Order 4096.

Only the 1577 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 642 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72314996	C₂	1	2	yes	maximal, complemented
2	#72314990	C₂	1	2	yes	maximal, complemented
3	#72314981	C₂	1	2	yes	maximal, complemented
4	#72314791	C₂	1	2	yes	maximal, complemented
5	#72314779	C₂	1	2	yes	maximal, complemented
6	#72314739	C₂²	1	2	yes	complemented
7	#72314734	C₂²	1	2	yes	complemented
8	#72314447	C₂	1	1	yes	maximal, characteristic, complemented
9	#72314440	C₂²	1	2	yes	complemented
10	#72313608	C₂	1	1	yes	maximal, characteristic, complemented
11	#72312503	C₂	1	2	yes	maximal, complemented
12	#72312216	C₂²	1	2	yes	complemented
13	#72310373	C₂	1	2	yes	maximal, complemented
14	#72310366	C₂²	1	2	yes	complemented
15	#72310205	C₂	1	1	yes	maximal, characteristic, complemented
16	#72309800	C₂²	1	1	yes	characteristic, complemented
17	#72309555	C₂²	1	2	yes	complemented
18	#72301923	C₂	1	2	yes	maximal, complemented
19	#72300151	C₂	1	1	yes	maximal, characteristic
20	#72300149	C₄	1	2	yes	complemented
21	#72300148	C₄	1	2	yes	complemented
22	#72271167	C₂²	1	1	yes	characteristic
23	#72266978	C₂	1	2	yes	maximal, complemented
24	#72266974	C₄	1	2	yes	complemented
25	#72266965	C₄	1	2	yes	complemented
26	#72266864	C₂²	1	1	yes	characteristic
27	#72266864	C₂²	1	1	yes	characteristic
28	#72266835	C₂²	1	2	yes	—
29	#72266446	C₂	1	1	yes	maximal, characteristic, complemented
30	#72266378	C₂²	1	2	yes	complemented
31	#72266368	C₂²	1	2	yes	complemented
32	#72265766	C₂²	1	1	yes	characteristic, complemented
33	#72260562	C₂²	1	1	yes	characteristic, complemented
34	#72258334	C₂²	1	2	yes	complemented
35	#72258028	C₂²	1	2	yes	—
36	#72258019	C₂²	1	2	yes	complemented
37	#72256303	C₂	1	2	yes	maximal, complemented
38	#72256119	C₂²	1	1	yes	characteristic, complemented
39	#72256113	C₂²	1	2	yes	complemented
40	#72255986	C₂²	1	2	yes	complemented
41	#72255977	C₂²	1	2	yes	complemented
42	#72255849	C₂²	1	2	yes	complemented
43	#72255793	C₂²	1	2	yes	complemented
44	#72255764	C₂²	1	2	yes	complemented
45	#72251580	C₂	1	2	yes	maximal, complemented
46	#72251550	C₂²	1	2	yes	complemented
47	#72251528	C₂²	1	2	yes	complemented
48	#72251528	C₂²	1	2	yes	complemented
49	#72251499	C₂²	1	2	yes	complemented
50	#72251485	C₂²	1	2	yes	complemented
51	#72251473	C₂²	1	2	yes	complemented
52	#72251462	C₂²	1	2	yes	complemented
53	#72251422	C₂²	1	2	yes	complemented
54	#72246304	C₂	1	2	yes	maximal, complemented
55	#72246301	C₂²	1	2	yes	complemented
56	#72246299	C₂²	1	2	yes	complemented
57	#72246299	C₂²	1	2	yes	complemented
58	#72246292	C₂²	1	2	yes	complemented
59	#72246288	C₂²	1	2	yes	complemented
60	#72246287	C₂²	1	2	yes	complemented
61	#72246286	C₂²	1	2	yes	complemented
62	#72240132	C₂²	1	1	yes	characteristic, complemented
63	#72238974	C₂²	1	2	yes	complemented
64	#72238614	C₂	1	1	yes	maximal, characteristic, complemented
65	#72238613	C₂²	1	2	yes	complemented
66	#72238612	C₂²	1	2	yes	complemented
67	#72238611	C₂²	1	2	yes	complemented
68	#72238609	C₂²	1	2	yes	—
69	#72238589	C₂²	1	2	yes	complemented
70	#72238349	C₂²	1	2	yes	complemented
71	#72238343	C₂²	1	2	yes	complemented
72	#72238343	C₂²	1	2	yes	complemented
73	#72237638	C₂²	1	2	yes	complemented
74	#72237480	C₂	1	1	yes	maximal, characteristic, complemented
75	#72237476	C₂²	1	2	yes	complemented
76	#72237476	C₂²	1	2	yes	complemented
77	#72237473	C₂²	1	2	yes	complemented
78	#72237472	C₂²	1	2	yes	—
79	#72237472	C₂²	1	2	yes	—
80	#72237467	C₂²	1	2	yes	complemented
81	#72237402	C₂²	1	2	yes	—
82	#72237302	C₂²	1	1	yes	characteristic
83	#72235242	C₂²	1	1	yes	characteristic, complemented
84	#72235186	C₂²	1	1	yes	characteristic, complemented
85	#72234668	C₂²	1	1	yes	characteristic, complemented
86	#72234607	C₄	1	2	yes	complemented
87	#72234516	C₄	1	2	yes	complemented
88	#72233581	C₂²	1	2	yes	—
89	#72225743	C₂²	1	2	yes	complemented
90	#72225713	C₂²	1	1	yes	characteristic, complemented
91	#72225639	C₂²	1	2	yes	complemented
92	#72224136	C₂²	1	1	yes	characteristic
93	#72224136	C₂²	1	1	yes	characteristic
94	C₂×#139748	C₂²	1	2	yes	complemented
95	#72219314	C₂²	1	1	yes	characteristic, complemented
96	C₂×#493474	C₂²	1	2	yes	complemented
97	C₂×#139716	C₂²	1	1	yes	characteristic, complemented
98	#72219264	C₂²	1	1	yes	characteristic
99	#72219241	C₂²	1	1	yes	characteristic, complemented
100	#72219162	C₂²	1	2	yes	complemented
101	#72218980	C₂²	1	2	yes	—
102	#72218980	C₂²	1	2	yes	—
103	#72218840	C₂²	1	2	yes	complemented
104	#72218521	C₂²	1	2	yes	complemented
105	#72218475	C₂²	1	2	yes	complemented
106	#72218475	C₂²	1	2	yes	complemented
107	#72218317	C₂²	1	2	yes	complemented
108	#72218206	C₂²	1	2	yes	complemented
109	#72218104	C₂²	1	2	yes	complemented
110	C₂×#139750	C₂²	1	2	yes	complemented
111	C₂×#139731	C₂²	1	2	yes	complemented
112	#72216323	C₄	1	2	yes	complemented
113	C₂×#347042	C₂²	1	2	yes	—
114	#72211144	C₄	1	2	yes	complemented
115	#10586797	C₂×C₄	1	2	yes	complemented
116	#10586796	C₂×C₄	1	2	yes	complemented
117	#10586489	C₂×C₄	1	2	yes	complemented
118	#10586472	C₂×C₄	1	2	yes	complemented
119	#10586422	C₂³	1	2	yes	—
120	#10586404	C₂³	1	1	yes	characteristic
121	#10586404	C₂³	1	1	yes	characteristic
122	C₂×#62817	C₂³	1	2	yes	—
123	C₂²×#3532	C₂³	1	1	yes	characteristic
124	#7630939	D₄	1	2	yes	—
125	C₂×#34980	C₂³	1	1	yes	characteristic
126	#7626202	C₂³	1	1	yes	characteristic, complemented
127	#6499871	C₂×C₄	1	2	yes	—
128	#6499871	C₂×C₄	1	2	yes	complemented
129	#6499871	D₄	1	2	yes	—
130	#6499870	C₂×C₄	1	2	yes	—
131	#6499870	C₂×C₄	1	2	yes	complemented
132	#6499870	D₄	1	2	yes	—
133	#6499869	C₂×C₄	1	2	yes	—
134	#6499869	C₂×C₄	1	2	yes	complemented
135	#6499869	D₄	1	2	yes	—
136	#6499867	C₂×C₄	1	2	yes	—
137	#6499867	C₂×C₄	1	2	yes	complemented
138	#6499867	D₄	1	2	yes	—
139	#6451874	D₄	1	2	yes	—
140	C₂×#23984	D₄	1	2	yes	—
141	#6437621	C₂³	1	2	yes	—
142	#6437621	C₂³	1	2	yes	—
143	C₂×#23900	C₂³	1	2	yes	—
144	C₂×#23900	C₂³	1	2	yes	—
145	#6374251	C₂³	1	1	yes	characteristic, complemented
146	#6374210	D₄	1	2	yes	—
147	C₂×#21778	C₂³	1	2	yes	—
148	#6374187	D₄	1	4	yes	complemented
149	C₂×#21776	C₂³	1	2	yes	—
150	C₂×#21776	C₂³	1	2	yes	—
151	#6374128	C₂³	1	1	yes	characteristic
152	#6374128	C₂³	1	1	yes	characteristic
153	#6374128	C₂³	1	1	yes	characteristic, complemented
154	C₂×#21746	C₂³	1	1	yes	characteristic, complemented
155	#6371558	C₂³	1	2	yes	—
156	#6371551	D₄	1	4	yes	complemented
157	#5025789	C₂×C₄	1	1	yes	characteristic, complemented
158	#5025782	C₂×C₄	1	1	yes	characteristic, complemented
159	#5021140	C₂×C₄	1	1	yes	characteristic, complemented
160	#5021138	C₂×C₄	1	1	yes	characteristic, complemented
161	#4422949	C₂×C₄	1	1	yes	characteristic, complemented
162	#4420586	C₂×C₄	1	1	yes	characteristic, complemented
163	#763333	C₂³	1	1	yes	characteristic
164	#686187	C₂×C₄	1	1	yes	characteristic, complemented
165	#647656	C₂×C₄	1	1	yes	characteristic, complemented
166	#616961	C₂³	1	1	yes	characteristic
167	#616960	C₂³	1	1	yes	characteristic
168	C₂×#15947	C₂³	1	1	yes	characteristic
169	#552670	C₂³	1	1	yes	characteristic
170	C₂×#12707	C₂³	1	2	yes	—
171	C₂×#12707	C₂³	1	2	yes	—
172	C₂×#12705	C₂³	1	2	yes	—
173	C₂×#12705	C₂³	1	2	yes	—
174	C₂×#12705	C₂³	1	2	yes	—
175	C₂×#12705	C₂³	1	2	yes	—
176	#493370	C₂³	1	2	yes	—
177	#493370	C₂³	1	2	yes	—
178	#493357	C₂³	1	2	yes	—
179	#493357	C₂³	1	2	yes	—
180	#493357	C₂³	1	2	yes	complemented
181	C₂×#12687	C₂³	1	2	yes	—
182	C₂×#12687	C₂³	1	2	yes	—
183	C₂×#12687	C₂³	1	2	yes	complemented
184	#392030	C₂³	1	2	yes	complemented
185	#373637	C₂³	1	2	yes	complemented
186	#363969	D₄	1	4	yes	complemented
187	#363969	D₄	1	4	yes	complemented
188	#359558	C₂³	1	2	yes	—
189	#359558	C₂³	1	2	yes	—
190	#359549	C₂³	1	2	yes	—
191	#359549	C₂³	1	2	yes	—
192	#359549	C₂³	1	2	yes	—
193	#359549	C₂³	1	2	yes	—
194	#359509	C₂³	1	2	yes	—
195	#359509	C₂³	1	2	yes	—
196	#359501	C₂³	1	2	yes	—
197	#359501	C₂³	1	2	yes	—
198	#359501	C₂³	1	2	yes	complemented
199	#359442	C₂³	1	2	yes	—
200	#359442	C₂³	1	2	yes	—
201	#359442	C₂³	1	2	yes	complemented
202	#355096	C₂³	1	2	yes	complemented
203	#355096	C₂³	1	2	yes	complemented
204	#347057	C₂×C₄	1	4	yes	complemented
205	#347056	C₂×C₄	1	4	yes	complemented
206	#347048	C₂×C₄	1	4	yes	complemented
207	#347048	C₂×C₄	1	4	yes	complemented
208	#347047	C₂×C₄	1	4	yes	complemented
209	#347047	C₂×C₄	1	4	yes	complemented
210	#347047	C₂×C₄	1	4	yes	complemented
211	#347045	C₂×C₄	1	4	yes	complemented
212	#347045	C₂×C₄	1	4	yes	complemented
213	#347045	C₂×C₄	1	4	yes	complemented
214	#347042	C₂×C₄	1	4	yes	complemented
215	#347042	C₂×C₄	1	4	yes	complemented
216	#347042	C₂×C₄	1	4	yes	complemented
217	#347042	C₂×C₄	1	4	yes	complemented
218	#347042	C₂×C₄	1	4	yes	complemented
219	#347042	C₂×C₄	1	4	yes	complemented
220	#188109	C₂³	1	1	yes	characteristic, complemented
221	C₂×#8547	C₂³	1	1	yes	characteristic, complemented
222	#188065	C₂×C₄	1	2	yes	complemented
223	#188062	C₂×C₄	1	2	yes	complemented
224	#188050	C₂³	1	2	yes	—
225	#188049	C₂³	1	1	yes	characteristic, complemented
226	#188046	C₂×C₄	1	2	yes	complemented
227	#188035	C₂×C₄	1	2	yes	complemented
228	C₂×#8541	C₂³	1	2	yes	—
229	C₂×#8541	C₂³	1	1	yes	characteristic, complemented
230	#187952	C₂×C₄	1	2	yes	complemented
231	#187952	C₂×C₄	1	2	yes	complemented
232	#187949	C₂×C₄	1	2	yes	complemented
233	#187949	C₂×C₄	1	2	yes	complemented
234	#187944	C₂³	1	2	yes	—
235	#187944	C₂³	1	2	yes	—
236	#187943	C₂×C₄	1	2	yes	complemented
237	#187943	C₂×C₄	1	2	yes	complemented
238	#187940	C₂×C₄	1	2	yes	complemented
239	#187940	C₂×C₄	1	2	yes	complemented
240	C₂×#8534	C₂³	1	2	yes	—
241	C₂×#8534	C₂³	1	2	yes	—
242	#146479	C₂³	1	2	yes	complemented
243	#146479	C₂³	1	2	yes	complemented
244	#146475	C₂³	1	2	yes	complemented
245	#146475	C₂³	1	2	yes	complemented
246	#128033	C₂³	1	2	yes	complemented
247	C₂×#7304	C₂³	1	2	yes	complemented
248	C₂×#7316	C₂³	1	2	yes	complemented
249	C₂×#7316	C₂³	1	2	yes	complemented
250	C₂×#7314	C₂³	1	2	yes	complemented
251	C₂×#7314	C₂³	1	2	yes	complemented
252	C₂×#7311	C₂³	1	2	yes	complemented
253	C₂×#7310	C₂³	1	2	yes	complemented
254	C₂×#7310	C₂³	1	2	yes	complemented
255	C₂×#7310	C₂³	1	2	yes	complemented
256	#128009	C₂³	1	2	yes	complemented
257	C₂×#7307	C₂³	1	2	yes	complemented
258	#108238	C₂³	1	2	yes	complemented
259	#108222	C₂³	1	2	yes	complemented
260	#107130	C₂³	1	2	yes	complemented
261	#107114	C₂³	1	2	yes	complemented
262	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
263	#62862	#41	1	8	yes	—
264	#62844	C₂×D₄	1	4	yes	—
265	#62842	C₂×D₄	1	4	yes	—
266	#62832	C₂²×C₄	1	4	yes	—
267	#62824	C₂²×C₄	1	4	yes	—
268	#62820	C₂²×C₄	1	2	yes	—
269	#62820	C₂²×C₄	1	2	yes	—
270	#62820	C₂×D₄	1	2	yes	—
271	#62817	C₂²×C₄	1	2	yes	—
272	#62817	C₂²×C₄	1	2	yes	—
273	#62817	C₂²×C₄	1	4	yes	—
274	#62817	C₂²×C₄	1	4	yes	—
275	#62817	C₂×D₄	1	2	yes	—
276	C₂×#3490	C₂×D₄	1	2	yes	—
277	C₂×#3484	C₂×D₄	1	2	yes	—
278	C₂×#3484	C₂⁴	1	2	yes	—
279	C₂×#3484	C₂⁴	1	2	yes	—
280	C₂²×#551	C₂²×C₄	1	1	yes	characteristic
281	C₂²×D₄²	C₂²×C₄	1	1	yes	characteristic
282	C₂²×H(3,𝔽₄)	C₂²×C₄	1	1	yes	characteristic
283	C₂²×#560	C₂²×C₄	1	1	yes	characteristic
284	C₂²×#535	C₂⁴	1	1	yes	characteristic
285	C₂²×#534	C₂⁴	1	1	yes	characteristic
286	C₂²×#534	C₂⁴	1	1	yes	characteristic
287	C₂³×#120	C₂⁴	1	1	yes	characteristic
288	C₂³×#120	C₂⁴	1	1	yes	characteristic
289	#62652	C₂×D₄	1	2	yes	complemented
290	C₂×#2883	C₂×D₄	1	4	yes	complemented
291	C₂×#2883	C₂×D₄	1	2	yes	complemented
292	#36614	C₂²⋊C₄	1	4	yes	complemented
293	C₂×#2849	C₂²×C₄	1	1	yes	characteristic
294	C₂×#2849	C₂×D₄	1	1	yes	characteristic
295	C₂×#2846	C₂²⋊C₄	1	4	yes	complemented
296	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
297	C₂×#2846	C₂×D₄	1	1	yes	characteristic
298	C₂×#2846	C₂×D₄	1	4	yes	—
299	#35222	C₂²⋊C₄	1	4	yes	complemented
300	#34980	C₂²⋊C₄	1	4	yes	complemented
301	#34980	C₂×D₄	1	4	yes	—
302	C₂×#2613	C₂²×C₄	1	1	yes	characteristic
303	C₂×#2613	C₂²×C₄	1	1	yes	characteristic
304	C₂×#2613	C₂×D₄	1	1	yes	characteristic
305	C₂×#2613	C₂×D₄	1	1	yes	characteristic
306	#34171	C₂×D₄	1	2	yes	—
307	#34171	C₂⁴	1	2	yes	—
308	#34171	C₂⁴	1	2	yes	—
309	C₂×#2308	C₂×D₄	1	1	yes	characteristic
310	C₂×#2308	C₂×D₄	1	1	yes	characteristic
311	C₂²×#379	C₂×D₄	1	1	yes	characteristic
312	#23985	C₂²⋊C₄	1	4	yes	complemented
313	#23985	C₂²⋊C₄	1	4	yes	complemented
314	#23984	C₂²⋊C₄	1	4	yes	complemented
315	#23984	C₂²⋊C₄	1	4	yes	complemented
316	#23984	C₂²⋊C₄	1	4	yes	complemented
317	#23984	C₂²⋊C₄	1	4	yes	complemented
318	#23984	C₂²⋊C₄	1	4	yes	complemented
319	#23984	C₂²⋊C₄	1	4	yes	complemented
320	#23901	C₂²×C₄	1	4	yes	—
321	#23901	C₂²×C₄	1	4	yes	—
322	#23901	C₂×D₄	1	4	yes	—
323	#23900	C₂²×C₄	1	4	yes	—
324	#23900	C₂²×C₄	1	4	yes	—
325	#23900	C₂²×C₄	1	4	yes	—
326	#23900	C₂²×C₄	1	4	yes	—
327	#23900	C₂²×C₄	1	4	yes	—
328	#23900	C₂²×C₄	1	4	yes	—
329	#23900	C₂×D₄	1	4	yes	—
330	#23900	C₂×D₄	1	4	yes	—
331	#23900	C₂×D₄	1	4	yes	—
332	#21748	C₂²⋊C₄	1	4	yes	complemented
333	#21748	C₂²⋊C₄	1	4	yes	complemented
334	#21747	C₂²×C₄	1	2	yes	—
335	#21747	C₂²×C₄	1	2	yes	—
336	#21747	C₂×D₄	1	2	yes	—
337	#21746	C₂²⋊C₄	1	4	yes	complemented
338	#21746	C₂²⋊C₄	1	4	yes	complemented
339	#21746	C₂²×C₄	1	2	yes	—
340	#21746	C₂²×C₄	1	2	yes	—
341	#21746	C₂×D₄	1	2	yes	—
342	C₂×#1913	C₂×D₄	1	4	yes	—
343	C₂×#1913	C₂×D₄	1	4	yes	—
344	C₂×#1913	C₂×D₄	1	4	yes	—
345	C₂×#1913	C₂×D₄	1	4	yes	—
346	C₂×#1913	C₂×D₄	1	4	yes	complemented
347	C₂×#1913	C₂×D₄	1	4	yes	complemented
348	C₂×#1898	C₂×D₄	1	4	yes	—
349	C₂×#1898	C₂×D₄	1	4	yes	—
350	#20960	C₂×D₄	1	4	yes	complemented
351	#20960	C₂×D₄	1	4	yes	complemented
352	C₂×#1828	C₂×D₄	1	4	yes	complemented
353	C₂×#1819	C₂×D₄	1	2	yes	—
354	C₂×#1783	C₂⁴	1	2	yes	—
355	C₂×#1783	C₂⁴	1	2	yes	—
356	C₂×#1781	C₂⁴	1	2	yes	—
357	C₂×#1781	C₂⁴	1	2	yes	—
358	C₂×#1781	C₂⁴	1	2	yes	—
359	C₂×#1781	C₂⁴	1	2	yes	—
360	C₂×#1781	C₂⁴	1	2	yes	—
361	C₂×#1781	C₂⁴	1	2	yes	—
362	#20354	C₂×D₄	1	2	yes	complemented
363	#20354	C₂×D₄	1	2	yes	complemented
364	#15948	C₂²×C₄	1	1	yes	characteristic
365	#15948	C₂²×C₄	1	1	yes	characteristic
366	#15947	C₂²×C₄	1	1	yes	characteristic
367	#15947	C₂²×C₄	1	1	yes	characteristic
368	#15947	C₂²×C₄	1	1	yes	characteristic
369	#15947	C₂²×C₄	1	1	yes	characteristic
370	#15947	C₂²×C₄	1	1	yes	characteristic
371	#15947	C₂²×C₄	1	1	yes	characteristic
372	#15262	C₂²×C₄	1	1	yes	characteristic
373	#15261	C₂²×C₄	1	1	yes	characteristic
374	#15259	C₂²×C₄	1	1	yes	characteristic
375	#15259	C₂²×C₄	1	1	yes	characteristic
376	#15259	C₂²×C₄	1	1	yes	characteristic
377	#15258	C₂²×C₄	1	1	yes	characteristic
378	#15258	C₂²×C₄	1	1	yes	characteristic
379	#15258	C₂²×C₄	1	1	yes	characteristic
380	#14658	C₂²×C₄	1	1	yes	characteristic
381	#14657	C₂²×C₄	1	1	yes	characteristic
382	#14335	C₂⁴	1	1	yes	characteristic
383	#14167	C₂²×C₄	1	1	yes	characteristic
384	#14134	C₂²×C₄	1	1	yes	characteristic
385	C₂×#1438	C₂⁴	1	1	yes	characteristic
386	#8546	C₂²×C₄	1	4	yes	—
387	#8544	C₂²×C₄	1	4	yes	—
388	#8541	C₂²×C₄	1	4	yes	—
389	#8541	C₂²×C₄	1	4	yes	—
390	#8534	C₂²×C₄	1	4	yes	—
391	#8534	C₂²×C₄	1	4	yes	—
392	#8534	C₂²×C₄	1	4	yes	—
393	#8534	C₂²×C₄	1	4	yes	—
394	#8534	C₂²×C₄	1	4	yes	—
395	#8534	C₂²×C₄	1	4	yes	—
396	#8534	C₂²×C₄	1	4	yes	—
397	#8534	C₂²×C₄	1	4	yes	—
398	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
399	C₂⁷	C₂²×D₄	1	1	yes	characteristic
400	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
402	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
403	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
404	C₂³×#41	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
406	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
407	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
408	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
409	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
410	C₂⁵×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
411	#3491	C₄×D₄	1	8	yes	—
412	#3491	#121	1	8	yes	—
413	#3490	C₂×C₂²⋊C₄	1	4	yes	—
414	#3490	C₂×C₂²⋊C₄	1	4	yes	—
415	#3490	C₄×D₄	1	8	yes	—
416	#3490	#121	1	8	yes	—
417	#3490	#123	1	4	yes	—
418	#3490	#123	1	4	yes	—
419	#3485	C₄×D₄	1	8	yes	—
420	#3485	#121	1	8	yes	—
421	#3484	C₄×D₄	1	8	yes	—
422	#3484	#121	1	8	yes	—
423	#3484	C₂³×C₄	1	4	yes	—
424	#3484	C₂³×C₄	1	4	yes	—
425	#3484	C₂²×D₄	1	4	yes	—
426	#3484	C₂×#41	1	4	yes	—
427	#3484	C₂×#41	1	4	yes	—
428	#3484	H(5,𝔽₂)	1	4	yes	—
429	C₂×#543	#120	1	2	yes	—
430	C₂×#535	#123	1	4	yes	—
431	C₂×#534	#120	1	4	yes	—
432	C₂×#534	#120	1	2	yes	—
433	C₂×#534	#123	1	4	yes	—
434	C₂×#534	C₂²×D₄	1	4	yes	—
435	C₂×#534	C₂²×D₄	1	4	yes	—
436	C₂×#534	C₂×#41	1	4	yes	—
437	C₂²×#127	C₂³×C₄	1	1	yes	characteristic
438	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×#124	C₂³×C₄	1	1	yes	characteristic
440	C₂²×#124	H(5,𝔽₂)	1	1	yes	characteristic
441	C₂×#525	C₂×C₂²⋊C₄	1	4	yes	—
442	C₂²×#123	C₂³×C₄	1	1	yes	characteristic
443	C₂²×#123	C₂³×C₄	1	1	yes	characteristic
444	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
445	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
446	C₂²×#120	C₂×C₂²⋊C₄	1	4	yes	—
447	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
448	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
449	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
450	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
451	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
452	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
453	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
454	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
455	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
456	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
457	C₂²×#120	C₂²×D₄	1	4	yes	—
458	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×#518	#120	1	2	yes	—
461	C₂×#518	#120	1	4	yes	—
462	C₂×#518	C₂²×D₄	1	2	yes	—
463	C₂×#518	C₂²×D₄	1	2	yes	—
464	C₂×#518	C₂²×D₄	1	2	yes	—
465	C₂×#518	C₂²×D₄	1	2	yes	—
466	C₂×#518	C₂²×D₄	1	2	yes	—
467	C₂×#518	H(5,𝔽₂)	1	2	yes	—
468	C₂²×#117	H(5,𝔽₂)	1	1	yes	characteristic
469	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
470	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×#99	C₂²×D₄	1	4	yes	—
474	C₂²×#99	C₂²×D₄	1	4	yes	—
475	#2849	C₂×C₂²⋊C₄	1	8	yes	complemented
476	#2846	C₂×C₂²⋊C₄	1	8	yes	complemented
477	#2846	C₂×C₂²⋊C₄	1	8	yes	complemented
478	#2846	C₂×C₂²⋊C₄	1	8	yes	complemented
479	#2280	C₂×C₂²⋊C₄	1	4	yes	complemented
480	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
481	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
482	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
483	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
484	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
485	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
486	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
487	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
488	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
489	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
490	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
491	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
492	C₂×#379	C₂×C₂²⋊C₄	1	4	yes	complemented
493	C₂×#379	C₂²×D₄	1	4	yes	—
494	#1898	C₂×C₂²⋊C₄	1	8	yes	complemented
495	#1898	C₂×C₂²⋊C₄	1	8	yes	complemented
496	#1898	C₂×C₂²⋊C₄	1	8	yes	complemented
497	#1898	C₂×C₂²⋊C₄	1	8	yes	complemented
498	#1819	C₂×C₂²⋊C₄	1	4	yes	complemented
499	#1819	C₂×C₂²⋊C₄	1	4	yes	complemented
500	#1781	C₂³×C₄	1	4	yes	—
501	#1781	C₂³×C₄	1	4	yes	—
502	#1781	C₂²×D₄	1	4	yes	—
503	#1438	C₂³×C₄	1	1	yes	characteristic
504	#1438	C₂³×C₄	1	1	yes	characteristic
505	#1438	C₂³×C₄	1	1	yes	characteristic
506	#1438	C₂³×C₄	1	1	yes	characteristic
507	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
508	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
509	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
510	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
511	C₂⁶	#518	1	1	yes	characteristic
512	C₂⁶	#518	1	1	yes	characteristic
513	C₂⁶	C₂³×D₄	1	1	yes	characteristic
514	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×H(5,𝔽₂)	C₂×C₄×D₄	1	4	yes	—
516	C₂×H(5,𝔽₂)	#518	1	4	yes	—
517	C₂×H(5,𝔽₂)	C₂×#121	1	4	yes	—
518	C₂²×#41	#386	1	4	yes	—
519	C₂²×#41	B(4,𝔽₂)	1	8	yes	—
520	C₂³×Q₈	#518	1	1	yes	characteristic
521	C₂³×D₄	#386	1	4	yes	—
522	C₂³×D₄	B(4,𝔽₂)	1	8	yes	—
523	C₂³×D₄	#518	1	1	yes	characteristic
524	C₂³×D₄	C₂×#120	1	4	yes	—
525	C₂³×D₄	C₂×#120	1	2	yes	—
526	C₂³×D₄	C₂×#123	1	2	yes	—
527	C₂³×D₄	C₂⁴×C₄	1	1	yes	characteristic
528	C₂³×D₄	C₂³×D₄	1	2	yes	—
529	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
530	C₂³×D₄	C₂²×#41	1	2	yes	—
531	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
533	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
535	C₂⁴×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
536	C₂⁴×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
537	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	#543	#386	1	4	yes	—
539	#543	#386	1	4	yes	—
540	#534	#386	1	4	yes	—
541	#534	#386	1	4	yes	—
542	#534	C₂×C₄×D₄	1	8	yes	—
543	#534	C₂×#121	1	8	yes	—
544	C₂×#123	#386	1	8	yes	—
545	C₂×#123	C₂×C₄×D₄	1	4	yes	—
546	C₂×#123	C₂×#121	1	4	yes	—
547	C₂×#120	#386	1	8	yes	—
548	C₂×#120	C₂²×C₂²⋊C₄	1	8	yes	—
549	C₂×#120	C₂×C₄×D₄	1	4	yes	—
550	C₂×#120	C₂×#121	1	4	yes	—
551	C₂×#120	C₂×#123	1	8	yes	—
552	#518	#386	1	8	yes	—
553	#518	#386	1	8	yes	—
554	#518	C₂×C₄×D₄	1	4	yes	—
555	#518	#518	1	4	yes	—
556	#518	C₂×#121	1	4	yes	—
557	C₂×#117	#386	1	4	yes	—
558	C₂²×C₂²⋊C₄	#386	1	4	yes	—
559	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
560	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
561	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
562	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
563	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
564	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
565	C₂²×C₂²⋊C₄	#518	1	1	yes	characteristic
566	C₂²×C₂²⋊C₄	#518	1	1	yes	characteristic
567	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
568	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
569	C₂²×C₂²⋊C₄	C₂×#123	1	2	yes	—
570	C₂²×C₄²	#518	1	1	yes	characteristic
571	C₂²×C₄²	#518	1	1	yes	characteristic
572	#379	C₂²×C₂²⋊C₄	1	8	yes	—
573	C₂⁵	#1889	1	4	yes	complemented
574	C₂⁵	C₂×#386	1	2	yes	—
575	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
576	C₂⁵	C₂³×C₂²⋊C₄	1	1	yes	characteristic
577	C₂⁵	C₂×#518	1	1	yes	characteristic
578	C₂⁵	C₂²×#120	1	1	yes	characteristic
579	C₂⁵	C₂²×#123	1	1	yes	characteristic
580	C₂⁵	#3484	1	1	yes	characteristic
581	C₂⁵	#3484	1	1	yes	characteristic
582	C₂⁵	#3484	1	2	yes	—
583	C₂⁵	#3484	1	1	yes	characteristic
584	C₂⁵	#3484	1	1	yes	characteristic
585	C₂⁵	#3484	1	1	yes	characteristic
586	C₂⁵	#3490	1	2	yes	—
587	C₂²×Q₈	#1889	1	4	yes	complemented
588	C₂²×D₄	#1889	1	8	yes	complemented
589	C₂²×D₄	#1889	1	4	yes	complemented
590	C₂²×D₄	C₂×#386	1	8	yes	—
591	C₂²×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
592	C₂²×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
593	C₂²×D₄	C₂²×C₄×D₄	1	2	yes	—
594	C₂²×D₄	C₂×#518	1	2	yes	—
595	C₂²×D₄	C₂²×#121	1	2	yes	—
596	C₂²×D₄	#3484	1	2	yes	—
597	C₂²×D₄	#3484	1	2	yes	—
598	C₂²×D₄	#3484	1	2	yes	—
599	C₂²×D₄	#3490	1	2	yes	—
600	C₂²×D₄	#3490	1	2	yes	—
601	C₂³×C₄	#1889	1	4	yes	complemented
602	C₂³×C₄	#1889	1	8	yes	complemented
603	C₂³×C₄	C₂×#386	1	2	yes	—
604	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
605	C₂³×C₄	C₂×#518	1	1	yes	characteristic
606	C₂³×C₄	#3484	1	1	yes	characteristic
607	C₂³×C₄	#3484	1	2	yes	—
608	C₂³×C₄	#3490	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂×#386	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂×#386	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂×#386	1	8	yes	—
612	C₂⁴	C₂×#1889	1	4	yes	—
613	C₂⁴	C₂×#1889	1	8	yes	—
614	C₂⁴	C₂²×#386	1	1	yes	characteristic
615	C₂⁴	#34171	1	1	yes	characteristic
616	C₂⁴	#34171	1	1	yes	characteristic
617	C₂⁴	#34198	1	2	yes	—
618	C₂⁴	#35346	1	1	yes	characteristic
619	C₂⁴	#35346	1	1	yes	characteristic
620	C₂⁴	#35348	1	2	yes	—
621	C₂⁴	#35350	1	1	yes	characteristic
622	C₂⁴	#35350	1	1	yes	characteristic
623	C₂⁴	C₂²×B(4,𝔽₂)	1	4	yes	—
624	C₂²×C₄	C₂×#1889	1	8	yes	—
625	C₂²×C₄	C₂×#1889	1	4	yes	—
626	C₂²×C₄	#34198	1	2	yes	—
627	C₂²×C₄	#35348	1	2	yes	—
628	C₂³	#515285	1	1	yes	characteristic
629	C₂³	C₂²×#1889	1	2	yes	—
630	C₂³	#6499867	1	2	yes	—
631	C₂³	#6499867	1	2	yes	—
632	C₂³	#6499874	1	1	yes	characteristic
633	C₂³	#6499875	1	1	yes	characteristic
634	C₂³	#6499876	1	2	yes	—
635	C₂²	#72217818	1	1	yes	characteristic
636	C₂²	#72234667	1	1	yes	characteristic
637	C₂²	#72241003	1	2	yes	—
638	C₂²	#72241004	1	2	yes	—
639	C₂²	#72258469	1	1	yes	characteristic
640	C₂	#72266211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266211
commutator	C₂³×D₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁵
prime radical	#72300151	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72314996	C₂	semidirect
2. #72314990	C₂	semidirect
3. #72314981	C₂	semidirect
4. #72314791	C₂	semidirect
5. #72314779	C₂	semidirect
6. #72314739	C₂²	semidirect
7. #72314734	C₂²	semidirect
8. #72314447	C₂	semidirect
9. #72314440	C₂²	semidirect
10. #72313608	C₂	semidirect
11. #72312503	C₂	semidirect
12. #72312216	C₂²	semidirect
13. #72310373	C₂	semidirect
14. #72310366	C₂²	semidirect
15. #72310205	C₂	semidirect
16. #72309800	C₂²	semidirect
17. #72309555	C₂²	semidirect
18. #72301923	C₂	semidirect
20. #72300149	C₄	semidirect
21. #72300148	C₄	semidirect
23. #72266978	C₂	semidirect
24. #72266974	C₄	semidirect
25. #72266965	C₄	semidirect
29. #72266446	C₂	semidirect
30. #72266378	C₂²	semidirect
31. #72266368	C₂²	semidirect
32. #72265766	C₂²	semidirect
33. #72260562	C₂²	semidirect
34. #72258334	C₂²	semidirect
36. #72258019	C₂²	semidirect
37. #72256303	C₂	semidirect
38. #72256119	C₂²	semidirect
39. #72256113	C₂²	semidirect
40. #72255986	C₂²	semidirect
41. #72255977	C₂²	semidirect
42. #72255849	C₂²	semidirect
43. #72255793	C₂²	semidirect
44. #72255764	C₂²	semidirect
45. #72251580	C₂	semidirect
46. #72251550	C₂²	semidirect
47. #72251528	C₂²	semidirect
48. #72251528	C₂²	semidirect
49. #72251499	C₂²	semidirect
50. #72251485	C₂²	semidirect
51. #72251473	C₂²	semidirect
52. #72251462	C₂²	semidirect
53. #72251422	C₂²	semidirect
54. #72246304	C₂	semidirect
55. #72246301	C₂²	semidirect
56. #72246299	C₂²	semidirect
57. #72246299	C₂²	semidirect
58. #72246292	C₂²	semidirect
59. #72246288	C₂²	semidirect
60. #72246287	C₂²	semidirect
61. #72246286	C₂²	semidirect
62. #72240132	C₂²	semidirect
63. #72238974	C₂²	semidirect
64. #72238614	C₂	semidirect
65. #72238613	C₂²	semidirect
66. #72238612	C₂²	semidirect
67. #72238611	C₂²	semidirect
69. #72238589	C₂²	semidirect
70. #72238349	C₂²	semidirect
71. #72238343	C₂²	semidirect
72. #72238343	C₂²	semidirect
73. #72237638	C₂²	semidirect
74. #72237480	C₂	semidirect
75. #72237476	C₂²	semidirect
76. #72237476	C₂²	semidirect
77. #72237473	C₂²	semidirect
80. #72237467	C₂²	semidirect
83. #72235242	C₂²	semidirect
84. #72235186	C₂²	semidirect
85. #72234668	C₂²	semidirect
86. #72234607	C₄	semidirect
87. #72234516	C₄	semidirect
89. #72225743	C₂²	semidirect
90. #72225713	C₂²	semidirect
91. #72225639	C₂²	semidirect
94. C₂×#139748	C₂²	semidirect
95. #72219314	C₂²	semidirect
96. C₂×#493474	C₂²	semidirect
97. C₂×#139716	C₂²	semidirect
99. #72219241	C₂²	semidirect
100. #72219162	C₂²	semidirect
103. #72218840	C₂²	semidirect
104. #72218521	C₂²	semidirect
105. #72218475	C₂²	semidirect
106. #72218475	C₂²	semidirect
107. #72218317	C₂²	semidirect
108. #72218206	C₂²	semidirect
109. #72218104	C₂²	semidirect
110. C₂×#139750	C₂²	semidirect
111. C₂×#139731	C₂²	semidirect
112. #72216323	C₄	semidirect
114. #72211144	C₄	semidirect
115. #10586797	C₂×C₄	semidirect
116. #10586796	C₂×C₄	semidirect
117. #10586489	C₂×C₄	semidirect
118. #10586472	C₂×C₄	semidirect
126. #7626202	C₂³	semidirect
128. #6499871	C₂×C₄	semidirect
131. #6499870	C₂×C₄	semidirect
134. #6499869	C₂×C₄	semidirect
137. #6499867	C₂×C₄	semidirect
145. #6374251	C₂³	semidirect
148. #6374187	D₄	semidirect
153. #6374128	C₂³	semidirect
154. C₂×#21746	C₂³	semidirect
156. #6371551	D₄	semidirect
157. #5025789	C₂×C₄	semidirect
158. #5025782	C₂×C₄	semidirect
159. #5021140	C₂×C₄	semidirect
160. #5021138	C₂×C₄	semidirect
161. #4422949	C₂×C₄	semidirect
162. #4420586	C₂×C₄	semidirect
164. #686187	C₂×C₄	semidirect
165. #647656	C₂×C₄	semidirect
180. #493357	C₂³	semidirect
183. C₂×#12687	C₂³	semidirect
184. #392030	C₂³	semidirect
185. #373637	C₂³	semidirect
186. #363969	D₄	semidirect
187. #363969	D₄	semidirect
198. #359501	C₂³	semidirect
201. #359442	C₂³	semidirect
202. #355096	C₂³	semidirect
203. #355096	C₂³	semidirect
204. #347057	C₂×C₄	semidirect
205. #347056	C₂×C₄	semidirect
206. #347048	C₂×C₄	semidirect
207. #347048	C₂×C₄	semidirect
208. #347047	C₂×C₄	semidirect
209. #347047	C₂×C₄	semidirect
210. #347047	C₂×C₄	semidirect
211. #347045	C₂×C₄	semidirect
212. #347045	C₂×C₄	semidirect
213. #347045	C₂×C₄	semidirect
214. #347042	C₂×C₄	semidirect
215. #347042	C₂×C₄	semidirect
216. #347042	C₂×C₄	semidirect
217. #347042	C₂×C₄	semidirect
218. #347042	C₂×C₄	semidirect
219. #347042	C₂×C₄	semidirect
220. #188109	C₂³	semidirect
221. C₂×#8547	C₂³	semidirect
222. #188065	C₂×C₄	semidirect
223. #188062	C₂×C₄	semidirect
225. #188049	C₂³	semidirect
226. #188046	C₂×C₄	semidirect
227. #188035	C₂×C₄	semidirect
229. C₂×#8541	C₂³	semidirect
230. #187952	C₂×C₄	semidirect
231. #187952	C₂×C₄	semidirect
232. #187949	C₂×C₄	semidirect
233. #187949	C₂×C₄	semidirect
236. #187943	C₂×C₄	semidirect
237. #187943	C₂×C₄	semidirect
238. #187940	C₂×C₄	semidirect
239. #187940	C₂×C₄	semidirect
242. #146479	C₂³	semidirect
243. #146479	C₂³	semidirect
244. #146475	C₂³	semidirect
245. #146475	C₂³	semidirect
246. #128033	C₂³	semidirect
247. C₂×#7304	C₂³	semidirect
248. C₂×#7316	C₂³	semidirect
249. C₂×#7316	C₂³	semidirect
250. C₂×#7314	C₂³	semidirect
251. C₂×#7314	C₂³	semidirect
252. C₂×#7311	C₂³	semidirect
253. C₂×#7310	C₂³	semidirect
254. C₂×#7310	C₂³	semidirect
255. C₂×#7310	C₂³	semidirect
256. #128009	C₂³	semidirect
257. C₂×#7307	C₂³	semidirect
258. #108238	C₂³	semidirect
259. #108222	C₂³	semidirect
260. #107130	C₂³	semidirect
261. #107114	C₂³	semidirect
289. #62652	C₂×D₄	semidirect
290. C₂×#2883	C₂×D₄	semidirect
291. C₂×#2883	C₂×D₄	semidirect
292. #36614	C₂²⋊C₄	semidirect
295. C₂×#2846	C₂²⋊C₄	semidirect
299. #35222	C₂²⋊C₄	semidirect
300. #34980	C₂²⋊C₄	semidirect
312. #23985	C₂²⋊C₄	semidirect
313. #23985	C₂²⋊C₄	semidirect
314. #23984	C₂²⋊C₄	semidirect
315. #23984	C₂²⋊C₄	semidirect
316. #23984	C₂²⋊C₄	semidirect
317. #23984	C₂²⋊C₄	semidirect
318. #23984	C₂²⋊C₄	semidirect
319. #23984	C₂²⋊C₄	semidirect
332. #21748	C₂²⋊C₄	semidirect
333. #21748	C₂²⋊C₄	semidirect
337. #21746	C₂²⋊C₄	semidirect
338. #21746	C₂²⋊C₄	semidirect
346. C₂×#1913	C₂×D₄	semidirect
347. C₂×#1913	C₂×D₄	semidirect
350. #20960	C₂×D₄	semidirect
351. #20960	C₂×D₄	semidirect
352. C₂×#1828	C₂×D₄	semidirect
362. #20354	C₂×D₄	semidirect
363. #20354	C₂×D₄	semidirect
398. C₂⁷	C₂×C₂²⋊C₄	semidirect
405. C₂⁴×D₄	C₂×C₂²⋊C₄	semidirect
406. C₂⁴×D₄	C₂×C₂²⋊C₄	semidirect
410. C₂⁵×C₄	C₂×C₂²⋊C₄	semidirect
475. #2849	C₂×C₂²⋊C₄	semidirect
476. #2846	C₂×C₂²⋊C₄	semidirect
477. #2846	C₂×C₂²⋊C₄	semidirect
478. #2846	C₂×C₂²⋊C₄	semidirect
479. #2280	C₂×C₂²⋊C₄	semidirect
480. C₂×#381	C₂×C₂²⋊C₄	semidirect
481. C₂×#381	C₂×C₂²⋊C₄	semidirect
482. C₂×#381	C₂×C₂²⋊C₄	semidirect
483. C₂×#381	C₂×C₂²⋊C₄	semidirect
484. C₂×#379	C₂×C₂²⋊C₄	semidirect
485. C₂×#379	C₂×C₂²⋊C₄	semidirect
486. C₂×#379	C₂×C₂²⋊C₄	semidirect
487. C₂×#379	C₂×C₂²⋊C₄	semidirect
488. C₂×#379	C₂×C₂²⋊C₄	semidirect
489. C₂×#379	C₂×C₂²⋊C₄	semidirect
490. C₂×#379	C₂×C₂²⋊C₄	semidirect
491. C₂×#379	C₂×C₂²⋊C₄	semidirect
492. C₂×#379	C₂×C₂²⋊C₄	semidirect
494. #1898	C₂×C₂²⋊C₄	semidirect
495. #1898	C₂×C₂²⋊C₄	semidirect
496. #1898	C₂×C₂²⋊C₄	semidirect
497. #1898	C₂×C₂²⋊C₄	semidirect
498. #1819	C₂×C₂²⋊C₄	semidirect
499. #1819	C₂×C₂²⋊C₄	semidirect
573. C₂⁵	#1889	semidirect
587. C₂²×Q₈	#1889	semidirect
588. C₂²×D₄	#1889	semidirect
589. C₂²×D₄	#1889	semidirect
601. C₂³×C₄	#1889	semidirect
602. C₂³×C₄	#1889	semidirect

Maximal subgroups

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

subgroup	index
#72314996	2
#72314990	2
#72314981	2
#72314791	2
#72314779	2
#72314447	2
#72313608	2
#72312503	2
#72310373	2
#72310205	2
#72301923	2
#72300151	2
#72266978	2
#72266446	2
#72256303	2
#72251580	2
#72246304	2
#72238614	2
#72237480	2