Subgroups — C₂×#19149160 #26003943

Order 11008.

7258 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149160	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583653	C₂	1	2	yes	maximal, complemented
3	C₂×#14583647	C₂	1	2	yes	maximal, complemented
4	C₂×#14583621	C₂	1	2	yes	maximal, complemented
5	C₂×#14583573	C₂	1	4	yes	maximal, complemented
6	C₂×#14583562	C₂	1	2	yes	maximal, complemented
7	C₂×#14583561	C₂	1	2	yes	maximal, complemented
8	C₂×#14583540	C₂	1	2	yes	maximal, complemented
9	C₂×#14583524	C₂	1	2	yes	maximal, complemented
10	C₂×#14583523	C₂	1	2	yes	maximal, complemented
11	C₂×#14583521	C₂	1	4	yes	maximal, complemented
12	C₂×#14583489	C₂	1	2	yes	maximal, complemented
13	C₂×#14583474	C₂	1	2	yes	maximal, complemented
14	C₂×#14583433	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13063313	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10621902	C₂²	1	2	yes	—
18	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×D₄₃	C₂²	1	2	yes	complemented
20	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
21	#14583653	C₂²	1	32	yes	complemented
22	#14583647	C₂²	1	32	yes	complemented
23	#14583621	C₂²	1	32	yes	complemented
24	#14583573	C₂²	1	64	yes	complemented
25	#14583562	C₂²	1	32	yes	complemented
26	#14583561	C₂²	1	32	yes	complemented
27	#14583540	C₂²	1	32	yes	complemented
28	#14583524	C₂²	1	32	yes	complemented
29	#14583523	C₂²	1	32	yes	complemented
30	#14583521	C₂²	1	64	yes	complemented
31	#14583489	C₂²	1	32	yes	complemented
32	#14583474	C₂²	1	32	yes	complemented
33	C₂×#13063324	C₂²	1	4	yes	complemented
34	C₂×#13063323	C₂²	1	2	yes	complemented
35	#14583433	C₂²	1	16	yes	complemented
36	C₂×#13063320	C₂²	1	4	yes	complemented
37	C₂×#13063320	C₂²	1	4	yes	complemented
38	C₂×#13063319	C₂²	1	4	yes	complemented
39	C₂×#13063319	C₂²	1	2	yes	complemented
40	C₂×#13063317	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13063314	C₂²	1	2	yes	—
42	C₂×#13063314	C₂²	1	4	yes	complemented
43	C₂×#13063313	C₂²	1	2	yes	—
44	C₂×#13063313	C₂²	1	2	yes	—
45	C₂×#13063313	C₂²	1	2	yes	—
46	C₂×#13063313	C₂²	1	2	yes	—
47	C₂×#13063313	C₂²	1	16	yes	complemented
48	C₂×#13063313	C₂²	1	4	yes	complemented
49	C₂×#13063313	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13063310	C₂²	1	4	yes	—
51	C₂×#13063310	C₂²	1	4	yes	complemented
52	C₂×#13063310	C₂²	1	4	yes	complemented
53	C₂×#13063310	C₂²	1	4	yes	complemented
54	C₂×#13063308	C₂²	1	2	yes	—
55	C₂×#13063305	C₂²	1	2	yes	complemented
56	C₂×#13063305	C₂²	1	4	yes	complemented
57	C₂×#13063304	C₂²	1	1	yes	characteristic
58	C₂×#13063303	C₂²	1	4	yes	complemented
59	C₂×#13063303	C₂²	1	4	yes	complemented
60	C₂×#13063303	C₂²	1	4	yes	complemented
61	C₂×#13063303	C₂²	1	4	yes	complemented
62	C₂×#13063302	C₂²	1	4	yes	—
63	C₂×#13063301	C₂²	1	4	yes	complemented
64	C₂×#13063300	C₂²	1	2	yes	—
65	C₂×#13063300	C₂²	1	4	yes	—
66	C₂×#13063300	C₂²	1	4	yes	complemented
67	C₂×#13063299	C₂²	1	1	yes	characteristic
68	C₂×#13063295	C₂²	1	4	yes	—
69	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
70	C₂×#13063290	C₂²	1	2	yes	complemented
71	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄×D₁₇₂	C₂²	1	4	yes	complemented
73	C₂×#13063287	C₂²	1	2	yes	—
74	C₂×C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
75	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
76	C₂×#13063282	C₂²	1	4	yes	complemented
77	C₂×#13063282	C₂²	1	2	yes	complemented
78	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
79	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
80	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
81	C₄₃×#533	C₂²	1	16	yes	complemented
82	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
84	C₂×#125×C₄₃	C₂²	1	2	yes	complemented
85	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
86	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
87	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
88	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
89	C₂×#117×C₄₃	C₂²	1	2	yes	—
90	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
91	C₂⁴×D₄₃	C₂³	1	2	yes	—
92	C₂×#10621902	—	4	8	no	—
93	C₂×#10621902	C₂³	1	16	yes	—
94	C₂²×Dic₈₆	—	4	4	no	—
95	C₂²×Dic₈₆	C₂³	1	2	yes	—
96	C₂²×Dic₈₆	C₂³	1	8	yes	—
97	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
98	C₂²×Dic₈₆	C₂³	1	4	yes	—
99	C₂²×Dic₈₆	C₂³	1	2	yes	—
100	C₂×Q₈×D₄₃	—	4	8	no	—
101	C₂×Q₈×D₄₃	C₂³	1	16	yes	complemented
102	C₂²×D₁₇₂	—	4	4	no	—
103	C₂²×D₁₇₂	C₂³	1	2	yes	—
104	C₂²×D₁₇₂	C₂³	1	4	yes	—
105	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
106	C₂²×D₁₇₂	C₂³	1	4	yes	—
107	C₂²×D₁₇₂	C₂³	1	2	yes	—
108	C₂²×D₁₇₂	C₂³	1	8	yes	—
109	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
110	C₂³×Dic₄₃	C₂³	1	2	yes	—
111	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
112	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
113	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
114	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
115	#13063324	C₂³	1	32	yes	complemented
116	#13063323	C₂³	1	16	yes	complemented
117	#13063320	C₂³	1	32	yes	complemented
118	#13063320	C₂³	1	32	yes	complemented
119	#13063319	C₂³	1	32	yes	complemented
120	#13063319	C₂³	1	16	yes	complemented
121	#13063317	C₂³	1	8	yes	complemented
122	#13063314	C₂³	1	16	yes	—
123	#13063314	C₂³	1	32	yes	complemented
124	#13063313	C₂³	1	16	yes	—
125	#13063313	C₂³	1	16	yes	—
126	#13063313	C₂³	1	16	yes	—
127	#13063313	C₂³	1	16	yes	—
128	#13063313	C₂³	1	32	yes	complemented
129	#13063313	C₂³	1	8	yes	complemented
130	#13063310	C₂³	1	32	yes	—
131	#13063310	C₂³	1	32	yes	complemented
132	#13063310	C₂³	1	32	yes	complemented
133	#13063310	C₂³	1	32	yes	complemented
134	#13063308	C₂³	1	16	yes	—
135	#13063305	C₂³	1	16	yes	complemented
136	#13063305	C₂³	1	32	yes	complemented
137	#13063304	C₂³	1	8	yes	—
138	#13063303	C₂³	1	32	yes	complemented
139	#13063303	C₂³	1	32	yes	complemented
140	#13063303	C₂³	1	32	yes	complemented
141	#13063303	C₂³	1	32	yes	complemented
142	#13063302	C₂³	1	32	yes	—
143	#13063301	C₂³	1	32	yes	complemented
144	#13063300	C₂³	1	16	yes	—
145	#13063300	C₂³	1	32	yes	—
146	#13063300	C₂³	1	32	yes	complemented
147	#13063299	C₂³	1	8	yes	—
148	#13063295	C₂³	1	32	yes	—
149	C₄×Dic₈₆	C₂³	1	8	yes	complemented
150	#13063290	C₂³	1	16	yes	complemented
151	C₄×D₁₇₂	C₂³	1	8	yes	complemented
152	C₄×D₁₇₂	C₂³	1	32	yes	complemented
153	#13063287	C₂³	1	16	yes	—
154	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	—
155	(C₂²⋊D₄₃)⋊C₄	C₂³	1	32	yes	—
156	#13063282	C₂³	1	32	yes	complemented
157	#13063282	C₂³	1	16	yes	complemented
158	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
159	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
161	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
162	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
163	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
164	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
165	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
166	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
167	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
168	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
169	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	16	yes	—
170	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
171	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
173	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
174	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
175	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
176	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	16	yes	—
177	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
179	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
180	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
181	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
182	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
183	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
184	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	—
185	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
186	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
187	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
188	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
189	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
192	C₄⋊Q₈×C₄₃	C₂³	1	8	yes	complemented
193	C₄⋊Q₈×C₄₃	C₂³	1	8	yes	complemented
194	#125×C₄₃	C₂³	1	16	yes	complemented
195	C₂²⋊Q₈×C₄₃	C₂³	1	16	yes	—
196	C₂²⋊Q₈×C₄₃	C₂³	1	16	yes	—
197	C₄×Q₈×C₄₃	C₂³	1	16	yes	complemented
198	C₄×Q₈×C₄₃	C₂³	1	16	yes	complemented
199	#117×C₄₃	C₂³	1	16	yes	—
200	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
207	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
212	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
213	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
214	C₂³×D₄₃	—	2	8	no	—
215	C₂³×D₄₃	—	4	4	no	—
216	C₂³×D₄₃	—	4	4	no	—
217	C₂³×D₄₃	C₂⁴	1	4	yes	—
218	C₂³×D₄₃	C₂⁴	1	2	yes	—
219	C₂³×D₄₃	C₂⁴	1	8	yes	—
220	C₂×Q₈×C₄₃	—	2	8	no	—
221	C₂×Q₈×C₄₃	—	4	4	no	—
222	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
223	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
224	C₂²×C₄×C₄₃	—	2	4	no	—
225	C₂²×C₄×C₄₃	—	2	4	no	—
226	C₂²×C₄×C₄₃	—	4	2	no	—
227	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
234	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₂²⋊D₄₃	—	2	8	no	—
239	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
240	C₂²×Dic₄₃	—	4	4	no	—
241	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
242	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
243	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
244	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
245	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
246	#10621902	—	4	32	no	—
247	Q₈×D₄₃	—	4	32	no	—
248	C₂×D₁₇₂	—	2	8	no	—
249	C₂×D₁₇₂	—	4	4	no	—
250	C₂×D₁₇₂	—	4	8	no	—
251	C₂×D₁₇₂	—	4	2	no	—
252	C₂×D₁₇₂	—	4	8	no	—
253	C₂×D₁₇₂	—	4	16	no	—
254	C₂×D₁₇₂	C₂⁴	1	8	yes	—
255	C₂×D₁₇₂	C₂⁴	1	16	yes	—
256	C₂×D₁₇₂	C₂⁴	1	4	yes	—
257	C₂×D₁₇₂	C₂⁴	1	16	yes	—
258	C₂×D₁₇₂	C₂⁴	1	8	yes	—
259	C₂×C₄×D₄₃	—	2	8	no	—
260	C₂×C₄×D₄₃	—	4	8	no	—
261	C₂×C₄×D₄₃	—	4	8	no	—
262	C₂×C₄×D₄₃	—	4	8	no	—
263	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
264	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
265	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
266	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
267	C₂×Dic₈₆	—	2	8	no	—
268	C₂×Dic₈₆	—	4	16	no	—
269	C₂×Dic₈₆	—	4	8	no	—
270	C₂×Dic₈₆	—	4	4	no	—
271	C₂×Dic₈₆	—	4	2	no	—
272	C₂×Dic₈₆	C₂⁴	1	8	yes	—
273	C₂×Dic₈₆	C₂⁴	1	4	yes	—
274	C₂×Dic₈₆	C₂⁴	1	16	yes	—
275	C₂×Dic₈₆	C₂⁴	1	8	yes	—
276	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
277	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
278	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
280	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
281	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
283	C₄²×C₄₃	C₂⁴	1	4	yes	—
284	C₄²×C₄₃	C₂⁴	1	4	yes	—
285	C₄²×C₄₃	C₂⁴	1	4	yes	—
286	C₄²×C₄₃	C₂⁴	1	4	yes	—
287	C₄²×C₄₃	C₂⁴	1	16	yes	—
288	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
289	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
290	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
291	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
292	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
293	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
294	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
295	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
296	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
297	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
298	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
299	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
300	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
301	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
302	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
303	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
304	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
305	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
306	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
307	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
308	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
309	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
310	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
311	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
312	C₄×Dic₄₃	C₂⁴	1	16	yes	—
313	C₄×Dic₄₃	C₂⁴	1	8	yes	—
314	C₂³×C₄₃	—	2	2	no	—
315	C₂³×C₄₃	—	2	2	no	—
316	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
317	C₂³×C₄₃	C₂⁵	1	2	yes	—
318	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
319	C₂²×D₄₃	—	2	4	no	—
320	C₂²×D₄₃	—	2	8	no	—
321	C₂²×D₄₃	—	2	4	no	—
322	C₂²×D₄₃	—	2	8	no	—
323	C₂²×D₄₃	—	2	8	no	—
324	C₂²×D₄₃	—	2	4	no	—
325	C₂²×D₄₃	—	2	16	no	—
326	C₂²×D₄₃	—	4	8	no	—
327	C₂²×D₄₃	—	4	8	no	—
328	C₂²×D₄₃	—	8	16	no	—
329	C₂²×D₄₃	C₂⁵	1	8	yes	—
330	C₂²×D₄₃	C₂⁵	1	4	yes	—
331	Q₈×C₄₃	—	2	16	no	—
332	Q₈×C₄₃	—	4	8	no	—
333	C₂×C₄×C₄₃	—	2	2	no	—
334	C₂×C₄×C₄₃	—	2	8	no	—
335	C₂×C₄×C₄₃	—	2	8	no	—
336	C₂×C₄×C₄₃	—	2	2	no	—
337	C₂×C₄×C₄₃	—	2	2	no	—
338	C₂×C₄×C₄₃	—	2	2	no	—
339	C₂×C₄×C₄₃	—	2	8	no	—
340	C₂×C₄×C₄₃	—	2	2	no	—
341	C₂×C₄×C₄₃	—	2	8	no	—
342	C₂×C₄×C₄₃	—	4	4	no	—
343	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
344	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
345	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
346	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
347	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
348	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
349	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
350	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
351	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
352	C₂²⋊D₄₃	—	2	16	no	—
353	C₂×Dic₄₃	—	2	8	no	—
354	C₂×Dic₄₃	—	2	4	no	—
355	C₂×Dic₄₃	—	2	4	no	—
356	C₂×Dic₄₃	—	2	4	no	—
357	C₂×Dic₄₃	—	4	8	no	—
358	C₂×Dic₄₃	C₂⁵	1	4	yes	—
359	C₂×Dic₄₃	C₂⁵	1	4	yes	—
360	C₂×Dic₄₃	C₂⁵	1	8	yes	—
361	C₂×Dic₄₃	C₂⁵	1	4	yes	—
362	D₁₇₂	—	2	16	no	—
363	D₁₇₂	—	4	8	no	—
364	D₁₇₂	—	4	4	no	—
365	D₁₇₂	—	4	16	no	—
366	D₁₇₂	—	4	16	no	—
367	C₄×D₄₃	—	2	16	no	—
368	C₄×D₄₃	—	4	16	no	—
369	C₄×D₄₃	—	4	16	no	—
370	C₄×D₄₃	—	4	16	no	—
371	Dic₈₆	—	2	16	no	—
372	Dic₈₆	—	4	8	no	—
373	Dic₈₆	—	4	4	no	—
374	Dic₈₆	—	4	16	no	—
375	C₂×#3561	—	43	1	no	maximal, Sylow
376	C₂²×C₄₃	—	2	2	no	—
377	C₂²×C₄₃	—	2	2	no	—
378	C₂²×C₄₃	—	2	8	no	—
379	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
380	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	4	yes	—
381	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
382	C₂²×C₄₃	#585	1	2	yes	—
383	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
384	C₂×D₄₃	—	2	8	no	—
385	C₂×D₄₃	—	2	4	no	—
386	C₂×D₄₃	—	2	8	no	—
387	C₂×D₄₃	—	2	4	no	—
388	C₂×D₄₃	—	2	8	no	—
389	C₂×D₄₃	—	2	4	no	—
390	C₂×D₄₃	—	4	8	no	—
391	C₂×D₄₃	—	4	16	no	—
392	C₂×D₄₃	—	8	16	no	—
393	C₄×C₄₃	—	2	2	no	—
394	C₄×C₄₃	—	2	8	no	—
395	C₄×C₄₃	—	2	2	no	—
396	C₄×C₄₃	—	2	2	no	—
397	C₄×C₄₃	—	2	2	no	—
398	C₄×C₄₃	—	2	8	no	—
399	C₄×C₄₃	—	2	2	no	—
400	C₄×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
401	Dic₄₃	—	2	8	no	—
402	Dic₄₃	—	2	4	no	—
403	Dic₄₃	—	2	4	no	—
404	Dic₄₃	—	2	4	no	—
405	#3561	—	43	32	no	—
406	C₂×#563	—	43	2	no	—
407	C₂×#562	—	43	2	no	—
408	C₂×#556	—	43	2	no	—
409	C₂×#551	—	43	4	no	—
410	C₂×D₄×Q₈	—	43	2	no	—
411	C₂×#548	—	43	2	no	—
412	C₂×#546	—	43	2	no	—
413	C₂×#543	—	43	2	no	—
414	C₂×#542	—	43	2	no	—
415	C₂×#542	—	43	4	no	—
416	C₂×#538	—	43	2	no	—
417	C₂×#536	—	43	2	no	—
418	C₂×#533	D₄₃	1	1	yes	characteristic, complemented
419	C₂×#529	—	43	1	no	—
420	C₂²×#124	—	43	1	no	—
421	C₂×C₄₃	—	2	4	no	—
422	C₂×C₄₃	#3561	1	4	yes	complemented
423	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
425	C₂×C₄₃	C₂×#585	1	1	yes	characteristic
426	D₄₃	—	4	4	no	—
427	D₄₃	—	4	8	no	—
428	C₂²×#41	—	43	2	no	—
429	C₂³×Q₈	—	43	2	no	—
430	C₂³×Q₈	—	43	1	no	—
431	C₂³×D₄	—	43	1	no	—
432	#563	—	43	32	no	—
433	#562	—	43	32	no	—
434	#556	—	43	32	no	—
435	#551	—	43	64	no	—
436	D₄×Q₈	—	43	32	no	—
437	#548	—	43	32	no	—
438	#546	—	43	32	no	—
439	#543	—	43	32	no	—
440	#542	—	43	32	no	—
441	#542	—	43	64	no	—
442	#538	—	43	32	no	—
443	#536	—	43	32	no	—
444	#533	C₂×D₄₃	1	16	yes	complemented
445	C₂×C₄⋊Q₈	—	43	2	no	—
446	C₂×C₄⋊Q₈	—	43	4	no	—
447	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
448	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
449	#529	—	43	16	no	—
450	C₂×#126	—	43	4	no	—
451	C₂×#126	—	43	4	no	—
452	C₂×#126	—	43	2	no	—
453	C₂×#126	—	43	4	no	—
454	C₂×#125	—	43	1	no	—
455	C₂×#125	C₂×D₄₃	1	2	yes	complemented
456	C₂×#124	—	43	2	no	—
457	C₂×#124	—	43	4	no	—
458	C₂×#124	—	43	2	no	—
459	C₂×#124	—	43	2	no	—
460	C₂×#124	—	43	2	no	—
461	C₂×#124	—	43	2	no	—
462	C₂×#124	—	43	16	no	—
463	C₂×#124	—	43	1	no	—
464	C₂×#124	—	43	4	no	—
465	C₂×#123	—	43	2	no	—
466	C₂×#123	—	43	4	no	—
467	C₂×#123	—	43	4	no	—
468	C₂×#123	—	43	4	no	—
469	C₂×#123	—	43	4	no	—
470	C₂×C₂²⋊Q₈	—	43	4	no	—
471	C₂×C₂²⋊Q₈	—	43	1	no	—
472	C₂×C₂²⋊Q₈	—	43	4	no	—
473	C₂×C₂²⋊Q₈	—	43	4	no	—
474	C₂×C₂²⋊Q₈	—	43	4	no	—
475	C₂×C₂²⋊Q₈	—	43	4	no	—
476	C₂×C₂²⋊Q₈	—	43	2	no	—
477	C₂×C₂²⋊Q₈	—	43	4	no	—
478	C₂×C₂²⋊Q₈	—	43	4	no	—
479	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
480	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
481	C₂×#121	—	43	1	no	—
482	C₂×#121	—	43	2	no	—
483	C₂×#121	—	43	4	no	—
484	C₂×#121	—	43	4	no	—
485	C₂×#120	—	43	4	no	—
486	C₂×C₄×Q₈	—	43	2	no	—
487	C₂×C₄×Q₈	—	43	1	no	—
488	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
489	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
490	C₂×C₄×D₄	—	43	2	no	—
491	C₂×C₄×D₄	—	43	2	no	—
492	C₂×C₄×D₄	—	43	4	no	—
493	C₂×C₄×D₄	—	43	1	no	—
494	C₂×C₄×D₄	—	43	4	no	—
495	C₂×#117	—	43	2	no	—
496	C₂×#117	—	43	4	no	—
497	C₂×#117	C₂×D₄₃	1	2	yes	—
498	C₂²×C₂²⋊C₄	—	43	2	no	—
499	C₂²×C₂²⋊C₄	—	43	2	no	—
500	C₂²×C₂²⋊C₄	—	43	4	no	—
501	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
502	C₄₃	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
503	C₂⁵	—	43	2	no	—
504	C₂×#41	—	43	16	no	—
505	C₂×#41	—	172	8	no	—
506	C₂²×Q₈	—	43	16	no	—
507	C₂²×Q₈	—	43	2	no	—
508	C₂²×Q₈	—	43	1	no	—
509	C₂²×Q₈	—	43	4	no	—
510	C₂²×Q₈	—	43	2	no	—
511	C₂²×Q₈	—	43	8	no	—
512	C₂²×Q₈	—	172	4	no	—
513	C₂²×Q₈	—	172	8	no	—
514	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
515	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
516	C₂²×D₄	—	43	2	no	—
517	C₂²×D₄	—	43	2	no	—
518	C₂²×D₄	—	43	4	no	—
519	C₂²×D₄	—	43	1	no	—
520	C₂²×D₄	—	43	4	no	—
521	C₂²×D₄	—	43	2	no	—
522	C₂²×D₄	—	43	8	no	—
523	C₂²×D₄	—	172	4	no	—
524	C₂³×C₄	—	43	2	no	—
525	C₂³×C₄	—	43	2	no	—
526	C₂³×C₄	—	43	4	no	—
527	C₂³×C₄	—	43	4	no	—
528	C₂³×C₄	—	43	4	no	—
529	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
530	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
531	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
532	C₄⋊Q₈	—	43	16	no	—
533	C₄⋊Q₈	—	43	32	no	—
534	C₄⋊Q₈	C₂²×D₄₃	1	8	yes	complemented
535	C₄⋊Q₈	C₂²×D₄₃	1	8	yes	complemented
536	#126	—	43	32	no	—
537	#126	—	43	32	no	—
538	#126	—	43	16	no	—
539	#126	—	43	32	no	—
540	#125	—	43	8	no	—
541	#125	C₂²×D₄₃	1	16	yes	complemented
542	#124	—	43	16	no	—
543	#124	—	43	32	no	—
544	#124	—	43	16	no	—
545	#124	—	43	16	no	—
546	#124	—	43	16	no	—
547	#124	—	43	16	no	—
548	#124	—	43	8	no	—
549	#124	—	43	32	no	—
550	#123	—	43	16	no	—
551	#123	—	43	32	no	—
552	#123	—	43	32	no	—
553	#123	—	43	32	no	—
554	#123	—	43	32	no	—
555	C₂²⋊Q₈	—	43	32	no	—
556	C₂²⋊Q₈	—	43	8	no	—
557	C₂²⋊Q₈	—	43	32	no	—
558	C₂²⋊Q₈	—	43	32	no	—
559	C₂²⋊Q₈	—	43	16	no	—
560	C₂²⋊Q₈	—	43	32	no	—
561	C₂²⋊Q₈	—	43	32	no	—
562	C₂²⋊Q₈	—	43	32	no	—
563	C₂²⋊Q₈	—	43	32	no	—
564	C₂²⋊Q₈	C₂²×D₄₃	1	16	yes	—
565	C₂²⋊Q₈	C₂²×D₄₃	1	16	yes	—
566	#121	—	43	8	no	—
567	#121	—	43	32	no	—
568	#121	—	43	16	no	—
569	#121	—	43	32	no	—
570	#120	—	43	32	no	—
571	C₄×Q₈	—	43	16	no	—
572	C₄×Q₈	—	43	8	no	—
573	C₄×Q₈	C₂²×D₄₃	1	16	yes	complemented
574	C₄×Q₈	C₂²×D₄₃	1	16	yes	complemented
575	C₄×D₄	—	43	16	no	—
576	C₄×D₄	—	43	16	no	—
577	C₄×D₄	—	43	32	no	—
578	C₄×D₄	—	43	8	no	—
579	C₄×D₄	—	43	32	no	—
580	#117	—	43	16	no	—
581	#117	—	43	32	no	—
582	#117	C₂²×D₄₃	1	16	yes	—
583	C₂×C₄⋊C₄	—	43	2	no	—
584	C₂×C₄⋊C₄	—	43	2	no	—
585	C₂×C₄⋊C₄	—	43	4	no	—
586	C₂×C₄⋊C₄	—	43	2	no	—
587	C₂×C₄⋊C₄	—	43	1	no	—
588	C₂×C₄⋊C₄	—	43	4	no	—
589	C₂×C₄⋊C₄	—	43	4	no	—
590	C₂×C₄⋊C₄	—	43	2	no	—
591	C₂×C₄⋊C₄	—	43	1	no	—
592	C₂×C₄⋊C₄	—	43	4	no	—
593	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
597	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
598	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
599	C₂×C₂²⋊C₄	—	43	2	no	—
600	C₂×C₂²⋊C₄	—	43	4	no	—
601	C₂×C₂²⋊C₄	—	43	4	no	—
602	C₂×C₂²⋊C₄	—	43	4	no	—
603	C₂×C₂²⋊C₄	—	43	4	no	—
604	C₂×C₂²⋊C₄	—	43	4	no	—
605	C₂×C₂²⋊C₄	—	43	4	no	—
606	C₂×C₂²⋊C₄	—	43	16	no	—
607	C₂×C₂²⋊C₄	—	43	16	no	—
608	C₂×C₂²⋊C₄	—	43	4	no	—
609	C₂×C₂²⋊C₄	—	43	2	no	—
610	C₂×C₂²⋊C₄	—	43	2	no	—
611	C₂×C₂²⋊C₄	—	43	2	no	—
612	C₂×C₂²⋊C₄	—	43	4	no	—
613	C₂×C₂²⋊C₄	—	43	2	no	—
614	C₂×C₂²⋊C₄	—	43	4	no	—
615	C₂×C₂²⋊C₄	—	43	32	no	—
616	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
617	C₂×C₄²	—	43	2	no	—
618	C₂×C₄²	—	43	4	no	—
619	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
620	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
621	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
622	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
623	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
624	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
625	C₂⁴	—	43	4	no	—
626	C₂⁴	—	43	2	no	—
627	C₂⁴	—	43	8	no	—
628	C₂⁴	—	86	8	no	—
629	C₂⁴	—	172	4	no	—
630	C₂⁴	—	172	4	no	—
631	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
632	#41	—	172	32	no	—
633	C₂×Q₈	—	2	8	no	—
634	C₂×Q₈	—	4	4	no	—
635	C₂×Q₈	—	43	8	no	—
636	C₂×Q₈	—	43	4	no	—
637	C₂×Q₈	—	43	16	no	—
638	C₂×Q₈	—	43	8	no	—
639	C₂×Q₈	—	86	8	no	—
640	C₂×Q₈	—	172	4	no	—
641	C₂×Q₈	—	172	8	no	—
642	C₂×Q₈	—	172	2	no	—
643	C₂×Q₈	—	172	16	no	—
644	C₂×Q₈	—	172	32	no	—
645	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
646	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
647	C₂×D₄	—	43	8	no	—
648	C₂×D₄	—	43	8	no	—
649	C₂×D₄	—	43	16	no	—
650	C₂×D₄	—	43	4	no	—
651	C₂×D₄	—	43	16	no	—
652	C₂×D₄	—	43	8	no	—
653	C₂×D₄	—	86	8	no	—
654	C₂×D₄	—	86	8	no	—
655	C₂×D₄	—	172	16	no	—
656	C₂×D₄	—	172	4	no	—
657	C₂×D₄	—	172	8	no	—
658	C₂×D₄	—	172	2	no	—
659	C₂×D₄	—	172	8	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	43	2	no	—
664	C₂²×C₄	—	43	2	no	—
665	C₂²×C₄	—	43	4	no	—
666	C₂²×C₄	—	43	2	no	—
667	C₂²×C₄	—	43	8	no	—
668	C₂²×C₄	—	43	8	no	—
669	C₂²×C₄	—	43	16	no	—
670	C₂²×C₄	—	43	16	no	—
671	C₂²×C₄	—	43	16	no	—
672	C₂²×C₄	—	86	8	no	—
673	C₂²×C₄	—	172	8	no	—
674	C₂²×C₄	—	172	8	no	—
675	C₂²×C₄	—	172	8	no	—
676	C₂²×C₄	—	172	4	no	—
677	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
678	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
679	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
680	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
681	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
682	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
683	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
684	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
685	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
686	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
687	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
688	C₄⋊C₄	—	43	8	no	—
689	C₄⋊C₄	—	43	8	no	—
690	C₄⋊C₄	—	43	16	no	—
691	C₄⋊C₄	—	43	8	no	—
692	C₄⋊C₄	—	43	4	no	—
693	C₄⋊C₄	—	43	16	no	—
694	C₄⋊C₄	—	43	16	no	—
695	C₄⋊C₄	—	43	8	no	—
696	C₄⋊C₄	—	43	4	no	—
697	C₄⋊C₄	—	43	16	no	—
698	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
699	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
700	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
701	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
702	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
703	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
704	C₂²⋊C₄	—	43	8	no	—
705	C₂²⋊C₄	—	43	16	no	—
706	C₂²⋊C₄	—	43	16	no	—
707	C₂²⋊C₄	—	43	16	no	—
708	C₂²⋊C₄	—	43	16	no	—
709	C₂²⋊C₄	—	43	16	no	—
710	C₂²⋊C₄	—	43	16	no	—
711	C₂²⋊C₄	—	43	16	no	—
712	C₂²⋊C₄	—	43	8	no	—
713	C₂²⋊C₄	—	43	8	no	—
714	C₂²⋊C₄	—	43	8	no	—
715	C₂²⋊C₄	—	43	16	no	—
716	C₂²⋊C₄	—	43	8	no	—
717	C₂²⋊C₄	—	43	16	no	—
718	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
719	C₄²	—	43	8	no	—
720	C₄²	—	43	16	no	—
721	C₄²	C₂³×D₄₃	1	4	yes	—
722	C₄²	C₂³×D₄₃	1	4	yes	—
723	C₄²	C₂³×D₄₃	1	4	yes	—
724	C₄²	C₂³×D₄₃	1	4	yes	—
725	C₄²	C₂³×D₄₃	1	16	yes	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	43	8	no	—
729	C₂³	—	43	4	no	—
730	C₂³	—	86	16	no	—
731	C₂³	—	86	4	no	—
732	C₂³	—	86	8	no	—
733	C₂³	—	86	4	no	—
734	C₂³	—	86	8	no	—
735	C₂³	—	86	8	no	—
736	C₂³	—	86	4	no	—
737	C₂³	—	344	16	no	—
738	C₂³	—	172	8	no	—
739	C₂³	—	172	8	no	—
740	C₂³	#13063373	1	4	yes	—
741	C₂³	C₂⁴×D₄₃	1	2	yes	—
742	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
743	Q₈	—	2	16	no	—
744	Q₈	—	4	8	no	—
745	Q₈	—	86	16	no	—
746	Q₈	—	172	8	no	—
747	Q₈	—	172	16	no	—
748	Q₈	—	172	4	no	—
749	D₄	—	86	16	no	—
750	D₄	—	86	16	no	—
751	D₄	—	172	8	no	—
752	D₄	—	172	16	no	—
753	D₄	—	172	4	no	—
754	D₄	—	172	16	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	8	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	8	no	—
763	C₂×C₄	—	2	8	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	43	4	no	—
766	C₂×C₄	—	43	4	no	—
767	C₂×C₄	—	43	8	no	—
768	C₂×C₄	—	43	4	no	—
769	C₂×C₄	—	86	4	no	—
770	C₂×C₄	—	86	8	no	—
771	C₂×C₄	—	86	4	no	—
772	C₂×C₄	—	86	4	no	—
773	C₂×C₄	—	86	16	no	—
774	C₂×C₄	—	172	16	no	—
775	C₂×C₄	—	172	16	no	—
776	C₂×C₄	—	172	16	no	—
777	C₂×C₄	—	172	8	no	—
778	C₂×C₄	#13063371	1	4	yes	—
779	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
780	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
781	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
782	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
783	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
784	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
785	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
786	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	8	no	—
790	C₂²	—	86	4	no	—
791	C₂²	—	86	8	no	—
792	C₂²	—	86	4	no	—
793	C₂²	—	86	8	no	—
794	C₂²	—	86	8	no	—
795	C₂²	—	86	4	no	—
796	C₂²	—	344	16	no	—
797	C₂²	—	172	16	no	—
798	C₂²	—	172	8	no	—
799	C₂²	C₂×#13063371	1	2	yes	—
800	C₂²	C₂×#13063373	1	4	yes	—
801	C₂²	C₂×#13063373	1	2	yes	—
802	C₂²	#14583735	1	2	yes	—
803	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	8	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	8	no	—
811	C₄	—	86	4	no	—
812	C₄	—	86	8	no	—
813	C₄	—	86	4	no	—
814	C₄	—	86	4	no	—
815	C₄	C₂×#13063371	1	4	yes	—
816	C₂	—	2	4	no	—
817	C₂	—	172	8	no	—
818	C₂	—	172	4	no	—
819	C₂	#19149160	1	4	yes	direct product factor
820	C₂	C₂²×#13063371	1	1	yes	characteristic
821	C₂	C₂²×#13063373	1	1	yes	characteristic
822	C₂	C₂×#14583735	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#533	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#533	D₄₃
hypocenter	C₄₃	C₂×#3561
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #19149160	C₂	direct (N × H)
2. C₂×#14583653	C₂	semidirect
3. C₂×#14583647	C₂	semidirect
4. C₂×#14583621	C₂	semidirect
5. C₂×#14583573	C₂	semidirect
6. C₂×#14583562	C₂	semidirect
7. C₂×#14583561	C₂	semidirect
8. C₂×#14583540	C₂	semidirect
9. C₂×#14583524	C₂	semidirect
10. C₂×#14583523	C₂	semidirect
11. C₂×#14583521	C₂	semidirect
12. C₂×#14583489	C₂	semidirect
13. C₂×#14583474	C₂	semidirect
14. C₂×#14583433	C₂	semidirect
15. C₂²×#13063313	C₂	semidirect
16. C₂×C₄₃×#533	C₂	semidirect
19. C₂²×Q₈×D₄₃	C₂²	semidirect
21. #14583653	C₂²	semidirect
22. #14583647	C₂²	semidirect
23. #14583621	C₂²	semidirect
24. #14583573	C₂²	semidirect
25. #14583562	C₂²	semidirect
26. #14583561	C₂²	semidirect
27. #14583540	C₂²	semidirect
28. #14583524	C₂²	semidirect
29. #14583523	C₂²	semidirect
30. #14583521	C₂²	semidirect
31. #14583489	C₂²	semidirect
32. #14583474	C₂²	semidirect
33. C₂×#13063324	C₂²	semidirect
34. C₂×#13063323	C₂²	semidirect
35. #14583433	C₂²	semidirect
36. C₂×#13063320	C₂²	semidirect
37. C₂×#13063320	C₂²	semidirect
38. C₂×#13063319	C₂²	semidirect
39. C₂×#13063319	C₂²	semidirect
40. C₂×#13063317	C₂²	semidirect
42. C₂×#13063314	C₂²	semidirect
47. C₂×#13063313	C₂²	semidirect
48. C₂×#13063313	C₂²	semidirect
49. C₂×#13063313	C₂²	semidirect
51. C₂×#13063310	C₂²	semidirect
52. C₂×#13063310	C₂²	semidirect
53. C₂×#13063310	C₂²	semidirect
55. C₂×#13063305	C₂²	semidirect
56. C₂×#13063305	C₂²	semidirect
58. C₂×#13063303	C₂²	semidirect
59. C₂×#13063303	C₂²	semidirect
60. C₂×#13063303	C₂²	semidirect
61. C₂×#13063303	C₂²	semidirect
63. C₂×#13063301	C₂²	semidirect
66. C₂×#13063300	C₂²	semidirect
69. C₂×C₄×Dic₈₆	C₂²	semidirect
70. C₂×#13063290	C₂²	semidirect
71. C₂×C₄×D₁₇₂	C₂²	semidirect
72. C₂×C₄×D₁₇₂	C₂²	semidirect
76. C₂×#13063282	C₂²	semidirect
77. C₂×#13063282	C₂²	semidirect
81. C₄₃×#533	C₂²	semidirect
82. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
83. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
84. C₂×#125×C₄₃	C₂²	semidirect
87. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
88. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
101. C₂×Q₈×D₄₃	C₂³	semidirect
115. #13063324	C₂³	semidirect
116. #13063323	C₂³	semidirect
117. #13063320	C₂³	semidirect
118. #13063320	C₂³	semidirect
119. #13063319	C₂³	semidirect
120. #13063319	C₂³	semidirect
121. #13063317	C₂³	semidirect
123. #13063314	C₂³	semidirect
128. #13063313	C₂³	semidirect
129. #13063313	C₂³	semidirect
131. #13063310	C₂³	semidirect
132. #13063310	C₂³	semidirect
133. #13063310	C₂³	semidirect
135. #13063305	C₂³	semidirect
136. #13063305	C₂³	semidirect
138. #13063303	C₂³	semidirect
139. #13063303	C₂³	semidirect
140. #13063303	C₂³	semidirect
141. #13063303	C₂³	semidirect
143. #13063301	C₂³	semidirect
146. #13063300	C₂³	semidirect
149. C₄×Dic₈₆	C₂³	semidirect
150. #13063290	C₂³	semidirect
151. C₄×D₁₇₂	C₂³	semidirect
152. C₄×D₁₇₂	C₂³	semidirect
156. #13063282	C₂³	semidirect
157. #13063282	C₂³	semidirect
192. C₄⋊Q₈×C₄₃	C₂³	semidirect
193. C₄⋊Q₈×C₄₃	C₂³	semidirect
194. #125×C₄₃	C₂³	semidirect
197. C₄×Q₈×C₄₃	C₂³	semidirect
198. C₄×Q₈×C₄₃	C₂³	semidirect
418. C₂×#533	D₄₃	semidirect
422. C₂×C₄₃	#3561	semidirect
444. #533	C₂×D₄₃	semidirect
447. C₂×C₄⋊Q₈	C₂×D₄₃	semidirect
448. C₂×C₄⋊Q₈	C₂×D₄₃	semidirect
455. C₂×#125	C₂×D₄₃	semidirect
488. C₂×C₄×Q₈	C₂×D₄₃	semidirect
489. C₂×C₄×Q₈	C₂×D₄₃	semidirect
502. C₄₃	C₂×#3561	semidirect
534. C₄⋊Q₈	C₂²×D₄₃	semidirect
535. C₄⋊Q₈	C₂²×D₄₃	semidirect
541. #125	C₂²×D₄₃	semidirect
573. C₄×Q₈	C₂²×D₄₃	semidirect
574. C₄×Q₈	C₂²×D₄₃	semidirect
819. C₂	#19149160	direct (N × H)

Maximal subgroups

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

subgroup	index
#19149160	2
C₂×#14583653	2
C₂×#14583647	2
C₂×#14583621	2
C₂×#14583573	2
C₂×#14583562	2
C₂×#14583561	2
C₂×#14583540	2
C₂×#14583524	2
C₂×#14583523	2
C₂×#14583521	2
C₂×#14583489	2
C₂×#14583474	2
C₂×#14583433	2
C₂²×#13063313	2
C₂×C₄₃×#533	2
C₂×#3561	43

Subgroups — C2×#19149160 #26003943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19149160 #26003943