Subgroups — #72261582

Order 2048.

At least 16825 conjugacy classes of subgroups; only the 1254 normal subgroups are shown.

The subgroup lattice has 609 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261568	C₂	1	2	yes	maximal, complemented
2	#72261560	C₂	1	2	yes	maximal, complemented
3	#72261545	C₂	1	4	yes	maximal, complemented
4	#72261400	C₂	1	1	yes	maximal, characteristic, complemented
5	#72261121	C₂	1	1	yes	maximal, characteristic, complemented
6	#72260976	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236728	C₂	1	2	yes	maximal, complemented
8	#72236720	C₂	1	1	yes	maximal, characteristic, complemented
9	#72234970	C₂	1	1	yes	maximal, characteristic, complemented
10	#72234959	C₂	1	4	yes	maximal, complemented
11	#72234164	C₂	1	1	yes	maximal, characteristic, complemented
12	#72234155	C₂	1	2	yes	maximal, complemented
13	#72234135	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233613	C₂	1	2	yes	maximal, complemented
15	#72233449	C₂	1	2	yes	maximal, complemented
16	#72233304	C₂	1	2	yes	maximal, complemented
17	#72233069	C₂	1	2	yes	maximal, complemented
18	C₂×#62818	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
21	#7804429	C₂²	1	2	yes	complemented
22	#7752089	C₂²	1	2	yes	complemented
23	#7733246	C₂²	1	2	yes	—
24	#7675391	C₂²	1	2	yes	—
25	#7644628	C₂²	1	1	yes	characteristic
26	C₂×#37646	C₂²	1	1	yes	characteristic
27	#7631287	C₂²	1	1	yes	characteristic, complemented
28	#7631286	C₂²	1	2	yes	complemented
29	#7631286	C₂²	1	1	yes	characteristic, complemented
30	C₂×#35347	C₂²	1	1	yes	characteristic, complemented
31	#7626663	C₂²	1	1	yes	characteristic, complemented
32	#6628892	C₂²	1	2	yes	complemented
33	C₂×#32900	C₂²	1	1	yes	characteristic, complemented
34	C₂×#32898	C₂²	1	2	yes	complemented
35	#6477580	C₂²	1	4	yes	complemented
36	#6470225	C₂²	1	2	yes	—
37	#6470225	C₂²	1	4	yes	complemented
38	#6470225	C₂²	1	2	yes	complemented
39	#6437621	C₂²	1	4	yes	complemented
40	#6385971	C₂²	1	1	yes	characteristic, complemented
41	#6385971	C₂²	1	2	yes	complemented
42	#616964	C₂²	1	2	yes	complemented
43	#394269	C₂²	1	2	yes	complemented
44	#394267	C₂²	1	4	yes	complemented
45	#394061	C₂²	1	2	yes	complemented
46	#393929	C₂²	1	4	yes	complemented
47	#392125	C₂²	1	2	yes	complemented
48	#374058	C₂²	1	2	yes	complemented
49	#374040	C₂²	1	1	yes	characteristic, complemented
50	#364471	C₂²	1	2	yes	complemented
51	#364440	C₂²	1	4	yes	complemented
52	#359579	C₂²	1	1	yes	characteristic, complemented
53	#359579	C₂²	1	2	yes	complemented
54	#359504	C₂²	1	1	yes	characteristic, complemented
55	#359442	C₂²	1	2	yes	complemented
56	#233549	C₂²	1	4	yes	complemented
57	#233541	C₂²	1	4	yes	complemented
58	C₂×#10337	C₂²	1	4	yes	complemented
59	#201701	C₂²	1	2	yes	complemented
60	#201701	C₂²	1	2	yes	complemented
61	#201678	C₂²	1	4	yes	complemented
62	#201668	C₂²	1	2	yes	complemented
63	C₂×#9495	C₂²	1	2	yes	complemented
64	#188035	C₂²	1	1	yes	characteristic, complemented
65	#188035	C₂²	1	2	yes	complemented
66	C₂×#8542	C₂²	1	2	yes	complemented
67	#187944	C₂²	1	4	yes	complemented
68	#187929	C₂²	1	4	yes	complemented
69	#187928	C₂²	1	2	yes	complemented
70	#187928	C₂²	1	2	yes	complemented
71	#187928	C₂²	1	4	yes	complemented
72	#115631	C₂²	1	2	yes	complemented
73	#115204	C₂²	1	4	yes	complemented
74	#115164	C₂²	1	2	yes	complemented
75	#115163	C₂²	1	4	yes	complemented
76	#115133	C₂²	1	4	yes	complemented
77	#111467	C₂²	1	4	yes	complemented
78	#111459	C₂²	1	4	yes	complemented
79	#107194	C₂²	1	4	yes	complemented
80	#106654	C₂²	1	2	yes	complemented
81	#106542	C₂²	1	2	yes	complemented
82	#105752	C₂²	1	4	yes	complemented
83	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
84	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
85	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
86	C₂×#3490	C₂³	1	2	yes	—
87	C₂×#3496	D₄	1	1	yes	characteristic, complemented
88	C₂×#3496	D₄	1	2	yes	complemented
89	C₂×#3484	D₄	1	2	yes	complemented
90	C₂×#3484	D₄	1	1	yes	characteristic, complemented
91	C₂×#3484	D₄	1	2	yes	complemented
92	C₂×#3484	C₂³	1	1	yes	characteristic
93	C₂×#3484	C₂³	1	2	yes	—
94	C₂×#3484	C₂³	1	1	yes	characteristic
95	C₂×#3484	C₂³	1	2	yes	—
96	C₂²×D₄²	C₂³	1	1	yes	characteristic
97	C₂²×D₄²	C₂³	1	2	yes	—
98	C₂²×#534	C₂³	1	1	yes	characteristic
99	C₂²×#534	C₂³	1	2	yes	complemented
100	C₂³×#123	D₄	1	1	yes	characteristic, complemented
101	C₂³×#121	C₂³	1	1	yes	characteristic
102	C₂×C₄×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
103	C₂³×#99	C₂³	1	1	yes	characteristic
104	C₂³×#99	C₂³	1	2	yes	complemented
105	#37436	C₂³	1	2	yes	—
106	#37232	D₄	1	2	yes	complemented
107	#37232	D₄	1	2	yes	complemented
108	#37117	D₄	1	2	yes	complemented
109	#36718	D₄	1	2	yes	complemented
110	#36718	D₄	1	2	yes	complemented
111	#36714	D₄	1	2	yes	complemented
112	C₂×#2849	D₄	1	1	yes	characteristic, complemented
113	#35554	D₄	1	2	yes	complemented
114	#35390	D₄	1	2	yes	complemented
115	#35358	D₄	1	2	yes	complemented
116	#35355	D₄	1	2	yes	complemented
117	#35355	D₄	1	2	yes	complemented
118	#35351	D₄	1	1	yes	characteristic, complemented
119	#35350	D₄	1	1	yes	characteristic, complemented
120	#35350	D₄	1	2	yes	complemented
121	#35348	D₄	1	2	yes	complemented
122	#35347	D₄	1	2	yes	complemented
123	#35347	D₄	1	1	yes	characteristic, complemented
124	#35346	D₄	1	1	yes	characteristic, complemented
125	#34984	D₄	1	2	yes	complemented
126	#34980	D₄	1	2	yes	complemented
127	#34980	C₂³	1	2	yes	—
128	#34980	C₂³	1	2	yes	—
129	#34980	C₂³	1	4	yes	—
130	#34980	C₂³	1	2	yes	—
131	#34980	C₂³	1	4	yes	complemented
132	C₂×#2539	D₄	1	1	yes	characteristic, complemented
133	C₂×#2534	D₄	1	1	yes	characteristic, complemented
134	C₂×#2412	C₂³	1	1	yes	characteristic
135	C₂×#2405	C₂³	1	2	yes	—
136	C₂×#2405	C₂³	1	1	yes	characteristic
137	C₂×#2405	C₂³	1	2	yes	complemented
138	C₂×#2410	D₄	1	1	yes	characteristic, complemented
139	C₂×#2410	C₂³	1	2	yes	—
140	C₂×#2403	D₄	1	1	yes	characteristic, complemented
141	C₂×#2403	C₂³	1	2	yes	—
142	C₂×#2403	C₂³	1	2	yes	—
143	C₂×#2403	C₂³	1	4	yes	—
144	C₂×#2618	D₄	1	1	yes	characteristic, complemented
145	C₂×#2613	C₂³	1	1	yes	characteristic
146	#34356	C₂³	1	2	yes	—
147	#34264	D₄	1	2	yes	complemented
148	#34198	C₂³	1	2	yes	—
149	#34171	C₂³	1	2	yes	—
150	#34171	C₂³	1	1	yes	characteristic
151	C₂×D₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×#2322	D₄	1	1	yes	characteristic, complemented
153	C₂×#2308	C₂³	1	1	yes	characteristic
154	#24056	D₄	1	8	yes	complemented
155	#23900	D₄	1	8	yes	complemented
156	#21746	C₂³	1	4	yes	—
157	#21746	C₂³	1	2	yes	—
158	#21746	C₂³	1	4	yes	—
159	#21746	C₂³	1	2	yes	—
160	#21746	C₂³	1	4	yes	complemented
161	#21746	C₂³	1	4	yes	complemented
162	C₂×#1898	C₂³	1	4	yes	—
163	C₂×#1898	C₂³	1	2	yes	—
164	C₂×#1898	C₂³	1	4	yes	complemented
165	C₂×#1819	C₂³	1	4	yes	complemented
166	C₂×#1781	C₂³	1	4	yes	—
167	C₂×#1781	C₂³	1	2	yes	—
168	C₂×#1781	C₂³	1	1	yes	characteristic
169	C₂×#1781	C₂³	1	2	yes	—
170	C₂×#1781	C₂³	1	2	yes	—
171	C₂×#1781	C₂³	1	4	yes	—
172	C₂×#1781	C₂³	1	2	yes	complemented
173	C₂×#1781	C₂³	1	4	yes	complemented
174	C₂×#1781	C₂³	1	4	yes	complemented
175	#14335	C₂³	1	2	yes	complemented
176	#13869	C₂³	1	2	yes	complemented
177	#13867	C₂³	1	2	yes	—
178	#13867	C₂³	1	4	yes	—
179	#10735	C₂³	1	2	yes	complemented
180	#10735	C₂³	1	4	yes	complemented
181	#10735	C₂³	1	2	yes	complemented
182	#10725	C₂³	1	4	yes	complemented
183	#8101	C₂³	1	4	yes	complemented
184	C₂×#1304	C₂³	1	4	yes	complemented
185	C₂×#1304	C₂³	1	4	yes	complemented
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
188	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
189	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
190	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
191	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
192	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
193	C₂⁴×D₄	C₂×D₄	1	2	yes	—
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	2	yes	—
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂⁴×D₄	C₂⁴	1	2	yes	—
199	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
200	C₂⁴×D₄	C₂⁴	1	2	yes	—
201	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
202	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
203	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
204	#3484	C₂×D₄	1	8	yes	—
205	C₂×#543	C₂×D₄	1	2	yes	complemented
206	C₂×#534	C₂×D₄	1	2	yes	—
207	C₂×#534	C₂×D₄	1	2	yes	—
208	C₂×#534	C₂×D₄	1	2	yes	—
209	C₂×#534	C₂×D₄	1	2	yes	—
210	C₂×#534	C₂×D₄	1	2	yes	—
211	C₂×#534	C₂×D₄	1	2	yes	—
212	C₂×#534	C₂×D₄	1	2	yes	—
213	C₂×#534	C₂×D₄	1	2	yes	—
214	C₂×#534	C₂×D₄	1	2	yes	—
215	C₂×#534	C₂×D₄	1	2	yes	complemented
216	C₂×#534	C₂×D₄	1	2	yes	complemented
217	C₂×#534	C₂×D₄	1	2	yes	complemented
218	C₂×#534	C₂×D₄	1	2	yes	complemented
219	C₂²×#127	C₂×D₄	1	1	yes	characteristic
220	C₂²×#127	C₂×D₄	1	2	yes	—
221	C₂²×#123	C₂×D₄	1	1	yes	characteristic
222	C₂²×#123	C₂×D₄	1	1	yes	characteristic
223	C₂²×#123	C₂×D₄	1	1	yes	characteristic
224	C₂²×#123	C₂×D₄	1	1	yes	characteristic
225	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
227	C₂²×#121	C₂×D₄	1	1	yes	characteristic
228	C₂²×#121	C₂×D₄	1	2	yes	—
229	C₂²×#121	C₂×D₄	1	2	yes	—
230	C₂²×#121	C₂×D₄	1	1	yes	characteristic
231	C₂²×#121	C₂×D₄	1	2	yes	—
232	C₂²×#121	C₂×D₄	1	1	yes	characteristic
233	C₂²×#121	C₂×D₄	1	1	yes	characteristic
234	C₂²×#121	C₂×D₄	1	2	yes	—
235	C₂²×#120	C₂×D₄	1	1	yes	characteristic
236	C₂²×#120	C₂×D₄	1	1	yes	characteristic
237	C₂²×#120	C₂×D₄	1	2	yes	—
238	C₂²×#120	C₂×D₄	1	1	yes	characteristic
239	C₂²×#120	C₂×D₄	1	1	yes	characteristic
240	C₂²×#120	C₂×D₄	1	2	yes	—
241	C₂²×#120	C₂×D₄	1	2	yes	—
242	C₂²×#120	C₂×D₄	1	1	yes	characteristic
243	C₂²×#120	C₂×D₄	1	2	yes	complemented
244	C₂²×#120	C₂×D₄	1	2	yes	complemented
245	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂²×#120	C₂×D₄	1	2	yes	complemented
247	C₂²×#120	C₂×D₄	1	4	yes	complemented
248	C₂²×#120	C₂⁴	1	2	yes	—
249	C₂²×#120	C₂⁴	1	1	yes	characteristic
250	C₂²×#120	C₂⁴	1	2	yes	—
251	C₂×#518	C₂×D₄	1	1	yes	characteristic
252	C₂×#518	C₂×D₄	1	2	yes	—
253	C₂×#518	C₂×D₄	1	2	yes	complemented
254	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
255	C₂×#518	C₂×D₄	1	2	yes	complemented
256	C₂×#518	C₂×D₄	1	2	yes	complemented
257	C₂×#518	C₂×D₄	1	2	yes	complemented
258	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
260	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
261	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
262	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
263	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
264	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
265	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
266	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
267	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
268	#2849	C₂×D₄	1	8	yes	complemented
269	#2846	C₂×D₄	1	8	yes	complemented
270	#2483	C₂×D₄	1	2	yes	complemented
271	#2405	C₂×D₄	1	2	yes	—
272	#2405	C₂×D₄	1	2	yes	—
273	#2405	C₂×D₄	1	2	yes	—
274	#2405	C₂×D₄	1	2	yes	—
275	#2405	C₂×D₄	1	2	yes	—
276	#2405	C₂×D₄	1	2	yes	—
277	#2405	C₂×D₄	1	2	yes	—
278	#2405	C₂×D₄	1	2	yes	—
279	#2405	C₂×D₄	1	2	yes	complemented
280	#2405	C₂×D₄	1	2	yes	complemented
281	#2405	C₂×D₄	1	2	yes	complemented
282	#2405	C₂×D₄	1	2	yes	complemented
283	#2405	C₂×D₄	1	2	yes	complemented
284	#2405	C₂×D₄	1	2	yes	complemented
285	#2405	C₂×D₄	1	2	yes	complemented
286	#2405	C₂×D₄	1	2	yes	complemented
287	#2403	C₂×D₄	1	2	yes	—
288	#2403	C₂×D₄	1	2	yes	—
289	#2403	C₂×D₄	1	2	yes	—
290	#2403	C₂×D₄	1	2	yes	—
291	#2403	C₂×D₄	1	2	yes	complemented
292	#2403	C₂×D₄	1	2	yes	complemented
293	#2403	C₂×D₄	1	2	yes	complemented
294	#2315	C₂×D₄	1	2	yes	complemented
295	#2312	C₂×D₄	1	2	yes	complemented
296	#2312	C₂×D₄	1	2	yes	complemented
297	#2309	C₂×D₄	1	2	yes	complemented
298	#2308	C₂×D₄	1	2	yes	—
299	#2308	C₂×D₄	1	2	yes	—
300	#2308	C₂×D₄	1	1	yes	characteristic, complemented
301	#2308	C₂×D₄	1	1	yes	characteristic, complemented
302	#2308	C₂×D₄	1	2	yes	complemented
303	#2308	C₂×D₄	1	2	yes	complemented
304	#2308	C₂×D₄	1	2	yes	complemented
305	C₂×#386	C₂×D₄	1	1	yes	characteristic
306	C₂×#386	C₂×D₄	1	1	yes	characteristic
307	C₂×#386	C₂×D₄	1	2	yes	complemented
308	C₂×#386	C₂×D₄	1	2	yes	complemented
309	C₂×#386	C₂×D₄	1	2	yes	complemented
310	C₂×#386	C₂×D₄	1	4	yes	complemented
311	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
312	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂×#385	C₂×D₄	1	2	yes	complemented
314	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
315	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
316	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
317	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
318	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
319	C₂×#379	C₂×D₄	1	2	yes	complemented
320	C₂×#379	C₂⁴	1	2	yes	—
321	C₂×#379	C₂⁴	1	4	yes	—
322	C₂×#379	C₂⁴	1	4	yes	—
323	C₂×#379	C₂⁴	1	2	yes	—
324	C₂×#379	C₂⁴	1	1	yes	characteristic
325	C₂×#379	C₂⁴	1	2	yes	—
326	#2273	C₂×D₄	1	2	yes	complemented
327	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
328	#1898	C₂×D₄	1	16	yes	complemented
329	#1781	C₂×D₄	1	8	yes	complemented
330	C₂⁶	#120	1	1	yes	characteristic
331	C₂⁶	#120	1	2	yes	—
332	C₂⁶	C₂²×D₄	1	2	yes	—
333	C₂⁶	C₂²×D₄	1	2	yes	—
334	C₂⁶	C₂²×D₄	1	1	yes	characteristic
335	C₂⁶	C₂²×D₄	1	1	yes	characteristic
336	C₂⁶	C₂²×D₄	1	1	yes	characteristic
337	C₂⁶	C₂⁵	1	1	yes	characteristic
338	C₂×H(5,𝔽₂)	#120	1	4	yes	—
339	C₂³×D₄	#120	1	1	yes	characteristic
340	C₂³×D₄	#120	1	2	yes	—
341	C₂³×D₄	#120	1	2	yes	—
342	C₂³×D₄	#120	1	1	yes	characteristic
343	C₂³×D₄	#120	1	1	yes	characteristic
344	C₂³×D₄	#120	1	1	yes	characteristic
345	C₂³×D₄	#120	1	2	yes	—
346	C₂³×D₄	#120	1	2	yes	—
347	C₂³×D₄	#120	1	2	yes	—
348	C₂³×D₄	#120	1	1	yes	characteristic
349	C₂³×D₄	C₂²×D₄	1	2	yes	—
350	C₂³×D₄	C₂²×D₄	1	2	yes	—
351	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
352	C₂³×D₄	C₂²×D₄	1	2	yes	—
353	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
354	C₂³×D₄	C₂²×D₄	1	2	yes	—
355	C₂³×D₄	C₂²×D₄	1	2	yes	—
356	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
357	C₂³×D₄	C₂²×D₄	1	2	yes	—
358	C₂³×D₄	C₂²×D₄	1	2	yes	—
359	C₂³×D₄	C₂²×D₄	1	2	yes	—
360	C₂³×D₄	C₂²×D₄	1	2	yes	—
361	C₂³×D₄	C₂²×D₄	1	2	yes	—
362	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
363	C₂³×D₄	C₂²×D₄	1	2	yes	—
364	C₂³×D₄	C₂²×D₄	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	2	yes	—
368	C₂³×D₄	C₂²×D₄	1	2	yes	—
369	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	2	yes	—
374	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
375	C₂³×D₄	C₂²×D₄	1	2	yes	—
376	C₂³×D₄	C₂²×D₄	1	4	yes	—
377	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
378	C₂⁴×C₄	#120	1	2	yes	—
379	C₂⁴×C₄	#120	1	1	yes	characteristic
380	C₂⁴×C₄	#120	1	2	yes	—
381	C₂⁴×C₄	#120	1	1	yes	characteristic
382	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
383	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
384	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
385	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
386	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
387	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
388	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
389	#534	#120	1	8	yes	—
390	C₂×#123	#120	1	1	yes	characteristic
391	C₂×#123	#120	1	1	yes	characteristic
392	C₂×#123	#120	1	1	yes	characteristic
393	C₂×#123	#120	1	2	yes	—
394	C₂×#123	#120	1	1	yes	characteristic
395	C₂×#123	#120	1	2	yes	—
396	C₂×#123	#120	1	1	yes	characteristic
397	C₂×#123	#120	1	1	yes	characteristic
398	C₂×#123	#120	1	1	yes	characteristic
399	C₂×#123	#120	1	1	yes	characteristic
400	C₂×#123	#120	1	2	yes	—
401	C₂×#123	#120	1	2	yes	—
402	C₂×#123	#120	1	2	yes	—
403	C₂×#123	#120	1	2	yes	—
404	C₂×#123	#120	1	2	yes	—
405	C₂×#123	#120	1	2	yes	—
406	C₂×#120	#120	1	2	yes	—
407	C₂×#120	#120	1	2	yes	—
408	C₂×#120	#120	1	2	yes	—
409	C₂×#120	#120	1	2	yes	—
410	C₂×#120	#120	1	2	yes	—
411	C₂×#120	#120	1	2	yes	—
412	C₂×#120	#120	1	2	yes	—
413	C₂×#120	#120	1	2	yes	—
414	C₂×#120	C₂²×D₄	1	8	yes	—
415	C₂×#120	H(5,𝔽₂)	1	8	yes	—
416	#518	#120	1	4	yes	—
417	C₂²×C₄⋊C₄	#120	1	2	yes	—
418	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
419	C₂²×C₄⋊C₄	#120	1	2	yes	—
420	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
421	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
422	C₂²×C₂²⋊C₄	#120	1	2	yes	—
423	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
424	C₂²×C₂²⋊C₄	#120	1	2	yes	—
425	C₂²×C₂²⋊C₄	#120	1	2	yes	—
426	C₂²×C₂²⋊C₄	#120	1	2	yes	—
427	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
430	C₂²×C₂²⋊C₄	#120	1	2	yes	—
431	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
433	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
434	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
436	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
438	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
439	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
440	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
441	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
442	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
443	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
444	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
445	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
447	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
448	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
450	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂²×C₄²	#120	1	1	yes	characteristic
452	C₂²×C₄²	#120	1	2	yes	—
453	#386	#120	1	2	yes	—
454	#386	#120	1	2	yes	—
455	#386	#120	1	2	yes	—
456	#386	#120	1	2	yes	—
457	#386	#120	1	2	yes	—
458	#386	#120	1	2	yes	—
459	#386	#120	1	2	yes	—
460	#386	#120	1	2	yes	—
461	#386	#120	1	2	yes	—
462	#386	#120	1	2	yes	—
463	#386	#120	1	2	yes	—
464	#386	#120	1	2	yes	—
465	#379	C₂²×D₄	1	8	yes	—
466	#379	C₂²×D₄	1	2	yes	—
467	#379	C₂²×D₄	1	2	yes	—
468	#379	C₂²×D₄	1	2	yes	—
469	#379	C₂²×D₄	1	2	yes	—
470	#379	C₂²×D₄	1	2	yes	—
471	#379	C₂²×D₄	1	2	yes	—
472	C₂⁵	C₂×#120	1	2	yes	—
473	C₂⁵	C₂×#120	1	1	yes	characteristic
474	C₂⁵	C₂×#120	1	1	yes	characteristic
475	C₂⁵	C₂×#120	1	2	yes	—
476	C₂⁵	C₂×#120	1	1	yes	characteristic
477	C₂⁵	C₂×#120	1	2	yes	—
478	C₂⁵	C₂×#120	1	2	yes	—
479	C₂⁵	C₂×#120	1	2	yes	—
480	C₂⁵	C₂×#120	1	1	yes	characteristic
481	C₂⁵	C₂×#120	1	1	yes	characteristic
482	C₂⁵	C₂×#120	1	2	yes	—
483	C₂⁵	C₂×#120	1	2	yes	—
484	C₂⁵	D₄²	1	4	yes	—
485	C₂⁵	C₂³×D₄	1	1	yes	characteristic
486	C₂⁵	C₂³×D₄	1	2	yes	—
487	C₂⁵	C₂³×D₄	1	1	yes	characteristic
488	C₂⁵	C₂³×D₄	1	1	yes	characteristic
489	C₂⁵	C₂³×D₄	1	2	yes	—
490	C₂⁵	C₂³×D₄	1	2	yes	—
491	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
492	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
493	C₂²×D₄	C₂×#120	1	2	yes	—
494	C₂²×D₄	C₂×#120	1	1	yes	characteristic
495	C₂²×D₄	C₂×#120	1	1	yes	characteristic
496	C₂²×D₄	C₂×#120	1	2	yes	—
497	C₂²×D₄	C₂×#120	1	1	yes	characteristic
498	C₂²×D₄	C₂×#120	1	2	yes	—
499	C₂²×D₄	C₂×#120	1	1	yes	characteristic
500	C₂²×D₄	C₂×#120	1	2	yes	—
501	C₂²×D₄	C₂×#120	1	2	yes	—
502	C₂²×D₄	C₂×#120	1	2	yes	—
503	C₂²×D₄	C₂×#120	1	2	yes	—
504	C₂²×D₄	C₂×#120	1	2	yes	—
505	C₂²×D₄	C₂×#120	1	4	yes	—
506	C₂²×D₄	#534	1	2	yes	—
507	C₂²×D₄	#534	1	2	yes	—
508	C₂²×D₄	#534	1	4	yes	—
509	C₂²×D₄	D₄²	1	4	yes	—
510	C₂²×D₄	D₄²	1	8	yes	—
511	C₂²×D₄	D₄²	1	4	yes	—
512	C₂²×D₄	D₄²	1	8	yes	—
513	C₂³×C₄	C₂×#120	1	1	yes	characteristic
514	C₂³×C₄	C₂×#120	1	1	yes	characteristic
515	C₂³×C₄	C₂×#120	1	1	yes	characteristic
516	C₂³×C₄	C₂×#120	1	2	yes	—
517	C₂³×C₄	C₂×#120	1	1	yes	characteristic
518	C₂³×C₄	C₂×#120	1	1	yes	characteristic
519	C₂³×C₄	C₂×#120	1	1	yes	characteristic
520	C₂³×C₄	C₂×#120	1	2	yes	—
521	C₂³×C₄	C₂×#120	1	1	yes	characteristic
522	C₂³×C₄	C₂×#120	1	2	yes	—
523	C₂³×C₄	C₂×#120	1	1	yes	characteristic
524	C₂³×C₄	C₂×#120	1	2	yes	—
525	C₂³×C₄	C₂×#120	1	2	yes	—
526	C₂³×C₄	C₂×#120	1	2	yes	—
527	C₂³×C₄	C₂×#120	1	2	yes	—
528	C₂³×C₄	C₂×#120	1	1	yes	characteristic
529	C₂³×C₄	C₂×#120	1	2	yes	—
530	C₂³×C₄	C₂×#120	1	1	yes	characteristic
531	C₂³×C₄	C₂×#120	1	1	yes	characteristic
532	C₂³×C₄	C₂×#120	1	2	yes	—
533	C₂³×C₄	C₂×#120	1	2	yes	—
534	C₂³×C₄	C₂×#120	1	2	yes	—
535	C₂³×C₄	D₄²	1	4	yes	—
536	#123	B(4,𝔽₂)	1	4	yes	complemented
537	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
548	C₂×C₂²⋊C₄	#534	1	4	yes	—
549	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
550	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
551	C₂⁴	#2403	1	2	yes	—
552	C₂⁴	#2403	1	2	yes	—
553	C₂⁴	#2403	1	4	yes	—
554	C₂⁴	#2846	1	1	yes	characteristic
555	C₂⁴	#2846	1	2	yes	—
556	C₂⁴	#2846	1	1	yes	characteristic
557	C₂⁴	C₂²×#120	1	1	yes	characteristic
558	C₂⁴	C₂²×#120	1	2	yes	—
559	C₂⁴	C₂²×#120	1	1	yes	characteristic
560	C₂⁴	C₂²×#120	1	2	yes	—
561	C₂⁴	C₂²×#120	1	1	yes	characteristic
562	C₂⁴	C₂²×#120	1	1	yes	characteristic
563	C₂⁴	C₂×#534	1	1	yes	characteristic
564	C₂⁴	C₂×#534	1	2	yes	—
565	C₂⁴	C₂×D₄²	1	2	yes	—
566	C₂⁴	C₂×D₄²	1	2	yes	—
567	C₂⁴	C₂×D₄²	1	4	yes	—
568	C₂⁴	C₂×D₄²	1	4	yes	—
569	C₂⁴	#3484	1	4	yes	—
570	C₂⁴	#3484	1	2	yes	—
571	C₂⁴	#3484	1	4	yes	—
572	C₂⁴	#3484	1	2	yes	—
573	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
574	C₂×D₄	#3026	1	2	yes	—
575	C₂²×C₄	#2403	1	2	yes	—
576	C₂²×C₄	#2403	1	2	yes	—
577	C₂²×C₄	#2403	1	4	yes	—
578	C₂²×C₄	#2403	1	4	yes	—
579	C₂²×C₄	#2403	1	4	yes	—
580	C₂²×C₄	#2846	1	2	yes	—
581	C₂²×C₄	#2846	1	1	yes	characteristic
582	C₂²×C₄	#2846	1	1	yes	characteristic
583	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	complemented
584	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	complemented
585	C₂³	#23895	1	4	yes	complemented
586	C₂³	#32898	1	2	yes	—
587	C₂³	C₂×#2403	1	2	yes	—
588	C₂³	C₂×#2403	1	1	yes	characteristic
589	C₂³	#34980	1	1	yes	characteristic
590	C₂³	#34980	1	2	yes	—
591	C₂³	D₄×#120	1	4	yes	—
592	C₂³	D₄×#120	1	2	yes	—
593	C₂³	D₄×#120	1	2	yes	—
594	C₂³	C₂×#2846	1	1	yes	characteristic
595	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
596	C₂³	C₂×#3026	1	1	yes	characteristic
597	C₂³	#60399	1	2	yes	—
598	C₂×C₄	#32898	1	2	yes	—
599	C₂²	#612424	1	1	yes	characteristic
600	C₂²	C₂×#23895	1	2	yes	—
601	C₂²	D₄×B(4,𝔽₂)	1	2	yes	—
602	C₂²	#6573715	1	2	yes	—
603	C₂²	C₂×#32898	1	1	yes	characteristic
604	C₂²	#6628896	1	1	yes	characteristic
605	C₂	#72213862	1	1	yes	characteristic
606	C₂	#72225691	1	1	yes	characteristic
607	C₂	#72260725	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261568	C₂	semidirect
2. #72261560	C₂	semidirect
3. #72261545	C₂	semidirect
4. #72261400	C₂	semidirect
5. #72261121	C₂	semidirect
6. #72260976	C₂	semidirect
7. #72236728	C₂	semidirect
8. #72236720	C₂	semidirect
9. #72234970	C₂	semidirect
10. #72234959	C₂	semidirect
11. #72234164	C₂	semidirect
12. #72234155	C₂	semidirect
13. #72234135	C₂	semidirect
14. #72233613	C₂	semidirect
15. #72233449	C₂	semidirect
16. #72233304	C₂	semidirect
17. #72233069	C₂	semidirect
18. C₂×#62818	C₂²	semidirect
20. C₂²×#3026	C₂²	semidirect
21. #7804429	C₂²	semidirect
22. #7752089	C₂²	semidirect
27. #7631287	C₂²	semidirect
28. #7631286	C₂²	semidirect
29. #7631286	C₂²	semidirect
30. C₂×#35347	C₂²	semidirect
31. #7626663	C₂²	semidirect
32. #6628892	C₂²	semidirect
33. C₂×#32900	C₂²	semidirect
34. C₂×#32898	C₂²	semidirect
35. #6477580	C₂²	semidirect
37. #6470225	C₂²	semidirect
38. #6470225	C₂²	semidirect
39. #6437621	C₂²	semidirect
40. #6385971	C₂²	semidirect
41. #6385971	C₂²	semidirect
42. #616964	C₂²	semidirect
43. #394269	C₂²	semidirect
44. #394267	C₂²	semidirect
45. #394061	C₂²	semidirect
46. #393929	C₂²	semidirect
47. #392125	C₂²	semidirect
48. #374058	C₂²	semidirect
49. #374040	C₂²	semidirect
50. #364471	C₂²	semidirect
51. #364440	C₂²	semidirect
52. #359579	C₂²	semidirect
53. #359579	C₂²	semidirect
54. #359504	C₂²	semidirect
55. #359442	C₂²	semidirect
56. #233549	C₂²	semidirect
57. #233541	C₂²	semidirect
58. C₂×#10337	C₂²	semidirect
59. #201701	C₂²	semidirect
60. #201701	C₂²	semidirect
61. #201678	C₂²	semidirect
62. #201668	C₂²	semidirect
63. C₂×#9495	C₂²	semidirect
64. #188035	C₂²	semidirect
65. #188035	C₂²	semidirect
66. C₂×#8542	C₂²	semidirect
67. #187944	C₂²	semidirect
68. #187929	C₂²	semidirect
69. #187928	C₂²	semidirect
70. #187928	C₂²	semidirect
71. #187928	C₂²	semidirect
72. #115631	C₂²	semidirect
73. #115204	C₂²	semidirect
74. #115164	C₂²	semidirect
75. #115163	C₂²	semidirect
76. #115133	C₂²	semidirect
77. #111467	C₂²	semidirect
78. #111459	C₂²	semidirect
79. #107194	C₂²	semidirect
80. #106654	C₂²	semidirect
81. #106542	C₂²	semidirect
82. #105752	C₂²	semidirect
83. C₂³×H(5,𝔽₂)	D₄	semidirect
87. C₂×#3496	D₄	semidirect
88. C₂×#3496	D₄	semidirect
89. C₂×#3484	D₄	semidirect
90. C₂×#3484	D₄	semidirect
91. C₂×#3484	D₄	semidirect
99. C₂²×#534	C₂³	semidirect
100. C₂³×#123	D₄	semidirect
102. C₂×C₄×H(5,𝔽₂)	D₄	semidirect
104. C₂³×#99	C₂³	semidirect
106. #37232	D₄	semidirect
107. #37232	D₄	semidirect
108. #37117	D₄	semidirect
109. #36718	D₄	semidirect
110. #36718	D₄	semidirect
111. #36714	D₄	semidirect
112. C₂×#2849	D₄	semidirect
113. #35554	D₄	semidirect
114. #35390	D₄	semidirect
115. #35358	D₄	semidirect
116. #35355	D₄	semidirect
117. #35355	D₄	semidirect
118. #35351	D₄	semidirect
119. #35350	D₄	semidirect
120. #35350	D₄	semidirect
121. #35348	D₄	semidirect
122. #35347	D₄	semidirect
123. #35347	D₄	semidirect
124. #35346	D₄	semidirect
125. #34984	D₄	semidirect
126. #34980	D₄	semidirect
131. #34980	C₂³	semidirect
132. C₂×#2539	D₄	semidirect
133. C₂×#2534	D₄	semidirect
137. C₂×#2405	C₂³	semidirect
138. C₂×#2410	D₄	semidirect
140. C₂×#2403	D₄	semidirect
144. C₂×#2618	D₄	semidirect
147. #34264	D₄	semidirect
152. C₂×#2322	D₄	semidirect
154. #24056	D₄	semidirect
155. #23900	D₄	semidirect
160. #21746	C₂³	semidirect
161. #21746	C₂³	semidirect
164. C₂×#1898	C₂³	semidirect
165. C₂×#1819	C₂³	semidirect
172. C₂×#1781	C₂³	semidirect
173. C₂×#1781	C₂³	semidirect
174. C₂×#1781	C₂³	semidirect
175. #14335	C₂³	semidirect
176. #13869	C₂³	semidirect
179. #10735	C₂³	semidirect
180. #10735	C₂³	semidirect
181. #10735	C₂³	semidirect
182. #10725	C₂³	semidirect
183. #8101	C₂³	semidirect
184. C₂×#1304	C₂³	semidirect
185. C₂×#1304	C₂³	semidirect
191. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
192. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
197. C₂⁴×D₄	C₂×D₄	semidirect
203. C₂⁵×C₄	C₂×D₄	semidirect
205. C₂×#543	C₂×D₄	semidirect
215. C₂×#534	C₂×D₄	semidirect
216. C₂×#534	C₂×D₄	semidirect
217. C₂×#534	C₂×D₄	semidirect
218. C₂×#534	C₂×D₄	semidirect
225. C₂²×#123	C₂×D₄	semidirect
226. C₂²×#123	C₂×D₄	semidirect
243. C₂²×#120	C₂×D₄	semidirect
244. C₂²×#120	C₂×D₄	semidirect
245. C₂²×#120	C₂×D₄	semidirect
246. C₂²×#120	C₂×D₄	semidirect
247. C₂²×#120	C₂×D₄	semidirect
253. C₂×#518	C₂×D₄	semidirect
254. C₂×#518	C₂×D₄	semidirect
255. C₂×#518	C₂×D₄	semidirect
256. C₂×#518	C₂×D₄	semidirect
257. C₂×#518	C₂×D₄	semidirect
262. C₂³×C₄⋊C₄	C₂×D₄	semidirect
263. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
264. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
268. #2849	C₂×D₄	semidirect
269. #2846	C₂×D₄	semidirect
270. #2483	C₂×D₄	semidirect
279. #2405	C₂×D₄	semidirect
280. #2405	C₂×D₄	semidirect
281. #2405	C₂×D₄	semidirect
282. #2405	C₂×D₄	semidirect
283. #2405	C₂×D₄	semidirect
284. #2405	C₂×D₄	semidirect
285. #2405	C₂×D₄	semidirect
286. #2405	C₂×D₄	semidirect
291. #2403	C₂×D₄	semidirect
292. #2403	C₂×D₄	semidirect
293. #2403	C₂×D₄	semidirect
294. #2315	C₂×D₄	semidirect
295. #2312	C₂×D₄	semidirect
296. #2312	C₂×D₄	semidirect
297. #2309	C₂×D₄	semidirect
300. #2308	C₂×D₄	semidirect
301. #2308	C₂×D₄	semidirect
302. #2308	C₂×D₄	semidirect
303. #2308	C₂×D₄	semidirect
304. #2308	C₂×D₄	semidirect
307. C₂×#386	C₂×D₄	semidirect
308. C₂×#386	C₂×D₄	semidirect
309. C₂×#386	C₂×D₄	semidirect
310. C₂×#386	C₂×D₄	semidirect
311. C₂×#386	C₂×D₄	semidirect
312. C₂×#385	C₂×D₄	semidirect
313. C₂×#385	C₂×D₄	semidirect
314. C₂×#381	C₂×D₄	semidirect
315. C₂×#381	C₂×D₄	semidirect
316. C₂×#380	C₂×D₄	semidirect
317. C₂×#379	C₂×D₄	semidirect
318. C₂×#379	C₂×D₄	semidirect
319. C₂×#379	C₂×D₄	semidirect
326. #2273	C₂×D₄	semidirect
327. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
328. #1898	C₂×D₄	semidirect
329. #1781	C₂×D₄	semidirect
536. #123	B(4,𝔽₂)	semidirect
583. C₂²×C₄	C₂×B(4,𝔽₂)	semidirect
584. C₂²⋊C₄	C₂×B(4,𝔽₂)	semidirect
585. C₂³	#23895	semidirect

Maximal subgroups

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

subgroup	index
#72261568	2
#72261560	2
#72261545	2
#72261400	2
#72261121	2
#72260976	2
#72236728	2
#72236720	2
#72234970	2
#72234959	2
#72234164	2
#72234155	2
#72234135	2
#72233613	2
#72233449	2
#72233304	2
#72233069	2