Subgroups — #72310354

Order 2048.

At least 7272 conjugacy classes of subgroups; only the 1158 normal subgroups are shown.

The subgroup lattice has 483 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72310350	C₂	1	4	yes	maximal, complemented
2	#72310347	C₂	1	4	yes	maximal, complemented
3	#72266864	C₂	1	1	yes	maximal, characteristic, complemented
4	#72266366	C₂	1	1	yes	maximal, characteristic, complemented
5	#72259125	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#135516	C₂	1	1	yes	maximal, characteristic, complemented
7	#72258229	C₂	1	4	yes	maximal, complemented
8	C₂×#139739	C₂	1	1	yes	maximal, characteristic, complemented
9	#72258028	C₂	1	1	yes	maximal, characteristic, complemented
10	#72256048	C₂	1	1	yes	maximal, characteristic, complemented
11	#72255841	C₂	1	1	yes	maximal, characteristic, complemented
12	#72240419	C₂	1	1	yes	maximal, characteristic, complemented
13	#72237374	C₂	1	1	yes	maximal, characteristic, complemented
14	#72237374	C₂	1	1	yes	maximal, characteristic, complemented
15	#72237003	C₂	1	1	yes	maximal, characteristic, complemented
16	#72234693	C₂	1	1	yes	maximal, characteristic
17	C₂×#139743	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#133839	C₂	1	1	yes	maximal, characteristic, complemented
19	#72216376	C₂	1	4	yes	maximal, complemented
20	#10586404	C₂²	1	1	yes	characteristic
21	#10574873	C₄	1	2	yes	complemented
22	C₂×#60399	C₂²	1	1	yes	characteristic
23	#6499876	C₄	1	8	yes	complemented
24	#6499875	C₂²	1	4	yes	—
25	#6499874	C₂²	1	4	yes	—
26	#6451863	C₄	1	2	yes	complemented
27	#6451863	C₄	1	2	yes	complemented
28	C₂×#23895	C₂²	1	1	yes	characteristic
29	C₂×#23895	C₂²	1	1	yes	characteristic
30	#6437621	C₂²	1	1	yes	characteristic
31	#6437621	C₂²	1	1	yes	characteristic
32	C₂×#21778	C₂²	1	1	yes	characteristic, complemented
33	#6374187	C₄	1	2	yes	complemented
34	C₂×#21776	C₂²	1	1	yes	characteristic
35	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
36	#6374128	C₂²	1	1	yes	characteristic, complemented
37	#552670	C₂²	1	1	yes	characteristic, complemented
38	#493475	C₂²	1	4	yes	complemented
39	#493474	C₂²	1	4	yes	complemented
40	C₂×#12707	C₂²	1	1	yes	characteristic, complemented
41	C₂×#12707	C₂²	1	1	yes	characteristic, complemented
42	C₂×#12705	C₂²	1	1	yes	characteristic
43	C₂×#12705	C₂²	1	1	yes	characteristic
44	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
45	C₂×#12705	C₂²	1	1	yes	characteristic, complemented
46	#493357	C₂²	1	1	yes	characteristic, complemented
47	#493357	C₂²	1	1	yes	characteristic, complemented
48	#187952	C₂²	1	2	yes	complemented
49	#187949	C₂²	1	2	yes	complemented
50	#187944	C₂²	1	1	yes	characteristic
51	#187944	C₂²	1	1	yes	characteristic, complemented
52	#187944	C₂²	1	1	yes	characteristic, complemented
53	#187943	C₂²	1	2	yes	complemented
54	#187940	C₂²	1	2	yes	complemented
55	C₂×#8534	C₂²	1	1	yes	characteristic
56	C₂×#8534	C₂²	1	1	yes	characteristic, complemented
57	C₂×#8534	C₂²	1	1	yes	characteristic, complemented
58	#186835	C₂²	1	1	yes	characteristic, complemented
59	C₂×#8453	C₂²	1	1	yes	characteristic, complemented
60	#139743	C₂²	1	4	yes	complemented
61	#139743	C₂²	1	4	yes	complemented
62	#139743	C₂²	1	4	yes	complemented
63	#139743	C₂²	1	4	yes	complemented
64	#139739	C₂²	1	4	yes	complemented
65	#139739	C₂²	1	4	yes	complemented
66	#139739	C₂²	1	4	yes	complemented
67	#139739	C₂²	1	4	yes	complemented
68	#139732	C₂²	1	4	yes	complemented
69	#139732	C₂²	1	4	yes	complemented
70	#139731	C₂²	1	4	yes	complemented
71	#139731	C₂²	1	4	yes	complemented
72	#139703	C₂²	1	2	yes	complemented
73	#139703	C₂²	1	2	yes	complemented
74	#139702	C₂²	1	2	yes	complemented
75	#139702	C₂²	1	2	yes	complemented
76	#139701	C₂²	1	2	yes	complemented
77	#139701	C₂²	1	2	yes	complemented
78	#139700	C₂²	1	2	yes	complemented
79	#139700	C₂²	1	2	yes	complemented
80	#135516	C₂²	1	4	yes	complemented
81	#135516	C₂²	1	4	yes	complemented
82	#135516	C₂²	1	4	yes	complemented
83	#135516	C₂²	1	4	yes	complemented
84	#133839	C₂²	1	4	yes	complemented
85	#133839	C₂²	1	4	yes	complemented
86	#133839	C₂²	1	4	yes	complemented
87	#133839	C₂²	1	4	yes	complemented
88	#128033	C₂²	1	1	yes	characteristic, complemented
89	C₂×#7304	C₂²	1	1	yes	characteristic, complemented
90	C₂×#7314	C₂²	1	1	yes	characteristic, complemented
91	C₂×#7314	C₂²	1	1	yes	characteristic, complemented
92	C₂×#7310	C₂²	1	1	yes	characteristic, complemented
93	C₂×#7310	C₂²	1	1	yes	characteristic, complemented
94	#128009	C₂²	1	1	yes	characteristic, complemented
95	C₂×#7307	C₂²	1	1	yes	characteristic, complemented
96	C₂×H(7,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
97	#62862	C₂×C₄	1	4	yes	—
98	#62862	D₄	1	4	yes	—
99	#62844	C₂×C₄	1	2	yes	—
100	#62844	D₄	1	2	yes	—
101	#62842	C₂×C₄	1	2	yes	—
102	#62842	D₄	1	2	yes	—
103	#62820	D₄	1	2	yes	—
104	#62820	C₂³	1	2	yes	—
105	#62817	D₄	1	2	yes	—
106	#62817	C₂³	1	2	yes	—
107	C₂×#3490	D₄	1	2	yes	—
108	C₂×#3484	D₄	1	2	yes	—
109	C₂×#3484	C₂³	1	1	yes	characteristic
110	C₂×#3484	C₂³	1	1	yes	characteristic
111	C₂×#3484	C₂³	1	1	yes	characteristic
112	C₂×#3484	C₂³	1	1	yes	characteristic
113	C₂²×#534	C₂³	1	1	yes	characteristic
114	#60401	C₂×C₄	1	8	yes	complemented
115	#60399	C₂×C₄	1	8	yes	complemented
116	#60399	C₂×C₄	1	4	yes	complemented
117	#60399	C₂³	1	4	yes	—
118	C₂×#3026	C₂×C₄	1	2	yes	complemented
119	C₂×#3026	C₂×C₄	1	2	yes	complemented
120	C₂×#3026	C₂×C₄	1	2	yes	complemented
121	C₂×#3026	C₂×C₄	1	2	yes	complemented
122	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
123	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×#2883	C₂×C₄	1	2	yes	complemented
126	#23997	C₂×C₄	1	8	yes	complemented
127	#23997	C₂×C₄	1	8	yes	complemented
128	#23996	C₂×C₄	1	8	yes	complemented
129	#23996	C₂×C₄	1	8	yes	complemented
130	#23903	C₂×C₄	1	4	yes	complemented
131	#23903	C₂×C₄	1	4	yes	complemented
132	#23901	C₂³	1	2	yes	—
133	#23901	C₂³	1	2	yes	—
134	#23900	C₂³	1	2	yes	—
135	#23900	C₂³	1	2	yes	—
136	#23895	C₂×C₄	1	4	yes	complemented
137	#23895	C₂×C₄	1	4	yes	complemented
138	#23895	C₂³	1	4	yes	—
139	#23895	C₂³	1	4	yes	—
140	#21778	C₂³	1	4	yes	complemented
141	#21777	C₂×C₄	1	8	yes	complemented
142	#21776	C₂×C₄	1	8	yes	complemented
143	#21776	C₂×C₄	1	4	yes	complemented
144	#21776	C₂³	1	4	yes	—
145	#21776	C₂³	1	4	yes	complemented
146	#21747	C₂³	1	2	yes	complemented
147	#21746	C₂³	1	2	yes	complemented
148	C₂×#1913	C₂×C₄	1	2	yes	complemented
149	C₂×#1913	C₂×C₄	1	2	yes	complemented
150	#20960	C₂×C₄	1	2	yes	complemented
151	#20960	C₂×C₄	1	2	yes	complemented
152	C₂×#1828	C₂×C₄	1	2	yes	complemented
153	C₂×#1783	C₂³	1	1	yes	characteristic
154	C₂×#1783	C₂³	1	1	yes	characteristic
155	C₂×#1781	C₂³	1	1	yes	characteristic
156	C₂×#1781	C₂³	1	1	yes	characteristic
157	C₂×#1781	C₂³	1	1	yes	characteristic
158	C₂×#1781	C₂³	1	1	yes	characteristic
159	C₂×#1781	C₂³	1	1	yes	characteristic
160	C₂×#1781	C₂³	1	1	yes	characteristic
161	#14658	C₂³	1	1	yes	characteristic, complemented
162	#14657	C₂³	1	1	yes	characteristic, complemented
163	#14335	C₂³	1	1	yes	characteristic
164	#14167	C₂³	1	1	yes	characteristic, complemented
165	#14134	C₂³	1	1	yes	characteristic, complemented
166	C₂×#1438	C₂³	1	1	yes	characteristic
167	#12707	C₂³	1	4	yes	—
168	#12707	C₂³	1	4	yes	—
169	#12705	C₂³	1	4	yes	—
170	#12705	C₂³	1	4	yes	—
171	#12705	C₂³	1	4	yes	—
172	#12705	C₂³	1	4	yes	—
173	#12688	C₂³	1	2	yes	complemented
174	#12688	C₂³	1	2	yes	complemented
175	#12687	C₂³	1	2	yes	complemented
176	#12687	C₂³	1	2	yes	complemented
177	#8534	C₂³	1	2	yes	—
178	#8534	C₂³	1	2	yes	—
179	#8534	C₂³	1	2	yes	—
180	#8534	C₂³	1	2	yes	—
181	#8534	C₂³	1	2	yes	—
182	#8534	C₂³	1	2	yes	—
183	#8534	C₂³	1	2	yes	—
184	#8534	C₂³	1	2	yes	—
185	#8534	C₂³	1	2	yes	complemented
186	#8534	C₂³	1	2	yes	complemented
187	#8534	C₂³	1	2	yes	complemented
188	#8534	C₂³	1	2	yes	complemented
189	#8453	C₂³	1	2	yes	—
190	#8453	C₂³	1	2	yes	—
191	#8453	C₂³	1	2	yes	—
192	#8453	C₂³	1	2	yes	—
193	#7314	C₂³	1	4	yes	complemented
194	#7314	C₂³	1	4	yes	complemented
195	#7310	C₂³	1	4	yes	complemented
196	#7310	C₂³	1	4	yes	complemented
197	#7307	C₂³	1	2	yes	complemented
198	#7307	C₂³	1	2	yes	complemented
199	#7307	C₂³	1	2	yes	complemented
200	#7307	C₂³	1	2	yes	complemented
201	#7304	C₂³	1	2	yes	complemented
202	#7304	C₂³	1	2	yes	complemented
203	#7304	C₂³	1	2	yes	complemented
204	#7304	C₂³	1	2	yes	complemented
205	H(7,𝔽₂)	C₂²×C₄	1	4	yes	complemented
206	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
207	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
208	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
209	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
210	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
211	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
213	#3491	C₂²⋊C₄	1	4	yes	—
214	#3491	C₂²⋊C₄	1	4	yes	—
215	#3491	C₂²×C₄	1	4	yes	—
216	#3491	C₂×D₄	1	4	yes	—
217	#3490	C₂²⋊C₄	1	4	yes	—
218	#3490	C₂²⋊C₄	1	4	yes	—
219	#3490	C₂²⋊C₄	1	4	yes	—
220	#3490	C₂²⋊C₄	1	4	yes	—
221	#3490	C₂²×C₄	1	4	yes	—
222	#3490	C₂×D₄	1	4	yes	—
223	#3490	C₂×D₄	1	4	yes	—
224	#3490	C₂×D₄	1	4	yes	—
225	#3485	C₂²⋊C₄	1	4	yes	—
226	#3485	C₂²⋊C₄	1	4	yes	—
227	#3485	C₂²×C₄	1	4	yes	—
228	#3485	C₂×D₄	1	4	yes	—
229	#3484	C₂²⋊C₄	1	4	yes	—
230	#3484	C₂²⋊C₄	1	4	yes	—
231	#3484	C₂²×C₄	1	2	yes	—
232	#3484	C₂²×C₄	1	4	yes	—
233	#3484	C₂²×C₄	1	2	yes	—
234	#3484	C₂²×C₄	1	2	yes	—
235	#3484	C₂²×C₄	1	2	yes	—
236	#3484	C₂×D₄	1	2	yes	—
237	#3484	C₂×D₄	1	4	yes	—
238	#3484	C₂×D₄	1	2	yes	—
239	#3484	C₂×D₄	1	2	yes	—
240	#3484	C₂×D₄	1	2	yes	—
241	#3484	C₂⁴	1	2	yes	—
242	#3484	C₂⁴	1	2	yes	—
243	#3484	C₂⁴	1	2	yes	—
244	#3484	C₂⁴	1	2	yes	—
245	C₂×#543	C₂²⋊C₄	1	2	yes	—
246	C₂×#535	C₂²⋊C₄	1	4	yes	—
247	C₂×#534	C₂²⋊C₄	1	2	yes	—
248	C₂×#534	C₂²⋊C₄	1	2	yes	—
249	C₂×#534	C₂²⋊C₄	1	2	yes	—
250	C₂×#534	C₂²⋊C₄	1	4	yes	—
251	C₂×#534	C₂²×C₄	1	2	yes	—
252	C₂×#534	C₂²×C₄	1	2	yes	—
253	C₂×#534	C₂²×C₄	1	2	yes	—
254	C₂×#534	C₂×D₄	1	2	yes	—
255	C₂×#534	C₂×D₄	1	2	yes	—
256	C₂×#534	C₂×D₄	1	2	yes	—
257	C₂×#525	C₂×D₄	1	4	yes	—
258	C₂²×#123	C₂×D₄	1	1	yes	characteristic
259	C₂²×#123	C₂⁴	1	1	yes	characteristic
260	C₂²×#120	C₂×D₄	1	2	yes	—
261	C₂²×#120	C₂×D₄	1	2	yes	—
262	C₂²×#120	C₂×D₄	1	4	yes	—
263	C₂²×#120	C₂×D₄	1	1	yes	characteristic
264	C₂²×#120	C₂⁴	1	1	yes	characteristic
265	C₂×#518	C₂²⋊C₄	1	2	yes	—
266	C₂×#518	C₂²⋊C₄	1	2	yes	—
267	C₂×#518	C₂²⋊C₄	1	2	yes	—
268	C₂×#518	C₂²×C₄	1	1	yes	characteristic
269	C₂×#518	C₂²×C₄	1	1	yes	characteristic
270	C₂×#518	C₂²×C₄	1	1	yes	characteristic
271	C₂×#518	C₂×D₄	1	1	yes	characteristic
272	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
273	#3026	C₂²×C₄	1	8	yes	—
274	#3026	C₂²×C₄	1	8	yes	—
275	C₂×#458	C₂²×C₄	1	4	yes	complemented
276	C₂×#458	C₂²×C₄	1	4	yes	complemented
277	C₂×B(4,𝔽₂)	C₂²×C₄	1	4	yes	complemented
278	C₂×B(4,𝔽₂)	C₂²×C₄	1	4	yes	complemented
279	#2883	C₂²×C₄	1	8	yes	complemented
280	#2883	C₂²×C₄	1	4	yes	complemented
281	#2883	C₂²×C₄	1	4	yes	complemented
282	#2883	C₂²×C₄	1	4	yes	complemented
283	C₂²×#99	C₂²×C₄	1	2	yes	—
284	C₂²×#99	C₂²×C₄	1	2	yes	—
285	#1913	C₂²×C₄	1	8	yes	—
286	#1913	C₂²×C₄	1	8	yes	—
287	#1890	C₂²×C₄	1	4	yes	complemented
288	#1890	C₂²×C₄	1	4	yes	complemented
289	#1889	C₂²×C₄	1	4	yes	complemented
290	#1889	C₂²×C₄	1	4	yes	complemented
291	#1828	C₂²×C₄	1	8	yes	complemented
292	#1783	C₂⁴	1	2	yes	—
293	#1783	C₂⁴	1	2	yes	—
294	#1781	C₂²×C₄	1	2	yes	—
295	#1781	C₂²×C₄	1	2	yes	—
296	#1781	C₂⁴	1	2	yes	—
297	#1781	C₂⁴	1	2	yes	—
298	#1781	C₂⁴	1	2	yes	—
299	#1781	C₂⁴	1	2	yes	—
300	#1781	C₂⁴	1	2	yes	—
301	#1781	C₂⁴	1	2	yes	—
302	#1438	C₂⁴	1	1	yes	characteristic
303	#1438	C₂⁴	1	1	yes	characteristic
304	#1438	C₂⁴	1	1	yes	characteristic
305	#1438	C₂⁴	1	1	yes	characteristic
306	C₂⁶	C₂²×D₄	1	1	yes	characteristic
307	C₂⁶	C₂²×D₄	1	1	yes	characteristic
308	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
311	C₂×H(5,𝔽₂)	C₂³×C₄	1	2	yes	—
312	C₂×H(5,𝔽₂)	C₂³×C₄	1	2	yes	—
313	C₂×H(5,𝔽₂)	C₂³×C₄	1	2	yes	—
314	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
315	C₂²×#41	#99	1	4	yes	complemented
316	C₂²×#41	#99	1	4	yes	complemented
317	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
318	C₂³×D₄	#99	1	4	yes	complemented
319	C₂³×D₄	#99	1	4	yes	complemented
320	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
323	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
324	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
325	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
326	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
327	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
328	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
329	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
330	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
331	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
335	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂³×D₄	C₂⁵	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
339	#543	C₂×C₂²⋊C₄	1	4	yes	—
340	#543	C₂×C₂²⋊C₄	1	4	yes	—
341	#534	C₂×C₂²⋊C₄	1	4	yes	—
342	#534	C₂×C₂²⋊C₄	1	4	yes	—
343	#534	C₂×C₂²⋊C₄	1	4	yes	—
344	#534	C₂×C₂²⋊C₄	1	4	yes	—
345	#534	C₂³×C₄	1	4	yes	—
346	#534	C₂²×D₄	1	4	yes	—
347	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
349	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
351	C₂×#123	C₂³×C₄	1	2	yes	—
352	C₂×#123	C₂²×D₄	1	2	yes	—
353	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
354	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
355	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
357	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
358	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
359	C₂×#120	C₂³×C₄	1	2	yes	—
360	C₂×#120	C₂²×D₄	1	4	yes	—
361	C₂×#120	C₂²×D₄	1	4	yes	—
362	C₂×#120	C₂²×D₄	1	2	yes	—
363	#518	C₂×C₂²⋊C₄	1	4	yes	—
364	#518	C₂×C₂²⋊C₄	1	4	yes	—
365	#518	C₂×C₂²⋊C₄	1	2	yes	—
366	#518	C₂×C₂²⋊C₄	1	4	yes	—
367	#518	C₂×C₂²⋊C₄	1	4	yes	—
368	#518	C₂×C₂²⋊C₄	1	2	yes	—
369	#518	C₂³×C₄	1	2	yes	—
370	#518	C₂³×C₄	1	2	yes	—
371	#518	C₂³×C₄	1	2	yes	—
372	#518	C₂²×D₄	1	2	yes	—
373	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
374	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
375	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
376	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
378	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
379	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂×#99	C₂³×C₄	1	4	yes	—
382	C₂×#99	C₂³×C₄	1	4	yes	—
383	C₂⁵	C₂×#99	1	2	yes	—
384	C₂⁵	C₂×#99	1	2	yes	—
385	C₂⁵	C₂×#99	1	4	yes	complemented
386	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
387	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
388	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
389	C₂⁵	#518	1	1	yes	characteristic
390	C₂⁵	#518	1	1	yes	characteristic
391	C₂⁵	#534	1	1	yes	characteristic
392	C₂⁵	#534	1	1	yes	characteristic
393	C₂⁵	#534	1	1	yes	characteristic
394	C₂⁵	#534	1	1	yes	characteristic
395	C₂⁵	#534	1	1	yes	characteristic
396	C₂⁵	#534	1	1	yes	characteristic
397	C₂⁵	#534	1	1	yes	characteristic
398	C₂⁵	C₂³×D₄	1	1	yes	characteristic
399	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×Q₈	C₂×#99	1	4	yes	complemented
401	C₂²×D₄	C₂×#99	1	4	yes	—
402	C₂²×D₄	C₂×#99	1	4	yes	—
403	C₂²×D₄	C₂×#99	1	4	yes	—
404	C₂²×D₄	C₂×#99	1	4	yes	—
405	C₂²×D₄	C₂×#99	1	4	yes	complemented
406	C₂²×D₄	C₂×#99	1	4	yes	complemented
407	C₂²×D₄	C₂×#99	1	4	yes	complemented
408	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
410	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
411	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
412	C₂²×D₄	#518	1	1	yes	characteristic
413	C₂²×D₄	#518	1	1	yes	characteristic
414	C₂²×D₄	#518	1	1	yes	characteristic
415	C₂²×D₄	#518	1	1	yes	characteristic
416	C₂²×D₄	#534	1	1	yes	characteristic
417	C₂²×D₄	#534	1	1	yes	characteristic
418	C₂²×D₄	#534	1	1	yes	characteristic
419	C₂²×D₄	#534	1	1	yes	characteristic
420	C₂²×D₄	#534	1	1	yes	characteristic
421	C₂²×D₄	#534	1	1	yes	characteristic
422	C₂²×D₄	C₂⁴×C₄	1	1	yes	characteristic
423	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
424	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂³×C₄	C₂×#99	1	2	yes	—
427	C₂³×C₄	C₂×#99	1	2	yes	—
428	C₂³×C₄	C₂×#99	1	4	yes	complemented
429	C₂³×C₄	C₂×#99	1	4	yes	complemented
430	C₂³×C₄	C₂×#99	1	4	yes	complemented
431	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
432	C₂³×C₄	#518	1	1	yes	characteristic
433	C₂³×C₄	#518	1	1	yes	characteristic
434	C₂³×C₄	#534	1	1	yes	characteristic
435	C₂³×C₄	#534	1	1	yes	characteristic
436	C₂³×C₄	#534	1	1	yes	characteristic
437	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
442	C₂⁴	#2308	1	1	yes	characteristic
443	C₂⁴	#2308	1	1	yes	characteristic
444	C₂⁴	#2308	1	1	yes	characteristic
445	C₂⁴	#2308	1	1	yes	characteristic
446	C₂⁴	#2308	1	1	yes	characteristic
447	C₂⁴	#2308	1	1	yes	characteristic
448	C₂⁴	C₂²×#99	1	2	yes	—
449	C₂⁴	C₂²×#99	1	2	yes	—
450	C₂⁴	C₂²×#99	1	4	yes	—
451	C₂⁴	C₂²×#99	1	4	yes	—
452	C₂⁴	C₂²×#99	1	4	yes	—
453	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
454	C₂⁴	C₂×#518	1	1	yes	characteristic
455	C₂⁴	C₂×#534	1	1	yes	characteristic
456	C₂⁴	C₂×#534	1	1	yes	characteristic
457	C₂⁴	C₂×#534	1	1	yes	characteristic
458	C₂²×C₄	#2308	1	1	yes	characteristic
459	C₂²×C₄	#2308	1	1	yes	characteristic
460	C₂²×C₄	C₂²×#99	1	4	yes	—
461	C₂²×C₄	C₂²×#99	1	4	yes	—
462	C₂²×C₄	C₂²×#99	1	4	yes	—
463	C₂²×C₄	C₂×#518	1	1	yes	characteristic
464	C₂²×C₄	C₂×#534	1	1	yes	characteristic
465	C₂³	#21746	1	2	yes	—
466	C₂³	#21746	1	1	yes	characteristic
467	C₂³	#21746	1	1	yes	characteristic
468	C₂³	#21776	1	1	yes	characteristic
469	C₂³	#21776	1	1	yes	characteristic
470	C₂³	#21776	1	1	yes	characteristic
471	C₂³	#21776	1	1	yes	characteristic
472	C₂³	C₂×#2308	1	1	yes	characteristic
473	C₂³	C₂³×#99	1	2	yes	—
474	C₂²	#213828	1	1	yes	characteristic
475	C₂²	#213828	1	1	yes	characteristic
476	C₂²	#213828	1	1	yes	characteristic
477	C₂²	#213828	1	1	yes	characteristic
478	C₂²	C₂×#21746	1	1	yes	characteristic
479	C₂²	C₂×#21776	1	1	yes	characteristic
480	C₂²	C₂×#21776	1	1	yes	characteristic
481	C₂	C₂×#213828	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#213828
commutator	C₂²×D₄	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72234693	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72310350	C₂	semidirect
2. #72310347	C₂	semidirect
3. #72266864	C₂	semidirect
4. #72266366	C₂	semidirect
5. #72259125	C₂	semidirect
6. C₂×#135516	C₂	semidirect
7. #72258229	C₂	semidirect
8. C₂×#139739	C₂	semidirect
9. #72258028	C₂	semidirect
10. #72256048	C₂	semidirect
11. #72255841	C₂	semidirect
12. #72240419	C₂	semidirect
13. #72237374	C₂	semidirect
14. #72237374	C₂	semidirect
15. #72237003	C₂	semidirect
17. C₂×#139743	C₂	semidirect
18. C₂×#133839	C₂	semidirect
19. #72216376	C₂	semidirect
21. #10574873	C₄	semidirect
23. #6499876	C₄	semidirect
26. #6451863	C₄	semidirect
27. #6451863	C₄	semidirect
32. C₂×#21778	C₂²	semidirect
33. #6374187	C₄	semidirect
35. C₂×#21776	C₂²	semidirect
36. #6374128	C₂²	semidirect
37. #552670	C₂²	semidirect
38. #493475	C₂²	semidirect
39. #493474	C₂²	semidirect
40. C₂×#12707	C₂²	semidirect
41. C₂×#12707	C₂²	semidirect
44. C₂×#12705	C₂²	semidirect
45. C₂×#12705	C₂²	semidirect
46. #493357	C₂²	semidirect
47. #493357	C₂²	semidirect
48. #187952	C₂²	semidirect
49. #187949	C₂²	semidirect
51. #187944	C₂²	semidirect
52. #187944	C₂²	semidirect
53. #187943	C₂²	semidirect
54. #187940	C₂²	semidirect
56. C₂×#8534	C₂²	semidirect
57. C₂×#8534	C₂²	semidirect
58. #186835	C₂²	semidirect
59. C₂×#8453	C₂²	semidirect
60. #139743	C₂²	semidirect
61. #139743	C₂²	semidirect
62. #139743	C₂²	semidirect
63. #139743	C₂²	semidirect
64. #139739	C₂²	semidirect
65. #139739	C₂²	semidirect
66. #139739	C₂²	semidirect
67. #139739	C₂²	semidirect
68. #139732	C₂²	semidirect
69. #139732	C₂²	semidirect
70. #139731	C₂²	semidirect
71. #139731	C₂²	semidirect
72. #139703	C₂²	semidirect
73. #139703	C₂²	semidirect
74. #139702	C₂²	semidirect
75. #139702	C₂²	semidirect
76. #139701	C₂²	semidirect
77. #139701	C₂²	semidirect
78. #139700	C₂²	semidirect
79. #139700	C₂²	semidirect
80. #135516	C₂²	semidirect
81. #135516	C₂²	semidirect
82. #135516	C₂²	semidirect
83. #135516	C₂²	semidirect
84. #133839	C₂²	semidirect
85. #133839	C₂²	semidirect
86. #133839	C₂²	semidirect
87. #133839	C₂²	semidirect
88. #128033	C₂²	semidirect
89. C₂×#7304	C₂²	semidirect
90. C₂×#7314	C₂²	semidirect
91. C₂×#7314	C₂²	semidirect
92. C₂×#7310	C₂²	semidirect
93. C₂×#7310	C₂²	semidirect
94. #128009	C₂²	semidirect
95. C₂×#7307	C₂²	semidirect
96. C₂×H(7,𝔽₂)	C₂×C₄	semidirect
114. #60401	C₂×C₄	semidirect
115. #60399	C₂×C₄	semidirect
116. #60399	C₂×C₄	semidirect
118. C₂×#3026	C₂×C₄	semidirect
119. C₂×#3026	C₂×C₄	semidirect
120. C₂×#3026	C₂×C₄	semidirect
121. C₂×#3026	C₂×C₄	semidirect
122. C₂×#2883	C₂×C₄	semidirect
123. C₂×#2883	C₂×C₄	semidirect
124. C₂×#2883	C₂×C₄	semidirect
125. C₂×#2883	C₂×C₄	semidirect
126. #23997	C₂×C₄	semidirect
127. #23997	C₂×C₄	semidirect
128. #23996	C₂×C₄	semidirect
129. #23996	C₂×C₄	semidirect
130. #23903	C₂×C₄	semidirect
131. #23903	C₂×C₄	semidirect
136. #23895	C₂×C₄	semidirect
137. #23895	C₂×C₄	semidirect
140. #21778	C₂³	semidirect
141. #21777	C₂×C₄	semidirect
142. #21776	C₂×C₄	semidirect
143. #21776	C₂×C₄	semidirect
145. #21776	C₂³	semidirect
146. #21747	C₂³	semidirect
147. #21746	C₂³	semidirect
148. C₂×#1913	C₂×C₄	semidirect
149. C₂×#1913	C₂×C₄	semidirect
150. #20960	C₂×C₄	semidirect
151. #20960	C₂×C₄	semidirect
152. C₂×#1828	C₂×C₄	semidirect
161. #14658	C₂³	semidirect
162. #14657	C₂³	semidirect
164. #14167	C₂³	semidirect
165. #14134	C₂³	semidirect
173. #12688	C₂³	semidirect
174. #12688	C₂³	semidirect
175. #12687	C₂³	semidirect
176. #12687	C₂³	semidirect
185. #8534	C₂³	semidirect
186. #8534	C₂³	semidirect
187. #8534	C₂³	semidirect
188. #8534	C₂³	semidirect
193. #7314	C₂³	semidirect
194. #7314	C₂³	semidirect
195. #7310	C₂³	semidirect
196. #7310	C₂³	semidirect
197. #7307	C₂³	semidirect
198. #7307	C₂³	semidirect
199. #7307	C₂³	semidirect
200. #7307	C₂³	semidirect
201. #7304	C₂³	semidirect
202. #7304	C₂³	semidirect
203. #7304	C₂³	semidirect
204. #7304	C₂³	semidirect
205. H(7,𝔽₂)	C₂²×C₄	semidirect
275. C₂×#458	C₂²×C₄	semidirect
276. C₂×#458	C₂²×C₄	semidirect
277. C₂×B(4,𝔽₂)	C₂²×C₄	semidirect
278. C₂×B(4,𝔽₂)	C₂²×C₄	semidirect
279. #2883	C₂²×C₄	semidirect
280. #2883	C₂²×C₄	semidirect
281. #2883	C₂²×C₄	semidirect
282. #2883	C₂²×C₄	semidirect
287. #1890	C₂²×C₄	semidirect
288. #1890	C₂²×C₄	semidirect
289. #1889	C₂²×C₄	semidirect
290. #1889	C₂²×C₄	semidirect
291. #1828	C₂²×C₄	semidirect
315. C₂²×#41	#99	semidirect
316. C₂²×#41	#99	semidirect
318. C₂³×D₄	#99	semidirect
319. C₂³×D₄	#99	semidirect
385. C₂⁵	C₂×#99	semidirect
400. C₂²×Q₈	C₂×#99	semidirect
405. C₂²×D₄	C₂×#99	semidirect
406. C₂²×D₄	C₂×#99	semidirect
407. C₂²×D₄	C₂×#99	semidirect
428. C₂³×C₄	C₂×#99	semidirect
429. C₂³×C₄	C₂×#99	semidirect
430. C₂³×C₄	C₂×#99	semidirect

Maximal subgroups

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

subgroup	index
#72310350	2
#72310347	2
#72266864	2
#72266366	2
#72259125	2
C₂×#135516	2
#72258229	2
C₂×#139739	2
#72258028	2
#72256048	2
#72255841	2
#72240419	2
#72237374	2
#72237003	2
#72234693	2
C₂×#139743	2
C₂×#133839	2
#72216376	2