Subgroups — #72341652

Order 4096.

Only the 2121 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 1014 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341642	C₂	1	1	yes	maximal, characteristic, complemented
2	#72341618	C₂	1	1	yes	maximal, characteristic
3	C₂×#72241333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72241304	C₂	1	1	yes	maximal, characteristic, complemented
5	#72341589	C₂	1	2	yes	maximal, complemented
6	#72341588	C₂	1	2	yes	maximal, complemented
7	#72341315	C₂	1	8	yes	maximal, complemented
8	#72341312	C₂²	1	4	yes	complemented
9	C₂×#10574064	C₂²	1	1	yes	characteristic, complemented
10	#72341290	C₂	1	4	yes	maximal, complemented
11	#72341286	C₂²	1	8	yes	complemented
12	C₂×#72241315	C₂	1	1	yes	maximal, characteristic, complemented
13	#72340255	C₂	1	2	yes	maximal, complemented
14	C₂×#356056	C₂²	1	1	yes	characteristic, complemented
15	#72340216	C₂²	1	2	yes	—
16	C₂×#494596	C₄	1	2	yes	complemented
17	#72312192	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#6379033	C₂²	1	1	yes	characteristic
19	#72312182	C₂²	1	1	yes	characteristic
20	#72312147	C₂²	1	2	yes	complemented
21	#72311401	C₂	1	2	yes	maximal, complemented
22	C₂×#360531	C₂²	1	1	yes	characteristic, complemented
23	#72311246	C₂²	1	4	yes	complemented
24	#72311172	C₂²	1	2	yes	—
25	#72311152	C₂²	1	8	yes	complemented
26	C₂×#128079	C₂²	1	2	yes	complemented
27	C₂×#72238010	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×#493430	C₂²	1	1	yes	characteristic
29	C₂×#493430	C₂²	1	1	yes	characteristic
30	C₂×#359605	C₂²	1	1	yes	characteristic
31	C₂×#146577	C₂²	1	2	yes	complemented
32	C₂×#146577	C₂²	1	2	yes	complemented
33	C₂×#146577	C₂²	1	2	yes	complemented
34	C₂×#128062	C₂²	1	2	yes	complemented
35	C₂×#6385980	C₂²	1	1	yes	characteristic
36	#72306899	C₄	1	2	yes	complemented
37	#72306899	C₂²	1	2	yes	—
38	#72306419	C₄	1	4	yes	complemented
39	#72306419	C₂²	1	4	yes	—
40	#72306279	C₂²	1	2	yes	—
41	#72306279	C₂²	1	2	yes	—
42	#72306279	C₂²	1	2	yes	—
43	#72303064	C₂²	1	2	yes	complemented
44	#72303055	C₂²	1	8	yes	complemented
45	#72283936	C₂²	1	8	yes	complemented
46	C₂×#392138	C₂²	1	1	yes	characteristic, complemented
47	#72256607	C₄	1	4	yes	complemented
48	C₂²×#33557	C₄	1	2	yes	complemented
49	C₂²×#60388	C₂²	1	1	yes	characteristic
50	#72241340	C₂	1	4	yes	maximal, complemented
51	#72241337	C₂²	1	8	yes	complemented
52	#72241333	C₂²	1	4	yes	complemented
53	#72241333	C₂²	1	4	yes	complemented
54	#72241332	C₂²	1	8	yes	complemented
55	#72241315	C₂²	1	4	yes	—
56	#72241315	C₂²	1	4	yes	complemented
57	#72241304	C₂²	1	4	yes	—
58	#72241304	C₂²	1	4	yes	complemented
59	#72240597	C₂²	1	2	yes	—
60	C₂×#392135	C₂²	1	2	yes	complemented
61	#72238013	C₂²	1	8	yes	complemented
62	#72238010	C₂²	1	4	yes	complemented
63	#72238010	C₂²	1	4	yes	complemented
64	#72236711	C₂²	1	2	yes	complemented
65	#72234146	C₄	1	2	yes	complemented
66	#72234146	C₂²	1	2	yes	—
67	#72233917	C₂²	1	2	yes	complemented
68	#72213513	C₂²	1	8	yes	complemented
69	C₂²×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
70	C₂²×#3543	C₂×C₄	1	1	yes	characteristic
71	C₂²×#3498	C₂³	1	1	yes	characteristic
72	C₂²×#3026	C₂×C₄	1	4	yes	complemented
73	C₂×#60388	C₂×C₄	1	2	yes	—
74	C₂×#60388	C₂×C₄	1	2	yes	—
75	C₂×#60388	D₄	1	2	yes	—
76	C₂×#60388	D₄	1	2	yes	—
77	C₂×#60388	D₄	1	2	yes	—
78	C₂×#60388	D₄	1	2	yes	—
79	C₂×#60388	C₂³	1	2	yes	—
80	C₂×#60388	C₂³	1	2	yes	—
81	C₂²×#3018	D₄	1	1	yes	characteristic
82	C₂²×#3018	D₄	1	1	yes	characteristic
83	C₂²×#3021	D₄	1	1	yes	characteristic
84	C₂²×#3021	D₄	1	1	yes	characteristic
85	C₂²×#3019	C₂×C₄	1	2	yes	—
86	C₂²×#3019	D₄	1	2	yes	—
87	C₂³×#453	C₂×C₄	1	2	yes	—
88	C₂³×#453	D₄	1	2	yes	—
89	#10574064	C₂³	1	4	yes	—
90	C₂²×#2888	D₄	1	1	yes	characteristic, complemented
91	C₂²×#2888	C₂³	1	1	yes	characteristic
92	C₂²×#2888	C₂³	1	1	yes	characteristic
93	C₂²×#2888	C₂³	1	1	yes	characteristic
94	#7743195	C₂×C₄	1	2	yes	—
95	#7743195	C₂³	1	2	yes	—
96	#7737652	C₂×C₄	1	1	yes	characteristic
97	#7737652	C₂³	1	1	yes	characteristic
98	#7737411	C₂×C₄	1	1	yes	characteristic
99	#7737411	C₂³	1	1	yes	characteristic
100	#7642008	C₂×C₄	1	2	yes	—
101	#7630442	C₂³	1	2	yes	—
102	C₂×#34364	C₂×C₄	1	1	yes	characteristic
103	C₂²×#2200	C₂×C₄	1	8	yes	complemented
104	C₂²×#2198	C₂×C₄	1	4	yes	complemented
105	C₂²×#2196	C₂×C₄	1	4	yes	complemented
106	C₂²×#2127	C₂×C₄	1	2	yes	—
107	C₂³×#353	C₂×C₄	1	2	yes	—
108	C₂²×#2121	C₂×C₄	1	4	yes	complemented
109	C₂²×#2121	D₄	1	4	yes	complemented
110	#6628897	C₂×C₄	1	4	yes	complemented
111	#6628897	C₂³	1	4	yes	—
112	#6628896	C₂×C₄	1	4	yes	complemented
113	#6628896	C₂³	1	4	yes	—
114	#6385980	C₂³	1	2	yes	—
115	#6385980	C₂³	1	2	yes	—
116	#6379033	D₄	1	2	yes	complemented
117	#6379033	D₄	1	2	yes	complemented
118	#6379033	C₂³	1	2	yes	—
119	#6379033	C₂³	1	2	yes	—
120	C₂×#20637	D₄	1	1	yes	characteristic, complemented
121	C₂×#20609	C₂×C₄	1	4	yes	complemented
122	C₂×#20592	D₄	1	1	yes	characteristic, complemented
123	C₂×#20592	C₂³	1	1	yes	characteristic
124	C₂×#20586	C₂³	1	1	yes	characteristic
125	C₂×#20585	C₂³	1	2	yes	—
126	C₂×#20585	C₂³	1	2	yes	—
127	C₂×#20585	C₂³	1	2	yes	—
128	C₂×C₄×#413	D₄	1	1	yes	characteristic, complemented
129	#498928	C₂×C₄	1	8	yes	complemented
130	#498928	C₂×C₄	1	8	yes	complemented
131	#498927	C₂×C₄	1	8	yes	complemented
132	#498927	C₂×C₄	1	8	yes	complemented
133	#496241	C₂³	1	4	yes	—
134	#496240	C₂³	1	4	yes	—
135	#494682	C₂×C₄	1	4	yes	complemented
136	#494682	D₄	1	4	yes	complemented
137	#494682	C₂³	1	4	yes	—
138	#494682	C₂³	1	4	yes	—
139	#494682	C₂³	1	4	yes	—
140	#494681	C₂×C₄	1	4	yes	complemented
141	#494681	D₄	1	4	yes	complemented
142	#494681	C₂³	1	4	yes	—
143	#494681	C₂³	1	4	yes	—
144	#494681	C₂³	1	4	yes	—
145	#494596	C₂×C₄	1	4	yes	complemented
146	#494596	C₂×C₄	1	4	yes	complemented
147	#494596	C₂×C₄	1	8	yes	complemented
148	#493430	C₂×C₄	1	2	yes	—
149	#493430	C₂×C₄	1	2	yes	—
150	#493430	C₂³	1	2	yes	—
151	#493430	C₂³	1	2	yes	—
152	#493430	C₂³	1	2	yes	—
153	#493430	C₂³	1	2	yes	—
154	C₂×#12574	C₂×C₄	1	4	yes	complemented
155	C₂×#12574	D₄	1	4	yes	complemented
156	#392138	C₂³	1	4	yes	—
157	#392135	C₂³	1	8	yes	—
158	#360531	C₂³	1	4	yes	—
159	#359605	D₄	1	2	yes	complemented
160	#359605	D₄	1	2	yes	complemented
161	#359605	C₂³	1	2	yes	—
162	#359605	C₂³	1	2	yes	—
163	C₂×#10989	D₄	1	2	yes	complemented
164	C₂×#10975	D₄	1	2	yes	complemented
165	#356056	C₂³	1	4	yes	—
166	#213855	C₂³	1	4	yes	—
167	#213854	C₂³	1	4	yes	—
168	#146577	C₂³	1	8	yes	—
169	#146577	C₂³	1	8	yes	—
170	#146577	C₂³	1	8	yes	—
171	#128079	C₂³	1	8	yes	—
172	#128062	C₂³	1	8	yes	—
173	C₂×H(7,𝔽₂)	C₂²×C₄	1	2	yes	—
174	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
175	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
176	C₂×H(7,𝔽₂)	C₂⁴	1	2	yes	—
177	C₂²×#585	C₂×D₄	1	1	yes	characteristic
178	C₂²×#585	C₂×D₄	1	1	yes	characteristic
179	C₂³×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
180	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
181	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
182	C₂³×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
183	C₂×#3498	C₂²×C₄	1	1	yes	characteristic
184	C₂×#3498	C₂²×C₄	1	1	yes	characteristic
185	C₂×#3498	C₂×D₄	1	1	yes	characteristic
186	C₂×#3498	C₂×D₄	1	1	yes	characteristic
187	C₂×#3498	C₂×D₄	1	1	yes	characteristic
188	C₂×#3498	C₂×D₄	1	1	yes	characteristic
189	C₂×#3498	C₂×D₄	1	1	yes	characteristic
190	C₂×#3498	C₂×D₄	1	1	yes	characteristic
191	C₂×#3498	C₂×D₄	1	1	yes	characteristic
192	C₂×#3498	C₂×D₄	1	1	yes	characteristic
193	C₂×#3498	#41	1	1	yes	characteristic
194	C₂×#3498	#41	1	1	yes	characteristic
195	C₂×#3498	#41	1	1	yes	characteristic
196	C₂×#3498	#41	1	1	yes	characteristic
197	C₂×#3498	C₂⁴	1	1	yes	characteristic
198	C₂×#3498	C₂⁴	1	1	yes	characteristic
199	C₂²×#559	C₂²×C₄	1	1	yes	characteristic
200	C₂²×D₄²	C₂²×C₄	1	1	yes	characteristic
201	C₂²×#560	C₂²×C₄	1	2	yes	—
202	C₂²×#535	C₂²×C₄	1	1	yes	characteristic
203	C₂²×#535	C₂×D₄	1	1	yes	characteristic
204	C₂²×#535	C₂×D₄	1	1	yes	characteristic
205	C₂²×#535	C₂×D₄	1	1	yes	characteristic
206	C₂²×#535	#41	1	1	yes	characteristic
207	C₂²×#535	#41	1	1	yes	characteristic
208	C₂²×#534	C₂²×C₄	1	2	yes	—
209	C₂²×#534	C₂×D₄	1	2	yes	—
210	C₂²×#534	#41	1	2	yes	—
211	C₂²×#532	C₂×D₄	1	1	yes	characteristic
212	C₂²×#532	#41	1	1	yes	characteristic
213	C₂²×#532	#41	1	1	yes	characteristic
214	C₂³×#127	C₂²×C₄	1	1	yes	characteristic
215	C₂³×#127	C₂×D₄	1	1	yes	characteristic
216	C₂³×#127	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×#41	C₂×D₄	1	1	yes	characteristic
218	C₂²×#458	C₂²×C₄	1	8	yes	complemented
219	C₂²×B(4,𝔽₂)	C₂²×C₄	1	8	yes	complemented
220	C₂×#3021	C₂²⋊C₄	1	2	yes	—
221	C₂×#3021	C₂²⋊C₄	1	2	yes	—
222	C₂×#3021	C₂²⋊C₄	1	2	yes	—
223	C₂×#3021	C₂²⋊C₄	1	2	yes	—
224	C₂×#3021	C₂×D₄	1	2	yes	—
225	C₂×#3021	C₂×D₄	1	2	yes	—
226	C₂×#3021	C₂×D₄	1	2	yes	—
227	C₂×#3021	C₂×D₄	1	2	yes	—
228	C₂×#3019	C₂²⋊C₄	1	4	yes	—
229	C₂×#3019	C₂²⋊C₄	1	4	yes	—
230	C₂×#3019	C₂²⋊C₄	1	4	yes	—
231	C₂×#3019	C₂²⋊C₄	1	4	yes	—
232	C₂×#3019	C₂²×C₄	1	4	yes	—
233	C₂×#3019	C₂²×C₄	1	4	yes	—
234	C₂×#3019	C₂×D₄	1	4	yes	—
235	C₂×#3019	C₂×D₄	1	4	yes	—
236	C₂×#3018	C₂²⋊C₄	1	2	yes	—
237	C₂×#3018	C₂²⋊C₄	1	2	yes	—
238	C₂×#3018	C₂²⋊C₄	1	2	yes	—
239	C₂×#3018	C₂²⋊C₄	1	2	yes	—
240	C₂×#3018	C₂×D₄	1	2	yes	—
241	C₂×#3018	C₂×D₄	1	2	yes	—
242	C₂×#3018	C₂×D₄	1	2	yes	—
243	C₂×#3018	C₂×D₄	1	2	yes	—
244	C₂²×#455	C₂²⋊C₄	1	2	yes	—
245	C₂²×#455	C₂²⋊C₄	1	2	yes	—
246	C₂²×#453	C₂²⋊C₄	1	2	yes	—
247	C₂²×#453	C₂²⋊C₄	1	2	yes	—
248	C₂²×#453	C₂²⋊C₄	1	2	yes	—
249	C₂²×#453	C₂²⋊C₄	1	2	yes	—
250	C₂²×#453	C₂²⋊C₄	1	4	yes	—
251	C₂²×#453	C₂²⋊C₄	1	4	yes	—
252	C₂²×#453	C₂²⋊C₄	1	2	yes	—
253	C₂²×#453	C₂²⋊C₄	1	2	yes	—
254	C₂²×#453	C₂²⋊C₄	1	4	yes	—
255	C₂²×#453	C₂²⋊C₄	1	4	yes	—
256	C₂²×#453	C₂²×C₄	1	4	yes	—
257	C₂²×#453	C₂²×C₄	1	4	yes	—
258	C₂²×#453	C₂×D₄	1	4	yes	—
259	C₂²×#453	C₂×D₄	1	4	yes	—
260	C₂×#2888	C₂²×C₄	1	2	yes	—
261	C₂×#2888	C₂×D₄	1	2	yes	—
262	C₂×#2888	C₂×D₄	1	2	yes	—
263	C₂×#2888	C₂×D₄	1	2	yes	—
264	C₂×#2888	C₂×D₄	1	4	yes	—
265	C₂×#2888	C₂×D₄	1	2	yes	—
266	C₂×#2888	C₂×D₄	1	2	yes	—
267	C₂×#2888	C₂×D₄	1	2	yes	—
268	C₂×#2888	C₂⁴	1	2	yes	—
269	C₂×#2888	C₂⁴	1	2	yes	—
270	C₂×#2888	C₂⁴	1	2	yes	—
271	C₂²×#413	C₂×D₄	1	1	yes	characteristic
272	C₂²×#413	C₂×D₄	1	1	yes	characteristic
273	C₂²×#413	C₂×D₄	1	1	yes	characteristic
274	C₂²×#413	C₂×D₄	1	1	yes	characteristic
275	C₂²×#413	C₂×D₄	1	1	yes	characteristic
276	C₂²×#413	C₂×D₄	1	1	yes	characteristic
277	C₂³×#100	C₂²×C₄	1	2	yes	—
278	C₂³×#100	C₂×D₄	1	2	yes	—
279	C₂³×#100	C₂×D₄	1	4	yes	—
280	C₂³×#100	C₂×D₄	1	2	yes	—
281	C₂³×#99	C₂²×C₄	1	4	yes	—
282	C₂³×#99	C₂×D₄	1	4	yes	—
283	#36955	C₂²×C₄	1	2	yes	—
284	#36955	C₂²×C₄	1	2	yes	—
285	#36702	C₂²×C₄	1	2	yes	—
286	#36702	C₂²×C₄	1	2	yes	—
287	#35446	C₂²×C₄	1	2	yes	—
288	#35446	C₂×D₄	1	2	yes	—
289	#35446	#41	1	2	yes	—
290	#35446	C₂⁴	1	2	yes	—
291	#35346	C₂²×C₄	1	2	yes	—
292	#35346	C₂×D₄	1	2	yes	—
293	#35346	#41	1	2	yes	—
294	#35346	C₂⁴	1	2	yes	—
295	#34364	C₂²×C₄	1	1	yes	characteristic
296	#34364	C₂²×C₄	1	1	yes	characteristic
297	#34364	C₂²×C₄	1	2	yes	—
298	C₂×#2309	C₂×D₄	1	2	yes	—
299	C₂×#2308	C₂²×C₄	1	2	yes	—
300	C₂×#2308	C₂×D₄	1	2	yes	—
301	C₂×#2308	#41	1	2	yes	—
302	C₂×#2127	C₂²×C₄	1	4	yes	—
303	C₂×#2127	C₂²×C₄	1	4	yes	—
304	C₂²×#353	C₂²×C₄	1	4	yes	—
305	C₂²×#353	C₂²×C₄	1	4	yes	—
306	C₂²×#352	C₂²×C₄	1	8	yes	complemented
307	C₂²×#352	C₂×D₄	1	8	yes	—
308	C₂²×AΣL(1,𝔽₁₆)	C₂²×C₄	1	8	yes	complemented
309	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	8	yes	—
310	#20637	C₂×D₄	1	2	yes	—
311	#20637	C₂×D₄	1	2	yes	—
312	#20609	C₂²×C₄	1	8	yes	complemented
313	#20609	C₂²×C₄	1	8	yes	complemented
314	#20592	C₂×D₄	1	2	yes	—
315	#20592	C₂×D₄	1	2	yes	—
316	#20592	C₂×D₄	1	2	yes	—
317	#20592	C₂⁴	1	2	yes	—
318	#20586	C₂×D₄	1	2	yes	—
319	#20586	C₂⁴	1	2	yes	—
320	#20585	C₂²×C₄	1	4	yes	—
321	#20585	C₂×D₄	1	4	yes	—
322	#20585	C₂⁴	1	4	yes	—
323	#20585	C₂⁴	1	4	yes	—
324	#20585	C₂⁴	1	4	yes	—
325	C₄×#413	C₂×D₄	1	2	yes	—
326	C₄×#413	C₂×D₄	1	2	yes	—
327	#12574	C₂²×C₄	1	8	yes	complemented
328	#12574	C₂²×C₄	1	8	yes	complemented
329	#12574	C₂×D₄	1	8	yes	—
330	#12574	C₂×D₄	1	8	yes	—
331	#10989	C₂×D₄	1	4	yes	—
332	#10989	C₂×D₄	1	4	yes	—
333	#10975	C₂×D₄	1	4	yes	—
334	#10975	C₂×D₄	1	4	yes	—
335	C₂×#585	C₂×C₂²⋊C₄	1	2	yes	—
336	C₂×#585	C₂×C₂²⋊C₄	1	2	yes	—
337	C₂×#585	C₂²×D₄	1	2	yes	—
338	C₂×#585	C₂²×D₄	1	2	yes	—
339	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
340	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
341	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
342	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂²×H(5,𝔽₂)	C₄×D₄	1	1	yes	characteristic
344	C₂²×H(5,𝔽₂)	C₄×D₄	1	1	yes	characteristic
345	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
346	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
347	C₂²×H(5,𝔽₂)	#121	1	1	yes	characteristic
348	C₂²×H(5,𝔽₂)	#121	1	1	yes	characteristic
349	C₂²×H(5,𝔽₂)	C₂³×C₄	1	1	yes	characteristic
350	C₂²×H(5,𝔽₂)	C₂³×C₄	1	4	yes	—
351	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
352	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
353	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
354	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
355	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
356	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
357	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
358	C₂²×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
359	C₂²×H(5,𝔽₂)	C₂×#41	1	1	yes	characteristic
360	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
361	C₂²×H(5,𝔽₂)	C₂×#41	1	1	yes	characteristic
362	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
363	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
364	C₂²×H(5,𝔽₂)	C₂⁵	1	1	yes	characteristic
365	C₂³×#41	C₄×D₄	1	1	yes	characteristic
366	C₂³×#41	#120	1	1	yes	characteristic
367	C₂³×#41	#121	1	1	yes	characteristic
368	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
369	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
370	C₂³×#41	C₂×#41	1	1	yes	characteristic
371	C₂³×#41	C₂×#41	1	1	yes	characteristic
372	C₂³×#41	H(5,𝔽₂)	1	2	yes	—
373	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
374	C₂⁴×D₄	C₄×D₄	1	2	yes	—
375	C₂⁴×D₄	#120	1	1	yes	characteristic
376	C₂⁴×D₄	#121	1	1	yes	characteristic
377	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
378	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
379	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
380	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
381	C₂⁴×D₄	C₂×#41	1	2	yes	—
382	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
383	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
386	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×#535	C₄×D₄	1	1	yes	characteristic
390	C₂×#535	C₄×D₄	1	1	yes	characteristic
391	C₂×#535	C₄×D₄	1	1	yes	characteristic
392	C₂×#535	C₄×D₄	1	1	yes	characteristic
393	C₂×#535	C₄×D₄	1	1	yes	characteristic
394	C₂×#535	C₄×D₄	1	1	yes	characteristic
395	C₂×#535	C₄×D₄	1	1	yes	characteristic
396	C₂×#535	C₄×D₄	1	1	yes	characteristic
397	C₂×#535	C₄×D₄	1	1	yes	characteristic
398	C₂×#535	C₄×D₄	1	1	yes	characteristic
399	C₂×#535	#120	1	1	yes	characteristic
400	C₂×#535	#120	1	1	yes	characteristic
401	C₂×#535	#120	1	1	yes	characteristic
402	C₂×#535	#120	1	1	yes	characteristic
403	C₂×#535	#121	1	1	yes	characteristic
404	C₂×#535	#121	1	1	yes	characteristic
405	C₂×#535	#121	1	1	yes	characteristic
406	C₂×#535	#121	1	1	yes	characteristic
407	C₂×#535	#121	1	1	yes	characteristic
408	C₂×#535	#121	1	1	yes	characteristic
409	C₂×#535	#121	1	1	yes	characteristic
410	C₂×#535	#121	1	1	yes	characteristic
411	C₂×#535	#121	1	1	yes	characteristic
412	C₂×#535	#121	1	1	yes	characteristic
413	C₂×#535	#123	1	1	yes	characteristic
414	C₂×#535	#123	1	1	yes	characteristic
415	C₂×#535	#123	1	1	yes	characteristic
416	C₂×#535	#123	1	1	yes	characteristic
417	C₂×#535	#123	1	1	yes	characteristic
418	C₂×#535	#123	1	1	yes	characteristic
419	C₂×#535	C₂³×C₄	1	1	yes	characteristic
420	C₂×#535	C₂³×C₄	1	1	yes	characteristic
421	C₂×#535	C₂²×D₄	1	1	yes	characteristic
422	C₂×#535	C₂²×D₄	1	1	yes	characteristic
423	C₂×#535	C₂²×D₄	1	1	yes	characteristic
424	C₂×#535	C₂²×D₄	1	1	yes	characteristic
425	C₂×#535	C₂²×D₄	1	1	yes	characteristic
426	C₂×#535	C₂²×D₄	1	1	yes	characteristic
427	C₂×#535	C₂×#41	1	1	yes	characteristic
428	C₂×#535	C₂×#41	1	1	yes	characteristic
429	C₂×#535	C₂×#41	1	1	yes	characteristic
430	C₂×#535	C₂×#41	1	1	yes	characteristic
431	C₂×#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
433	C₂×#532	C₄×D₄	1	1	yes	characteristic
434	C₂×#532	C₄×D₄	1	1	yes	characteristic
435	C₂×#532	C₄×D₄	1	1	yes	characteristic
436	C₂×#532	C₄×D₄	1	1	yes	characteristic
437	C₂×#532	#120	1	1	yes	characteristic
438	C₂×#532	#120	1	1	yes	characteristic
439	C₂×#532	#121	1	1	yes	characteristic
440	C₂×#532	#121	1	1	yes	characteristic
441	C₂×#532	#121	1	1	yes	characteristic
442	C₂×#532	#121	1	1	yes	characteristic
443	C₂×#532	#123	1	1	yes	characteristic
444	C₂×#532	#123	1	1	yes	characteristic
445	C₂×#532	#123	1	1	yes	characteristic
446	C₂×#532	#123	1	1	yes	characteristic
447	C₂×#532	#123	1	1	yes	characteristic
448	C₂×#532	#123	1	1	yes	characteristic
449	C₂×#532	C₂²×D₄	1	1	yes	characteristic
450	C₂×#532	C₂²×D₄	1	1	yes	characteristic
451	C₂×#532	C₂×#41	1	1	yes	characteristic
452	C₂×#532	C₂×#41	1	1	yes	characteristic
453	C₂×#532	C₂×#41	1	1	yes	characteristic
454	C₂×#532	C₂×#41	1	1	yes	characteristic
455	C₂²×C₄⋊Q₈	#123	1	1	yes	characteristic
456	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²×#127	C₄×D₄	1	1	yes	characteristic
464	C₂²×#127	C₄×D₄	1	1	yes	characteristic
465	C₂²×#127	C₄×D₄	1	1	yes	characteristic
466	C₂²×#127	C₄×D₄	1	1	yes	characteristic
467	C₂²×#127	C₄×D₄	1	1	yes	characteristic
468	C₂²×#127	C₄×D₄	1	1	yes	characteristic
469	C₂²×#127	C₄×D₄	1	1	yes	characteristic
470	C₂²×#127	C₄×D₄	1	1	yes	characteristic
471	C₂²×#127	C₄×D₄	1	1	yes	characteristic
472	C₂²×#127	#120	1	1	yes	characteristic
473	C₂²×#127	#120	1	1	yes	characteristic
474	C₂²×#127	#121	1	1	yes	characteristic
475	C₂²×#127	#121	1	1	yes	characteristic
476	C₂²×#127	#121	1	1	yes	characteristic
477	C₂²×#127	#121	1	1	yes	characteristic
478	C₂²×#127	#121	1	1	yes	characteristic
479	C₂²×#127	#121	1	1	yes	characteristic
480	C₂²×#127	#121	1	1	yes	characteristic
481	C₂²×#127	#121	1	1	yes	characteristic
482	C₂²×#127	#121	1	1	yes	characteristic
483	C₂²×#127	C₂³×C₄	1	1	yes	characteristic
484	C₂²×#127	C₂³×C₄	1	1	yes	characteristic
485	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
486	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
487	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
488	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
489	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
490	C₂²×#124	C₄×D₄	1	1	yes	characteristic
491	C₂²×#124	#121	1	1	yes	characteristic
492	C₂²×#124	#123	1	1	yes	characteristic
493	C₂²×#124	#123	1	1	yes	characteristic
494	C₂²×#124	#123	1	1	yes	characteristic
495	C₂²×#123	C₄×D₄	1	2	yes	—
496	C₂²×#123	C₄×D₄	1	2	yes	—
497	C₂²×#123	C₄×D₄	1	2	yes	—
498	C₂²×#123	C₂³×C₄	1	2	yes	—
499	C₂²×#123	C₂²×D₄	1	2	yes	—
500	C₂²×#123	C₂×#41	1	2	yes	—
501	C₂²×#120	C₄×D₄	1	2	yes	—
502	C₂²×#120	C₄×D₄	1	2	yes	—
503	C₂²×#120	C₄×D₄	1	2	yes	—
504	C₂²×#120	C₂³×C₄	1	2	yes	—
505	C₂²×#120	C₂²×D₄	1	2	yes	—
506	C₂²×#120	C₂×#41	1	2	yes	—
507	C₂×C₄×#41	C₄×D₄	1	1	yes	characteristic
508	C₂×C₄×#41	C₄×D₄	1	1	yes	characteristic
509	C₂×C₄×#41	#120	1	1	yes	characteristic
510	C₂×C₄×#41	#120	1	1	yes	characteristic
511	C₂×C₄×#41	#121	1	1	yes	characteristic
512	C₂×C₄×#41	#121	1	1	yes	characteristic
513	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
515	C₂²×#117	C₄×D₄	1	1	yes	characteristic
516	C₂²×#117	#120	1	1	yes	characteristic
517	C₂²×#117	#121	1	1	yes	characteristic
518	C₂³×C₂²⋊C₄	C₄×D₄	1	2	yes	—
519	C₂³×C₂²⋊C₄	C₄×D₄	1	2	yes	—
520	C₂³×C₂²⋊C₄	C₄×D₄	1	2	yes	—
521	C₂³×C₄²	C₄×D₄	1	1	yes	characteristic
522	C₂³×C₄²	#120	1	1	yes	characteristic
523	C₂³×C₄²	#121	1	1	yes	characteristic
524	C₂×#455	C₂×C₂²⋊C₄	1	4	yes	—
525	C₂×#455	C₂×C₂²⋊C₄	1	4	yes	—
526	C₂×#455	C₂×C₂²⋊C₄	1	4	yes	—
527	C₂×#455	C₂×C₂²⋊C₄	1	4	yes	—
528	C₂×#453	#99	1	16	yes	complemented
529	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
530	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
531	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
532	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
533	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
534	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
535	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
536	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
537	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
538	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
539	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
540	C₂×#453	C₂×C₂²⋊C₄	1	4	yes	—
541	C₂×#413	C₂×C₂²⋊C₄	1	2	yes	—
542	C₂×#413	C₂×C₂²⋊C₄	1	2	yes	—
543	C₂×#413	#120	1	2	yes	—
544	C₂×#413	#120	1	2	yes	—
545	C₂×#413	C₂²×D₄	1	2	yes	—
546	C₂×#413	C₂²×D₄	1	2	yes	—
547	C₂×#413	C₂²×D₄	1	2	yes	—
548	C₂×#413	C₂²×D₄	1	2	yes	—
549	C₂×#413	C₂²×D₄	1	2	yes	—
550	C₂×#413	C₂²×D₄	1	2	yes	—
551	C₂²×#100	C₂×C₂²⋊C₄	1	2	yes	—
552	C₂²×#100	C₂×C₂²⋊C₄	1	4	yes	—
553	C₂²×#100	C₂×C₂²⋊C₄	1	4	yes	—
554	C₂²×#100	C₂×C₂²⋊C₄	1	2	yes	—
555	C₂²×#100	#120	1	2	yes	—
556	C₂²×#100	#120	1	8	yes	—
557	C₂²×#100	#120	1	2	yes	—
558	C₂²×#100	C₂³×C₄	1	4	yes	—
559	C₂²×#100	C₂²×D₄	1	4	yes	—
560	C₂²×#100	C₂²×D₄	1	4	yes	—
561	C₂²×#100	C₂²×D₄	1	8	yes	—
562	C₂²×#99	C₂³×C₄	1	8	yes	—
563	C₂²×#99	C₂²×D₄	1	8	yes	—
564	#2309	C₂²×D₄	1	4	yes	—
565	#2308	C₄×D₄	1	2	yes	—
566	#2308	C₄×D₄	1	2	yes	—
567	#2308	C₄×D₄	1	2	yes	—
568	#2308	C₄×D₄	1	2	yes	—
569	#2308	C₄×D₄	1	2	yes	—
570	#2308	C₄×D₄	1	2	yes	—
571	#2308	C₂³×C₄	1	2	yes	—
572	#2308	C₂³×C₄	1	2	yes	—
573	#2308	C₂²×D₄	1	2	yes	—
574	#2308	C₂²×D₄	1	2	yes	—
575	#2308	C₂×#41	1	2	yes	—
576	#2308	C₂×#41	1	2	yes	—
577	C₂⁶	C₂×C₄×D₄	1	2	yes	—
578	C₂⁶	C₂×C₄×D₄	1	2	yes	—
579	C₂⁶	D₄²	1	2	yes	—
580	C₂⁶	#546	1	2	yes	—
581	C₂×H(5,𝔽₂)	C₂×#99	1	8	yes	—
582	C₂×H(5,𝔽₂)	C₂²×C₂²⋊C₄	1	4	yes	—
583	C₂×H(5,𝔽₂)	C₂²×C₂²⋊C₄	1	4	yes	—
584	C₂²×#41	#386	1	1	yes	characteristic
585	C₂²×#41	#386	1	1	yes	characteristic
586	C₂²×#41	#386	1	1	yes	characteristic
587	C₂²×#41	#386	1	1	yes	characteristic
588	C₂²×#41	#386	1	1	yes	characteristic
589	C₂²×#41	#386	1	1	yes	characteristic
590	C₂²×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
591	C₂²×#41	C₂×C₄×D₄	1	1	yes	characteristic
592	C₂²×#41	C₂×C₄×D₄	1	1	yes	characteristic
593	C₂²×#41	C₂×C₄×D₄	1	1	yes	characteristic
594	C₂²×#41	C₂×C₄×D₄	1	1	yes	characteristic
595	C₂²×#41	C₂×C₄×D₄	1	1	yes	characteristic
596	C₂²×#41	#518	1	2	yes	—
597	C₂²×#41	C₂×#120	1	1	yes	characteristic
598	C₂²×#41	C₂×#120	1	1	yes	characteristic
599	C₂²×#41	C₂×#120	1	1	yes	characteristic
600	C₂²×#41	C₂×#120	1	1	yes	characteristic
601	C₂²×#41	C₂×#120	1	1	yes	characteristic
602	C₂²×#41	C₂×#121	1	1	yes	characteristic
603	C₂²×#41	C₂×#121	1	1	yes	characteristic
604	C₂²×#41	C₂×#121	1	1	yes	characteristic
605	C₂²×#41	C₂×#121	1	1	yes	characteristic
606	C₂²×#41	C₂×#121	1	1	yes	characteristic
607	C₂²×#41	C₂×#123	1	1	yes	characteristic
608	C₂²×#41	C₂×#123	1	1	yes	characteristic
609	C₂²×#41	C₂×#123	1	1	yes	characteristic
610	C₂²×#41	#525	1	1	yes	characteristic
611	C₂²×#41	#525	1	2	yes	—
612	C₂²×#41	#534	1	1	yes	characteristic
613	C₂²×#41	#534	1	2	yes	—
614	C₂²×#41	#535	1	1	yes	characteristic
615	C₂²×#41	#538	1	2	yes	—
616	C₂²×#41	#538	1	2	yes	—
617	C₂²×#41	D₄²	1	2	yes	—
618	C₂²×#41	D₄²	1	2	yes	—
619	C₂²×#41	D₄²	1	2	yes	—
620	C₂²×#41	#546	1	2	yes	—
621	C₂²×#41	#546	1	2	yes	—
622	C₂²×#41	#546	1	2	yes	—
623	C₂²×#41	#551	1	2	yes	—
624	C₂²×#41	#551	1	2	yes	—
625	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
626	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
627	C₂²×#41	C₂²×#41	1	1	yes	characteristic
628	C₂²×#41	C₂²×#41	1	1	yes	characteristic
629	C₂²×#41	C₂×H(5,𝔽₂)	1	2	yes	—
630	C₂³×Q₈	#386	1	1	yes	characteristic
631	C₂³×Q₈	C₂×#123	1	1	yes	characteristic
632	C₂³×Q₈	#534	1	1	yes	characteristic
633	C₂³×D₄	#386	1	1	yes	characteristic
634	C₂³×D₄	#386	1	1	yes	characteristic
635	C₂³×D₄	#386	1	1	yes	characteristic
636	C₂³×D₄	#386	1	1	yes	characteristic
637	C₂³×D₄	#386	1	1	yes	characteristic
638	C₂³×D₄	#386	1	1	yes	characteristic
639	C₂³×D₄	#386	1	1	yes	characteristic
640	C₂³×D₄	#386	1	1	yes	characteristic
641	C₂³×D₄	#386	1	1	yes	characteristic
642	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
643	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
644	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
645	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
646	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
647	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
648	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
649	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
650	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
651	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
652	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
653	C₂³×D₄	C₂×C₄×D₄	1	2	yes	—
654	C₂³×D₄	#518	1	2	yes	—
655	C₂³×D₄	#518	1	2	yes	—
656	C₂³×D₄	#518	1	2	yes	—
657	C₂³×D₄	C₂×#120	1	1	yes	characteristic
658	C₂³×D₄	C₂×#120	1	2	yes	—
659	C₂³×D₄	C₂×#120	1	1	yes	characteristic
660	C₂³×D₄	C₂×#120	1	1	yes	characteristic
661	C₂³×D₄	C₂×#120	1	1	yes	characteristic
662	C₂³×D₄	C₂×#121	1	1	yes	characteristic
663	C₂³×D₄	C₂×#121	1	1	yes	characteristic
664	C₂³×D₄	C₂×#121	1	1	yes	characteristic
665	C₂³×D₄	C₂×#121	1	1	yes	characteristic
666	C₂³×D₄	C₂×#121	1	1	yes	characteristic
667	C₂³×D₄	C₂×#121	1	1	yes	characteristic
668	C₂³×D₄	#525	1	2	yes	—
669	C₂³×D₄	#525	1	2	yes	—
670	C₂³×D₄	#525	1	2	yes	—
671	C₂³×D₄	#525	1	1	yes	characteristic
672	C₂³×D₄	#525	1	2	yes	—
673	C₂³×D₄	#535	1	1	yes	characteristic
674	C₂³×D₄	#535	1	2	yes	—
675	C₂³×D₄	#538	1	2	yes	—
676	C₂³×D₄	D₄²	1	2	yes	—
677	C₂³×D₄	D₄²	1	2	yes	—
678	C₂³×D₄	D₄²	1	2	yes	—
679	C₂³×D₄	D₄²	1	2	yes	—
680	C₂³×D₄	D₄²	1	2	yes	—
681	C₂³×D₄	D₄²	1	2	yes	—
682	C₂³×D₄	D₄²	1	2	yes	—
683	C₂³×D₄	#546	1	2	yes	—
684	C₂³×D₄	#546	1	2	yes	—
685	C₂³×D₄	#546	1	2	yes	—
686	C₂³×D₄	#546	1	2	yes	—
687	C₂³×D₄	#546	1	2	yes	—
688	C₂³×D₄	#546	1	2	yes	—
689	C₂³×D₄	#546	1	2	yes	—
690	C₂³×D₄	#546	1	2	yes	—
691	C₂³×D₄	#546	1	2	yes	—
692	C₂³×D₄	#546	1	2	yes	—
693	C₂³×D₄	#546	1	2	yes	—
694	C₂³×D₄	#546	1	2	yes	—
695	C₂³×D₄	#551	1	2	yes	—
696	C₂³×D₄	C₂⁴×C₄	1	1	yes	characteristic
697	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
698	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
699	C₂³×D₄	C₂³×D₄	1	2	yes	—
700	C₂³×D₄	C₂²×#41	1	2	yes	—
701	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
702	C₂⁴×C₄	C₂×C₄×D₄	1	1	yes	characteristic
703	C₂⁴×C₄	C₂×C₄×D₄	1	2	yes	—
704	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
705	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
706	C₂⁴×C₄	#538	1	2	yes	—
707	C₂⁴×C₄	D₄²	1	2	yes	—
708	C₂⁴×C₄	#551	1	2	yes	—
709	C₂×C₄⋊Q₈	#386	1	1	yes	characteristic
710	C₂×C₄⋊Q₈	#386	1	1	yes	characteristic
711	C₂×C₄⋊Q₈	C₂×#123	1	1	yes	characteristic
712	C₂×C₄⋊Q₈	C₂×#123	1	1	yes	characteristic
713	C₂×#127	#386	1	1	yes	characteristic
714	C₂×#127	#386	1	1	yes	characteristic
715	C₂×#127	#386	1	1	yes	characteristic
716	C₂×#127	#386	1	1	yes	characteristic
717	C₂×#127	#386	1	1	yes	characteristic
718	C₂×#127	#386	1	1	yes	characteristic
719	C₂×#127	#386	1	1	yes	characteristic
720	C₂×#127	#386	1	1	yes	characteristic
721	C₂×#127	#386	1	1	yes	characteristic
722	C₂×#127	#386	1	1	yes	characteristic
723	C₂×#127	#386	1	1	yes	characteristic
724	C₂×#127	#386	1	1	yes	characteristic
725	C₂×#127	#386	1	1	yes	characteristic
726	C₂×#127	#386	1	1	yes	characteristic
727	C₂×#127	#386	1	1	yes	characteristic
728	C₂×#127	#386	1	1	yes	characteristic
729	C₂×#127	#386	1	1	yes	characteristic
730	C₂×#127	#386	1	1	yes	characteristic
731	C₂×#127	C₂×#99	1	8	yes	—
732	C₂×#127	C₂²×C₂²⋊C₄	1	1	yes	characteristic
733	C₂×#127	C₂²×C₂²⋊C₄	1	1	yes	characteristic
734	C₂×#127	C₂²×C₂²⋊C₄	1	1	yes	characteristic
735	C₂×#127	C₂²×C₂²⋊C₄	1	1	yes	characteristic
736	C₂×#127	C₂²×C₂²⋊C₄	1	1	yes	characteristic
737	C₂×#127	C₂²×C₂²⋊C₄	1	1	yes	characteristic
738	C₂×#127	C₂×C₄×D₄	1	1	yes	characteristic
739	C₂×#127	C₂×C₄×D₄	1	1	yes	characteristic
740	C₂×#127	C₂×C₄×D₄	1	1	yes	characteristic
741	C₂×#127	C₂×C₄×D₄	1	1	yes	characteristic
742	C₂×#127	C₂×C₄×D₄	1	1	yes	characteristic
743	C₂×#127	C₂×C₄×D₄	1	1	yes	characteristic
744	C₂×#127	C₂×#121	1	1	yes	characteristic
745	C₂×#127	C₂×#121	1	1	yes	characteristic
746	C₂×#127	C₂×#121	1	1	yes	characteristic
747	C₂×#127	C₂×#121	1	1	yes	characteristic
748	C₂×#127	C₂×#121	1	1	yes	characteristic
749	C₂×#127	C₂×#121	1	1	yes	characteristic
750	C₂×#124	#386	1	1	yes	characteristic
751	C₂×#124	#386	1	1	yes	characteristic
752	C₂×#124	#386	1	1	yes	characteristic
753	C₂×#124	#386	1	1	yes	characteristic
754	C₂×#124	#386	1	1	yes	characteristic
755	C₂×#124	#386	1	1	yes	characteristic
756	C₂×#124	#386	1	1	yes	characteristic
757	C₂×#124	#386	1	1	yes	characteristic
758	C₂×#124	#386	1	1	yes	characteristic
759	C₂×#124	#386	1	1	yes	characteristic
760	C₂×#124	#386	1	1	yes	characteristic
761	C₂×#124	#386	1	1	yes	characteristic
762	C₂×#124	C₂²×C₂²⋊C₄	1	1	yes	characteristic
763	C₂×#124	C₂²×C₂²⋊C₄	1	1	yes	characteristic
764	C₂×#124	C₂×C₄×D₄	1	1	yes	characteristic
765	C₂×#124	C₂×C₄×D₄	1	1	yes	characteristic
766	C₂×#124	C₂×#121	1	1	yes	characteristic
767	C₂×#124	C₂×#121	1	1	yes	characteristic
768	C₂×#124	C₂×#123	1	1	yes	characteristic
769	C₂×#124	C₂×#123	1	1	yes	characteristic
770	C₂×#124	C₂×#123	1	1	yes	characteristic
771	C₂×#124	C₂×#123	1	1	yes	characteristic
772	C₂×#124	C₂×#123	1	1	yes	characteristic
773	C₂×#124	C₂×#123	1	1	yes	characteristic
774	C₂×#117	#386	1	1	yes	characteristic
775	C₂×#117	#386	1	1	yes	characteristic
776	C₂×#117	#386	1	1	yes	characteristic
777	C₂×#117	#386	1	1	yes	characteristic
778	C₂×#117	#386	1	1	yes	characteristic
779	C₂×#117	#386	1	1	yes	characteristic
780	C₂×#117	C₂×C₄×D₄	1	1	yes	characteristic
781	C₂×#117	C₂×C₄×D₄	1	1	yes	characteristic
782	C₂×#117	C₂×#120	1	1	yes	characteristic
783	C₂×#117	C₂×#120	1	1	yes	characteristic
784	C₂×#117	C₂×#121	1	1	yes	characteristic
785	C₂×#117	C₂×#121	1	1	yes	characteristic
786	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
787	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
788	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
789	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
790	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
791	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
792	C₂²×C₄²	#386	1	1	yes	characteristic
793	C₂²×C₄²	#386	1	1	yes	characteristic
794	C₂²×C₄²	#386	1	1	yes	characteristic
795	C₂²×C₄²	#386	1	1	yes	characteristic
796	C₂²×C₄²	#386	1	1	yes	characteristic
797	C₂²×C₄²	#386	1	1	yes	characteristic
798	C₂²×C₄²	#386	1	1	yes	characteristic
799	C₂²×C₄²	#386	1	1	yes	characteristic
800	C₂²×C₄²	#386	1	1	yes	characteristic
801	C₂²×C₄²	#386	1	1	yes	characteristic
802	C₂²×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
803	C₂²×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
804	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
805	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
806	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
807	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
808	#453	C₂×#99	1	16	yes	—
809	#453	C₂×#99	1	16	yes	—
810	C₂×#100	C₂×#99	1	8	yes	—
811	C₂×#100	B(4,𝔽₂)	1	8	yes	—
812	C₂×#100	C₂²×C₂²⋊C₄	1	4	yes	—
813	C₂×#100	C₂²×C₂²⋊C₄	1	4	yes	—
814	C₂×#100	C₂×#120	1	4	yes	—
815	C₂×#100	C₂×#120	1	4	yes	—
816	C₂⁵	C₄×#120	1	2	yes	—
817	C₂⁵	C₄×#120	1	1	yes	characteristic
818	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
819	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
820	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
821	C₂⁵	#2358	1	2	yes	—
822	C₂⁵	#2358	1	2	yes	—
823	C₂⁵	#2358	1	2	yes	—
824	C₂⁵	#2404	1	2	yes	—
825	C₂⁵	#2404	1	1	yes	characteristic
826	C₂⁵	#2408	1	2	yes	—
827	C₂⁵	#2408	1	1	yes	characteristic
828	C₂⁵	#2424	1	2	yes	—
829	C₂⁵	#2424	1	2	yes	—
830	C₂⁵	#2424	1	2	yes	—
831	C₂⁵	C₂²×C₄×D₄	1	2	yes	—
832	C₂⁵	C₂×D₄²	1	2	yes	—
833	C₂⁵	C₂×#546	1	2	yes	—
834	H(5,𝔽₂)	C₂²×#99	1	8	yes	—
835	C₂²×Q₈	C₂×#386	1	1	yes	characteristic
836	C₂²×Q₈	C₂×#386	1	1	yes	characteristic
837	C₂²×Q₈	C₂×#386	1	1	yes	characteristic
838	C₂²×Q₈	#2321	1	1	yes	characteristic
839	C₂²×Q₈	#2403	1	1	yes	characteristic
840	C₂²×Q₈	#2418	1	2	yes	—
841	C₂²×Q₈	#2534	1	1	yes	characteristic
842	C₂²×Q₈	C₂²×#123	1	1	yes	characteristic
843	C₂²×Q₈	C₂×#534	1	1	yes	characteristic
844	C₂²×D₄	#1898	1	4	yes	—
845	C₂²×D₄	C₂×#386	1	1	yes	characteristic
846	C₂²×D₄	C₂×#386	1	1	yes	characteristic
847	C₂²×D₄	C₂×#386	1	1	yes	characteristic
848	C₂²×D₄	C₂×#386	1	1	yes	characteristic
849	C₂²×D₄	C₂×#386	1	1	yes	characteristic
850	C₂²×D₄	C₂×#386	1	1	yes	characteristic
851	C₂²×D₄	C₂×#386	1	1	yes	characteristic
852	C₂²×D₄	C₂×#386	1	1	yes	characteristic
853	C₂²×D₄	C₂×#386	1	1	yes	characteristic
854	C₂²×D₄	C₄×#120	1	1	yes	characteristic
855	C₂²×D₄	C₄×#120	1	2	yes	—
856	C₂²×D₄	C₄×#120	1	1	yes	characteristic
857	C₂²×D₄	#2321	1	2	yes	—
858	C₂²×D₄	#2321	1	1	yes	characteristic
859	C₂²×D₄	D₄×C₂²⋊C₄	1	2	yes	—
860	C₂²×D₄	D₄×C₂²⋊C₄	1	2	yes	—
861	C₂²×D₄	D₄×C₂²⋊C₄	1	2	yes	—
862	C₂²×D₄	D₄×C₂²⋊C₄	1	2	yes	—
863	C₂²×D₄	#2358	1	2	yes	—
864	C₂²×D₄	#2358	1	2	yes	—
865	C₂²×D₄	#2358	1	2	yes	—
866	C₂²×D₄	#2358	1	2	yes	—
867	C₂²×D₄	#2403	1	1	yes	characteristic
868	C₂²×D₄	#2403	1	2	yes	—
869	C₂²×D₄	#2404	1	2	yes	—
870	C₂²×D₄	#2404	1	1	yes	characteristic
871	C₂²×D₄	#2404	1	1	yes	characteristic
872	C₂²×D₄	#2408	1	1	yes	characteristic
873	C₂²×D₄	#2408	1	2	yes	—
874	C₂²×D₄	#2408	1	1	yes	characteristic
875	C₂²×D₄	#2418	1	2	yes	—
876	C₂²×D₄	#2418	1	2	yes	—
877	C₂²×D₄	#2418	1	2	yes	—
878	C₂²×D₄	#2424	1	2	yes	—
879	C₂²×D₄	#2424	1	2	yes	—
880	C₂²×D₄	#2424	1	2	yes	—
881	C₂²×D₄	#2424	1	2	yes	—
882	C₂²×D₄	#2534	1	2	yes	—
883	C₂²×D₄	#2534	1	1	yes	characteristic
884	C₂²×D₄	C₂²×#99	1	4	yes	—
885	C₂²×D₄	#2883	1	4	yes	—
886	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
887	C₂²×D₄	#3025	1	4	yes	—
888	C₂²×D₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
889	C₂²×D₄	C₂²×C₄×D₄	1	1	yes	characteristic
890	C₂²×D₄	C₂×#518	1	2	yes	—
891	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
892	C₂²×D₄	C₂²×#121	1	1	yes	characteristic
893	C₂²×D₄	C₂×#525	1	1	yes	characteristic
894	C₂²×D₄	C₂×#525	1	2	yes	—
895	C₂²×D₄	C₂×#535	1	1	yes	characteristic
896	C₂²×D₄	C₂×D₄²	1	2	yes	—
897	C₂²×D₄	C₂×#546	1	2	yes	—
898	C₂²×D₄	C₂×#546	1	2	yes	—
899	C₂²×D₄	C₂×#546	1	2	yes	—
900	C₂³×C₄	C₂×#386	1	1	yes	characteristic
901	C₂³×C₄	C₂×#386	1	1	yes	characteristic
902	C₂³×C₄	C₂×#386	1	1	yes	characteristic
903	C₂³×C₄	C₂×#386	1	1	yes	characteristic
904	C₂³×C₄	C₄×#120	1	1	yes	characteristic
905	C₂³×C₄	#2321	1	1	yes	characteristic
906	C₂³×C₄	#2321	1	2	yes	—
907	C₂³×C₄	#2321	1	1	yes	characteristic
908	C₂³×C₄	D₄×C₂²⋊C₄	1	2	yes	—
909	C₂³×C₄	#2358	1	2	yes	—
910	C₂³×C₄	#2403	1	1	yes	characteristic
911	C₂³×C₄	#2403	1	1	yes	characteristic
912	C₂³×C₄	#2403	1	2	yes	—
913	C₂³×C₄	#2404	1	1	yes	characteristic
914	C₂³×C₄	#2408	1	1	yes	characteristic
915	C₂³×C₄	#2418	1	2	yes	—
916	C₂³×C₄	#2418	1	2	yes	—
917	C₂³×C₄	#2418	1	2	yes	—
918	C₂³×C₄	#2418	1	2	yes	—
919	C₂³×C₄	#2424	1	2	yes	—
920	C₂³×C₄	#2534	1	1	yes	characteristic
921	C₂³×C₄	#2534	1	2	yes	—
922	C₂³×C₄	#2534	1	1	yes	characteristic
923	C₂³×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
924	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
925	C₂³×C₄	C₂²×#121	1	1	yes	characteristic
926	C₂³×C₄	C₂×#538	1	2	yes	—
927	C₂³×C₄	C₂×D₄²	1	2	yes	—
928	C₂³×C₄	C₂×#551	1	2	yes	—
929	#127	#1898	1	4	yes	—
930	#127	#1898	1	4	yes	—
931	#127	C₂²×#99	1	4	yes	—
932	#127	C₂²×#99	1	4	yes	—
933	C₂×C₄²	#1898	1	4	yes	—
934	C₂×C₄²	C₂×#386	1	1	yes	characteristic
935	C₂×C₄²	C₂×#386	1	1	yes	characteristic
936	C₂×C₄²	C₂×#386	1	1	yes	characteristic
937	C₂×C₄²	C₂×#386	1	1	yes	characteristic
938	C₂×C₄²	C₂×#386	1	1	yes	characteristic
939	C₂×C₄²	C₂×#386	1	1	yes	characteristic
940	C₂×C₄²	C₂×#386	1	1	yes	characteristic
941	C₂×C₄²	C₂×#386	1	1	yes	characteristic
942	#100	C₂²×#99	1	8	yes	—
943	#100	C₂×B(4,𝔽₂)	1	8	yes	—
944	C₂⁴	#13967	1	2	yes	—
945	C₂⁴	#13967	1	2	yes	—
946	C₂⁴	#13967	1	2	yes	—
947	C₂⁴	#13967	1	1	yes	characteristic
948	C₂⁴	#13967	1	1	yes	characteristic
949	C₂⁴	#13967	1	1	yes	characteristic
950	C₂⁴	#13967	1	1	yes	characteristic
951	C₂⁴	C₄×B(4,𝔽₂)	1	4	yes	—
952	C₂⁴	D₄×#99	1	8	yes	—
953	C₂⁴	#23996	1	4	yes	—
954	C₂⁴	#24260	1	4	yes	—
955	C₂⁴	C₂×C₄×#120	1	1	yes	characteristic
956	C₂⁴	C₂×D₄×C₂²⋊C₄	1	2	yes	—
957	C₂⁴	C₂×#2358	1	2	yes	—
958	C₂⁴	C₂×#2424	1	2	yes	—
959	C₂⁴	C₂×#2408	1	1	yes	characteristic
960	C₂⁴	C₂×#2404	1	1	yes	characteristic
961	C₂×D₄	C₂×#1898	1	2	yes	—
962	C₂×D₄	C₂×#1898	1	2	yes	—
963	C₂×D₄	C₂×#1898	1	2	yes	—
964	C₂×D₄	#20984	1	2	yes	—
965	C₂×D₄	C₄×B(4,𝔽₂)	1	4	yes	—
966	C₂×D₄	D₄×#99	1	8	yes	—
967	C₂×D₄	#23900	1	2	yes	—
968	C₂×D₄	#23902	1	2	yes	—
969	C₂×D₄	#24260	1	4	yes	—
970	C₂×D₄	C₂³×#99	1	2	yes	—
971	C₂×D₄	C₂×#2883	1	2	yes	—
972	C₂×D₄	C₂²×B(4,𝔽₂)	1	2	yes	—
973	C₂×D₄	C₂×#3025	1	2	yes	—
974	C₂²×C₄	#13967	1	1	yes	characteristic
975	C₂²×C₄	#13967	1	1	yes	characteristic
976	C₂²×C₄	#13967	1	2	yes	—
977	C₂²×C₄	#13967	1	1	yes	characteristic
978	C₂²×C₄	#13967	1	1	yes	characteristic
979	C₂²×C₄	C₂×#1898	1	2	yes	—
980	C₂²×C₄	#20984	1	2	yes	—
981	C₂²×C₄	#23900	1	2	yes	—
982	C₂²×C₄	#23902	1	2	yes	—
983	C₂²×C₄	C₂²×#386	1	1	yes	characteristic
984	C₂²×C₄	C₂×#2321	1	1	yes	characteristic
985	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
986	C₂²×C₄	C₂×#2418	1	2	yes	—
987	C₂²×C₄	C₂×#2534	1	1	yes	characteristic
988	C₄²	C₂×#1898	1	2	yes	—
989	C₄²	C₂×#1898	1	2	yes	—
990	C₂³	#364471	1	2	yes	—
991	C₂³	#364471	1	4	yes	—
992	C₂³	#364513	1	2	yes	—
993	C₂³	#364513	1	2	yes	—
994	C₂³	#364513	1	2	yes	—
995	C₂³	#364532	1	2	yes	—
996	C₂³	#364532	1	2	yes	—
997	C₂³	C₂×#13967	1	1	yes	characteristic
998	C₂³	C₂×C₄×B(4,𝔽₂)	1	2	yes	—
999	C₂³	C₂×D₄×#99	1	4	yes	—
1000	C₂³	C₂×#24260	1	2	yes	—
1001	C₂³	C₂×#23996	1	2	yes	—
1002	C₂×C₄	#364471	1	2	yes	—
1003	C₂×C₄	#364513	1	2	yes	—
1004	C₂×C₄	C₂²×#1898	1	1	yes	characteristic
1005	C₂×C₄	C₂×#20984	1	1	yes	characteristic
1006	C₂×C₄	C₂×#23900	1	1	yes	characteristic
1007	C₂×C₄	C₂×#23902	1	1	yes	characteristic
1008	C₂²	#72216620	1	4	yes	—
1009	C₂²	C₂×#364532	1	1	yes	characteristic
1010	C₂²	C₂×#364471	1	1	yes	characteristic
1011	C₂²	C₂×#364513	1	1	yes	characteristic
1012	C₂	C₂×#72216620	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#72216620
commutator	C₂³×D₄	C₂⁴×C₄
Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁵
prime radical	#72341618	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341642	C₂	semidirect
3. C₂×#72241333	C₂	semidirect
4. C₂×#72241304	C₂	semidirect
5. #72341589	C₂	semidirect
6. #72341588	C₂	semidirect
7. #72341315	C₂	semidirect
8. #72341312	C₂²	semidirect
9. C₂×#10574064	C₂²	semidirect
10. #72341290	C₂	semidirect
11. #72341286	C₂²	semidirect
12. C₂×#72241315	C₂	semidirect
13. #72340255	C₂	semidirect
14. C₂×#356056	C₂²	semidirect
16. C₂×#494596	C₄	semidirect
17. #72312192	C₂	semidirect
20. #72312147	C₂²	semidirect
21. #72311401	C₂	semidirect
22. C₂×#360531	C₂²	semidirect
23. #72311246	C₂²	semidirect
25. #72311152	C₂²	semidirect
26. C₂×#128079	C₂²	semidirect
27. C₂×#72238010	C₂	semidirect
31. C₂×#146577	C₂²	semidirect
32. C₂×#146577	C₂²	semidirect
33. C₂×#146577	C₂²	semidirect
34. C₂×#128062	C₂²	semidirect
36. #72306899	C₄	semidirect
38. #72306419	C₄	semidirect
43. #72303064	C₂²	semidirect
44. #72303055	C₂²	semidirect
45. #72283936	C₂²	semidirect
46. C₂×#392138	C₂²	semidirect
47. #72256607	C₄	semidirect
48. C₂²×#33557	C₄	semidirect
50. #72241340	C₂	semidirect
51. #72241337	C₂²	semidirect
52. #72241333	C₂²	semidirect
53. #72241333	C₂²	semidirect
54. #72241332	C₂²	semidirect
56. #72241315	C₂²	semidirect
58. #72241304	C₂²	semidirect
60. C₂×#392135	C₂²	semidirect
61. #72238013	C₂²	semidirect
62. #72238010	C₂²	semidirect
63. #72238010	C₂²	semidirect
64. #72236711	C₂²	semidirect
65. #72234146	C₄	semidirect
67. #72233917	C₂²	semidirect
68. #72213513	C₂²	semidirect
72. C₂²×#3026	C₂×C₄	semidirect
90. C₂²×#2888	D₄	semidirect
103. C₂²×#2200	C₂×C₄	semidirect
104. C₂²×#2198	C₂×C₄	semidirect
105. C₂²×#2196	C₂×C₄	semidirect
108. C₂²×#2121	C₂×C₄	semidirect
109. C₂²×#2121	D₄	semidirect
110. #6628897	C₂×C₄	semidirect
112. #6628896	C₂×C₄	semidirect
116. #6379033	D₄	semidirect
117. #6379033	D₄	semidirect
120. C₂×#20637	D₄	semidirect
121. C₂×#20609	C₂×C₄	semidirect
122. C₂×#20592	D₄	semidirect
128. C₂×C₄×#413	D₄	semidirect
129. #498928	C₂×C₄	semidirect
130. #498928	C₂×C₄	semidirect
131. #498927	C₂×C₄	semidirect
132. #498927	C₂×C₄	semidirect
135. #494682	C₂×C₄	semidirect
136. #494682	D₄	semidirect
140. #494681	C₂×C₄	semidirect
141. #494681	D₄	semidirect
145. #494596	C₂×C₄	semidirect
146. #494596	C₂×C₄	semidirect
147. #494596	C₂×C₄	semidirect
154. C₂×#12574	C₂×C₄	semidirect
155. C₂×#12574	D₄	semidirect
159. #359605	D₄	semidirect
160. #359605	D₄	semidirect
163. C₂×#10989	D₄	semidirect
164. C₂×#10975	D₄	semidirect
218. C₂²×#458	C₂²×C₄	semidirect
219. C₂²×B(4,𝔽₂)	C₂²×C₄	semidirect
306. C₂²×#352	C₂²×C₄	semidirect
308. C₂²×AΣL(1,𝔽₁₆)	C₂²×C₄	semidirect
312. #20609	C₂²×C₄	semidirect
313. #20609	C₂²×C₄	semidirect
327. #12574	C₂²×C₄	semidirect
328. #12574	C₂²×C₄	semidirect
528. C₂×#453	#99	semidirect

Maximal subgroups

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

subgroup	index
#72341642	2
#72341618	2
C₂×#72241333	2
C₂×#72241304	2
#72341589	2
#72341588	2
#72341315	2
#72341290	2
C₂×#72241315	2
#72340255	2
#72312192	2
#72311401	2
C₂×#72238010	2
#72241340	2