Subgroups — #26005257

Order 11008.

7382 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148808	C₂	1	8	yes	maximal, complemented
2	#19148789	C₂	1	8	yes	maximal, complemented
3	#19148766	C₂	1	8	yes	maximal, complemented
4	#19148527	C₂	1	16	yes	maximal, complemented
5	#19148304	C₂	1	4	yes	maximal, complemented
6	#19148291	C₂	1	4	yes	maximal, complemented
7	#19148284	C₂	1	4	yes	maximal, complemented
8	#19148284	C₂	1	2	yes	maximal, complemented
9	#19148233	C₂	1	4	yes	maximal, complemented
10	#19148230	C₂	1	2	yes	maximal, complemented
11	C₂×#14583410	C₂	1	2	yes	maximal, complemented
12	C₂²×#123×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13063370	C₂²	1	2	yes	complemented
14	C₂²×#10621898	C₂²	1	2	yes	complemented
15	#14583652	C₂²	1	8	yes	complemented
16	#14583646	C₂²	1	16	yes	complemented
17	#14583639	C₂²	1	8	yes	complemented
18	#14583633	C₂²	1	8	yes	complemented
19	#14583604	C₂²	1	16	yes	complemented
20	#14583597	C₂²	1	16	yes	complemented
21	#14583594	C₂²	1	16	yes	complemented
22	#14583586	C₂²	1	16	yes	complemented
23	#14583584	C₂²	1	16	yes	complemented
24	#14583577	C₂²	1	8	yes	complemented
25	#14583575	C₂²	1	16	yes	complemented
26	#14583575	C₂²	1	16	yes	complemented
27	#14583575	C₂²	1	16	yes	complemented
28	#14583572	C₂²	1	16	yes	complemented
29	#14583550	C₂²	1	16	yes	complemented
30	#14583547	C₂²	1	16	yes	complemented
31	#14583543	C₂²	1	16	yes	complemented
32	#14583541	C₂²	1	16	yes	complemented
33	#14583539	C₂²	1	16	yes	complemented
34	#14583539	C₂²	1	16	yes	complemented
35	#14583539	C₂²	1	16	yes	complemented
36	D₄×C₂²⋊D₄₃	C₂²	1	16	yes	complemented
37	#14583530	C₂²	1	4	yes	complemented
38	#14583525	C₂²	1	2	yes	complemented
39	#14583525	C₂²	1	4	yes	complemented
40	#14583517	C₂²	1	16	yes	complemented
41	#14583501	C₂²	1	16	yes	complemented
42	#14583496	C₂²	1	8	yes	complemented
43	#14583496	C₂²	1	8	yes	complemented
44	#14583493	C₂²	1	16	yes	complemented
45	#14583492	C₂²	1	16	yes	complemented
46	#14583487	C₂²	1	8	yes	complemented
47	#14583487	C₂²	1	8	yes	complemented
48	#14583487	C₂²	1	8	yes	complemented
49	#14583485	C₂²	1	16	yes	complemented
50	#14583480	C₂²	1	4	yes	complemented
51	#14583471	C₂²	1	8	yes	complemented
52	#14583466	C₂²	1	4	yes	complemented
53	#14583461	C₂²	1	2	yes	complemented
54	#14583461	C₂²	1	4	yes	complemented
55	#14583460	C₂²	1	8	yes	complemented
56	#14583458	C₂²	1	4	yes	—
57	#14583458	C₂²	1	4	yes	complemented
58	#14583426	C₂²	1	16	yes	complemented
59	#14583410	C₂²	1	4	yes	complemented
60	#14583410	C₂²	1	8	yes	complemented
61	#14583410	C₂²	1	8	yes	complemented
62	#14583410	C₂²	1	8	yes	complemented
63	#14583410	C₂²	1	8	yes	complemented
64	#14583410	C₂²	1	8	yes	complemented
65	#14583407	C₂²	1	8	yes	complemented
66	C₂×#13063308	C₂²	1	4	yes	complemented
67	#123×D₄₃	C₂²	1	8	yes	complemented
68	C₂×#13063304	C₂²	1	4	yes	complemented
69	C₂×#13063299	C₂²	1	4	yes	complemented
70	C₂×#13063294	C₂²	1	4	yes	complemented
71	C₂×#13063294	C₂²	1	4	yes	complemented
72	#14583380	C₂²	1	8	yes	complemented
73	#14583374	C₂²	1	2	yes	complemented
74	#14583372	C₂²	1	4	yes	complemented
75	#14583372	C₂²	1	8	yes	complemented
76	C₂×C₄×C₂²⋊D₄₃	C₂²	1	8	yes	complemented
77	C₂×#13063284	C₂²	1	2	yes	complemented
78	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
79	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×#123×C₄₃	C₂²	1	4	yes	complemented
81	C₂×#123×C₄₃	C₂²	1	8	yes	complemented
82	C₂×#123×C₄₃	C₂²	1	4	yes	complemented
83	C₂×#123×C₄₃	C₂²	1	8	yes	complemented
84	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
85	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
86	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	complemented
87	#13063370	—	4	8	no	—
88	C₂×#10621898	—	4	8	no	—
89	C₂×#10621898	C₂³	1	8	yes	—
90	C₂×#10621898	C₂³	1	8	yes	—
91	C₂×#10621898	C₂³	1	4	yes	—
92	C₂×#10621898	C₂³	1	8	yes	complemented
93	C₂×#10621900	C₂³	1	8	yes	—
94	C₂²×Dic₈₆	C₂³	1	2	yes	complemented
95	C₂²×D₁₇₂	C₂³	1	2	yes	complemented
96	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
97	C₂²×C₂²⋊D₄₃	C₂³	1	8	yes	—
98	C₂²×C₂²⋊D₄₃	C₂³	1	8	yes	—
99	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
100	C₂×D₄×D₄₃	C₂³	1	8	yes	—
101	C₂²×C₄×D₄₃	C₂³	1	4	yes	complemented
102	#13063324	C₂³	1	16	yes	complemented
103	#13063321	C₂³	1	8	yes	—
104	#13063320	C₂³	1	16	yes	complemented
105	#13063320	C₂³	1	16	yes	complemented
106	#13063318	C₂³	1	16	yes	complemented
107	#13063318	C₂³	1	16	yes	complemented
108	#13063318	C₂³	1	16	yes	complemented
109	#13063316	C₂³	1	16	yes	complemented
110	#13063315	C₂³	1	16	yes	complemented
111	#13063315	C₂³	1	16	yes	complemented
112	#13063312	C₂³	1	8	yes	—
113	#13063311	C₂³	1	16	yes	complemented
114	#13063311	C₂³	1	16	yes	complemented
115	#13063311	C₂³	1	16	yes	complemented
116	#13063310	C₂³	1	16	yes	complemented
117	#13063310	C₂³	1	16	yes	complemented
118	#13063309	C₂³	1	16	yes	complemented
119	#13063309	C₂³	1	8	yes	complemented
120	#13063308	C₂³	1	16	yes	—
121	#13063308	C₂³	1	16	yes	—
122	#13063308	C₂³	1	8	yes	—
123	#13063308	C₂³	1	8	yes	complemented
124	#13063308	C₂³	1	8	yes	complemented
125	#13063307	C₂³	1	16	yes	complemented
126	#13063307	C₂³	1	16	yes	complemented
127	#13063307	C₂³	1	16	yes	complemented
128	#13063306	C₂³	1	8	yes	—
129	#13063306	C₂³	1	8	yes	—
130	#13063305	C₂³	1	16	yes	complemented
131	#13063304	C₂³	1	8	yes	—
132	#13063304	C₂³	1	8	yes	—
133	#13063304	C₂³	1	8	yes	—
134	#13063304	C₂³	1	8	yes	—
135	#13063304	C₂³	1	8	yes	—
136	#13063304	C₂³	1	8	yes	complemented
137	#13063304	C₂³	1	8	yes	complemented
138	#13063303	C₂³	1	16	yes	complemented
139	#13063303	C₂³	1	16	yes	complemented
140	#13063302	C₂³	1	16	yes	complemented
141	#13063302	C₂³	1	16	yes	complemented
142	#13063302	C₂³	1	16	yes	complemented
143	#13063300	C₂³	1	16	yes	complemented
144	#13063299	C₂³	1	8	yes	—
145	#13063299	C₂³	1	8	yes	—
146	#13063299	C₂³	1	8	yes	—
147	#13063299	C₂³	1	8	yes	—
148	#13063299	C₂³	1	8	yes	—
149	#13063299	C₂³	1	8	yes	complemented
150	#13063299	C₂³	1	8	yes	complemented
151	#13063298	C₂³	1	16	yes	complemented
152	#13063298	C₂³	1	16	yes	complemented
153	#13063298	C₂³	1	16	yes	complemented
154	#13063297	C₂³	1	16	yes	—
155	#13063297	C₂³	1	16	yes	—
156	#13063296	C₂³	1	16	yes	—
157	#13063295	C₂³	1	16	yes	complemented
158	#13063295	C₂³	1	8	yes	complemented
159	#13063294	C₂³	1	8	yes	—
160	#13063294	C₂³	1	16	yes	—
161	#13063294	C₂³	1	16	yes	—
162	#13063294	C₂³	1	8	yes	—
163	#13063294	C₂³	1	8	yes	—
164	#13063293	C₂³	1	8	yes	—
165	#13063293	C₂³	1	8	yes	—
166	#13063290	C₂³	1	16	yes	complemented
167	D₄×Dic₄₃	C₂³	1	16	yes	—
168	#13063287	C₂³	1	16	yes	complemented
169	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	—
170	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	—
171	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	—
172	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	—
173	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	—
174	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	complemented
175	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	complemented
176	(C₂²⋊D₄₃)⋊C₄	C₂³	1	16	yes	complemented
177	(C₂²⋊D₄₃)⋊C₄	C₂³	1	16	yes	complemented
178	(C₂²⋊D₄₃)⋊C₄	C₂³	1	16	yes	complemented
179	#13063284	C₂³	1	8	yes	—
180	#13063284	C₂³	1	8	yes	—
181	#13063284	C₂³	1	4	yes	—
182	#13063284	C₂³	1	8	yes	complemented
183	#13063283	C₂³	1	16	yes	complemented
184	#13063281	C₂³	1	8	yes	complemented
185	#13063281	C₂³	1	16	yes	complemented
186	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	complemented
187	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	complemented
188	C₄⋊C₄×D₄₃	C₂³	1	16	yes	complemented
189	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
190	C₂×C₂²⋊Dic₄₃	C₂³	1	8	yes	—
191	C₂×C₂²⋊Dic₄₃	C₂³	1	8	yes	—
192	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
193	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	complemented
194	C₂²⋊C₄×D₄₃	C₂³	1	8	yes	complemented
195	C₂²⋊C₄×D₄₃	C₂³	1	16	yes	complemented
196	C₂×C₄×Dic₄₃	C₂³	1	4	yes	complemented
197	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
198	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₄₃	—	4	4	no	—
200	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
201	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
202	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
203	C₂³×C₄×C₄₃	—	4	4	no	—
204	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
205	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
206	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
207	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
209	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
210	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
211	#123×C₄₃	C₂³	1	16	yes	—
212	#123×C₄₃	C₂³	1	8	yes	—
213	#123×C₄₃	C₂³	1	8	yes	—
214	#123×C₄₃	C₂³	1	8	yes	—
215	#123×C₄₃	C₂³	1	8	yes	—
216	#123×C₄₃	C₂³	1	16	yes	—
217	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
218	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
219	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
220	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
222	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
223	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
224	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
226	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
228	C₂⁴×C₄₃	—	2	4	no	—
229	C₂⁴×C₄₃	—	4	4	no	—
230	C₂⁴×C₄₃	—	4	2	no	—
231	C₂⁴×C₄₃	—	4	4	no	—
232	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
234	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
235	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
236	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂³×D₄₃	C₂⁴	1	4	yes	—
239	C₂³×D₄₃	C₂⁴	1	4	yes	—
240	C₂×D₄×C₄₃	—	2	8	no	—
241	C₂×D₄×C₄₃	—	4	4	no	—
242	C₂×D₄×C₄₃	—	4	16	no	—
243	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
244	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
245	C₂²×C₄×C₄₃	—	2	8	no	—
246	C₂²×C₄×C₄₃	—	4	4	no	—
247	C₂²×C₄×C₄₃	—	4	8	no	—
248	C₂²×C₄×C₄₃	—	4	8	no	—
249	C₂²×C₄×C₄₃	—	4	4	no	—
250	C₂²×C₄×C₄₃	—	4	4	no	—
251	C₂²×C₄×C₄₃	—	4	2	no	—
252	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
267	C₂×C₂²⋊D₄₃	—	2	16	no	—
268	C₂×C₂²⋊D₄₃	—	4	16	no	—
269	C₂×C₂²⋊D₄₃	—	4	16	no	—
270	C₂×C₂²⋊D₄₃	—	4	8	no	—
271	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
272	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
273	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
274	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
275	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
276	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
277	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
278	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
279	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
280	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
281	#10621900	—	4	16	no	—
282	D₄×D₄₃	—	4	16	no	—
283	#10621898	—	4	16	no	—
284	#10621898	—	4	16	no	—
285	#10621898	—	4	16	no	—
286	#10621898	—	4	8	no	—
287	C₂×D₁₇₂	—	4	4	no	—
288	C₂×D₁₇₂	C₂⁴	1	8	yes	—
289	C₂×D₁₇₂	C₂⁴	1	8	yes	—
290	C₂×D₁₇₂	C₂⁴	1	4	yes	—
291	C₂×C₄×D₄₃	—	4	8	no	—
292	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
293	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
294	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
295	C₂×Dic₈₆	—	4	4	no	—
296	C₂×Dic₈₆	C₂⁴	1	8	yes	—
297	C₂×Dic₈₆	C₂⁴	1	8	yes	—
298	C₂×Dic₈₆	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
300	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
301	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
302	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
303	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
304	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
305	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
306	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
307	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
308	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
309	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
310	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
311	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
312	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
313	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
314	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
315	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
316	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
317	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
318	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
319	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
320	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
321	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
322	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
323	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
324	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
325	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
326	C₄×Dic₄₃	C₂⁴	1	16	yes	—
327	C₄×Dic₄₃	C₂⁴	1	16	yes	—
328	C₄×Dic₄₃	C₂⁴	1	8	yes	—
329	C₂³×C₄₃	—	2	2	no	—
330	C₂³×C₄₃	—	2	4	no	—
331	C₂³×C₄₃	—	2	8	no	—
332	C₂³×C₄₃	—	2	2	no	—
333	C₂³×C₄₃	—	2	8	no	—
334	C₂³×C₄₃	—	2	4	no	—
335	C₂³×C₄₃	—	2	8	no	—
336	C₂³×C₄₃	—	4	2	no	—
337	C₂³×C₄₃	—	4	4	no	—
338	C₂³×C₄₃	—	4	2	no	—
339	C₂³×C₄₃	—	4	4	no	—
340	C₂³×C₄₃	—	4	4	no	—
341	C₂³×C₄₃	—	4	4	no	—
342	C₂³×C₄₃	—	4	16	no	—
343	C₂³×C₄₃	—	8	8	no	—
344	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
345	C₂³×C₄₃	C₂⁵	1	2	yes	—
346	C₂³×C₄₃	C₂⁵	1	4	yes	—
347	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
348	C₂³×C₄₃	C₂⁵	1	2	yes	—
349	C₂³×C₄₃	C₂⁵	1	2	yes	—
350	C₂²×D₄₃	—	2	8	no	—
351	C₂²×D₄₃	—	4	8	no	—
352	C₂²×D₄₃	—	4	4	no	—
353	C₂²×D₄₃	—	4	8	no	—
354	C₂²×D₄₃	C₂⁵	1	8	yes	—
355	D₄×C₄₃	—	2	16	no	—
356	D₄×C₄₃	—	4	8	no	—
357	C₂×C₄×C₄₃	—	2	4	no	—
358	C₂×C₄×C₄₃	—	2	4	no	—
359	C₂×C₄×C₄₃	—	2	8	no	—
360	C₂×C₄×C₄₃	—	2	8	no	—
361	C₂×C₄×C₄₃	—	2	4	no	—
362	C₂×C₄×C₄₃	—	2	8	no	—
363	C₂×C₄×C₄₃	—	4	2	no	—
364	C₂×C₄×C₄₃	—	4	2	no	—
365	C₂×C₄×C₄₃	—	4	4	no	—
366	C₂×C₄×C₄₃	—	4	4	no	—
367	C₂×C₄×C₄₃	—	4	2	no	—
368	C₂×C₄×C₄₃	—	4	2	no	—
369	C₂×C₄×C₄₃	—	4	4	no	—
370	C₂×C₄×C₄₃	—	4	4	no	—
371	C₂×C₄×C₄₃	—	4	4	no	—
372	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
373	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
374	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
375	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
376	C₂²⋊D₄₃	—	2	16	no	—
377	C₂²⋊D₄₃	—	2	16	no	—
378	C₂²⋊D₄₃	—	2	32	no	—
379	C₂²⋊D₄₃	—	4	8	no	—
380	C₂²⋊D₄₃	—	4	16	no	—
381	C₂²⋊D₄₃	—	4	16	no	—
382	C₂×Dic₄₃	—	2	8	no	—
383	C₂×Dic₄₃	—	4	4	no	—
384	C₂×Dic₄₃	—	4	8	no	—
385	C₂×Dic₄₃	—	4	8	no	—
386	C₂×Dic₄₃	C₂⁵	1	16	yes	—
387	C₂×Dic₄₃	C₂⁵	1	8	yes	—
388	D₁₇₂	—	4	8	no	—
389	D₁₇₂	—	4	8	no	—
390	D₁₇₂	—	4	4	no	—
391	C₄×D₄₃	—	4	16	no	—
392	C₄×D₄₃	—	4	16	no	—
393	C₄×D₄₃	—	4	8	no	—
394	Dic₈₆	—	4	8	no	—
395	Dic₈₆	—	4	8	no	—
396	Dic₈₆	—	4	4	no	—
397	#62820	—	43	1	no	maximal, Sylow
398	C₂²×C₄₃	—	2	8	no	—
399	C₂²×C₄₃	—	2	2	no	—
400	C₂²×C₄₃	—	2	4	no	—
401	C₂²×C₄₃	—	2	2	no	—
402	C₂²×C₄₃	—	2	2	no	—
403	C₂²×C₄₃	—	2	4	no	—
404	C₂²×C₄₃	—	2	2	no	—
405	C₂²×C₄₃	—	2	8	no	—
406	C₂²×C₄₃	—	2	4	no	—
407	C₂²×C₄₃	—	4	4	no	—
408	C₂²×C₄₃	—	4	16	no	—
409	C₂²×C₄₃	—	4	4	no	—
410	C₂²×C₄₃	—	8	4	no	—
411	C₂²×C₄₃	—	8	8	no	—
412	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
413	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
414	C₂²×C₄₃	#585	1	4	yes	—
415	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
416	C₂×D₄₃	—	2	8	no	—
417	C₂×D₄₃	—	2	16	no	—
418	C₂×D₄₃	—	8	8	no	—
419	C₂×D₄₃	—	16	4	no	—
420	C₄×C₄₃	—	2	4	no	—
421	C₄×C₄₃	—	2	4	no	—
422	C₄×C₄₃	—	2	4	no	—
423	C₄×C₄₃	—	2	8	no	—
424	Dic₄₃	—	2	8	no	—
425	Dic₄₃	—	2	16	no	—
426	#3535	—	43	8	no	—
427	#3534	—	43	8	no	—
428	#3533	—	43	8	no	—
429	#3513	—	43	16	no	—
430	#3492	—	43	4	no	—
431	#3491	—	43	4	no	—
432	#3490	—	43	2	no	—
433	#3490	—	43	4	no	—
434	#3485	—	43	4	no	—
435	#3484	—	43	2	no	—
436	C₂×#525	—	43	2	no	—
437	C₂²×#123	D₄₃	1	1	yes	characteristic, complemented
438	C₂×C₄₃	—	2	4	no	—
439	C₂×C₄₃	—	2	2	no	—
440	C₂×C₄₃	—	2	4	no	—
441	C₂×C₄₃	—	4	4	no	—
442	C₂×C₄₃	—	4	2	no	—
443	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂×C₄₃	C₂×#585	1	2	yes	—
445	D₄₃	—	4	8	no	—
446	C₂×H(5,𝔽₂)	—	43	2	no	—
447	C₂²×#41	—	43	2	no	—
448	C₂³×D₄	C₂×D₄₃	1	1	yes	characteristic
449	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
450	#563	—	43	8	no	—
451	#562	—	43	16	no	—
452	#560	—	43	8	no	—
453	#559	—	43	8	no	—
454	#554	—	43	16	no	—
455	#553	—	43	16	no	—
456	#553	—	43	16	no	—
457	#552	—	43	16	no	—
458	#552	—	43	16	no	—
459	#551	—	43	16	no	—
460	#551	—	43	8	no	—
461	#551	—	43	16	no	—
462	#551	—	43	16	no	—
463	#551	—	43	16	no	—
464	#547	—	43	16	no	—
465	#547	—	43	16	no	—
466	#546	—	43	16	no	—
467	#546	—	43	16	no	—
468	#546	—	43	16	no	—
469	#546	—	43	16	no	—
470	#546	—	43	16	no	—
471	D₄²	—	43	16	no	—
472	#544	—	43	4	no	—
473	#543	—	43	2	no	—
474	#543	—	43	4	no	—
475	#542	—	43	16	no	—
476	#540	—	43	16	no	—
477	#539	—	43	16	no	—
478	#539	—	43	16	no	—
479	#539	—	43	8	no	—
480	#539	—	43	8	no	—
481	#538	—	43	16	no	—
482	#538	—	43	8	no	—
483	#538	—	43	8	no	—
484	#538	—	43	8	no	—
485	#537	—	43	4	no	—
486	#536	—	43	8	no	—
487	#535	—	43	4	no	—
488	#534	—	43	4	no	—
489	#534	—	43	4	no	—
490	#534	—	43	8	no	—
491	#534	—	43	2	no	—
492	#534	—	43	4	no	—
493	#529	—	43	16	no	—
494	#525	—	43	8	no	—
495	#525	—	43	8	no	—
496	#525	—	43	8	no	—
497	#525	—	43	8	no	—
498	#525	—	43	4	no	—
499	#525	—	43	8	no	—
500	#525	—	43	8	no	—
501	C₂×#123	—	43	4	no	—
502	C₂×#123	—	43	8	no	—
503	C₂×#123	C₂×D₄₃	1	4	yes	complemented
504	C₂×#123	C₂×D₄₃	1	8	yes	complemented
505	C₂×#123	C₂×D₄₃	1	4	yes	complemented
506	C₂×#123	C₂×D₄₃	1	8	yes	complemented
507	C₂×C₂²⋊Q₈	—	43	4	no	—
508	C₂×#121	—	43	4	no	—
509	C₂×#120	—	43	4	no	—
510	C₂×#120	—	43	4	no	—
511	#520	—	43	8	no	—
512	#518	—	43	2	no	—
513	#518	—	43	4	no	—
514	#518	—	43	8	no	—
515	C₂×C₄×D₄	—	43	8	no	—
516	C₂×#117	—	43	2	no	—
517	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	complemented
518	C₂²×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
519	C₂²×C₂²⋊C₄	C₂×D₄₃	1	2	yes	complemented
520	C₄₃	#62820	1	1	yes	characteristic, complemented, Sylow
521	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
522	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
523	H(5,𝔽₂)	—	172	8	no	—
524	C₂×#41	—	43	8	no	—
525	C₂×#41	—	43	8	no	—
526	C₂×#41	—	43	8	no	—
527	C₂×#41	—	43	8	no	—
528	C₂×#41	—	43	4	no	—
529	C₂×#41	—	172	8	no	—
530	C₂²×Q₈	—	43	2	no	—
531	C₂²×D₄	—	4	4	no	—
532	C₂²×D₄	—	43	4	no	—
533	C₂²×D₄	—	43	8	no	—
534	C₂²×D₄	—	43	8	no	—
535	C₂²×D₄	—	43	4	no	—
536	C₂²×D₄	—	43	8	no	—
537	C₂²×D₄	—	43	2	no	—
538	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
539	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
540	C₂²×D₄	C₂²×D₄₃	1	8	yes	—
541	C₂³×C₄	—	4	4	no	—
542	C₂³×C₄	—	43	4	no	—
543	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
544	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
545	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
546	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
547	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
548	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
549	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
550	C₄⋊Q₈	—	43	16	no	—
551	#127	—	43	8	no	—
552	#126	—	43	16	no	—
553	#126	—	43	16	no	—
554	#126	—	43	16	no	—
555	#126	—	43	16	no	—
556	#126	—	43	16	no	—
557	#125	—	43	16	no	—
558	#125	—	43	16	no	—
559	#125	—	43	16	no	—
560	#124	—	43	8	no	—
561	#124	—	43	16	no	—
562	#124	—	43	16	no	—
563	#124	—	43	16	no	—
564	#123	—	43	8	no	—
565	#123	—	43	8	no	—
566	#123	—	43	8	no	—
567	#123	—	43	8	no	—
568	#123	—	43	16	no	—
569	#123	—	43	8	no	—
570	#123	—	43	16	no	—
571	#123	—	43	16	no	—
572	#123	—	43	16	no	—
573	#123	—	43	8	no	—
574	#123	—	43	16	no	—
575	#123	—	43	16	no	—
576	#123	—	43	16	no	—
577	#123	—	43	16	no	—
578	#123	C₂²×D₄₃	1	8	yes	—
579	#123	C₂²×D₄₃	1	8	yes	—
580	#123	C₂²×D₄₃	1	16	yes	—
581	#123	C₂²×D₄₃	1	16	yes	—
582	#123	C₂²×D₄₃	1	8	yes	—
583	#123	C₂²×D₄₃	1	8	yes	—
584	C₂²⋊Q₈	—	43	8	no	—
585	C₂²⋊Q₈	—	43	8	no	—
586	C₂²⋊Q₈	—	43	8	no	—
587	C₂²⋊Q₈	—	43	8	no	—
588	C₂²⋊Q₈	—	43	8	no	—
589	C₂²⋊Q₈	—	43	8	no	—
590	C₂²⋊Q₈	—	43	8	no	—
591	C₂²⋊Q₈	—	43	16	no	—
592	C₂²⋊Q₈	—	43	16	no	—
593	C₂²⋊Q₈	—	43	16	no	—
594	C₂²⋊Q₈	—	43	16	no	—
595	C₂²⋊Q₈	—	43	16	no	—
596	C₂²⋊Q₈	—	43	16	no	—
597	#121	—	43	16	no	—
598	#121	—	43	16	no	—
599	#121	—	43	16	no	—
600	#121	—	43	8	no	—
601	#121	—	43	8	no	—
602	#121	—	43	8	no	—
603	#121	—	43	8	no	—
604	#121	—	43	8	no	—
605	#121	—	43	8	no	—
606	#121	—	43	8	no	—
607	#121	—	43	16	no	—
608	#121	—	43	16	no	—
609	#121	—	43	16	no	—
610	#121	—	43	16	no	—
611	#120	—	43	8	no	—
612	#120	—	43	8	no	—
613	#120	—	43	16	no	—
614	#120	—	43	8	no	—
615	#120	—	43	16	no	—
616	#120	—	43	8	no	—
617	#120	—	43	8	no	—
618	#120	—	43	8	no	—
619	#120	—	43	16	no	—
620	C₄×Q₈	—	43	16	no	—
621	C₄×D₄	—	43	16	no	—
622	C₄×D₄	—	43	16	no	—
623	C₄×D₄	—	43	16	no	—
624	C₄×D₄	—	43	16	no	—
625	C₄×D₄	—	43	16	no	—
626	C₄×D₄	—	43	16	no	—
627	C₄×D₄	—	43	16	no	—
628	C₄×D₄	—	43	16	no	—
629	C₄×D₄	—	43	16	no	—
630	C₄×D₄	—	43	16	no	—
631	C₄×D₄	—	43	16	no	—
632	C₄×D₄	—	43	16	no	—
633	#117	—	43	8	no	—
634	#117	—	43	8	no	—
635	#117	—	43	4	no	—
636	#117	—	43	8	no	—
637	#117	—	43	16	no	—
638	#117	—	43	8	no	—
639	#117	—	43	16	no	—
640	C₂×C₄⋊C₄	—	43	4	no	—
641	C₂×C₄⋊C₄	—	43	8	no	—
642	C₂×C₄⋊C₄	—	43	16	no	—
643	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
644	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
645	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
646	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
647	C₂×C₂²⋊C₄	—	43	4	no	—
648	C₂×C₂²⋊C₄	—	43	8	no	—
649	C₂×C₂²⋊C₄	—	43	4	no	—
650	C₂×C₂²⋊C₄	—	43	8	no	—
651	C₂×C₂²⋊C₄	—	43	8	no	—
652	C₂×C₂²⋊C₄	—	43	8	no	—
653	C₂×C₂²⋊C₄	—	43	16	no	—
654	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
659	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
660	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
661	C₂×C₄²	—	43	4	no	—
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	4	4	no	—
664	C₂⁴	—	4	2	no	—
665	C₂⁴	—	4	4	no	—
666	C₂⁴	—	43	4	no	—
667	C₂⁴	—	43	4	no	—
668	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
669	C₂⁴	C₂³×D₄₃	1	4	yes	—
670	C₂⁴	C₂³×D₄₃	1	2	yes	—
671	C₂⁴	C₂³×D₄₃	1	4	yes	—
672	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
673	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
674	#41	—	172	16	no	—
675	#41	—	172	16	no	—
676	#41	—	172	8	no	—
677	#41	—	172	16	no	—
678	#41	—	172	16	no	—
679	C₂×Q₈	—	43	8	no	—
680	C₂×Q₈	—	43	8	no	—
681	C₂×Q₈	—	43	4	no	—
682	C₂×Q₈	—	172	4	no	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	16	no	—
686	C₂×D₄	—	43	16	no	—
687	C₂×D₄	—	43	8	no	—
688	C₂×D₄	—	43	8	no	—
689	C₂×D₄	—	43	16	no	—
690	C₂×D₄	—	43	16	no	—
691	C₂×D₄	—	43	8	no	—
692	C₂×D₄	—	43	8	no	—
693	C₂×D₄	—	43	8	no	—
694	C₂×D₄	—	43	4	no	—
695	C₂×D₄	—	86	16	no	—
696	C₂×D₄	—	172	4	no	—
697	C₂×D₄	—	172	16	no	—
698	C₂×D₄	—	172	8	no	—
699	C₂×D₄	—	172	16	no	—
700	C₂×D₄	—	172	16	no	—
701	C₂×D₄	C₂³×D₄₃	1	8	yes	—
702	C₂×D₄	C₂³×D₄₃	1	8	yes	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	4	8	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	—	4	4	no	—
707	C₂²×C₄	—	4	4	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	4	no	—
710	C₂²×C₄	—	43	4	no	—
711	C₂²×C₄	—	43	8	no	—
712	C₂²×C₄	—	43	8	no	—
713	C₂²×C₄	—	43	4	no	—
714	C₂²×C₄	—	43	16	no	—
715	C₂²×C₄	—	43	16	no	—
716	C₂²×C₄	—	43	8	no	—
717	C₂²×C₄	—	172	8	no	—
718	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
719	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
720	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
721	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
722	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
723	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
724	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
725	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
726	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
727	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
728	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
729	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
730	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
731	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
732	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
733	C₄⋊C₄	—	43	16	no	—
734	C₄⋊C₄	—	43	8	no	—
735	C₄⋊C₄	—	43	8	no	—
736	C₄⋊C₄	—	43	8	no	—
737	C₄⋊C₄	—	43	16	no	—
738	C₄⋊C₄	—	43	16	no	—
739	C₄⋊C₄	—	43	8	no	—
740	C₄⋊C₄	—	43	8	no	—
741	C₄⋊C₄	—	43	16	no	—
742	C₄⋊C₄	—	43	16	no	—
743	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
744	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
745	C₂²⋊C₄	—	43	8	no	—
746	C₂²⋊C₄	—	43	8	no	—
747	C₂²⋊C₄	—	43	16	no	—
748	C₂²⋊C₄	—	43	16	no	—
749	C₂²⋊C₄	—	43	8	no	—
750	C₂²⋊C₄	—	43	16	no	—
751	C₂²⋊C₄	—	43	16	no	—
752	C₂²⋊C₄	—	43	16	no	—
753	C₂²⋊C₄	—	43	16	no	—
754	C₂²⋊C₄	—	43	16	no	—
755	C₂²⋊C₄	—	43	16	no	—
756	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
757	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
758	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
759	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
760	C₄²	—	43	16	no	—
761	C₄²	—	43	16	no	—
762	C₄²	—	43	8	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	4	no	—
765	C₂³	—	2	8	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	8	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	4	4	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	16	no	—
777	C₂³	—	8	8	no	—
778	C₂³	—	43	8	no	—
779	C₂³	—	86	8	no	—
780	C₂³	—	172	8	no	—
781	C₂³	—	172	4	no	—
782	C₂³	—	172	8	no	—
783	C₂³	#13063370	1	4	yes	—
784	C₂³	C₂⁴×D₄₃	1	2	yes	—
785	C₂³	C₂⁴×D₄₃	1	4	yes	—
786	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
787	C₂³	C₂⁴×D₄₃	1	2	yes	—
788	C₂³	C₂⁴×D₄₃	1	2	yes	—
789	Q₈	—	172	8	no	—
790	Q₈	—	172	4	no	—
791	Q₈	—	172	8	no	—
792	D₄	—	2	16	no	—
793	D₄	—	4	8	no	—
794	D₄	—	86	16	no	—
795	D₄	—	86	16	no	—
796	D₄	—	86	32	no	—
797	D₄	—	172	4	no	—
798	D₄	—	172	8	no	—
799	D₄	—	172	8	no	—
800	D₄	—	172	8	no	—
801	D₄	—	172	16	no	—
802	D₄	—	172	16	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	43	16	no	—
819	C₂×C₄	—	43	8	no	—
820	C₂×C₄	—	86	8	no	—
821	C₂×C₄	—	172	16	no	—
822	C₂×C₄	—	172	8	no	—
823	C₂×C₄	—	172	16	no	—
824	C₂×C₄	—	172	4	no	—
825	C₂×C₄	—	172	8	no	—
826	C₂×C₄	—	172	8	no	—
827	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
828	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
829	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
830	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
831	C₂²	—	2	8	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	8	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	16	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	8	4	no	—
844	C₂²	—	8	8	no	—
845	C₂²	—	86	8	no	—
846	C₂²	—	86	16	no	—
847	C₂²	—	344	8	no	—
848	C₂²	—	688	4	no	—
849	C₂²	C₂×#13063370	1	2	yes	—
850	C₂²	C₂×#13063370	1	4	yes	—
851	C₂²	#14583735	1	4	yes	—
852	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	86	8	no	—
858	C₄	—	86	16	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	4	no	—
861	C₂	—	2	4	no	—
862	C₂	—	4	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	172	8	no	—
865	C₂	C₂²×#13063370	1	1	yes	characteristic
866	C₂	C₂×#14583735	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁶
Fitting	C₂²×#123×C₄₃	C₂
hypercenter	C₂²×#123	D₄₃
hypocenter	C₄₃	#62820
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×#123

Complements

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

N	H ≅ G/N	type
1. #19148808	C₂	semidirect
2. #19148789	C₂	semidirect
3. #19148766	C₂	semidirect
4. #19148527	C₂	semidirect
5. #19148304	C₂	semidirect
6. #19148291	C₂	semidirect
7. #19148284	C₂	semidirect
8. #19148284	C₂	semidirect
9. #19148233	C₂	semidirect
10. #19148230	C₂	semidirect
11. C₂×#14583410	C₂	semidirect
12. C₂²×#123×C₄₃	C₂	semidirect
13. C₂×#13063370	C₂²	semidirect
14. C₂²×#10621898	C₂²	semidirect
15. #14583652	C₂²	semidirect
16. #14583646	C₂²	semidirect
17. #14583639	C₂²	semidirect
18. #14583633	C₂²	semidirect
19. #14583604	C₂²	semidirect
20. #14583597	C₂²	semidirect
21. #14583594	C₂²	semidirect
22. #14583586	C₂²	semidirect
23. #14583584	C₂²	semidirect
24. #14583577	C₂²	semidirect
25. #14583575	C₂²	semidirect
26. #14583575	C₂²	semidirect
27. #14583575	C₂²	semidirect
28. #14583572	C₂²	semidirect
29. #14583550	C₂²	semidirect
30. #14583547	C₂²	semidirect
31. #14583543	C₂²	semidirect
32. #14583541	C₂²	semidirect
33. #14583539	C₂²	semidirect
34. #14583539	C₂²	semidirect
35. #14583539	C₂²	semidirect
36. D₄×C₂²⋊D₄₃	C₂²	semidirect
37. #14583530	C₂²	semidirect
38. #14583525	C₂²	semidirect
39. #14583525	C₂²	semidirect
40. #14583517	C₂²	semidirect
41. #14583501	C₂²	semidirect
42. #14583496	C₂²	semidirect
43. #14583496	C₂²	semidirect
44. #14583493	C₂²	semidirect
45. #14583492	C₂²	semidirect
46. #14583487	C₂²	semidirect
47. #14583487	C₂²	semidirect
48. #14583487	C₂²	semidirect
49. #14583485	C₂²	semidirect
50. #14583480	C₂²	semidirect
51. #14583471	C₂²	semidirect
52. #14583466	C₂²	semidirect
53. #14583461	C₂²	semidirect
54. #14583461	C₂²	semidirect
55. #14583460	C₂²	semidirect
57. #14583458	C₂²	semidirect
58. #14583426	C₂²	semidirect
59. #14583410	C₂²	semidirect
60. #14583410	C₂²	semidirect
61. #14583410	C₂²	semidirect
62. #14583410	C₂²	semidirect
63. #14583410	C₂²	semidirect
64. #14583410	C₂²	semidirect
65. #14583407	C₂²	semidirect
66. C₂×#13063308	C₂²	semidirect
67. #123×D₄₃	C₂²	semidirect
68. C₂×#13063304	C₂²	semidirect
69. C₂×#13063299	C₂²	semidirect
70. C₂×#13063294	C₂²	semidirect
71. C₂×#13063294	C₂²	semidirect
72. #14583380	C₂²	semidirect
73. #14583374	C₂²	semidirect
74. #14583372	C₂²	semidirect
75. #14583372	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
77. C₂×#13063284	C₂²	semidirect
79. C₂⁴×C₄×C₄₃	C₂²	semidirect
80. C₂×#123×C₄₃	C₂²	semidirect
81. C₂×#123×C₄₃	C₂²	semidirect
82. C₂×#123×C₄₃	C₂²	semidirect
83. C₂×#123×C₄₃	C₂²	semidirect
84. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
85. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
86. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
92. C₂×#10621898	C₂³	semidirect
94. C₂²×Dic₈₆	C₂³	semidirect
95. C₂²×D₁₇₂	C₂³	semidirect
101. C₂²×C₄×D₄₃	C₂³	semidirect
102. #13063324	C₂³	semidirect
104. #13063320	C₂³	semidirect
105. #13063320	C₂³	semidirect
106. #13063318	C₂³	semidirect
107. #13063318	C₂³	semidirect
108. #13063318	C₂³	semidirect
109. #13063316	C₂³	semidirect
110. #13063315	C₂³	semidirect
111. #13063315	C₂³	semidirect
113. #13063311	C₂³	semidirect
114. #13063311	C₂³	semidirect
115. #13063311	C₂³	semidirect
116. #13063310	C₂³	semidirect
117. #13063310	C₂³	semidirect
118. #13063309	C₂³	semidirect
119. #13063309	C₂³	semidirect
123. #13063308	C₂³	semidirect
124. #13063308	C₂³	semidirect
125. #13063307	C₂³	semidirect
126. #13063307	C₂³	semidirect
127. #13063307	C₂³	semidirect
130. #13063305	C₂³	semidirect
136. #13063304	C₂³	semidirect
137. #13063304	C₂³	semidirect
138. #13063303	C₂³	semidirect
139. #13063303	C₂³	semidirect
140. #13063302	C₂³	semidirect
141. #13063302	C₂³	semidirect
142. #13063302	C₂³	semidirect
143. #13063300	C₂³	semidirect
149. #13063299	C₂³	semidirect
150. #13063299	C₂³	semidirect
151. #13063298	C₂³	semidirect
152. #13063298	C₂³	semidirect
153. #13063298	C₂³	semidirect
157. #13063295	C₂³	semidirect
158. #13063295	C₂³	semidirect
166. #13063290	C₂³	semidirect
168. #13063287	C₂³	semidirect
174. C₄×C₂²⋊D₄₃	C₂³	semidirect
175. C₄×C₂²⋊D₄₃	C₂³	semidirect
176. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
177. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
178. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
182. #13063284	C₂³	semidirect
183. #13063283	C₂³	semidirect
184. #13063281	C₂³	semidirect
185. #13063281	C₂³	semidirect
186. C₂×C₄⋊Dic₄₃	C₂³	semidirect
187. C₂×Dic₄₃⋊C₄	C₂³	semidirect
188. C₄⋊C₄×D₄₃	C₂³	semidirect
193. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
194. C₂²⋊C₄×D₄₃	C₂³	semidirect
195. C₂²⋊C₄×D₄₃	C₂³	semidirect
196. C₂×C₄×Dic₄₃	C₂³	semidirect
437. C₂²×#123	D₄₃	semidirect
449. C₂⁴×C₄	C₂×D₄₃	semidirect
503. C₂×#123	C₂×D₄₃	semidirect
504. C₂×#123	C₂×D₄₃	semidirect
505. C₂×#123	C₂×D₄₃	semidirect
506. C₂×#123	C₂×D₄₃	semidirect
517. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
518. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
519. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
520. C₄₃	#62820	semidirect

Maximal subgroups

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

subgroup	index
#19148808	2
#19148789	2
#19148766	2
#19148527	2
#19148304	2
#19148291	2
#19148284	2
#19148233	2
#19148230	2
C₂×#14583410	2
C₂²×#123×C₄₃	2
#62820	43