Subgroups — #72341751

Order 2048.

At least 13116 conjugacy classes of subgroups; only the 1142 normal subgroups are shown.

The subgroup lattice has 819 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341739	C₂	1	1	yes	maximal, characteristic, complemented
2	#72315284	C₂	1	1	yes	maximal, characteristic, complemented
3	#72315283	C₂	1	1	yes	maximal, characteristic, complemented
4	#72312474	C₂	1	1	yes	maximal, characteristic, complemented
5	#72303719	C₂	1	2	yes	maximal, complemented
6	#72303713	C₂	1	2	yes	maximal, complemented
7	#72303706	C₂	1	2	yes	maximal, complemented
8	C₂×#6437584	C₂	1	1	yes	maximal, characteristic
9	#72303051	C₂	1	2	yes	maximal, complemented
10	C₂×#493419	C₂	1	1	yes	maximal, characteristic, complemented
11	#72302906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#63090	C₂²	1	1	yes	characteristic
13	C₂×#62812	C₂²	1	1	yes	characteristic
14	C₂×#60398	C₂²	1	1	yes	characteristic
15	C₂²×#3018	C₂²	1	1	yes	characteristic
16	#7625999	C₂²	1	1	yes	characteristic
17	#7625999	C₂²	1	1	yes	characteristic
18	C₂²×#2132	C₂²	1	1	yes	characteristic
19	C₂²×#2126	C₂²	1	1	yes	characteristic
20	C₂×#33347	C₂²	1	2	yes	—
21	C₂×#23873	C₄	1	2	yes	complemented
22	C₂×#23875	C₄	1	2	yes	complemented
23	C₂×#23874	C₄	1	2	yes	complemented
24	C₂×#23872	C₄	1	2	yes	complemented
25	#6374127	C₂²	1	2	yes	—
26	C₂×#21017	C₂²	1	1	yes	characteristic
27	C₂²×#1884	C₂²	1	1	yes	characteristic
28	C₂×#20623	C₂²	1	2	yes	—
29	C₂×#20623	C₂²	1	1	yes	characteristic
30	#6370746	C₂²	1	2	yes	complemented
31	#6370734	C₂²	1	2	yes	complemented
32	#6370692	C₂²	1	2	yes	—
33	#492906	C₂²	1	2	yes	complemented
34	#492899	C₂²	1	2	yes	complemented
35	#492886	C₂²	1	2	yes	complemented
36	#492886	C₂²	1	2	yes	complemented
37	#353430	C₂²	1	2	yes	complemented
38	#353422	C₂²	1	2	yes	complemented
39	C₂²×#585	D₄	1	1	yes	characteristic
40	C₂²×#585	C₂³	1	1	yes	characteristic
41	C₂²×#585	C₂³	1	1	yes	characteristic
42	C₂×#3586	C₂×C₄	1	2	yes	complemented
43	C₂×#3585	C₂×C₄	1	2	yes	complemented
44	C₂²×#568	C₂³	1	1	yes	characteristic
45	C₂×#3500	C₂×C₄	1	1	yes	characteristic
46	C₂×#3500	C₂×C₄	1	1	yes	characteristic
47	C₂×#3500	D₄	1	1	yes	characteristic
48	C₂×#3500	D₄	1	1	yes	characteristic
49	C₂×#3499	C₂×C₄	1	1	yes	characteristic
50	C₂×#3499	D₄	1	1	yes	characteristic
51	C₂×#3498	C₂×C₄	1	1	yes	characteristic
52	C₂×#3498	D₄	1	1	yes	characteristic
53	C₂×#3449	D₄	1	1	yes	characteristic
54	C₂×#3449	C₂³	1	1	yes	characteristic
55	C₂²×#532	D₄	1	1	yes	characteristic
56	C₂²×#532	C₂³	1	1	yes	characteristic
57	C₂²×C₄×#41	D₄	1	1	yes	characteristic
58	C₂×#3028	C₂×C₄	1	2	yes	complemented
59	C₂×#3027	C₂×C₄	1	2	yes	complemented
60	C₂×#3018	C₂×C₄	1	2	yes	—
61	C₂×#3018	C₂×C₄	1	2	yes	—
62	C₂×#3018	D₄	1	2	yes	—
63	C₂×#3018	D₄	1	2	yes	—
64	C₂×#3018	D₄	1	2	yes	—
65	C₂×#3018	D₄	1	2	yes	—
66	C₂²×#413	C₂³	1	2	yes	—
67	C₂²×#413	C₂³	1	1	yes	characteristic
68	C₂²×#410	D₄	1	2	yes	complemented
69	C₂²×#410	D₄	1	2	yes	complemented
70	C₂²×#410	D₄	1	2	yes	complemented
71	C₂²×#410	D₄	1	2	yes	complemented
72	C₂²×#410	C₂³	1	2	yes	—
73	C₂²×#410	C₂³	1	1	yes	characteristic
74	#34366	D₄	1	2	yes	complemented
75	#34366	D₄	1	2	yes	complemented
76	#34365	D₄	1	2	yes	complemented
77	#34364	D₄	1	2	yes	complemented
78	#34044	C₂³	1	2	yes	—
79	#34044	C₂³	1	2	yes	—
80	C₂×#2132	D₄	1	2	yes	complemented
81	C₂×#2132	D₄	1	2	yes	complemented
82	C₂×#2126	D₄	1	2	yes	complemented
83	C₂×#2126	D₄	1	2	yes	complemented
84	#21749	D₄	1	8	yes	—
85	C₂×#1915	C₂×C₄	1	2	yes	complemented
86	C₂×#1914	C₂×C₄	1	2	yes	complemented
87	C₂×#1884	C₂×C₄	1	2	yes	—
88	C₂×#1884	C₂×C₄	1	2	yes	—
89	C₂×#1884	D₄	1	2	yes	—
90	C₂×#1884	D₄	1	2	yes	—
91	C₂×#1884	D₄	1	2	yes	—
92	C₂×#1884	D₄	1	2	yes	—
93	C₂×#1796	C₂×C₄	1	2	yes	complemented
94	C₂×#1795	C₂×C₄	1	2	yes	complemented
95	C₂×#585	C₂²×C₄	1	2	yes	—
96	C₂×#585	C₂×D₄	1	2	yes	—
97	C₂×#585	C₂×D₄	1	2	yes	—
98	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic, complemented
99	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic, complemented
100	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
101	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
102	C₂²×2₋¹⁺⁴	#41	1	2	yes	—
103	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
105	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
106	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
107	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
108	C₂³×#41	C₂×D₄	1	1	yes	characteristic
109	C₂³×#41	C₂×D₄	1	2	yes	—
110	C₂³×#41	C₂×D₄	1	1	yes	characteristic
111	C₂³×#41	C₂×D₄	1	2	yes	—
112	C₂³×#41	C₂×D₄	1	1	yes	characteristic
113	C₂³×#41	C₂×D₄	1	1	yes	characteristic
114	C₂³×#41	C₂⁴	1	1	yes	characteristic
115	C₂×#568	C₂²×C₄	1	2	yes	—
116	C₂×#568	C₂×D₄	1	2	yes	—
117	C₂×#568	C₂×D₄	1	2	yes	—
118	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic, complemented
119	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic, complemented
120	C₂×#536	C₂²×C₄	1	1	yes	characteristic
121	C₂×#536	C₂×D₄	1	1	yes	characteristic
122	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic, complemented
123	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic, complemented
124	C₂×#535	C₂²×C₄	1	1	yes	characteristic
125	C₂×#535	C₂×D₄	1	1	yes	characteristic
126	C₂×#534	C₂×D₄	1	4	yes	—
127	C₂×#532	C₂²×C₄	1	1	yes	characteristic
128	C₂×#532	C₂²×C₄	1	1	yes	characteristic
129	C₂×#532	C₂×D₄	1	1	yes	characteristic
130	C₂×#532	C₂×D₄	1	1	yes	characteristic
131	C₂×#532	C₂×D₄	1	1	yes	characteristic
132	C₂×#532	C₂×D₄	1	1	yes	characteristic
133	C₂×#532	C₂×D₄	1	1	yes	characteristic
134	C₂×#532	C₂×D₄	1	1	yes	characteristic
135	C₂×#532	C₂×D₄	1	1	yes	characteristic
136	C₂×#532	C₂×D₄	1	1	yes	characteristic
137	C₂×#532	C₂×D₄	1	1	yes	characteristic
138	C₂×#532	C₂×D₄	1	1	yes	characteristic
139	C₂×#532	C₂×D₄	1	1	yes	characteristic
140	C₂×#532	C₂×D₄	1	1	yes	characteristic
141	C₂×#532	C₂×D₄	1	1	yes	characteristic
142	C₂×#532	C₂×D₄	1	1	yes	characteristic
143	C₂×#532	#41	1	1	yes	characteristic
144	C₂×#532	#41	1	1	yes	characteristic
145	C₂×#532	#41	1	1	yes	characteristic
146	C₂×#532	#41	1	1	yes	characteristic
147	C₂×#532	#41	1	1	yes	characteristic
148	C₂×#532	#41	1	1	yes	characteristic
149	C₂×#532	#41	1	1	yes	characteristic
150	C₂×#532	#41	1	1	yes	characteristic
151	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic, complemented
152	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
153	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
154	C₂²×#127	C₂×D₄	1	1	yes	characteristic
155	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	C₂²×#124	C₂×D₄	1	1	yes	characteristic
158	C₂²×#124	C₂×D₄	1	1	yes	characteristic
159	C₂×#525	#41	1	4	yes	—
160	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
161	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	C₂²×#117	C₂×D₄	1	2	yes	—
165	C₂²×#117	C₂×D₄	1	2	yes	—
166	C₂²×#117	C₂×D₄	1	1	yes	characteristic
167	C₂²×#117	C₂×D₄	1	2	yes	—
168	C₂²×#117	C₂×D₄	1	2	yes	—
169	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
170	#3018	C₂²⋊C₄	1	4	yes	—
171	#3018	C₂²⋊C₄	1	4	yes	—
172	#3018	C₂²⋊C₄	1	4	yes	—
173	#3018	C₂²⋊C₄	1	4	yes	—
174	C₂×#413	C₂²×C₄	1	2	yes	—
175	C₂×#413	C₂×D₄	1	4	yes	—
176	C₂×#413	C₂×D₄	1	2	yes	—
177	C₂×#413	C₂×D₄	1	2	yes	—
178	C₂×#410	C₂²×C₄	1	2	yes	—
179	C₂×#410	C₂×D₄	1	4	yes	—
180	C₂×#410	C₂×D₄	1	2	yes	—
181	C₂×#410	C₂×D₄	1	2	yes	—
182	#2310	C₂×D₄	1	4	yes	—
183	#2309	C₂×D₄	1	4	yes	—
184	#2308	C₂×D₄	1	4	yes	—
185	#2308	C₂×D₄	1	4	yes	—
186	#1884	C₂²⋊C₄	1	4	yes	complemented
187	#1884	C₂²⋊C₄	1	4	yes	complemented
188	#1884	C₂²⋊C₄	1	4	yes	complemented
189	#1884	C₂²⋊C₄	1	4	yes	complemented
190	#585	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×#41	C₄×D₄	1	2	yes	—
196	C₂²×#41	C₄×D₄	1	2	yes	—
197	C₂²×#41	#120	1	1	yes	characteristic
198	C₂²×#41	#120	1	1	yes	characteristic
199	C₂²×#41	#120	1	1	yes	characteristic
200	C₂²×#41	#120	1	1	yes	characteristic
201	C₂²×#41	#120	1	2	yes	—
202	C₂²×#41	#120	1	1	yes	characteristic
203	C₂²×#41	#120	1	1	yes	characteristic
204	C₂²×#41	#121	1	2	yes	—
205	C₂²×#41	#121	1	2	yes	—
206	C₂²×#41	#121	1	1	yes	characteristic
207	C₂²×#41	#121	1	1	yes	characteristic
208	C₂²×#41	#121	1	1	yes	characteristic
209	C₂²×#41	#121	1	1	yes	characteristic
210	C₂²×#41	#123	1	2	yes	—
211	C₂²×#41	#123	1	1	yes	characteristic
212	C₂²×#41	#123	1	1	yes	characteristic
213	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
214	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
215	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
216	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
217	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
218	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
219	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
220	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
221	C₂²×#41	C₂×#41	1	2	yes	—
222	C₂²×#41	C₂×#41	1	1	yes	characteristic
223	C₂²×#41	C₂×#41	1	1	yes	characteristic
224	C₂²×#41	C₂×#41	1	2	yes	—
225	C₂²×#41	C₂×#41	1	1	yes	characteristic
226	C₂²×#41	C₂×#41	1	1	yes	characteristic
227	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
228	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
229	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
230	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
231	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂³×Q₈	C₄×D₄	1	2	yes	—
234	C₂³×Q₈	#120	1	1	yes	characteristic
235	C₂³×Q₈	#121	1	2	yes	—
236	C₂³×Q₈	#123	1	1	yes	characteristic
237	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
238	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂³×D₄	C₄×D₄	1	2	yes	—
241	C₂³×D₄	#120	1	1	yes	characteristic
242	C₂³×D₄	#120	1	2	yes	—
243	C₂³×D₄	#121	1	2	yes	—
244	C₂³×D₄	#123	1	1	yes	characteristic
245	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
246	C₂³×D₄	C₂²×D₄	1	2	yes	—
247	C₂⁴×C₄	#123	1	2	yes	—
248	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
249	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
250	#568	C₂×C₂²⋊C₄	1	4	yes	—
251	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	#532	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	#532	C₄×D₄	1	1	yes	characteristic
260	#532	C₄×D₄	1	1	yes	characteristic
261	#532	C₄×D₄	1	1	yes	characteristic
262	#532	C₄×D₄	1	1	yes	characteristic
263	#532	C₄×D₄	1	1	yes	characteristic
264	#532	C₄×D₄	1	1	yes	characteristic
265	#532	C₄×D₄	1	1	yes	characteristic
266	#532	C₄×D₄	1	1	yes	characteristic
267	#532	#120	1	1	yes	characteristic
268	#532	#120	1	1	yes	characteristic
269	#532	#120	1	1	yes	characteristic
270	#532	#120	1	1	yes	characteristic
271	#532	#120	1	1	yes	characteristic
272	#532	#120	1	1	yes	characteristic
273	#532	#120	1	1	yes	characteristic
274	#532	#120	1	1	yes	characteristic
275	#532	#120	1	1	yes	characteristic
276	#532	#120	1	1	yes	characteristic
277	#532	#120	1	1	yes	characteristic
278	#532	#120	1	1	yes	characteristic
279	#532	#121	1	1	yes	characteristic
280	#532	#121	1	1	yes	characteristic
281	#532	#121	1	1	yes	characteristic
282	#532	#121	1	1	yes	characteristic
283	#532	#121	1	1	yes	characteristic
284	#532	#121	1	1	yes	characteristic
285	#532	#121	1	1	yes	characteristic
286	#532	#121	1	1	yes	characteristic
287	#532	#121	1	1	yes	characteristic
288	#532	#121	1	1	yes	characteristic
289	#532	#121	1	1	yes	characteristic
290	#532	#121	1	1	yes	characteristic
291	#532	#121	1	1	yes	characteristic
292	#532	#121	1	1	yes	characteristic
293	#532	#121	1	1	yes	characteristic
294	#532	#121	1	1	yes	characteristic
295	#532	#123	1	1	yes	characteristic
296	#532	#123	1	1	yes	characteristic
297	#532	#123	1	1	yes	characteristic
298	#532	#123	1	1	yes	characteristic
299	#532	#123	1	1	yes	characteristic
300	#532	#123	1	1	yes	characteristic
301	#532	#123	1	1	yes	characteristic
302	#532	#123	1	1	yes	characteristic
303	#532	#123	1	1	yes	characteristic
304	#532	#123	1	1	yes	characteristic
305	#532	#123	1	1	yes	characteristic
306	#532	#123	1	1	yes	characteristic
307	#532	#124	1	1	yes	characteristic
308	#532	#124	1	1	yes	characteristic
309	#532	#124	1	1	yes	characteristic
310	#532	#124	1	1	yes	characteristic
311	#532	#124	1	1	yes	characteristic
312	#532	#124	1	1	yes	characteristic
313	#532	#124	1	1	yes	characteristic
314	#532	#124	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
316	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
317	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
318	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
319	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
320	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
321	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
322	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
324	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	#127	1	1	yes	characteristic
326	C₂×C₄⋊Q₈	#127	1	1	yes	characteristic
327	C₂×#127	C₄×D₄	1	1	yes	characteristic
328	C₂×#127	C₄×D₄	1	1	yes	characteristic
329	C₂×#127	#120	1	1	yes	characteristic
330	C₂×#127	#120	1	1	yes	characteristic
331	C₂×#127	#121	1	1	yes	characteristic
332	C₂×#127	#121	1	1	yes	characteristic
333	C₂×#127	#121	1	1	yes	characteristic
334	C₂×#127	#121	1	1	yes	characteristic
335	C₂×#127	#121	1	1	yes	characteristic
336	C₂×#127	#121	1	1	yes	characteristic
337	C₂×#127	#127	1	1	yes	characteristic
338	C₂×#127	#127	1	1	yes	characteristic
339	C₂×#124	C₄×D₄	1	1	yes	characteristic
340	C₂×#124	C₄×D₄	1	1	yes	characteristic
341	C₂×#124	C₄×D₄	1	1	yes	characteristic
342	C₂×#124	C₄×D₄	1	1	yes	characteristic
343	C₂×#124	#120	1	1	yes	characteristic
344	C₂×#124	#120	1	1	yes	characteristic
345	C₂×#124	#120	1	1	yes	characteristic
346	C₂×#124	#120	1	1	yes	characteristic
347	C₂×#124	#121	1	1	yes	characteristic
348	C₂×#124	#121	1	1	yes	characteristic
349	C₂×#124	#121	1	1	yes	characteristic
350	C₂×#124	#121	1	1	yes	characteristic
351	C₂×#124	#121	1	1	yes	characteristic
352	C₂×#124	#121	1	1	yes	characteristic
353	C₂×#124	#121	1	1	yes	characteristic
354	C₂×#124	#121	1	1	yes	characteristic
355	C₂×#124	#121	1	1	yes	characteristic
356	C₂×#124	#121	1	1	yes	characteristic
357	C₂×#124	#121	1	1	yes	characteristic
358	C₂×#124	#121	1	1	yes	characteristic
359	C₂×#124	#127	1	1	yes	characteristic
360	C₂×#124	#127	1	1	yes	characteristic
361	C₂×#124	#127	1	1	yes	characteristic
362	C₂×#124	#127	1	1	yes	characteristic
363	C₂×#123	C₄×D₄	1	4	yes	—
364	C₂×#123	#121	1	4	yes	—
365	C₂×#120	C₄×D₄	1	4	yes	—
366	C₂×#120	#121	1	4	yes	—
367	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×#117	#120	1	4	yes	—
370	C₂×#117	#120	1	4	yes	—
371	C₂×#117	#123	1	2	yes	—
372	C₂²×C₂²⋊C₄	#120	1	2	yes	—
373	C₂²×C₂²⋊C₄	#120	1	4	yes	—
374	C₂²×C₂²⋊C₄	#120	1	4	yes	—
375	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
377	C₂²×C₄²	#120	1	1	yes	characteristic
378	C₂²×C₄²	#120	1	1	yes	characteristic
379	C₂²×C₄²	#120	1	1	yes	characteristic
380	C₂²×C₄²	#120	1	1	yes	characteristic
381	C₂²×C₄²	#120	1	1	yes	characteristic
382	C₂²×C₄²	#120	1	1	yes	characteristic
383	C₂²×C₄²	#121	1	1	yes	characteristic
384	C₂²×C₄²	#121	1	1	yes	characteristic
385	C₂²×C₄²	#121	1	1	yes	characteristic
386	C₂²×C₄²	#121	1	1	yes	characteristic
387	C₂²×C₄²	#123	1	1	yes	characteristic
388	C₂²×C₄²	#123	1	1	yes	characteristic
389	#413	C₂×C₂²⋊C₄	1	4	yes	—
390	#410	C₂×C₂²⋊C₄	1	4	yes	—
391	C₂⁵	#386	1	2	yes	—
392	C₂⁵	C₂×#120	1	2	yes	—
393	C₂⁵	C₂×#120	1	1	yes	characteristic
394	C₂×#41	#379	1	1	yes	characteristic
395	C₂×#41	#379	1	1	yes	characteristic
396	C₂×#41	#379	1	1	yes	characteristic
397	C₂×#41	#379	1	1	yes	characteristic
398	C₂×#41	#386	1	1	yes	characteristic
399	C₂×#41	#386	1	1	yes	characteristic
400	C₂×#41	#386	1	1	yes	characteristic
401	C₂×#41	#386	1	1	yes	characteristic
402	C₂×#41	#394	1	1	yes	characteristic
403	C₂×#41	#394	1	1	yes	characteristic
404	C₂×#41	#394	1	1	yes	characteristic
405	C₂×#41	#394	1	1	yes	characteristic
406	C₂×#41	#394	1	1	yes	characteristic
407	C₂×#41	#394	1	1	yes	characteristic
408	C₂×#41	#394	1	1	yes	characteristic
409	C₂×#41	#394	1	1	yes	characteristic
410	C₂×#41	B(4,𝔽₂)	1	2	yes	—
411	C₂×#41	B(4,𝔽₂)	1	2	yes	—
412	C₂×#41	B(4,𝔽₂)	1	2	yes	—
413	C₂×#41	B(4,𝔽₂)	1	2	yes	—
414	C₂×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
415	C₂×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
416	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
417	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂×#41	#518	1	2	yes	—
419	C₂×#41	#518	1	2	yes	—
420	C₂×#41	C₂×#120	1	1	yes	characteristic
421	C₂×#41	C₂×#120	1	1	yes	characteristic
422	C₂×#41	C₂×#120	1	1	yes	characteristic
423	C₂×#41	C₂×#121	1	1	yes	characteristic
424	C₂×#41	C₂×#121	1	1	yes	characteristic
425	C₂×#41	C₂×#121	1	1	yes	characteristic
426	C₂×#41	C₂×#121	1	1	yes	characteristic
427	C₂×#41	C₂×#123	1	1	yes	characteristic
428	C₂×#41	C₂×#123	1	1	yes	characteristic
429	C₂×#41	C₂×#123	1	1	yes	characteristic
430	C₂×#41	C₂×#124	1	1	yes	characteristic
431	C₂×#41	C₂×#124	1	1	yes	characteristic
432	C₂×#41	#534	1	2	yes	—
433	C₂×#41	#534	1	2	yes	—
434	C₂×#41	#538	1	2	yes	—
435	C₂×#41	#538	1	2	yes	—
436	C₂×#41	#538	1	2	yes	—
437	C₂×#41	#538	1	2	yes	—
438	C₂×#41	#546	1	2	yes	—
439	C₂×#41	#546	1	2	yes	—
440	C₂×#41	#546	1	2	yes	—
441	C₂×#41	#546	1	2	yes	—
442	C₂×#41	#546	1	2	yes	—
443	C₂×#41	#546	1	2	yes	—
444	C₂×#41	#546	1	2	yes	—
445	C₂×#41	#546	1	2	yes	—
446	C₂×#41	#546	1	2	yes	—
447	C₂×#41	#546	1	2	yes	—
448	C₂×#41	#546	1	2	yes	—
449	C₂×#41	#546	1	2	yes	—
450	C₂×#41	#551	1	2	yes	—
451	C₂×#41	#551	1	2	yes	—
452	C₂×#41	#551	1	2	yes	—
453	C₂×#41	#551	1	2	yes	—
454	C₂²×Q₈	#386	1	2	yes	—
455	C₂²×Q₈	#386	1	1	yes	characteristic
456	C₂²×Q₈	#386	1	1	yes	characteristic
457	C₂²×Q₈	#386	1	1	yes	characteristic
458	C₂²×Q₈	#386	1	1	yes	characteristic
459	C₂²×Q₈	#392	1	1	yes	characteristic
460	C₂²×Q₈	#392	1	1	yes	characteristic
461	C₂²×Q₈	#392	1	1	yes	characteristic
462	C₂²×Q₈	#392	1	1	yes	characteristic
463	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
464	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
465	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
466	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
467	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
468	C₂²×Q₈	#525	1	2	yes	—
469	C₂²×Q₈	C₂×#127	1	1	yes	characteristic
470	C₂²×Q₈	#534	1	2	yes	—
471	C₂²×Q₈	#535	1	2	yes	—
472	C₂²×D₄	#386	1	2	yes	—
473	C₂²×D₄	#386	1	1	yes	characteristic
474	C₂²×D₄	#386	1	1	yes	characteristic
475	C₂²×D₄	#386	1	1	yes	characteristic
476	C₂²×D₄	#386	1	1	yes	characteristic
477	C₂²×D₄	#392	1	1	yes	characteristic
478	C₂²×D₄	#392	1	1	yes	characteristic
479	C₂²×D₄	#392	1	1	yes	characteristic
480	C₂²×D₄	#392	1	1	yes	characteristic
481	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
482	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
483	C₂²×D₄	C₂×#120	1	1	yes	characteristic
484	C₂²×D₄	C₂×#121	1	2	yes	—
485	C₂²×D₄	C₂×#121	1	1	yes	characteristic
486	C₂²×D₄	C₂×#121	1	1	yes	characteristic
487	C₂²×D₄	C₂×#121	1	1	yes	characteristic
488	C₂²×D₄	#525	1	2	yes	—
489	C₂²×D₄	#525	1	2	yes	—
490	C₂²×D₄	#525	1	2	yes	—
491	C₂²×D₄	C₂×#127	1	1	yes	characteristic
492	C₂²×D₄	#534	1	2	yes	—
493	C₂²×D₄	#535	1	2	yes	—
494	C₂²×D₄	D₄²	1	2	yes	—
495	C₂²×D₄	D₄²	1	2	yes	—
496	C₂²×D₄	D₄²	1	2	yes	—
497	C₂²×D₄	D₄²	1	2	yes	—
498	C₂²×D₄	D₄²	1	2	yes	—
499	C₂²×D₄	D₄²	1	2	yes	—
500	C₂²×D₄	#546	1	2	yes	—
501	C₂²×D₄	#546	1	2	yes	—
502	C₂³×C₄	#386	1	2	yes	—
503	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
505	C₂³×C₄	C₂×#120	1	2	yes	—
506	C₂³×C₄	C₂×#120	1	1	yes	characteristic
507	C₂³×C₄	C₂×#120	1	1	yes	characteristic
508	C₂³×C₄	C₂×#120	1	1	yes	characteristic
509	C₂³×C₄	C₂×#120	1	1	yes	characteristic
510	C₂³×C₄	C₂×#121	1	2	yes	—
511	C₂³×C₄	C₂×#121	1	1	yes	characteristic
512	C₂³×C₄	C₂×#121	1	1	yes	characteristic
513	C₂³×C₄	C₂×#123	1	1	yes	characteristic
514	C₂³×C₄	C₂×#123	1	1	yes	characteristic
515	C₂³×C₄	C₂×#123	1	1	yes	characteristic
516	C₂³×C₄	#525	1	2	yes	—
517	C₂³×C₄	#525	1	2	yes	—
518	C₂³×C₄	#534	1	1	yes	characteristic
519	C₂³×C₄	#534	1	1	yes	characteristic
520	C₂³×C₄	#534	1	1	yes	characteristic
521	C₂³×C₄	#534	1	1	yes	characteristic
522	C₂³×C₄	D₄²	1	2	yes	—
523	C₂³×C₄	D₄²	1	2	yes	—
524	C₂³×C₄	D₄²	1	2	yes	—
525	C₂³×C₄	D₄²	1	2	yes	—
526	C₂³×C₄	D₄²	1	2	yes	—
527	C₂³×C₄	D₄²	1	2	yes	—
528	C₂³×C₄	#546	1	2	yes	—
529	C₂³×C₄	#546	1	2	yes	—
530	C₄⋊Q₈	#386	1	1	yes	characteristic
531	C₄⋊Q₈	#386	1	1	yes	characteristic
532	C₄⋊Q₈	#386	1	1	yes	characteristic
533	C₄⋊Q₈	#386	1	1	yes	characteristic
534	C₄⋊Q₈	#390	1	1	yes	characteristic
535	C₄⋊Q₈	#390	1	1	yes	characteristic
536	C₄⋊Q₈	#390	1	1	yes	characteristic
537	C₄⋊Q₈	#390	1	1	yes	characteristic
538	C₄⋊Q₈	#392	1	1	yes	characteristic
539	C₄⋊Q₈	#392	1	1	yes	characteristic
540	C₄⋊Q₈	#392	1	1	yes	characteristic
541	C₄⋊Q₈	#392	1	1	yes	characteristic
542	C₄⋊Q₈	#394	1	1	yes	characteristic
543	C₄⋊Q₈	#394	1	1	yes	characteristic
544	C₄⋊Q₈	#394	1	1	yes	characteristic
545	C₄⋊Q₈	#394	1	1	yes	characteristic
546	#127	#386	1	1	yes	characteristic
547	#127	#386	1	1	yes	characteristic
548	#127	#386	1	1	yes	characteristic
549	#127	#386	1	1	yes	characteristic
550	#127	#390	1	1	yes	characteristic
551	#127	#390	1	1	yes	characteristic
552	#127	#390	1	1	yes	characteristic
553	#127	#390	1	1	yes	characteristic
554	#127	#392	1	1	yes	characteristic
555	#127	#392	1	1	yes	characteristic
556	#127	#392	1	1	yes	characteristic
557	#127	#392	1	1	yes	characteristic
558	#127	#394	1	1	yes	characteristic
559	#127	#394	1	1	yes	characteristic
560	#127	#394	1	1	yes	characteristic
561	#127	#394	1	1	yes	characteristic
562	#124	#386	1	1	yes	characteristic
563	#124	#386	1	1	yes	characteristic
564	#124	#386	1	1	yes	characteristic
565	#124	#386	1	1	yes	characteristic
566	#124	#386	1	1	yes	characteristic
567	#124	#386	1	1	yes	characteristic
568	#124	#386	1	1	yes	characteristic
569	#124	#386	1	1	yes	characteristic
570	#124	#390	1	1	yes	characteristic
571	#124	#390	1	1	yes	characteristic
572	#124	#390	1	1	yes	characteristic
573	#124	#390	1	1	yes	characteristic
574	#124	#390	1	1	yes	characteristic
575	#124	#390	1	1	yes	characteristic
576	#124	#390	1	1	yes	characteristic
577	#124	#390	1	1	yes	characteristic
578	#124	#392	1	1	yes	characteristic
579	#124	#392	1	1	yes	characteristic
580	#124	#392	1	1	yes	characteristic
581	#124	#392	1	1	yes	characteristic
582	#124	#392	1	1	yes	characteristic
583	#124	#392	1	1	yes	characteristic
584	#124	#392	1	1	yes	characteristic
585	#124	#392	1	1	yes	characteristic
586	#124	#394	1	1	yes	characteristic
587	#124	#394	1	1	yes	characteristic
588	#124	#394	1	1	yes	characteristic
589	#124	#394	1	1	yes	characteristic
590	#124	#394	1	1	yes	characteristic
591	#124	#394	1	1	yes	characteristic
592	#124	#394	1	1	yes	characteristic
593	#124	#394	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	#386	1	2	yes	—
595	C₂×C₂²⋊C₄	#386	1	2	yes	—
596	C₂×C₄²	#379	1	1	yes	characteristic
597	C₂×C₄²	#379	1	1	yes	characteristic
598	C₂×C₄²	#379	1	1	yes	characteristic
599	C₂×C₄²	#379	1	1	yes	characteristic
600	C₂×C₄²	#386	1	1	yes	characteristic
601	C₂×C₄²	#386	1	1	yes	characteristic
602	C₂×C₄²	#386	1	1	yes	characteristic
603	C₂×C₄²	#386	1	1	yes	characteristic
604	C₂×C₄²	#386	1	1	yes	characteristic
605	C₂×C₄²	#386	1	1	yes	characteristic
606	C₂×C₄²	#386	1	1	yes	characteristic
607	C₂×C₄²	#386	1	1	yes	characteristic
608	C₂×C₄²	#392	1	1	yes	characteristic
609	C₂×C₄²	#392	1	1	yes	characteristic
610	C₂×C₄²	#392	1	1	yes	characteristic
611	C₂×C₄²	#392	1	1	yes	characteristic
612	C₂×C₄²	#392	1	1	yes	characteristic
613	C₂×C₄²	#392	1	1	yes	characteristic
614	C₂×C₄²	#392	1	1	yes	characteristic
615	C₂×C₄²	#392	1	1	yes	characteristic
616	C₂×C₄²	#394	1	1	yes	characteristic
617	C₂×C₄²	#394	1	1	yes	characteristic
618	C₂×C₄²	#394	1	1	yes	characteristic
619	C₂×C₄²	#394	1	1	yes	characteristic
620	C₂×C₄²	#394	1	1	yes	characteristic
621	C₂×C₄²	#394	1	1	yes	characteristic
622	C₂×C₄²	#394	1	1	yes	characteristic
623	C₂×C₄²	#394	1	1	yes	characteristic
624	C₂⁴	C₂×#386	1	1	yes	characteristic
625	C₂⁴	C₄×#120	1	2	yes	—
626	C₂⁴	#2403	1	1	yes	characteristic
627	C₂⁴	#2403	1	1	yes	characteristic
628	C₂⁴	#2403	1	2	yes	—
629	C₂⁴	#2408	1	2	yes	—
630	C₂⁴	#2410	1	1	yes	characteristic
631	C₂⁴	#2410	1	1	yes	characteristic
632	C₂⁴	#2410	1	2	yes	—
633	C₂⁴	#2433	1	2	yes	—
634	C₂⁴	#2846	1	1	yes	characteristic
635	C₂⁴	#2847	1	2	yes	—
636	C₂⁴	#2849	1	1	yes	characteristic
637	C₂×Q₈	#1438	1	1	yes	characteristic
638	C₂×Q₈	#1438	1	1	yes	characteristic
639	C₂×Q₈	#1438	1	1	yes	characteristic
640	C₂×Q₈	#1438	1	1	yes	characteristic
641	C₂×Q₈	#1889	1	2	yes	—
642	C₂×Q₈	#1889	1	2	yes	—
643	C₂×Q₈	C₂×#386	1	1	yes	characteristic
644	C₂×Q₈	C₂×#390	1	1	yes	characteristic
645	C₂×Q₈	#2321	1	2	yes	—
646	C₂×Q₈	C₂×#392	1	1	yes	characteristic
647	C₂×Q₈	C₂×#394	1	1	yes	characteristic
648	C₂×Q₈	#2404	1	2	yes	—
649	C₂×Q₈	#2411	1	2	yes	—
650	C₂×Q₈	#2534	1	2	yes	—
651	C₂×Q₈	#2539	1	2	yes	—
652	C₂×Q₈	#2617	1	2	yes	—
653	C₂×D₄	#1438	1	1	yes	characteristic
654	C₂×D₄	#1438	1	1	yes	characteristic
655	C₂×D₄	#1438	1	1	yes	characteristic
656	C₂×D₄	#1438	1	1	yes	characteristic
657	C₂×D₄	#1889	1	2	yes	—
658	C₂×D₄	#1889	1	2	yes	—
659	C₂×D₄	C₂×#386	1	1	yes	characteristic
660	C₂×D₄	C₂×#390	1	1	yes	characteristic
661	C₂×D₄	#2321	1	2	yes	—
662	C₂×D₄	D₄×C₂²⋊C₄	1	2	yes	—
663	C₂×D₄	D₄×C₂²⋊C₄	1	2	yes	—
664	C₂×D₄	#2358	1	2	yes	—
665	C₂×D₄	#2358	1	2	yes	—
666	C₂×D₄	C₂×#392	1	1	yes	characteristic
667	C₂×D₄	C₂×#394	1	1	yes	characteristic
668	C₂×D₄	#2404	1	2	yes	—
669	C₂×D₄	#2410	1	2	yes	—
670	C₂×D₄	#2410	1	2	yes	—
671	C₂×D₄	#2410	1	2	yes	—
672	C₂×D₄	#2411	1	2	yes	—
673	C₂×D₄	#2412	1	2	yes	—
674	C₂×D₄	#2418	1	2	yes	—
675	C₂×D₄	#2418	1	2	yes	—
676	C₂×D₄	#2424	1	2	yes	—
677	C₂×D₄	#2424	1	2	yes	—
678	C₂×D₄	#2424	1	2	yes	—
679	C₂×D₄	#2424	1	2	yes	—
680	C₂×D₄	#2472	1	2	yes	—
681	C₂×D₄	#2472	1	2	yes	—
682	C₂×D₄	#2534	1	2	yes	—
683	C₂×D₄	#2539	1	2	yes	—
684	C₂×D₄	#2617	1	2	yes	—
685	C₂²×C₄	C₂×#379	1	1	yes	characteristic
686	C₂²×C₄	C₂×#386	1	1	yes	characteristic
687	C₂²×C₄	C₂×#386	1	1	yes	characteristic
688	C₂²×C₄	C₂×#386	1	1	yes	characteristic
689	C₂²×C₄	C₄×#120	1	2	yes	—
690	C₂²×C₄	#2308	1	1	yes	characteristic
691	C₂²×C₄	#2308	1	1	yes	characteristic
692	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
693	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
694	C₂²×C₄	#2358	1	2	yes	—
695	C₂²×C₄	#2358	1	2	yes	—
696	C₂²×C₄	C₂×#392	1	1	yes	characteristic
697	C₂²×C₄	C₂×#392	1	1	yes	characteristic
698	C₂²×C₄	C₂×#394	1	1	yes	characteristic
699	C₂²×C₄	C₂×#394	1	1	yes	characteristic
700	C₂²×C₄	#2403	1	2	yes	—
701	C₂²×C₄	#2403	1	1	yes	characteristic
702	C₂²×C₄	#2403	1	1	yes	characteristic
703	C₂²×C₄	#2405	1	1	yes	characteristic
704	C₂²×C₄	#2405	1	1	yes	characteristic
705	C₂²×C₄	#2405	1	1	yes	characteristic
706	C₂²×C₄	#2405	1	1	yes	characteristic
707	C₂²×C₄	#2408	1	2	yes	—
708	C₂²×C₄	#2410	1	2	yes	—
709	C₂²×C₄	#2410	1	2	yes	—
710	C₂²×C₄	#2410	1	2	yes	—
711	C₂²×C₄	#2410	1	2	yes	—
712	C₂²×C₄	#2410	1	1	yes	characteristic
713	C₂²×C₄	#2410	1	1	yes	characteristic
714	C₂²×C₄	#2412	1	1	yes	characteristic
715	C₂²×C₄	#2412	1	1	yes	characteristic
716	C₂²×C₄	#2412	1	2	yes	—
717	C₂²×C₄	#2412	1	1	yes	characteristic
718	C₂²×C₄	#2412	1	1	yes	characteristic
719	C₂²×C₄	#2418	1	2	yes	—
720	C₂²×C₄	#2418	1	2	yes	—
721	C₂²×C₄	#2424	1	2	yes	—
722	C₂²×C₄	#2424	1	2	yes	—
723	C₂²×C₄	#2424	1	2	yes	—
724	C₂²×C₄	#2424	1	2	yes	—
725	C₂²×C₄	#2433	1	2	yes	—
726	C₂²×C₄	#2472	1	2	yes	—
727	C₂²×C₄	#2472	1	2	yes	—
728	C₂²×C₄	#2613	1	1	yes	characteristic
729	C₂²×C₄	#2613	1	1	yes	characteristic
730	C₂²×C₄	#2622	1	1	yes	characteristic
731	C₂²×C₄	#2622	1	1	yes	characteristic
732	C₂²×C₄	#2847	1	2	yes	—
733	C₂²×C₄	#2849	1	1	yes	characteristic
734	C₂²×C₄	#2849	1	1	yes	characteristic
735	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
736	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
737	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
738	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
739	C₂²×C₄	#3026	1	1	yes	characteristic
740	C₂²×C₄	#3026	1	1	yes	characteristic
741	C₂²×C₄	#3026	1	1	yes	characteristic
742	C₂²×C₄	#3026	1	1	yes	characteristic
743	C₄²	#1438	1	1	yes	characteristic
744	C₄²	#1438	1	1	yes	characteristic
745	C₄²	#1438	1	1	yes	characteristic
746	C₄²	#1438	1	1	yes	characteristic
747	C₄²	#1438	1	1	yes	characteristic
748	C₄²	#1438	1	1	yes	characteristic
749	C₄²	#1438	1	1	yes	characteristic
750	C₄²	#1438	1	1	yes	characteristic
751	C₂³	#13867	1	1	yes	characteristic
752	C₂³	#13967	1	2	yes	—
753	C₂³	#13995	1	2	yes	—
754	C₂³	#14134	1	1	yes	characteristic
755	C₂³	#14694	1	1	yes	characteristic
756	C₂³	#14715	1	1	yes	characteristic
757	C₂³	#14715	1	1	yes	characteristic
758	C₂³	#14716	1	2	yes	—
759	C₂³	#14718	1	1	yes	characteristic
760	C₂³	#14718	1	1	yes	characteristic
761	C₂³	#14725	1	2	yes	—
762	C₂³	#32898	1	1	yes	characteristic
763	C₂³	#32898	1	1	yes	characteristic
764	C₂³	#32898	1	1	yes	characteristic
765	C₂³	#32898	1	1	yes	characteristic
766	C₂×C₄	C₂×#1438	1	1	yes	characteristic
767	C₂×C₄	#13867	1	1	yes	characteristic
768	C₂×C₄	#13967	1	2	yes	—
769	C₂×C₄	#13995	1	2	yes	—
770	C₂×C₄	#14134	1	1	yes	characteristic
771	C₂×C₄	#14255	1	1	yes	characteristic
772	C₂×C₄	#14716	1	2	yes	—
773	C₂×C₄	#14718	1	1	yes	characteristic
774	C₂×C₄	#14718	1	1	yes	characteristic
775	C₂×C₄	#14725	1	2	yes	—
776	C₂×C₄	#14911	1	1	yes	characteristic
777	C₂×C₄	#14911	1	1	yes	characteristic
778	C₂×C₄	C₂×#1889	1	1	yes	characteristic
779	C₂×C₄	C₂×#1889	1	1	yes	characteristic
780	C₂×C₄	#20960	1	1	yes	characteristic
781	C₂×C₄	#20960	1	1	yes	characteristic
782	C₂×C₄	#23900	1	1	yes	characteristic
783	C₂×C₄	#23900	1	1	yes	characteristic
784	C₂×C₄	#23900	1	1	yes	characteristic
785	C₂×C₄	#23900	1	1	yes	characteristic
786	C₂×C₄	#23903	1	1	yes	characteristic
787	C₂×C₄	#23903	1	1	yes	characteristic
788	C₂×C₄	#23903	1	1	yes	characteristic
789	C₂×C₄	#23903	1	1	yes	characteristic
790	C₂×C₄	#24404	1	1	yes	characteristic
791	C₂×C₄	#24404	1	1	yes	characteristic
792	C₂×C₄	#24404	1	1	yes	characteristic
793	C₂×C₄	#24404	1	1	yes	characteristic
794	C₂×C₄	#24404	1	1	yes	characteristic
795	C₂×C₄	#24404	1	1	yes	characteristic
796	C₂×C₄	#24404	1	1	yes	characteristic
797	C₂×C₄	#24404	1	1	yes	characteristic
798	C₂×C₄	#33020	1	1	yes	characteristic
799	C₂×C₄	#33020	1	1	yes	characteristic
800	C₂×C₄	#33020	1	1	yes	characteristic
801	C₂×C₄	#33020	1	1	yes	characteristic
802	C₂²	#154195	1	1	yes	characteristic
803	C₂²	#392658	1	1	yes	characteristic
804	C₂²	#392658	1	1	yes	characteristic
805	C₂²	#394066	1	1	yes	characteristic
806	C₂²	#394066	1	1	yes	characteristic
807	C₂²	#394066	1	1	yes	characteristic
808	C₂²	#394066	1	1	yes	characteristic
809	C₄	#359501	1	1	yes	characteristic
810	C₄	#359504	1	1	yes	characteristic
811	C₄	#374038	1	1	yes	characteristic
812	C₄	#374038	1	1	yes	characteristic
813	C₄	#394557	1	1	yes	characteristic
814	C₄	#394557	1	1	yes	characteristic
815	C₄	#394557	1	1	yes	characteristic
816	C₄	#394557	1	1	yes	characteristic
817	C₂	#72219232	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#394557
commutator	C₂²×#41	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
socle	C₂	#72219232
prime radical	C₂×#6437584	C₂
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341739	C₂	semidirect
2. #72315284	C₂	semidirect
3. #72315283	C₂	semidirect
4. #72312474	C₂	semidirect
5. #72303719	C₂	semidirect
6. #72303713	C₂	semidirect
7. #72303706	C₂	semidirect
9. #72303051	C₂	semidirect
10. C₂×#493419	C₂	semidirect
11. #72302906	C₂	semidirect
21. C₂×#23873	C₄	semidirect
22. C₂×#23875	C₄	semidirect
23. C₂×#23874	C₄	semidirect
24. C₂×#23872	C₄	semidirect
30. #6370746	C₂²	semidirect
31. #6370734	C₂²	semidirect
33. #492906	C₂²	semidirect
34. #492899	C₂²	semidirect
35. #492886	C₂²	semidirect
36. #492886	C₂²	semidirect
37. #353430	C₂²	semidirect
38. #353422	C₂²	semidirect
42. C₂×#3586	C₂×C₄	semidirect
43. C₂×#3585	C₂×C₄	semidirect
58. C₂×#3028	C₂×C₄	semidirect
59. C₂×#3027	C₂×C₄	semidirect
68. C₂²×#410	D₄	semidirect
69. C₂²×#410	D₄	semidirect
70. C₂²×#410	D₄	semidirect
71. C₂²×#410	D₄	semidirect
74. #34366	D₄	semidirect
75. #34366	D₄	semidirect
76. #34365	D₄	semidirect
77. #34364	D₄	semidirect
80. C₂×#2132	D₄	semidirect
81. C₂×#2132	D₄	semidirect
82. C₂×#2126	D₄	semidirect
83. C₂×#2126	D₄	semidirect
85. C₂×#1915	C₂×C₄	semidirect
86. C₂×#1914	C₂×C₄	semidirect
93. C₂×#1796	C₂×C₄	semidirect
94. C₂×#1795	C₂×C₄	semidirect
98. C₂²×2₋¹⁺⁴	C₂²⋊C₄	semidirect
99. C₂²×2₋¹⁺⁴	C₂²⋊C₄	semidirect
103. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
104. C₂²×H(5,𝔽₂)	C₂²⋊C₄	semidirect
118. C₂×#536	C₂²⋊C₄	semidirect
119. C₂×#536	C₂²⋊C₄	semidirect
122. C₂×#535	C₂²⋊C₄	semidirect
123. C₂×#535	C₂²⋊C₄	semidirect
151. C₂²×C₄⋊Q₈	C₂²⋊C₄	semidirect
153. C₂²×#127	C₂²⋊C₄	semidirect
155. C₂²×#124	C₂²⋊C₄	semidirect
156. C₂²×#124	C₂²⋊C₄	semidirect
160. C₂×C₄×#41	C₂²⋊C₄	semidirect
161. C₂×C₄×#41	C₂²⋊C₄	semidirect
162. C₂×C₄×#41	C₂²⋊C₄	semidirect
163. C₂×C₄×#41	C₂²⋊C₄	semidirect
186. #1884	C₂²⋊C₄	semidirect
187. #1884	C₂²⋊C₄	semidirect
188. #1884	C₂²⋊C₄	semidirect
189. #1884	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72341739	2
#72315284	2
#72315283	2
#72312474	2
#72303719	2
#72303713	2
#72303706	2
C₂×#6437584	2
#72303051	2
C₂×#493419	2
#72302906	2