Subgroups — #72311100

Order 2048.

At least 11032 conjugacy classes of subgroups; only the 1968 normal subgroups are shown.

The subgroup lattice has 941 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72311068	C₂	1	2	yes	maximal, complemented
2	#72310819	C₂	1	2	yes	maximal, complemented
3	#72310800	C₂	1	4	yes	maximal, complemented
4	#72310748	C₂	1	2	yes	maximal, complemented
5	#72310726	C₂	1	1	yes	maximal, characteristic, complemented
6	#72306399	C₂	1	4	yes	maximal, complemented
7	#72306339	C₂	1	4	yes	maximal, complemented
8	#72303390	C₂	1	4	yes	maximal, complemented
9	#72303382	C₂	1	4	yes	maximal, complemented
10	#72302959	C₂	1	1	yes	maximal, characteristic, complemented
11	#72302947	C₂	1	2	yes	maximal, complemented
12	#72257321	C₂	1	1	yes	maximal, characteristic
13	C₂×#62812	C₂²	1	1	yes	characteristic
14	C₂²×#3481	C₄	1	1	yes	characteristic, complemented
15	#7739384	C₂²	1	2	yes	—
16	#7739315	C₄	1	2	yes	complemented
17	#7739265	C₄	1	2	yes	complemented
18	#7739265	C₂²	1	2	yes	—
19	#7737652	C₄	1	1	yes	characteristic, complemented
20	#7737652	C₂²	1	1	yes	characteristic
21	#7737411	C₄	1	1	yes	characteristic, complemented
22	#7737411	C₂²	1	1	yes	characteristic
23	#7737041	C₄	1	2	yes	complemented
24	#7737041	C₂²	1	2	yes	—
25	#7708257	C₄	1	2	yes	complemented
26	#7708257	C₂²	1	2	yes	—
27	#7666965	C₄	1	2	yes	complemented
28	#7666965	C₂²	1	2	yes	—
29	#7634872	C₄	1	2	yes	complemented
30	#7629120	C₂²	1	2	yes	—
31	#7625999	C₄	1	1	yes	characteristic, complemented
32	#6370703	C₂²	1	1	yes	characteristic, complemented
33	#6370692	C₂²	1	1	yes	characteristic, complemented
34	#6370692	C₂²	1	2	yes	complemented
35	#496239	C₂²	1	8	yes	complemented
36	#496238	C₂²	1	4	yes	complemented
37	#496237	C₂²	1	4	yes	complemented
38	#494676	C₂²	1	8	yes	complemented
39	#493434	C₂²	1	2	yes	complemented
40	#493433	C₂²	1	2	yes	complemented
41	#493431	C₂²	1	2	yes	—
42	#493430	C₂²	1	2	yes	complemented
43	#493369	C₂²	1	2	yes	complemented
44	#493365	C₂²	1	2	yes	complemented
45	#382444	C₂²	1	2	yes	complemented
46	#382444	C₂²	1	2	yes	complemented
47	#382443	C₂²	1	2	yes	—
48	#382443	C₂²	1	2	yes	complemented
49	#357478	C₂²	1	2	yes	complemented
50	#357451	C₂²	1	2	yes	complemented
51	#213832	C₂²	1	8	yes	complemented
52	#213831	C₂²	1	4	yes	complemented
53	#213829	C₂²	1	4	yes	complemented
54	#201660	C₂²	1	8	yes	complemented
55	#133358	C₂²	1	16	yes	complemented
56	#133357	C₂²	1	8	yes	complemented
57	#133356	C₂²	1	8	yes	complemented
58	#133334	C₂²	1	16	yes	complemented
59	#133333	C₂²	1	8	yes	complemented
60	#133332	C₂²	1	8	yes	complemented
61	C₂²×#585	D₄	1	1	yes	characteristic
62	C₂²×#585	C₂³	1	1	yes	characteristic
63	C₂×#3500	C₂×C₄	1	1	yes	characteristic
64	C₂×#3500	C₂×C₄	1	1	yes	characteristic
65	C₂×#3500	D₄	1	1	yes	characteristic
66	C₂×#3500	D₄	1	1	yes	characteristic
67	C₂×#3500	D₄	1	1	yes	characteristic
68	C₂×#3500	D₄	1	1	yes	characteristic
69	C₂×#3500	C₂³	1	1	yes	characteristic
70	C₂×#3500	C₂³	1	1	yes	characteristic
71	C₂×#3499	C₂×C₄	1	1	yes	characteristic
72	C₂×#3499	D₄	1	1	yes	characteristic
73	C₂×#3499	D₄	1	1	yes	characteristic
74	C₂×#3499	D₄	1	1	yes	characteristic
75	C₂×#3498	C₂×C₄	1	1	yes	characteristic
76	C₂×#3498	D₄	1	1	yes	characteristic
77	C₂×#3498	C₂³	1	1	yes	characteristic
78	C₂×#3498	C₂³	1	1	yes	characteristic
79	C₂×#3481	C₂×C₄	1	2	yes	complemented
80	C₂×#3481	C₂×C₄	1	2	yes	complemented
81	C₂×#3481	C₂×C₄	1	2	yes	complemented
82	C₂×#3481	C₂×C₄	1	2	yes	complemented
83	C₂²×#559	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂²×#551	C₂×C₄	1	2	yes	complemented
85	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×#3449	C₂×C₄	1	1	yes	characteristic
87	C₂×#3449	C₂×C₄	1	1	yes	characteristic
88	C₂×#3449	D₄	1	1	yes	characteristic
89	C₂×#3449	D₄	1	1	yes	characteristic
90	C₂×#3449	D₄	1	1	yes	characteristic
91	C₂×#3449	C₂³	1	1	yes	characteristic
92	C₂²×#532	C₂×C₄	1	1	yes	characteristic
93	C₂²×#532	C₂×C₄	1	1	yes	characteristic
94	C₂²×#532	D₄	1	1	yes	characteristic
95	C₂²×#532	D₄	1	1	yes	characteristic
96	C₂²×#532	D₄	1	1	yes	characteristic
97	C₂²×#532	C₂³	1	1	yes	characteristic
98	C₂²×#525	C₂×C₄	1	2	yes	—
99	C₂²×#525	D₄	1	2	yes	—
100	C₂²×#525	D₄	1	2	yes	—
101	C₂²×C₄×#41	D₄	1	1	yes	characteristic
102	C₂²×#413	C₂³	1	2	yes	complemented
103	#59184	C₂×C₄	1	4	yes	complemented
104	#59184	C₂×C₄	1	4	yes	complemented
105	#59162	C₂×C₄	1	4	yes	complemented
106	#59162	C₂³	1	4	yes	—
107	#59143	C₂×C₄	1	2	yes	complemented
108	#59143	C₂³	1	2	yes	—
109	#59126	C₂×C₄	1	2	yes	complemented
110	#59126	C₂³	1	2	yes	—
111	#59070	C₂×C₄	1	2	yes	complemented
112	#59070	C₂×C₄	1	2	yes	complemented
113	#59041	C₂×C₄	1	2	yes	complemented
114	#59041	C₂×C₄	1	2	yes	complemented
115	#52165	C₂×C₄	1	4	yes	complemented
116	#52165	C₂×C₄	1	4	yes	complemented
117	#52054	C₂×C₄	1	2	yes	complemented
118	#52054	C₂×C₄	1	2	yes	complemented
119	#52054	C₂×C₄	1	2	yes	complemented
120	#52054	C₂³	1	2	yes	—
121	#52004	C₂×C₄	1	2	yes	complemented
122	#52004	C₂×C₄	1	2	yes	complemented
123	#52004	C₂×C₄	1	2	yes	complemented
124	#52004	C₂³	1	2	yes	—
125	#51895	C₂×C₄	1	4	yes	complemented
126	#51895	C₂³	1	4	yes	—
127	#51530	C₂×C₄	1	4	yes	complemented
128	#51530	C₂×C₄	1	4	yes	complemented
129	#37374	C₂×C₄	1	4	yes	complemented
130	#37269	C₂×C₄	1	4	yes	complemented
131	#36955	C₂×C₄	1	2	yes	complemented
132	#36955	C₂×C₄	1	2	yes	complemented
133	#36702	C₂×C₄	1	2	yes	complemented
134	#36702	C₂×C₄	1	2	yes	complemented
135	#35659	C₂×C₄	1	4	yes	—
136	#35659	D₄	1	4	yes	—
137	#35512	D₄	1	4	yes	—
138	#35512	C₂³	1	4	yes	—
139	#35446	C₂×C₄	1	2	yes	—
140	#35446	D₄	1	2	yes	—
141	#35446	D₄	1	2	yes	—
142	#35446	C₂³	1	2	yes	—
143	#35346	C₂×C₄	1	2	yes	—
144	#35346	D₄	1	2	yes	—
145	#35346	D₄	1	2	yes	—
146	#35346	C₂³	1	2	yes	—
147	#34736	C₂×C₄	1	4	yes	—
148	#34736	D₄	1	4	yes	—
149	#34736	D₄	1	4	yes	—
150	#34736	C₂³	1	4	yes	—
151	#34369	C₂×C₄	1	2	yes	complemented
152	#34368	C₂×C₄	1	2	yes	complemented
153	#34366	C₂×C₄	1	2	yes	complemented
154	#34364	C₂×C₄	1	1	yes	characteristic, complemented
155	#34364	C₂×C₄	1	1	yes	characteristic, complemented
156	#34346	C₂×C₄	1	2	yes	complemented
157	#34155	C₂×C₄	1	2	yes	complemented
158	#34044	C₂×C₄	1	2	yes	—
159	#34044	D₄	1	2	yes	—
160	#34044	D₄	1	2	yes	—
161	#34044	C₂³	1	2	yes	complemented
162	#20592	C₂³	1	2	yes	—
163	#20592	C₂³	1	2	yes	complemented
164	#20586	C₂³	1	4	yes	—
165	#20586	C₂³	1	2	yes	—
166	#20586	C₂³	1	2	yes	complemented
167	#20585	C₂³	1	4	yes	complemented
168	#20584	C₂³	1	4	yes	complemented
169	#13082	C₂³	1	16	yes	—
170	#13080	C₂³	1	16	yes	complemented
171	#12696	C₂³	1	4	yes	—
172	#12696	C₂³	1	4	yes	complemented
173	#12694	C₂³	1	4	yes	complemented
174	#12693	C₂³	1	4	yes	—
175	#10989	C₂³	1	4	yes	—
176	#10989	C₂³	1	4	yes	complemented
177	#10977	C₂³	1	4	yes	complemented
178	#10975	C₂³	1	4	yes	—
179	#9501	C₂³	1	16	yes	complemented
180	#9497	C₂³	1	16	yes	—
181	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
184	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
185	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
186	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
187	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
188	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
189	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
190	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
193	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
194	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
195	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
196	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
197	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
198	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
199	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
200	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
201	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
203	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
206	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
207	C₂³×#41	C₂×D₄	1	1	yes	characteristic
208	C₂³×#41	C₂×D₄	1	1	yes	characteristic
209	C₂³×#41	C₂×D₄	1	2	yes	—
210	C₂³×#41	C₂×D₄	1	1	yes	characteristic
211	C₂³×#41	C₂×D₄	1	2	yes	—
212	C₂³×#41	C₂×D₄	1	2	yes	—
213	C₂³×#41	C₂×D₄	1	1	yes	characteristic
214	C₂³×#41	C₂×D₄	1	1	yes	characteristic
215	C₂³×#41	C₂×D₄	1	1	yes	characteristic
216	C₂³×#41	C₂×D₄	1	2	yes	—
217	C₂³×#41	C₂⁴	1	1	yes	characteristic
218	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	—
219	C₂×#559	C₂²×C₄	1	2	yes	—
220	C₂×#559	C₂²×C₄	1	2	yes	—
221	C₂×#551	C₂²×C₄	1	4	yes	—
222	C₂×#551	C₂²×C₄	1	4	yes	—
223	C₂×D₄²	C₂²×C₄	1	2	yes	—
224	C₂×D₄²	C₂²×C₄	1	2	yes	—
225	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
226	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
227	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
228	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
229	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
230	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
231	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
235	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
236	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
237	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
238	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
239	C₂×#536	C₂²×C₄	1	1	yes	characteristic
240	C₂×#536	C₂²×C₄	1	1	yes	characteristic
241	C₂×#536	C₂²×C₄	1	1	yes	characteristic
242	C₂×#536	C₂×D₄	1	1	yes	characteristic
243	C₂×#536	C₂×D₄	1	1	yes	characteristic
244	C₂×#536	C₂×D₄	1	1	yes	characteristic
245	C₂×#536	C₂×D₄	1	1	yes	characteristic
246	C₂×#536	C₂×D₄	1	1	yes	characteristic
247	C₂×#536	C₂×D₄	1	1	yes	characteristic
248	C₂×#536	C₂×D₄	1	1	yes	characteristic
249	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
250	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
251	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
252	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
253	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
254	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
255	C₂×#535	C₂²×C₄	1	1	yes	characteristic
256	C₂×#535	C₂²×C₄	1	1	yes	characteristic
257	C₂×#535	C₂²×C₄	1	1	yes	characteristic
258	C₂×#535	C₂²×C₄	1	1	yes	characteristic
259	C₂×#535	C₂²×C₄	1	1	yes	characteristic
260	C₂×#535	C₂²×C₄	1	1	yes	characteristic
261	C₂×#535	C₂²×C₄	1	1	yes	characteristic
262	C₂×#535	C₂×D₄	1	1	yes	characteristic
263	C₂×#535	C₂×D₄	1	1	yes	characteristic
264	C₂×#535	C₂×D₄	1	1	yes	characteristic
265	C₂×#535	C₂×D₄	1	1	yes	characteristic
266	C₂×#535	C₂×D₄	1	1	yes	characteristic
267	C₂×#535	C₂×D₄	1	1	yes	characteristic
268	C₂×#535	C₂×D₄	1	1	yes	characteristic
269	C₂×#535	C₂×D₄	1	1	yes	characteristic
270	C₂×#535	C₂×D₄	1	1	yes	characteristic
271	C₂×#535	C₂⁴	1	1	yes	characteristic
272	C₂×#535	C₂⁴	1	1	yes	characteristic
273	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
274	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
275	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
276	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
277	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
278	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
279	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
280	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
281	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
282	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
283	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
284	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
285	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
286	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
287	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
288	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
289	C₂×#532	C₂²×C₄	1	1	yes	characteristic
290	C₂×#532	C₂²×C₄	1	1	yes	characteristic
291	C₂×#532	C₂²×C₄	1	1	yes	characteristic
292	C₂×#532	C₂²×C₄	1	1	yes	characteristic
293	C₂×#532	C₂²×C₄	1	1	yes	characteristic
294	C₂×#532	C₂²×C₄	1	1	yes	characteristic
295	C₂×#532	C₂²×C₄	1	1	yes	characteristic
296	C₂×#532	C₂²×C₄	1	1	yes	characteristic
297	C₂×#532	C₂²×C₄	1	1	yes	characteristic
298	C₂×#532	C₂²×C₄	1	1	yes	characteristic
299	C₂×#532	C₂×D₄	1	1	yes	characteristic
300	C₂×#532	C₂×D₄	1	1	yes	characteristic
301	C₂×#532	C₂×D₄	1	1	yes	characteristic
302	C₂×#532	C₂×D₄	1	1	yes	characteristic
303	C₂×#532	C₂×D₄	1	1	yes	characteristic
304	C₂×#532	C₂×D₄	1	1	yes	characteristic
305	C₂×#532	C₂×D₄	1	1	yes	characteristic
306	C₂×#532	C₂×D₄	1	1	yes	characteristic
307	C₂×#532	C₂×D₄	1	1	yes	characteristic
308	C₂×#532	C₂×D₄	1	1	yes	characteristic
309	C₂×#532	C₂×D₄	1	1	yes	characteristic
310	C₂×#532	C₂×D₄	1	1	yes	characteristic
311	C₂×#532	C₂×D₄	1	1	yes	characteristic
312	C₂×#532	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
314	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
319	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
320	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
321	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
322	C₂²×#127	C₂×D₄	1	1	yes	characteristic
323	C₂²×#127	C₂×D₄	1	1	yes	characteristic
324	C₂²×#127	C₂⁴	1	1	yes	characteristic
325	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
327	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
328	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
329	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
331	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
332	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
333	C₂²×#124	C₂×D₄	1	1	yes	characteristic
334	C₂²×#124	C₂×D₄	1	1	yes	characteristic
335	C₂²×#124	C₂×D₄	1	1	yes	characteristic
336	C₂²×#124	C₂⁴	1	1	yes	characteristic
337	C₂×#525	C₂²⋊C₄	1	4	yes	—
338	C₂×#525	C₂²⋊C₄	1	4	yes	—
339	C₂×#525	C₂²⋊C₄	1	4	yes	—
340	C₂×#525	C₂²⋊C₄	1	4	yes	—
341	C₂×#525	C₂²×C₄	1	4	yes	—
342	C₂×#525	C₂²×C₄	1	4	yes	—
343	C₂×#525	C₂×D₄	1	4	yes	—
344	C₂×#525	C₂×D₄	1	4	yes	—
345	C₂²×#123	C₂²⋊C₄	1	2	yes	—
346	C₂²×#123	C₂²⋊C₄	1	2	yes	—
347	C₂²×#123	C₂²⋊C₄	1	2	yes	—
348	C₂²×#123	C₂²×C₄	1	2	yes	—
349	C₂²×#123	C₂×D₄	1	2	yes	—
350	C₂²×#123	C₂×D₄	1	2	yes	—
351	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	4	yes	—
352	C₂²×#121	C₂×D₄	1	4	yes	—
353	C₂²×#120	C₂²⋊C₄	1	2	yes	—
354	C₂²×#120	C₂²⋊C₄	1	2	yes	—
355	C₂²×#120	C₂²⋊C₄	1	2	yes	—
356	C₂²×#120	C₂²×C₄	1	2	yes	—
357	C₂²×#120	C₂×D₄	1	2	yes	—
358	C₂²×#120	C₂×D₄	1	2	yes	—
359	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
364	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
365	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
366	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×D₄	C₂²⋊C₄	1	4	yes	—
368	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
369	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×#117	C₂²⋊C₄	1	2	yes	—
372	C₂²×#117	C₂²⋊C₄	1	2	yes	—
373	C₂²×#117	C₂²⋊C₄	1	2	yes	—
374	C₂²×#117	C₂×D₄	1	1	yes	characteristic
375	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
376	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
377	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
378	C₂²×#100	C₂⁴	1	4	yes	—
379	#2717	C₂²×C₄	1	4	yes	—
380	#2717	C₂²×C₄	1	4	yes	—
381	#2709	C₂²×C₄	1	4	yes	—
382	#2709	C₂²×C₄	1	4	yes	—
383	#2684	C₂²×C₄	1	4	yes	—
384	#2684	C₂²×C₄	1	4	yes	—
385	#2669	C₂²×C₄	1	4	yes	—
386	#2669	C₂²×C₄	1	4	yes	—
387	#2406	C₂²⋊C₄	1	4	yes	—
388	#2406	C₂²⋊C₄	1	4	yes	—
389	#2406	C₂²⋊C₄	1	4	yes	—
390	#2406	C₂²⋊C₄	1	4	yes	—
391	#2406	C₂²×C₄	1	4	yes	—
392	#2406	C₂²×C₄	1	4	yes	—
393	#2406	C₂×D₄	1	4	yes	—
394	#2406	C₂×D₄	1	4	yes	—
395	#2405	C₂²⋊C₄	1	4	yes	—
396	#2405	C₂²⋊C₄	1	4	yes	—
397	#2405	C₂²×C₄	1	4	yes	—
398	#2405	C₂×D₄	1	4	yes	—
399	#2405	C₂×D₄	1	4	yes	—
400	#2405	C₂×D₄	1	4	yes	—
401	#2405	C₂×D₄	1	4	yes	—
402	#2405	C₂⁴	1	4	yes	—
403	#2404	C₂²⋊C₄	1	4	yes	—
404	#2404	C₂²⋊C₄	1	4	yes	—
405	#2404	C₂²⋊C₄	1	4	yes	—
406	#2404	C₂²⋊C₄	1	4	yes	—
407	#2404	C₂²×C₄	1	4	yes	—
408	#2404	C₂²×C₄	1	4	yes	—
409	#2404	C₂×D₄	1	4	yes	—
410	#2404	C₂×D₄	1	4	yes	—
411	#2403	C₂²⋊C₄	1	4	yes	—
412	#2403	C₂²⋊C₄	1	4	yes	—
413	#2403	C₂²×C₄	1	4	yes	—
414	#2403	C₂×D₄	1	4	yes	—
415	#2403	C₂×D₄	1	4	yes	—
416	#2403	C₂×D₄	1	4	yes	—
417	#2403	C₂×D₄	1	4	yes	—
418	#2403	C₂⁴	1	4	yes	—
419	#2380	C₂²×C₄	1	2	yes	—
420	#2380	C₂²×C₄	1	2	yes	—
421	#2379	C₂²×C₄	1	4	yes	—
422	#2372	C₂²×C₄	1	4	yes	—
423	#2366	C₂²×C₄	1	2	yes	—
424	#2366	C₂²×C₄	1	2	yes	—
425	#2311	C₂²⋊C₄	1	4	yes	—
426	#2311	C₂²⋊C₄	1	4	yes	—
427	#2311	C₂²×C₄	1	4	yes	—
428	#2311	C₂×D₄	1	4	yes	—
429	#2310	C₂²⋊C₄	1	4	yes	—
430	#2309	C₂×D₄	1	4	yes	—
431	#2309	C₂⁴	1	4	yes	—
432	#2308	C₂²⋊C₄	1	2	yes	—
433	#2308	C₂²⋊C₄	1	2	yes	—
434	#2308	C₂²⋊C₄	1	2	yes	—
435	#2308	C₂²⋊C₄	1	2	yes	—
436	#2308	C₂²⋊C₄	1	2	yes	—
437	#2308	C₂²⋊C₄	1	2	yes	—
438	#2308	C₂²×C₄	1	2	yes	—
439	#2308	C₂²×C₄	1	2	yes	—
440	#2308	C₂×D₄	1	2	yes	—
441	#2308	C₂×D₄	1	2	yes	—
442	#2308	C₂×D₄	1	2	yes	—
443	#2308	C₂×D₄	1	2	yes	—
444	#2297	C₂²⋊C₄	1	4	yes	—
445	#2297	C₂²⋊C₄	1	4	yes	—
446	#2297	C₂²×C₄	1	4	yes	—
447	#2297	C₂×D₄	1	4	yes	—
448	#2280	C₂²⋊C₄	1	4	yes	—
449	#2280	C₂×D₄	1	4	yes	—
450	#1781	C₂⁴	1	8	yes	—
451	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
452	C₂²×#41	#99	1	8	yes	complemented
453	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
470	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
471	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
472	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
473	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
474	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
475	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
476	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
477	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
478	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
479	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
480	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
481	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
482	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
483	C₂²×#41	#120	1	2	yes	—
484	C₂²×#41	#120	1	2	yes	—
485	C₂²×#41	#120	1	2	yes	—
486	C₂²×#41	#120	1	2	yes	—
487	C₂²×#41	#120	1	2	yes	—
488	C₂²×#41	#120	1	2	yes	—
489	C₂²×#41	#120	1	2	yes	—
490	C₂²×#41	#120	1	2	yes	—
491	C₂²×#41	#120	1	2	yes	—
492	C₂²×#41	#120	1	2	yes	—
493	C₂²×#41	#120	1	2	yes	—
494	C₂²×#41	#120	1	2	yes	—
495	C₂²×#41	#120	1	2	yes	—
496	C₂²×#41	#120	1	1	yes	characteristic
497	C₂²×#41	#120	1	1	yes	characteristic
498	C₂²×#41	#120	1	2	yes	—
499	C₂²×#41	#120	1	2	yes	—
500	C₂²×#41	#120	1	1	yes	characteristic
501	C₂²×#41	#120	1	1	yes	characteristic
502	C₂²×#41	#120	1	2	yes	—
503	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
504	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
505	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
506	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
507	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
508	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
509	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
510	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
511	C₂²×#41	C₂²×D₄	1	2	yes	—
512	C₂²×#41	C₂²×D₄	1	2	yes	—
513	C₂²×#41	C₂²×D₄	1	2	yes	—
514	C₂²×#41	C₂²×D₄	1	2	yes	—
515	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
516	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
517	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
518	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
519	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
520	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
521	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
522	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
523	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
524	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
525	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
526	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
527	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
528	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
529	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
530	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
531	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
532	C₂³×Q₈	#120	1	2	yes	—
533	C₂³×Q₈	#120	1	1	yes	characteristic
534	C₂³×Q₈	#120	1	2	yes	—
535	C₂³×Q₈	#120	1	2	yes	—
536	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
537	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
538	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
539	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
540	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
541	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
542	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
543	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
544	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
545	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
546	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
547	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
548	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
549	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
550	C₂³×D₄	#120	1	1	yes	characteristic
551	C₂³×D₄	#120	1	2	yes	—
552	C₂³×D₄	#120	1	1	yes	characteristic
553	C₂³×D₄	#120	1	1	yes	characteristic
554	C₂³×D₄	#120	1	2	yes	—
555	C₂³×D₄	#120	1	2	yes	—
556	C₂³×D₄	#120	1	2	yes	—
557	C₂³×D₄	#120	1	2	yes	—
558	C₂³×D₄	#120	1	2	yes	—
559	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
560	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
561	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
562	C₂³×D₄	C₂²×D₄	1	4	yes	—
563	C₂³×D₄	C₂²×D₄	1	2	yes	—
564	C₂³×D₄	C₂²×D₄	1	2	yes	—
565	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
566	C₂³×D₄	C₂²×D₄	1	2	yes	—
567	C₂³×D₄	C₂²×D₄	1	2	yes	—
568	C₂³×D₄	C₂²×D₄	1	2	yes	—
569	C₂³×D₄	C₂²×D₄	1	2	yes	—
570	C₂³×D₄	C₂²×D₄	1	2	yes	—
571	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
572	C₂³×D₄	C₂⁵	1	1	yes	characteristic
573	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
574	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
575	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
576	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
577	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
578	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
579	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
580	C₂⁴×C₄	#120	1	2	yes	—
581	C₂⁴×C₄	#120	1	2	yes	—
582	C₂⁴×C₄	#120	1	2	yes	—
583	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
584	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
585	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
588	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
589	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
590	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
591	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
592	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
593	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
594	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
595	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
596	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
597	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
598	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
599	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
600	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
601	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
602	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
603	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
604	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
605	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
606	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
607	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
608	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
609	C₂×#127	C₂³×C₄	1	1	yes	characteristic
610	C₂×#127	C₂³×C₄	1	1	yes	characteristic
611	C₂×#127	C₂³×C₄	1	1	yes	characteristic
612	C₂×#127	C₂³×C₄	1	1	yes	characteristic
613	C₂×#127	C₂²×D₄	1	1	yes	characteristic
614	C₂×#127	C₂²×D₄	1	1	yes	characteristic
615	C₂×#127	C₂²×D₄	1	1	yes	characteristic
616	C₂×#127	C₂²×D₄	1	1	yes	characteristic
617	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
618	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
619	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
620	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
621	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
622	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
623	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
624	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
625	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
626	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
627	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
628	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
629	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
630	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
631	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
632	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
633	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
634	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
635	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
636	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
637	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
638	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
639	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
640	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
641	C₂×#124	C₂³×C₄	1	1	yes	characteristic
642	C₂×#124	C₂³×C₄	1	1	yes	characteristic
643	C₂×#124	C₂³×C₄	1	1	yes	characteristic
644	C₂×#124	C₂³×C₄	1	1	yes	characteristic
645	C₂×#124	C₂²×D₄	1	1	yes	characteristic
646	C₂×#124	C₂²×D₄	1	1	yes	characteristic
647	C₂×#124	C₂²×D₄	1	1	yes	characteristic
648	C₂×#124	C₂²×D₄	1	1	yes	characteristic
649	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
650	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
651	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
652	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
653	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
654	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
655	C₂×#123	C₂³×C₄	1	4	yes	—
656	C₂×#123	C₂²×D₄	1	4	yes	—
657	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
658	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
659	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
660	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
661	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
662	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
663	C₂×#120	C₂³×C₄	1	4	yes	—
664	C₂×#120	C₂²×D₄	1	4	yes	—
665	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
666	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
667	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
668	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
669	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
670	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
671	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
672	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
673	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
674	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
675	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
676	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
677	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
678	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
679	C₂×#117	C₂²×D₄	1	1	yes	characteristic
680	C₂×#117	C₂²×D₄	1	1	yes	characteristic
681	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
682	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
683	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
684	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
685	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
686	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
687	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
688	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
689	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
690	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
691	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
692	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
693	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
694	C₂²×C₄²	#99	1	8	yes	complemented
695	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
696	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
697	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
698	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
699	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
700	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
701	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
702	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
703	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
704	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
705	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
706	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
707	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
708	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
709	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	—
710	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
711	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
712	#386	C₂×C₂²⋊C₄	1	4	yes	—
713	#386	C₂×C₂²⋊C₄	1	4	yes	—
714	#386	C₂×C₂²⋊C₄	1	4	yes	—
715	#386	C₂×C₂²⋊C₄	1	4	yes	—
716	#386	C₂×C₂²⋊C₄	1	4	yes	—
717	#386	C₂×C₂²⋊C₄	1	4	yes	—
718	#386	C₂×C₂²⋊C₄	1	4	yes	—
719	#386	C₂×C₂²⋊C₄	1	4	yes	—
720	#386	C₂×C₂²⋊C₄	1	4	yes	—
721	#386	C₂×C₂²⋊C₄	1	4	yes	—
722	#386	C₂×C₂²⋊C₄	1	4	yes	—
723	#386	C₂×C₂²⋊C₄	1	4	yes	—
724	#386	C₂³×C₄	1	4	yes	—
725	#386	C₂³×C₄	1	4	yes	—
726	#386	C₂²×D₄	1	4	yes	—
727	#386	C₂²×D₄	1	4	yes	—
728	#381	C₂×C₂²⋊C₄	1	4	yes	—
729	#381	C₂×C₂²⋊C₄	1	4	yes	—
730	#381	C₂×C₂²⋊C₄	1	4	yes	—
731	#381	C₂×C₂²⋊C₄	1	4	yes	—
732	#379	C₂×C₂²⋊C₄	1	4	yes	—
733	#379	C₂×C₂²⋊C₄	1	4	yes	—
734	#379	C₂²×D₄	1	4	yes	—
735	#379	C₂²×D₄	1	4	yes	—
736	C₂⁵	#379	1	2	yes	—
737	C₂⁵	#379	1	1	yes	characteristic
738	C₂⁵	#379	1	1	yes	characteristic
739	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
740	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
741	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
742	C₂⁵	C₂×#120	1	1	yes	characteristic
743	C₂⁵	C₂×#120	1	2	yes	—
744	C₂⁵	C₂×#120	1	2	yes	—
745	C₂⁵	C₂³×D₄	1	2	yes	—
746	C₂×#41	C₂×#99	1	4	yes	—
747	C₂×#41	C₂×#99	1	4	yes	—
748	C₂×#41	C₂×#99	1	4	yes	—
749	C₂×#41	C₂×#99	1	4	yes	—
750	C₂²×Q₈	#379	1	1	yes	characteristic
751	C₂²×Q₈	#379	1	1	yes	characteristic
752	C₂²×Q₈	#379	1	2	yes	—
753	C₂²×Q₈	#379	1	2	yes	—
754	C₂²×Q₈	#379	1	2	yes	—
755	C₂²×Q₈	#379	1	2	yes	—
756	C₂²×Q₈	#379	1	2	yes	—
757	C₂²×Q₈	C₂×#99	1	4	yes	—
758	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
759	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
760	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
761	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
762	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
763	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
764	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
765	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
766	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
767	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
768	C₂²×Q₈	C₂×#120	1	2	yes	—
769	C₂²×D₄	#379	1	1	yes	characteristic
770	C₂²×D₄	#379	1	1	yes	characteristic
771	C₂²×D₄	#379	1	1	yes	characteristic
772	C₂²×D₄	#379	1	1	yes	characteristic
773	C₂²×D₄	#379	1	1	yes	characteristic
774	C₂²×D₄	#379	1	1	yes	characteristic
775	C₂²×D₄	#379	1	2	yes	—
776	C₂²×D₄	#379	1	2	yes	—
777	C₂²×D₄	#379	1	2	yes	—
778	C₂²×D₄	#379	1	2	yes	—
779	C₂²×D₄	#379	1	2	yes	—
780	C₂²×D₄	#379	1	2	yes	—
781	C₂²×D₄	#379	1	2	yes	—
782	C₂²×D₄	C₂×#99	1	4	yes	—
783	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
784	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
785	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
786	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
787	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
788	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
789	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
790	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
791	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
792	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
793	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
794	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
795	C₂²×D₄	C₂×#120	1	1	yes	characteristic
796	C₂²×D₄	C₂×#120	1	1	yes	characteristic
797	C₂²×D₄	C₂×#120	1	1	yes	characteristic
798	C₂²×D₄	C₂×#120	1	1	yes	characteristic
799	C₂²×D₄	C₂×#120	1	1	yes	characteristic
800	C₂²×D₄	C₂×#120	1	1	yes	characteristic
801	C₂²×D₄	C₂×#120	1	2	yes	—
802	C₂²×D₄	C₂×#120	1	2	yes	—
803	C₂²×D₄	C₂×#120	1	2	yes	—
804	C₂²×D₄	C₂×#120	1	2	yes	—
805	C₂²×D₄	C₂×#120	1	2	yes	—
806	C₂²×D₄	C₂×#120	1	2	yes	—
807	C₂²×D₄	C₂×#120	1	2	yes	—
808	C₂²×D₄	C₂×#120	1	2	yes	—
809	C₂²×D₄	C₂⁴×C₄	1	1	yes	characteristic
810	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
811	C₂²×D₄	C₂³×D₄	1	2	yes	—
812	C₂³×C₄	#379	1	2	yes	—
813	C₂³×C₄	#379	1	1	yes	characteristic
814	C₂³×C₄	#379	1	1	yes	characteristic
815	C₂³×C₄	#379	1	2	yes	—
816	C₂³×C₄	#379	1	1	yes	characteristic
817	C₂³×C₄	#379	1	1	yes	characteristic
818	C₂³×C₄	#379	1	2	yes	—
819	C₂³×C₄	#379	1	2	yes	—
820	C₂³×C₄	#379	1	2	yes	—
821	C₂³×C₄	#379	1	2	yes	—
822	C₂³×C₄	#379	1	1	yes	characteristic
823	C₂³×C₄	#379	1	2	yes	—
824	C₂³×C₄	#379	1	2	yes	—
825	C₂³×C₄	#379	1	2	yes	—
826	C₂³×C₄	#379	1	2	yes	—
827	C₂³×C₄	#379	1	2	yes	—
828	C₂³×C₄	#379	1	1	yes	characteristic
829	C₂³×C₄	C₂×#99	1	4	yes	—
830	C₂³×C₄	C₂×#99	1	4	yes	—
831	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
832	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
833	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
834	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
835	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
836	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
837	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
838	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
839	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
840	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
841	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
842	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
843	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
844	C₂³×C₄	C₂×#120	1	1	yes	characteristic
845	C₂³×C₄	C₂×#120	1	2	yes	—
846	C₂³×C₄	C₂×#120	1	1	yes	characteristic
847	C₂³×C₄	C₂×#120	1	2	yes	—
848	C₂³×C₄	C₂×#120	1	2	yes	—
849	C₂³×C₄	C₂×#120	1	2	yes	—
850	C₂³×C₄	C₂×#120	1	2	yes	—
851	C₂³×C₄	C₂×#120	1	2	yes	—
852	C₂³×C₄	C₂×#120	1	2	yes	—
853	C₂³×C₄	C₂×#120	1	1	yes	characteristic
854	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
856	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
857	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
858	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
859	C₂×C₄²	C₂×#99	1	4	yes	—
860	C₂×C₄²	C₂×#99	1	4	yes	—
861	C₂×C₄²	C₂×#99	1	4	yes	—
862	C₂×C₄²	C₂×#99	1	4	yes	—
863	C₂×C₄²	C₂×#99	1	4	yes	—
864	C₂×C₄²	C₂×#99	1	4	yes	—
865	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
866	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
867	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
868	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
869	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
870	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
871	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
872	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
873	C₂⁴	#1781	1	4	yes	—
874	C₂⁴	C₂×#379	1	2	yes	—
875	C₂⁴	C₂×#379	1	1	yes	characteristic
876	C₂⁴	C₂×#379	1	1	yes	characteristic
877	C₂⁴	C₂×#379	1	2	yes	—
878	C₂⁴	C₂×#379	1	1	yes	characteristic
879	C₂⁴	C₂×#379	1	1	yes	characteristic
880	C₂⁴	C₂×#379	1	1	yes	characteristic
881	C₂⁴	C₂×#379	1	1	yes	characteristic
882	C₂⁴	C₂³×C₂²⋊C₄	1	2	yes	—
883	C₂⁴	C₂²×#120	1	2	yes	—
884	C₂⁴	C₂²×#120	1	1	yes	characteristic
885	C₂×Q₈	C₂²×#99	1	2	yes	—
886	C₂×Q₈	C₂²×#99	1	2	yes	—
887	C₂×D₄	C₂²×#99	1	2	yes	—
888	C₂×D₄	C₂²×#99	1	2	yes	—
889	C₂²×C₄	#1781	1	4	yes	—
890	C₂²×C₄	#1781	1	4	yes	—
891	C₂²×C₄	#1781	1	4	yes	—
892	C₂²×C₄	C₂×#379	1	1	yes	characteristic
893	C₂²×C₄	C₂×#379	1	1	yes	characteristic
894	C₂²×C₄	C₂×#379	1	2	yes	—
895	C₂²×C₄	C₂×#379	1	2	yes	—
896	C₂²×C₄	C₂×#379	1	2	yes	—
897	C₂²×C₄	C₂×#379	1	2	yes	—
898	C₂²×C₄	C₂×#379	1	1	yes	characteristic
899	C₂²×C₄	C₂×#379	1	1	yes	characteristic
900	C₂²×C₄	C₂×#379	1	1	yes	characteristic
901	C₂²×C₄	C₂×#379	1	1	yes	characteristic
902	C₂²×C₄	C₂²×#99	1	2	yes	—
903	C₂²×C₄	C₂²×#99	1	2	yes	—
904	C₂²×C₄	C₂²×#99	1	2	yes	—
905	C₂²×C₄	C₂²×#99	1	2	yes	—
906	C₂²×C₄	C₂²×#99	1	2	yes	—
907	C₂²×C₄	C₂²×#99	1	2	yes	—
908	C₂²×C₄	#3026	1	2	yes	—
909	C₂²×C₄	#3026	1	2	yes	—
910	C₂²×C₄	#3026	1	4	yes	—
911	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
912	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
913	C₄²	C₂²×#99	1	2	yes	—
914	C₄²	C₂²×#99	1	2	yes	—
915	C₄²	C₂²×#99	1	2	yes	—
916	C₄²	C₂²×#99	1	2	yes	—
917	C₂³	C₂×#1781	1	2	yes	—
918	C₂³	C₂×#1781	1	2	yes	—
919	C₂³	C₂×#1781	1	2	yes	—
920	C₂³	#20609	1	2	yes	—
921	C₂³	C₂²×#379	1	1	yes	characteristic
922	C₂³	C₂×#3026	1	2	yes	—
923	C₂×C₄	C₂×#1781	1	2	yes	—
924	C₂×C₄	C₂×#1781	1	2	yes	—
925	C₂×C₄	C₂×#1781	1	2	yes	—
926	C₂×C₄	#20609	1	2	yes	—
927	C₂×C₄	#20609	1	1	yes	characteristic
928	C₂×C₄	#20609	1	2	yes	—
929	C₂×C₄	#20609	1	1	yes	characteristic
930	C₂×C₄	C₂³×#99	1	1	yes	characteristic
931	C₂×C₄	C₂³×#99	1	1	yes	characteristic
932	C₂×C₄	C₂×#3026	1	2	yes	—
933	C₂²	C₂²×#1781	1	1	yes	characteristic
934	C₂²	C₂×#20609	1	1	yes	characteristic
935	C₂²	C₂×#20609	1	1	yes	characteristic
936	C₄	#187944	1	2	yes	—
937	C₄	#187944	1	2	yes	—
938	C₂	#72303375	1	2	yes	—
939	C₂	C₂×#187944	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#20609
commutator	C₂²×D₄	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
socle	C₂²	C₂×#20609
prime radical	#72257321	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#585 ◁ 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. #72311068	C₂	semidirect
2. #72310819	C₂	semidirect
3. #72310800	C₂	semidirect
4. #72310748	C₂	semidirect
5. #72310726	C₂	semidirect
6. #72306399	C₂	semidirect
7. #72306339	C₂	semidirect
8. #72303390	C₂	semidirect
9. #72303382	C₂	semidirect
10. #72302959	C₂	semidirect
11. #72302947	C₂	semidirect
14. C₂²×#3481	C₄	semidirect
16. #7739315	C₄	semidirect
17. #7739265	C₄	semidirect
19. #7737652	C₄	semidirect
21. #7737411	C₄	semidirect
23. #7737041	C₄	semidirect
25. #7708257	C₄	semidirect
27. #7666965	C₄	semidirect
29. #7634872	C₄	semidirect
31. #7625999	C₄	semidirect
32. #6370703	C₂²	semidirect
33. #6370692	C₂²	semidirect
34. #6370692	C₂²	semidirect
35. #496239	C₂²	semidirect
36. #496238	C₂²	semidirect
37. #496237	C₂²	semidirect
38. #494676	C₂²	semidirect
39. #493434	C₂²	semidirect
40. #493433	C₂²	semidirect
42. #493430	C₂²	semidirect
43. #493369	C₂²	semidirect
44. #493365	C₂²	semidirect
45. #382444	C₂²	semidirect
46. #382444	C₂²	semidirect
48. #382443	C₂²	semidirect
49. #357478	C₂²	semidirect
50. #357451	C₂²	semidirect
51. #213832	C₂²	semidirect
52. #213831	C₂²	semidirect
53. #213829	C₂²	semidirect
54. #201660	C₂²	semidirect
55. #133358	C₂²	semidirect
56. #133357	C₂²	semidirect
57. #133356	C₂²	semidirect
58. #133334	C₂²	semidirect
59. #133333	C₂²	semidirect
60. #133332	C₂²	semidirect
79. C₂×#3481	C₂×C₄	semidirect
80. C₂×#3481	C₂×C₄	semidirect
81. C₂×#3481	C₂×C₄	semidirect
82. C₂×#3481	C₂×C₄	semidirect
83. C₂²×#559	C₂×C₄	semidirect
84. C₂²×#551	C₂×C₄	semidirect
85. C₂²×D₄²	C₂×C₄	semidirect
102. C₂²×#413	C₂³	semidirect
103. #59184	C₂×C₄	semidirect
104. #59184	C₂×C₄	semidirect
105. #59162	C₂×C₄	semidirect
107. #59143	C₂×C₄	semidirect
109. #59126	C₂×C₄	semidirect
111. #59070	C₂×C₄	semidirect
112. #59070	C₂×C₄	semidirect
113. #59041	C₂×C₄	semidirect
114. #59041	C₂×C₄	semidirect
115. #52165	C₂×C₄	semidirect
116. #52165	C₂×C₄	semidirect
117. #52054	C₂×C₄	semidirect
118. #52054	C₂×C₄	semidirect
119. #52054	C₂×C₄	semidirect
121. #52004	C₂×C₄	semidirect
122. #52004	C₂×C₄	semidirect
123. #52004	C₂×C₄	semidirect
125. #51895	C₂×C₄	semidirect
127. #51530	C₂×C₄	semidirect
128. #51530	C₂×C₄	semidirect
129. #37374	C₂×C₄	semidirect
130. #37269	C₂×C₄	semidirect
131. #36955	C₂×C₄	semidirect
132. #36955	C₂×C₄	semidirect
133. #36702	C₂×C₄	semidirect
134. #36702	C₂×C₄	semidirect
151. #34369	C₂×C₄	semidirect
152. #34368	C₂×C₄	semidirect
153. #34366	C₂×C₄	semidirect
154. #34364	C₂×C₄	semidirect
155. #34364	C₂×C₄	semidirect
156. #34346	C₂×C₄	semidirect
157. #34155	C₂×C₄	semidirect
161. #34044	C₂³	semidirect
163. #20592	C₂³	semidirect
166. #20586	C₂³	semidirect
167. #20585	C₂³	semidirect
168. #20584	C₂³	semidirect
170. #13080	C₂³	semidirect
172. #12696	C₂³	semidirect
173. #12694	C₂³	semidirect
176. #10989	C₂³	semidirect
177. #10977	C₂³	semidirect
179. #9501	C₂³	semidirect
452. C₂²×#41	#99	semidirect
694. C₂²×C₄²	#99	semidirect

Maximal subgroups

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

subgroup	index
#72311068	2
#72310819	2
#72310800	2
#72310748	2
#72310726	2
#72306399	2
#72306339	2
#72303390	2
#72303382	2
#72302959	2
#72302947	2
#72257321	2