Subgroups — C₂×#19149364 #26010426

Order 11008.

10858 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583735	C₂	1	2	yes	maximal, complemented
2	#19149364	C₂	1	32	yes	maximal, direct product factor
3	C₂×#14583713	C₂	1	2	yes	maximal, complemented
4	C₂×#14583712	C₂	1	2	yes	maximal, complemented
5	C₂×#14583706	C₂	1	4	yes	maximal, complemented
6	C₂×#14583705	C₂	1	4	yes	maximal, complemented
7	C₂×#14583701	C₂	1	2	yes	maximal, complemented
8	C₂×#14583700	C₂	1	2	yes	maximal, complemented
9	C₂×#14583697	C₂	1	2	yes	maximal, complemented
10	C₂×#14583696	C₂	1	4	yes	maximal, complemented
11	C₂²×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×D₄₃	C₂	1	4	yes	maximal, complemented
13	C₂²×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583735	—	2	16	no	—
16	#14583735	C₂²	1	32	yes	complemented
17	C₂×#13063373	C₂²	1	4	yes	complemented
18	C₂×#13063372	—	2	2	no	—
19	C₂×#13063372	C₂²	1	4	yes	complemented
20	C₂×#13063371	—	2	2	no	—
21	C₂×#13063371	C₂²	1	4	yes	complemented
22	C₂×#13063370	—	2	4	no	—
23	C₂×#13063370	C₂²	1	4	yes	complemented
24	C₂²×#10621898	—	2	4	no	—
25	C₂²×#10621898	C₂²	1	1	yes	characteristic
26	C₂²×#10621898	C₂²	1	2	yes	complemented
27	C₂×#41×D₄₃	—	2	4	no	—
28	C₂×#41×D₄₃	C₂²	1	8	yes	complemented
29	#14583713	C₂²	1	32	yes	complemented
30	#14583712	C₂²	1	32	yes	complemented
31	#14583706	C₂²	1	64	yes	complemented
32	#14583705	C₂²	1	64	yes	complemented
33	#14583701	C₂²	1	32	yes	complemented
34	#14583700	C₂²	1	32	yes	complemented
35	#14583697	C₂²	1	32	yes	complemented
36	#14583696	C₂²	1	64	yes	complemented
37	C₂×#13063357	C₂²	1	8	yes	complemented
38	C₂×#13063356	C₂²	1	4	yes	complemented
39	C₂×#13063355	C₂²	1	4	yes	complemented
40	C₂×#13063354	C₂²	1	8	yes	complemented
41	C₂×#13063352	C₂²	1	8	yes	complemented
42	C₂×#13063351	C₂²	1	4	yes	complemented
43	C₂×#13063350	C₂²	1	4	yes	complemented
44	C₂×#13063349	C₂²	1	8	yes	complemented
45	C₂×#13063348	C₂²	1	4	yes	complemented
46	C₂×#13063347	C₂²	1	2	yes	complemented
47	C₂×#13063347	C₂²	1	2	yes	complemented
48	C₂×#13063347	C₂²	1	2	yes	complemented
49	C₂×#13063347	C₂²	1	2	yes	complemented
50	C₂×#13063347	C₂²	1	16	yes	complemented
51	C₂×#13063346	C₂²	1	8	yes	complemented
52	C₂×#13063345	C₂²	1	8	yes	complemented
53	C₂×#13063344	C₂²	1	4	yes	complemented
54	#135×D₄₃	C₂²	1	64	yes	complemented
55	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
56	C₂×Q₁₆×D₄₃	C₂²	1	4	yes	complemented
57	C₂²×#10621873	C₂²	1	2	yes	complemented
58	C₂×SD₁₆×D₄₃	C₂²	1	8	yes	complemented
59	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×D₈×D₄₃	C₂²	1	4	yes	complemented
61	C₂×#13063331	C₂²	1	2	yes	complemented
62	C₂×#13063331	C₂²	1	2	yes	complemented
63	C₂×#13063331	C₂²	1	2	yes	complemented
64	C₂×#13063331	C₂²	1	2	yes	complemented
65	C₂×#13063331	C₂²	1	16	yes	complemented
66	C₂²×#10621877	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#10621872	C₂²	1	2	yes	complemented
68	C₂²×C₈×D₄₃	C₂²	1	2	yes	complemented
69	C₂²×#41×C₄₃	C₂²	1	2	yes	complemented
70	C₂×#135×C₄₃	C₂²	1	2	yes	complemented
71	C₂×#135×C₄₃	C₂²	1	2	yes	complemented
72	C₂×#135×C₄₃	C₂²	1	2	yes	complemented
73	C₂×#135×C₄₃	C₂²	1	2	yes	complemented
74	C₂×#135×C₄₃	C₂²	1	16	yes	complemented
75	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
76	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
77	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
78	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
79	#13063373	—	2	16	no	—
80	#13063373	C₂³	1	32	yes	complemented
81	#13063372	—	2	16	no	—
82	#13063372	—	2	32	no	—
83	#13063372	C₂³	1	32	yes	complemented
84	#13063371	—	2	16	no	—
85	#13063371	—	2	32	no	—
86	#13063371	C₂³	1	32	yes	complemented
87	#13063370	—	2	64	no	—
88	#13063370	—	2	16	no	—
89	#13063370	C₂³	1	32	yes	complemented
90	C₂×#10621902	—	2	4	no	—
91	C₂×#10621902	C₂³	1	8	yes	—
92	C₂×#10621898	—	2	2	no	—
93	C₂×#10621898	—	2	2	no	—
94	C₂×#10621898	—	2	8	no	—
95	C₂×#10621898	—	2	8	no	—
96	C₂×#10621898	—	2	64	no	—
97	C₂×#10621898	—	2	4	no	—
98	C₂×#10621898	—	2	8	no	—
99	C₂×#10621898	—	2	4	no	—
100	C₂×#10621898	D₄	1	2	yes	—
101	C₂×#10621898	D₄	1	2	yes	—
102	C₂×#10621898	D₄	1	8	yes	—
103	C₂×#10621898	C₂³	1	2	yes	—
104	C₂×#10621898	C₂³	1	2	yes	—
105	C₂×#10621898	C₂³	1	8	yes	—
106	C₂×#10621898	C₂³	1	4	yes	—
107	C₂×#10621898	C₂³	1	4	yes	—
108	C₂×#10621898	C₂³	1	16	yes	complemented
109	C₂×#10621900	—	2	8	no	—
110	C₂×#10621900	—	2	8	no	—
111	C₂×#10621900	—	2	4	no	—
112	C₂×#10621900	C₂³	1	8	yes	—
113	#41×D₄₃	—	2	64	no	—
114	#41×D₄₃	—	2	32	no	—
115	#41×D₄₃	C₂³	1	64	yes	complemented
116	C₂²×Dic₈₆	—	2	4	no	—
117	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
118	C₂²×Dic₈₆	C₂³	1	2	yes	—
119	C₂×Q₈×D₄₃	—	2	4	no	—
120	C₂×Q₈×D₄₃	C₂³	1	8	yes	—
121	C₂²×D₁₇₂	—	2	4	no	—
122	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
123	C₂²×D₁₇₂	C₂³	1	2	yes	—
124	C₂²×C₂²⋊D₄₃	—	2	2	no	—
125	C₂²×C₂²⋊D₄₃	—	2	8	no	—
126	C₂²×C₂²⋊D₄₃	D₄	1	2	yes	—
127	C₂×D₄×D₄₃	—	2	8	no	—
128	C₂×D₄×D₄₃	—	2	8	no	—
129	C₂×D₄×D₄₃	—	2	4	no	—
130	C₂×D₄×D₄₃	C₂³	1	8	yes	—
131	C₂²×C₄×D₄₃	—	2	2	no	—
132	C₂²×C₄×D₄₃	—	2	8	no	—
133	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
134	#13063357	C₂³	1	64	yes	complemented
135	#13063356	C₂³	1	32	yes	complemented
136	#13063355	C₂³	1	32	yes	complemented
137	#13063354	C₂³	1	64	yes	complemented
138	#13063352	C₂³	1	64	yes	complemented
139	#13063351	C₂³	1	32	yes	complemented
140	#13063350	C₂³	1	32	yes	complemented
141	#13063349	C₂³	1	64	yes	complemented
142	#13063348	C₂³	1	32	yes	complemented
143	#13063347	C₂³	1	16	yes	complemented
144	#13063347	C₂³	1	16	yes	complemented
145	#13063347	C₂³	1	16	yes	complemented
146	#13063347	C₂³	1	16	yes	complemented
147	#13063346	C₂³	1	64	yes	complemented
148	#13063345	C₂³	1	64	yes	complemented
149	#13063344	C₂³	1	32	yes	complemented
150	C₂×Dic₁₇₂	C₂³	1	2	yes	—
151	C₂×Dic₁₇₂	C₂³	1	2	yes	—
152	C₂×Dic₁₇₂	C₂³	1	8	yes	complemented
153	C₂×#10621885	C₂³	1	8	yes	—
154	Q₁₆×D₄₃	C₂³	1	32	yes	complemented
155	C₂×#10621873	C₂³	1	4	yes	—
156	C₂×#10621873	C₂³	1	4	yes	—
157	C₂×#10621873	C₂³	1	16	yes	complemented
158	C₂×#10621883	C₂³	1	8	yes	—
159	C₂×#10621884	C₂³	1	8	yes	—
160	SD₁₆×D₄₃	C₂³	1	64	yes	complemented
161	C₂×D₃₄₄	C₂³	1	2	yes	—
162	C₂×D₃₄₄	C₂³	1	2	yes	—
163	C₂×D₃₄₄	C₂³	1	8	yes	complemented
164	C₂×#10621882	C₂³	1	8	yes	—
165	D₈×D₄₃	C₂³	1	32	yes	complemented
166	#13063331	C₂³	1	16	yes	complemented
167	#13063331	C₂³	1	16	yes	complemented
168	#13063331	C₂³	1	16	yes	complemented
169	#13063331	C₂³	1	16	yes	complemented
170	C₂×#10621877	C₂³	1	2	yes	—
171	C₂×#10621877	C₂³	1	2	yes	—
172	C₂×#10621877	C₂³	1	8	yes	complemented
173	C₂×#10621872	C₂³	1	4	yes	—
174	C₂×#10621872	C₂³	1	4	yes	—
175	C₂×#10621872	C₂³	1	16	yes	complemented
176	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
177	C₂×C₈×D₄₃	C₂³	1	4	yes	—
178	C₂×C₈×D₄₃	C₂³	1	4	yes	—
179	C₂×C₈×D₄₃	C₂³	1	16	yes	complemented
180	C₂×#41×C₄₃	—	2	2	no	—
181	C₂×#41×C₄₃	—	2	2	no	—
182	C₂×#41×C₄₃	—	2	8	no	—
183	C₂×#41×C₄₃	C₂³	1	4	yes	—
184	C₂×#41×C₄₃	C₂³	1	4	yes	—
185	C₂×#41×C₄₃	C₂³	1	16	yes	complemented
186	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
187	C₂²×D₄×C₄₃	—	2	2	no	—
188	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
189	C₂³×C₄×C₄₃	—	2	2	no	—
190	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
191	#135×C₄₃	C₂³	1	16	yes	complemented
192	#135×C₄₃	C₂³	1	16	yes	complemented
193	#135×C₄₃	C₂³	1	16	yes	complemented
194	#135×C₄₃	C₂³	1	16	yes	complemented
195	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
196	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
197	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	complemented
198	C₂×SD₁₆×C₄₃	C₂³	1	4	yes	—
199	C₂×SD₁₆×C₄₃	C₂³	1	4	yes	—
200	C₂×SD₁₆×C₄₃	C₂³	1	16	yes	complemented
201	C₂×D₈×C₄₃	C₂³	1	2	yes	—
202	C₂×D₈×C₄₃	C₂³	1	2	yes	—
203	C₂×D₈×C₄₃	C₂³	1	8	yes	complemented
204	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
205	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
206	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
207	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
208	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
209	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
210	C₂²×C₈×C₄₃	C₂³	1	8	yes	complemented
211	C₂⁴×C₄₃	—	2	2	no	—
212	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
213	C₂³×D₄₃	—	2	2	no	—
214	C₂³×D₄₃	—	2	8	no	—
215	C₂³×D₄₃	C₂×D₄	1	2	yes	—
216	#41×C₄₃	—	2	8	no	—
217	#41×C₄₃	—	2	8	no	—
218	#41×C₄₃	—	2	16	no	—
219	#41×C₄₃	—	2	16	no	—
220	#41×C₄₃	C₂⁴	1	16	yes	—
221	#41×C₄₃	C₂⁴	1	16	yes	—
222	C₂×Q₈×C₄₃	—	2	2	no	—
223	C₂×Q₈×C₄₃	—	2	4	no	—
224	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
225	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
226	C₂×D₄×C₄₃	—	2	2	no	—
227	C₂×D₄×C₄₃	—	2	4	no	—
228	C₂×D₄×C₄₃	—	2	4	no	—
229	C₂×D₄×C₄₃	—	2	4	no	—
230	C₂×D₄×C₄₃	—	2	16	no	—
231	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
232	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
233	C₂²×C₄×C₄₃	—	2	4	no	—
234	C₂²×C₄×C₄₃	—	2	4	no	—
235	C₂²×C₄×C₄₃	—	2	16	no	—
236	C₂²×C₄×C₄₃	—	2	2	no	—
237	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
245	C₂×C₂²⋊D₄₃	—	2	64	no	—
246	C₂×C₂²⋊D₄₃	—	2	8	no	—
247	C₂×C₂²⋊D₄₃	—	2	4	no	—
248	C₂×C₂²⋊D₄₃	—	2	4	no	—
249	C₂×C₂²⋊D₄₃	—	2	16	no	—
250	C₂×C₂²⋊D₄₃	—	2	8	no	—
251	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
252	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
253	C₂×C₂²⋊D₄₃	C₂×D₄	1	16	yes	—
254	C₂²×Dic₄₃	—	2	8	no	—
255	C₂²×Dic₄₃	—	2	2	no	—
256	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
257	#10621902	—	2	32	no	—
258	#10621902	—	2	16	no	—
259	#10621902	C₂⁴	1	32	yes	—
260	Q₈×D₄₃	—	2	16	no	—
261	Q₈×D₄₃	—	2	32	no	—
262	Q₈×D₄₃	C₂⁴	1	32	yes	—
263	#10621900	—	2	64	no	—
264	#10621900	—	2	64	no	—
265	#10621900	—	2	16	no	—
266	#10621900	—	2	32	no	—
267	#10621900	C₂⁴	1	32	yes	—
268	D₄×D₄₃	—	2	64	no	—
269	D₄×D₄₃	—	2	32	no	—
270	D₄×D₄₃	—	2	16	no	—
271	D₄×D₄₃	—	2	64	no	—
272	D₄×D₄₃	C₂⁴	1	32	yes	—
273	#10621898	—	2	8	no	—
274	#10621898	—	2	16	no	—
275	#10621898	—	2	8	no	—
276	#10621898	—	2	16	no	—
277	#10621898	—	2	64	no	—
278	#10621898	—	2	32	no	—
279	#10621898	—	2	64	no	—
280	#10621898	—	2	32	no	—
281	#10621898	C₂×D₄	1	16	yes	—
282	#10621898	C₂×D₄	1	16	yes	—
283	#10621898	C₂×D₄	1	8	yes	—
284	#10621898	C₂×D₄	1	8	yes	—
285	#10621898	C₂⁴	1	8	yes	—
286	#10621898	C₂⁴	1	8	yes	—
287	#10621898	C₂⁴	1	16	yes	—
288	#10621898	C₂⁴	1	16	yes	—
289	C₂×D₁₇₂	—	2	2	no	—
290	C₂×D₁₇₂	—	2	4	no	—
291	C₂×D₁₇₂	—	2	32	no	—
292	C₂×D₁₇₂	—	2	8	no	—
293	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
294	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
295	C₂×D₁₇₂	C₂×D₄	1	8	yes	—
296	C₂×D₁₇₂	C₂⁴	1	4	yes	—
297	C₂×D₁₇₂	C₂⁴	1	8	yes	—
298	C₂×C₄×D₄₃	—	2	4	no	—
299	C₂×C₄×D₄₃	—	2	4	no	—
300	C₂×C₄×D₄₃	—	2	16	no	—
301	C₂×C₄×D₄₃	—	2	8	no	—
302	C₂×C₄×D₄₃	—	2	64	no	—
303	C₂×C₄×D₄₃	—	2	8	no	—
304	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
305	C₂×C₄×D₄₃	C₂×D₄	1	8	yes	—
306	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
307	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
308	C₂×Dic₈₆	—	2	2	no	—
309	C₂×Dic₈₆	—	2	4	no	—
310	C₂×Dic₈₆	—	2	8	no	—
311	C₂×Dic₈₆	—	2	32	no	—
312	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
313	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
314	C₂×Dic₈₆	C₂×D₄	1	8	yes	—
315	C₂×Dic₈₆	C₂⁴	1	4	yes	—
316	C₂×Dic₈₆	C₂⁴	1	8	yes	—
317	Q₁₆×C₄₃	C₂⁴	1	8	yes	—
318	Q₁₆×C₄₃	C₂⁴	1	8	yes	—
319	SD₁₆×C₄₃	C₂⁴	1	16	yes	—
320	SD₁₆×C₄₃	C₂⁴	1	16	yes	—
321	D₈×C₄₃	C₂⁴	1	8	yes	—
322	D₈×C₄₃	C₂⁴	1	8	yes	—
323	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
327	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
328	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
329	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
330	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
331	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
332	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
333	#10621885	C₂⁴	1	32	yes	—
334	#10621884	C₂⁴	1	32	yes	—
335	#10621883	C₂⁴	1	32	yes	—
336	#10621882	C₂⁴	1	32	yes	—
337	#10621877	C₂⁴	1	8	yes	—
338	#10621877	C₂⁴	1	8	yes	—
339	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
340	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
341	Dic₁₇₂	C₂⁴	1	8	yes	—
342	Dic₁₇₂	C₂⁴	1	8	yes	—
343	D₃₄₄	C₂⁴	1	8	yes	—
344	D₃₄₄	C₂⁴	1	8	yes	—
345	#10621873	C₂⁴	1	16	yes	—
346	#10621873	C₂⁴	1	16	yes	—
347	#10621872	C₂⁴	1	16	yes	—
348	#10621872	C₂⁴	1	16	yes	—
349	C₈×D₄₃	C₂⁴	1	16	yes	—
350	C₈×D₄₃	C₂⁴	1	16	yes	—
351	C₂³×C₄₃	—	2	4	no	—
352	C₂³×C₄₃	—	2	8	no	—
353	C₂³×C₄₃	—	4	2	no	—
354	C₂³×C₄₃	—	8	4	no	—
355	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
358	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
359	C₂²×D₄₃	—	2	4	no	—
360	C₂²×D₄₃	—	2	8	no	—
361	C₂²×D₄₃	—	2	32	no	—
362	C₂²×D₄₃	—	4	4	no	—
363	C₂²×D₄₃	—	8	16	no	—
364	C₂²×D₄₃	—	8	4	no	—
365	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
366	C₂²×D₄₃	C₂²×D₄	1	8	yes	—
367	Q₈×C₄₃	—	2	4	no	—
368	Q₈×C₄₃	—	2	8	no	—
369	Q₈×C₄₃	C₂⁵	1	8	yes	—
370	D₄×C₄₃	—	2	16	no	—
371	D₄×C₄₃	—	2	16	no	—
372	D₄×C₄₃	—	2	4	no	—
373	D₄×C₄₃	—	2	8	no	—
374	D₄×C₄₃	C₂⁵	1	8	yes	—
375	C₂×C₄×C₄₃	—	2	4	no	—
376	C₂×C₄×C₄₃	—	2	8	no	—
377	C₂×C₄×C₄₃	—	2	16	no	—
378	C₂×C₄×C₄₃	—	2	16	no	—
379	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
389	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
390	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
391	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
392	C₂²⋊D₄₃	—	2	16	no	—
393	C₂²⋊D₄₃	—	2	16	no	—
394	C₂²⋊D₄₃	—	2	32	no	—
395	C₂²⋊D₄₃	—	2	32	no	—
396	C₂²⋊D₄₃	C₂²×D₄	1	16	yes	—
397	C₂²⋊D₄₃	C₂²×D₄	1	16	yes	—
398	C₂×Dic₄₃	—	2	4	no	—
399	C₂×Dic₄₃	—	2	8	no	—
400	C₂×Dic₄₃	—	2	32	no	—
401	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
402	C₂×Dic₄₃	C₂²×D₄	1	8	yes	—
403	D₁₇₂	—	2	32	no	—
404	D₁₇₂	—	2	8	no	—
405	D₁₇₂	—	2	4	no	—
406	D₁₇₂	C₂²×D₄	1	8	yes	—
407	D₁₇₂	C₂²×D₄	1	8	yes	—
408	D₁₇₂	C₂⁵	1	8	yes	—
409	C₄×D₄₃	—	2	32	no	—
410	C₄×D₄₃	—	2	16	no	—
411	C₄×D₄₃	—	2	16	no	—
412	C₄×D₄₃	—	2	32	no	—
413	C₄×D₄₃	C₂²×D₄	1	16	yes	—
414	C₄×D₄₃	C₂²×D₄	1	8	yes	—
415	C₄×D₄₃	C₂⁵	1	8	yes	—
416	Dic₈₆	—	2	8	no	—
417	Dic₈₆	—	2	4	no	—
418	Dic₈₆	—	2	32	no	—
419	Dic₈₆	C₂²×D₄	1	8	yes	—
420	Dic₈₆	C₂²×D₄	1	8	yes	—
421	Dic₈₆	C₂⁵	1	8	yes	—
422	C₈×C₄₃	C₂⁵	1	2	yes	—
423	C₈×C₄₃	C₂⁵	1	2	yes	—
424	C₈×C₄₃	C₂⁵	1	2	yes	—
425	C₈×C₄₃	C₂⁵	1	2	yes	—
426	C₄₃⋊C₈	C₂⁵	1	8	yes	—
427	C₂×#3584	—	43	1	no	maximal, Sylow
428	C₂²×C₄₃	—	2	2	no	—
429	C₂²×C₄₃	—	2	2	no	—
430	C₂²×C₄₃	—	2	2	no	—
431	C₂²×C₄₃	—	2	8	no	—
432	C₂²×C₄₃	—	4	4	no	—
433	C₂²×C₄₃	—	4	8	no	—
434	C₂²×C₄₃	—	8	8	no	—
435	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
436	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
437	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
438	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
439	C₂×D₄₃	—	2	8	no	—
440	C₂×D₄₃	—	2	8	no	—
441	C₂×D₄₃	—	4	8	no	—
442	C₂×D₄₃	—	4	8	no	—
443	C₂×D₄₃	—	8	32	no	—
444	C₂×D₄₃	—	8	8	no	—
445	C₂×D₄₃	C₂³×D₄	1	8	yes	—
446	C₄×C₄₃	—	2	8	no	—
447	C₄×C₄₃	C₂³×D₄	1	2	yes	—
448	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
449	C₄×C₄₃	C₂³×D₄	1	2	yes	—
450	C₄×C₄₃	C₂³×D₄	1	2	yes	—
451	C₄×C₄₃	C₂⁶	1	1	yes	characteristic
452	Dic₄₃	—	2	8	no	—
453	Dic₄₃	C₂³×D₄	1	8	yes	—
454	C₂×#585	—	43	2	no	—
455	#3584	—	43	32	no	—
456	C₂×#578	—	43	2	no	—
457	C₂×#578	—	43	2	no	—
458	C₂×#577	—	43	4	no	—
459	C₂×#577	—	43	4	no	—
460	C₂×#576	—	43	2	no	—
461	C₂×#576	—	43	2	no	—
462	C₂×#575	—	43	2	no	—
463	C₂×#575	—	43	4	no	—
464	C₂²×#135	—	43	4	no	—
465	C₂²×#135	—	43	1	no	—
466	C₂²×#135	D₄₃	1	1	yes	characteristic, complemented
467	C₂²×#131	—	43	1	no	—
468	C₂×C₄₃	—	2	2	no	—
469	C₂×C₄₃	—	2	2	no	—
470	C₂×C₄₃	—	2	2	no	—
471	C₂×C₄₃	—	4	8	no	—
472	C₂×C₄₃	#3584	1	2	yes	complemented
473	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
474	D₄₃	—	2	8	no	—
475	D₄₃	—	4	8	no	—
476	#585	—	43	32	no	—
477	#585	—	86	16	no	—
478	C₂×2₋¹⁺⁴	—	43	4	no	—
479	C₂×2₋¹⁺⁴	—	43	4	no	—
480	C₂×2₋¹⁺⁴	—	86	2	no	—
481	C₂×H(5,𝔽₂)	—	43	4	no	—
482	C₂×H(5,𝔽₂)	—	43	4	no	—
483	C₂×H(5,𝔽₂)	—	86	4	no	—
484	C₂×H(5,𝔽₂)	—	86	2	no	—
485	C₂²×#41	—	43	1	no	—
486	C₂²×#41	—	43	8	no	—
487	C₂²×#41	—	43	2	no	—
488	C₂²×#41	—	86	4	no	—
489	C₂²×#41	—	86	4	no	—
490	C₂²×#41	C₂×D₄₃	1	2	yes	complemented
491	#578	—	43	32	no	—
492	#578	—	43	32	no	—
493	#577	—	43	64	no	—
494	#577	—	43	64	no	—
495	#576	—	43	32	no	—
496	#576	—	43	32	no	—
497	#575	—	43	32	no	—
498	#575	—	43	64	no	—
499	C₂×#137	—	43	4	no	—
500	C₂×#137	—	43	4	no	—
501	C₂×#137	—	43	8	no	—
502	C₂×#137	—	43	8	no	—
503	C₂×AGL(1,ℤ/8)	—	43	4	no	—
504	C₂×AGL(1,ℤ/8)	—	43	4	no	—
505	C₂×AGL(1,ℤ/8)	—	43	8	no	—
506	C₂×AGL(1,ℤ/8)	—	43	8	no	—
507	C₂×#135	—	43	8	no	—
508	C₂×#135	—	43	64	no	—
509	C₂×#135	—	43	4	no	—
510	C₂×#135	—	43	8	no	—
511	C₂×#135	—	43	4	no	—
512	C₂×#135	—	43	2	no	—
513	C₂×#135	—	43	2	no	—
514	C₂×#135	—	43	2	no	—
515	C₂×#135	—	43	2	no	—
516	C₂×#135	—	43	16	no	—
517	C₂×#135	C₂×D₄₃	1	2	yes	complemented
518	C₂×#135	C₂×D₄₃	1	2	yes	complemented
519	C₂×#135	C₂×D₄₃	1	2	yes	complemented
520	C₂×#135	C₂×D₄₃	1	2	yes	complemented
521	C₂×#135	C₂×D₄₃	1	16	yes	complemented
522	C₂²×Q₁₆	—	43	4	no	—
523	C₂²×Q₁₆	—	43	1	no	—
524	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
525	C₂²×SD₁₆	—	43	8	no	—
526	C₂²×SD₁₆	—	43	2	no	—
527	C₂²×SD₁₆	C₂×D₄₃	1	2	yes	complemented
528	C₂²×D₈	—	43	4	no	—
529	C₂²×D₈	—	43	1	no	—
530	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
531	C₂×#131	—	43	2	no	—
532	C₂×#131	—	43	2	no	—
533	C₂×#131	—	43	2	no	—
534	C₂×#131	—	43	2	no	—
535	C₂×#131	—	43	16	no	—
536	C₂²×M₁₆	—	43	1	no	—
537	C₂²×M₁₆	—	43	2	no	—
538	C₂³×C₈	—	43	2	no	—
539	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
540	C₄₃	C₂×#3584	1	1	yes	characteristic, complemented, Sylow
541	2₋¹⁺⁴	—	43	32	no	—
542	2₋¹⁺⁴	—	43	32	no	—
543	2₋¹⁺⁴	—	86	16	no	—
544	2₋¹⁺⁴	—	86	32	no	—
545	2₋¹⁺⁴	—	86	16	no	—
546	H(5,𝔽₂)	—	43	32	no	—
547	H(5,𝔽₂)	—	43	32	no	—
548	H(5,𝔽₂)	—	86	64	no	—
549	H(5,𝔽₂)	—	86	16	no	—
550	H(5,𝔽₂)	—	86	32	no	—
551	H(5,𝔽₂)	—	86	16	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	8	no	—
555	C₂×#41	—	43	2	no	—
556	C₂×#41	—	43	2	no	—
557	C₂×#41	—	43	8	no	—
558	C₂×#41	—	43	2	no	—
559	C₂×#41	—	43	2	no	—
560	C₂×#41	—	43	8	no	—
561	C₂×#41	—	43	64	no	—
562	C₂×#41	—	43	8	no	—
563	C₂×#41	—	43	8	no	—
564	C₂×#41	—	43	4	no	—
565	C₂×#41	—	43	4	no	—
566	C₂×#41	—	43	16	no	—
567	C₂×#41	—	86	8	no	—
568	C₂×#41	—	86	8	no	—
569	C₂×#41	—	86	4	no	—
570	C₂×#41	—	86	4	no	—
571	C₂×#41	—	86	64	no	—
572	C₂×#41	—	86	8	no	—
573	C₂×#41	—	86	32	no	—
574	C₂×#41	—	86	8	no	—
575	C₂×#41	—	86	4	no	—
576	C₂×#41	—	86	4	no	—
577	C₂×#41	—	86	64	no	—
578	C₂×#41	—	86	2	no	—
579	C₂×#41	—	86	2	no	—
580	C₂×#41	—	86	8	no	—
581	C₂×#41	C₂²×D₄₃	1	4	yes	—
582	C₂×#41	C₂²×D₄₃	1	4	yes	—
583	C₂×#41	C₂²×D₄₃	1	16	yes	complemented
584	C₂²×Q₈	—	43	1	no	—
585	C₂²×Q₈	—	43	8	no	—
586	C₂²×Q₈	—	43	2	no	—
587	C₂²×Q₈	—	86	4	no	—
588	C₂²×Q₈	—	86	4	no	—
589	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	43	2	no	—
592	C₂²×D₄	—	43	8	no	—
593	C₂²×D₄	—	43	1	no	—
594	C₂²×D₄	—	43	2	no	—
595	C₂²×D₄	—	86	4	no	—
596	C₂²×D₄	—	86	8	no	—
597	C₂²×D₄	—	86	4	no	—
598	C₂²×D₄	—	86	8	no	—
599	C₂²×D₄	—	86	8	no	—
600	C₂²×D₄	—	86	2	no	—
601	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
602	C₂³×C₄	—	2	2	no	—
603	C₂³×C₄	—	43	2	no	—
604	C₂³×C₄	—	86	8	no	—
605	C₂³×C₄	—	86	2	no	—
606	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
607	#137	—	43	32	no	—
608	#137	—	43	32	no	—
609	#137	—	43	64	no	—
610	#137	—	43	64	no	—
611	AGL(1,ℤ/8)	—	43	32	no	—
612	AGL(1,ℤ/8)	—	43	32	no	—
613	AGL(1,ℤ/8)	—	43	64	no	—
614	AGL(1,ℤ/8)	—	43	64	no	—
615	#135	—	43	64	no	—
616	#135	—	43	32	no	—
617	#135	—	43	64	no	—
618	#135	—	43	32	no	—
619	#135	—	43	16	no	—
620	#135	—	43	16	no	—
621	#135	—	43	16	no	—
622	#135	—	43	16	no	—
623	#135	C₂²×D₄₃	1	16	yes	complemented
624	#135	C₂²×D₄₃	1	16	yes	complemented
625	#135	C₂²×D₄₃	1	16	yes	complemented
626	#135	C₂²×D₄₃	1	16	yes	complemented
627	C₂×Q₁₆	—	43	8	no	—
628	C₂×Q₁₆	—	43	32	no	—
629	C₂×Q₁₆	—	43	2	no	—
630	C₂×Q₁₆	—	43	2	no	—
631	C₂×Q₁₆	—	43	8	no	—
632	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
633	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
634	C₂×Q₁₆	C₂²×D₄₃	1	8	yes	complemented
635	C₂×SD₁₆	—	43	8	no	—
636	C₂×SD₁₆	—	43	8	no	—
637	C₂×SD₁₆	—	43	64	no	—
638	C₂×SD₁₆	—	43	4	no	—
639	C₂×SD₁₆	—	43	4	no	—
640	C₂×SD₁₆	—	43	16	no	—
641	C₂×SD₁₆	C₂²×D₄₃	1	4	yes	—
642	C₂×SD₁₆	C₂²×D₄₃	1	4	yes	—
643	C₂×SD₁₆	C₂²×D₄₃	1	16	yes	complemented
644	C₂×D₈	—	43	8	no	—
645	C₂×D₈	—	43	32	no	—
646	C₂×D₈	—	43	2	no	—
647	C₂×D₈	—	43	2	no	—
648	C₂×D₈	—	43	8	no	—
649	C₂×D₈	C₂²×D₄₃	1	2	yes	—
650	C₂×D₈	C₂²×D₄₃	1	2	yes	—
651	C₂×D₈	C₂²×D₄₃	1	8	yes	complemented
652	#131	—	43	16	no	—
653	#131	—	43	16	no	—
654	#131	—	43	16	no	—
655	#131	—	43	16	no	—
656	C₂×M₁₆	—	43	2	no	—
657	C₂×M₁₆	—	43	2	no	—
658	C₂×M₁₆	—	43	8	no	—
659	C₂×M₁₆	—	43	4	no	—
660	C₂×M₁₆	—	43	4	no	—
661	C₂×M₁₆	—	43	16	no	—
662	C₂²×C₈	—	43	2	no	—
663	C₂²×C₈	—	43	4	no	—
664	C₂²×C₈	—	43	4	no	—
665	C₂²×C₈	—	43	16	no	—
666	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
667	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
668	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
669	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
670	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
671	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
672	C₂²×C₈	C₂²×D₄₃	1	8	yes	complemented
673	C₂⁴	—	2	2	no	—
674	C₂⁴	—	43	2	no	—
675	C₂⁴	—	86	8	no	—
676	C₂⁴	—	86	2	no	—
677	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
678	#41	—	2	8	no	—
679	#41	—	2	16	no	—
680	#41	—	2	8	no	—
681	#41	—	2	16	no	—
682	#41	—	43	16	no	—
683	#41	—	43	16	no	—
684	#41	—	43	8	no	—
685	#41	—	43	8	no	—
686	#41	—	43	8	no	—
687	#41	—	43	8	no	—
688	#41	—	43	32	no	—
689	#41	—	43	32	no	—
690	#41	—	43	16	no	—
691	#41	—	43	16	no	—
692	#41	—	86	64	no	—
693	#41	—	86	64	no	—
694	#41	—	86	32	no	—
695	#41	—	86	32	no	—
696	#41	—	86	64	no	—
697	#41	—	86	16	no	—
698	#41	—	86	16	no	—
699	#41	—	86	64	no	—
700	#41	—	86	32	no	—
701	#41	—	86	32	no	—
702	#41	—	86	16	no	—
703	#41	—	86	8	no	—
704	#41	—	86	8	no	—
705	#41	—	86	16	no	—
706	#41	C₂³×D₄₃	1	16	yes	—
707	#41	C₂³×D₄₃	1	16	yes	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	43	2	no	—
711	C₂×Q₈	—	43	2	no	—
712	C₂×Q₈	—	43	8	no	—
713	C₂×Q₈	—	43	32	no	—
714	C₂×Q₈	—	43	4	no	—
715	C₂×Q₈	—	43	8	no	—
716	C₂×Q₈	—	86	8	no	—
717	C₂×Q₈	—	86	32	no	—
718	C₂×Q₈	—	86	16	no	—
719	C₂×Q₈	—	86	32	no	—
720	C₂×Q₈	—	86	2	no	—
721	C₂×Q₈	—	86	4	no	—
722	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
723	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	16	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	43	4	no	—
730	C₂×D₄	—	43	4	no	—
731	C₂×D₄	—	43	16	no	—
732	C₂×D₄	—	43	32	no	—
733	C₂×D₄	—	43	2	no	—
734	C₂×D₄	—	43	2	no	—
735	C₂×D₄	—	43	8	no	—
736	C₂×D₄	—	43	4	no	—
737	C₂×D₄	—	43	8	no	—
738	C₂×D₄	—	86	32	no	—
739	C₂×D₄	—	86	8	no	—
740	C₂×D₄	—	86	16	no	—
741	C₂×D₄	—	86	8	no	—
742	C₂×D₄	—	86	64	no	—
743	C₂×D₄	—	86	32	no	—
744	C₂×D₄	—	86	64	no	—
745	C₂×D₄	—	86	64	no	—
746	C₂×D₄	—	86	8	no	—
747	C₂×D₄	—	86	4	no	—
748	C₂×D₄	—	86	4	no	—
749	C₂×D₄	—	86	16	no	—
750	C₂×D₄	—	86	2	no	—
751	C₂×D₄	—	86	4	no	—
752	C₂×D₄	C₂³×D₄₃	1	4	yes	—
753	C₂×D₄	C₂³×D₄₃	1	8	yes	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	16	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	43	2	no	—
759	C₂²×C₄	—	43	8	no	—
760	C₂²×C₄	—	43	4	no	—
761	C₂²×C₄	—	43	4	no	—
762	C₂²×C₄	—	43	8	no	—
763	C₂²×C₄	—	86	8	no	—
764	C₂²×C₄	—	86	64	no	—
765	C₂²×C₄	—	86	8	no	—
766	C₂²×C₄	—	86	8	no	—
767	C₂²×C₄	—	86	2	no	—
768	C₂²×C₄	—	86	4	no	—
769	C₂²×C₄	—	86	16	no	—
770	C₂²×C₄	—	86	4	no	—
771	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
772	C₂²×C₄	D₄×D₄₃	1	4	yes	—
773	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
774	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
775	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
776	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
777	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
778	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
779	Q₁₆	—	43	32	no	—
780	Q₁₆	—	43	8	no	—
781	Q₁₆	—	43	8	no	—
782	Q₁₆	C₂³×D₄₃	1	8	yes	—
783	Q₁₆	C₂³×D₄₃	1	8	yes	—
784	SD₁₆	—	43	32	no	—
785	SD₁₆	—	43	32	no	—
786	SD₁₆	—	43	16	no	—
787	SD₁₆	—	43	16	no	—
788	SD₁₆	C₂³×D₄₃	1	16	yes	—
789	SD₁₆	C₂³×D₄₃	1	16	yes	—
790	D₈	—	43	32	no	—
791	D₈	—	43	8	no	—
792	D₈	—	43	8	no	—
793	D₈	C₂³×D₄₃	1	8	yes	—
794	D₈	C₂³×D₄₃	1	8	yes	—
795	M₁₆	—	43	8	no	—
796	M₁₆	—	43	8	no	—
797	M₁₆	—	43	16	no	—
798	M₁₆	—	43	16	no	—
799	C₂×C₈	—	43	4	no	—
800	C₂×C₈	—	43	8	no	—
801	C₂×C₈	—	43	16	no	—
802	C₂×C₈	—	43	16	no	—
803	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
804	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
805	C₂×C₈	C₂³×D₄₃	1	4	yes	—
806	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
807	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
808	C₂×C₈	C₂³×D₄₃	1	4	yes	—
809	C₂×C₈	C₂³×D₄₃	1	4	yes	—
810	C₂×C₈	C₂³×D₄₃	1	4	yes	—
811	C₂×C₈	C₂³×D₄₃	1	4	yes	—
812	C₂×C₈	C₂³×D₄₃	1	4	yes	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	8	no	—
815	C₂³	—	4	2	no	—
816	C₂³	—	8	4	no	—
817	C₂³	—	43	4	no	—
818	C₂³	—	43	8	no	—
819	C₂³	—	86	32	no	—
820	C₂³	—	86	8	no	—
821	C₂³	—	86	4	no	—
822	C₂³	—	344	4	no	—
823	C₂³	—	344	16	no	—
824	C₂³	—	172	4	no	—
825	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
826	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
827	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
828	C₂³	C₂×D₄×D₄₃	1	4	yes	—
829	Q₈	—	2	4	no	—
830	Q₈	—	2	8	no	—
831	Q₈	—	43	8	no	—
832	Q₈	—	43	8	no	—
833	Q₈	—	43	8	no	—
834	Q₈	—	86	32	no	—
835	Q₈	—	86	8	no	—
836	Q₈	—	86	4	no	—
837	Q₈	C₂⁴×D₄₃	1	8	yes	—
838	D₄	—	2	16	no	—
839	D₄	—	2	16	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	8	no	—
842	D₄	—	43	16	no	—
843	D₄	—	43	16	no	—
844	D₄	—	43	8	no	—
845	D₄	—	43	8	no	—
846	D₄	—	43	8	no	—
847	D₄	—	86	32	no	—
848	D₄	—	86	32	no	—
849	D₄	—	86	32	no	—
850	D₄	—	86	16	no	—
851	D₄	—	86	16	no	—
852	D₄	—	86	8	no	—
853	D₄	—	86	4	no	—
854	D₄	C₂⁴×D₄₃	1	8	yes	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	8	no	—
857	C₂×C₄	—	2	16	no	—
858	C₂×C₄	—	2	16	no	—
859	C₂×C₄	—	43	4	no	—
860	C₂×C₄	—	43	8	no	—
861	C₂×C₄	—	43	16	no	—
862	C₂×C₄	—	43	8	no	—
863	C₂×C₄	—	43	8	no	—
864	C₂×C₄	—	86	32	no	—
865	C₂×C₄	—	86	32	no	—
866	C₂×C₄	—	86	32	no	—
867	C₂×C₄	—	86	4	no	—
868	C₂×C₄	—	86	8	no	—
869	C₂×C₄	—	86	16	no	—
870	C₂×C₄	—	86	16	no	—
871	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
872	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
873	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
874	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
875	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
876	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
877	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
878	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
879	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
880	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
881	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
882	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
883	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
884	C₈	—	43	8	no	—
885	C₈	C₂⁴×D₄₃	1	2	yes	—
886	C₈	C₂⁴×D₄₃	1	2	yes	—
887	C₈	C₂⁴×D₄₃	1	2	yes	—
888	C₈	C₂⁴×D₄₃	1	2	yes	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	8	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	8	no	—
895	C₂²	—	8	8	no	—
896	C₂²	—	43	8	no	—
897	C₂²	—	86	8	no	—
898	C₂²	—	86	8	no	—
899	C₂²	—	344	8	no	—
900	C₂²	—	344	32	no	—
901	C₂²	—	172	8	no	—
902	C₂²	—	172	8	no	—
903	C₂²	C₂²×D₄×D₄₃	1	2	yes	—
904	C₂²	C₂²×D₄×D₄₃	1	2	yes	—
905	C₂²	C₂²×D₄×D₄₃	1	2	yes	—
906	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
907	C₄	—	2	8	no	—
908	C₄	—	43	8	no	—
909	C₄	—	86	8	no	—
910	C₄	C₂²×D₄×D₄₃	1	2	yes	—
911	C₄	C₂²×D₄×D₄₃	1	2	yes	—
912	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
913	C₄	C₂²×D₄×D₄₃	1	2	yes	—
914	C₄	C₂⁵×D₄₃	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	2	2	no	—
917	C₂	—	2	2	no	—
918	C₂	—	4	8	no	—
919	C₂	—	86	8	no	—
920	C₂	—	172	8	no	—
921	C₂	#19149364	1	2	yes	direct product factor
922	C₂	C₂³×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₄×C₄₃	C₂⁶
Frattini	C₄	C₂⁵×D₄₃
Fitting	C₂²×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂²×#135	D₄₃
hypocenter	C₄₃	C₂×#3584
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#14583735	C₂	semidirect
2. #19149364	C₂	direct (N × H)
3. C₂×#14583713	C₂	semidirect
4. C₂×#14583712	C₂	semidirect
5. C₂×#14583706	C₂	semidirect
6. C₂×#14583705	C₂	semidirect
7. C₂×#14583701	C₂	semidirect
8. C₂×#14583700	C₂	semidirect
9. C₂×#14583697	C₂	semidirect
10. C₂×#14583696	C₂	semidirect
11. C₂²×#13063347	C₂	semidirect
12. C₂×#135×D₄₃	C₂	semidirect
13. C₂²×#13063331	C₂	semidirect
14. C₂²×#135×C₄₃	C₂	semidirect
16. #14583735	C₂²	semidirect
17. C₂×#13063373	C₂²	semidirect
19. C₂×#13063372	C₂²	semidirect
21. C₂×#13063371	C₂²	semidirect
23. C₂×#13063370	C₂²	semidirect
26. C₂²×#10621898	C₂²	semidirect
28. C₂×#41×D₄₃	C₂²	semidirect
29. #14583713	C₂²	semidirect
30. #14583712	C₂²	semidirect
31. #14583706	C₂²	semidirect
32. #14583705	C₂²	semidirect
33. #14583701	C₂²	semidirect
34. #14583700	C₂²	semidirect
35. #14583697	C₂²	semidirect
36. #14583696	C₂²	semidirect
37. C₂×#13063357	C₂²	semidirect
38. C₂×#13063356	C₂²	semidirect
39. C₂×#13063355	C₂²	semidirect
40. C₂×#13063354	C₂²	semidirect
41. C₂×#13063352	C₂²	semidirect
42. C₂×#13063351	C₂²	semidirect
43. C₂×#13063350	C₂²	semidirect
44. C₂×#13063349	C₂²	semidirect
45. C₂×#13063348	C₂²	semidirect
46. C₂×#13063347	C₂²	semidirect
47. C₂×#13063347	C₂²	semidirect
48. C₂×#13063347	C₂²	semidirect
49. C₂×#13063347	C₂²	semidirect
50. C₂×#13063347	C₂²	semidirect
51. C₂×#13063346	C₂²	semidirect
52. C₂×#13063345	C₂²	semidirect
53. C₂×#13063344	C₂²	semidirect
54. #135×D₄₃	C₂²	semidirect
55. C₂²×Dic₁₇₂	C₂²	semidirect
56. C₂×Q₁₆×D₄₃	C₂²	semidirect
57. C₂²×#10621873	C₂²	semidirect
58. C₂×SD₁₆×D₄₃	C₂²	semidirect
59. C₂²×D₃₄₄	C₂²	semidirect
60. C₂×D₈×D₄₃	C₂²	semidirect
61. C₂×#13063331	C₂²	semidirect
62. C₂×#13063331	C₂²	semidirect
63. C₂×#13063331	C₂²	semidirect
64. C₂×#13063331	C₂²	semidirect
65. C₂×#13063331	C₂²	semidirect
66. C₂²×#10621877	C₂²	semidirect
67. C₂²×#10621872	C₂²	semidirect
68. C₂²×C₈×D₄₃	C₂²	semidirect
69. C₂²×#41×C₄₃	C₂²	semidirect
70. C₂×#135×C₄₃	C₂²	semidirect
71. C₂×#135×C₄₃	C₂²	semidirect
72. C₂×#135×C₄₃	C₂²	semidirect
73. C₂×#135×C₄₃	C₂²	semidirect
74. C₂×#135×C₄₃	C₂²	semidirect
75. C₂²×Q₁₆×C₄₃	C₂²	semidirect
76. C₂²×SD₁₆×C₄₃	C₂²	semidirect
77. C₂²×D₈×C₄₃	C₂²	semidirect
78. C₂³×C₈×C₄₃	C₂²	semidirect
80. #13063373	C₂³	semidirect
83. #13063372	C₂³	semidirect
86. #13063371	C₂³	semidirect
89. #13063370	C₂³	semidirect
108. C₂×#10621898	C₂³	semidirect
115. #41×D₄₃	C₂³	semidirect
134. #13063357	C₂³	semidirect
135. #13063356	C₂³	semidirect
136. #13063355	C₂³	semidirect
137. #13063354	C₂³	semidirect
138. #13063352	C₂³	semidirect
139. #13063351	C₂³	semidirect
140. #13063350	C₂³	semidirect
141. #13063349	C₂³	semidirect
142. #13063348	C₂³	semidirect
143. #13063347	C₂³	semidirect
144. #13063347	C₂³	semidirect
145. #13063347	C₂³	semidirect
146. #13063347	C₂³	semidirect
147. #13063346	C₂³	semidirect
148. #13063345	C₂³	semidirect
149. #13063344	C₂³	semidirect
152. C₂×Dic₁₇₂	C₂³	semidirect
154. Q₁₆×D₄₃	C₂³	semidirect
157. C₂×#10621873	C₂³	semidirect
160. SD₁₆×D₄₃	C₂³	semidirect
163. C₂×D₃₄₄	C₂³	semidirect
165. D₈×D₄₃	C₂³	semidirect
166. #13063331	C₂³	semidirect
167. #13063331	C₂³	semidirect
168. #13063331	C₂³	semidirect
169. #13063331	C₂³	semidirect
172. C₂×#10621877	C₂³	semidirect
175. C₂×#10621872	C₂³	semidirect
179. C₂×C₈×D₄₃	C₂³	semidirect
185. C₂×#41×C₄₃	C₂³	semidirect
191. #135×C₄₃	C₂³	semidirect
192. #135×C₄₃	C₂³	semidirect
193. #135×C₄₃	C₂³	semidirect
194. #135×C₄₃	C₂³	semidirect
197. C₂×Q₁₆×C₄₃	C₂³	semidirect
200. C₂×SD₁₆×C₄₃	C₂³	semidirect
203. C₂×D₈×C₄₃	C₂³	semidirect
210. C₂²×C₈×C₄₃	C₂³	semidirect
466. C₂²×#135	D₄₃	semidirect
472. C₂×C₄₃	#3584	semidirect
490. C₂²×#41	C₂×D₄₃	semidirect
517. C₂×#135	C₂×D₄₃	semidirect
518. C₂×#135	C₂×D₄₃	semidirect
519. C₂×#135	C₂×D₄₃	semidirect
520. C₂×#135	C₂×D₄₃	semidirect
521. C₂×#135	C₂×D₄₃	semidirect
524. C₂²×Q₁₆	C₂×D₄₃	semidirect
527. C₂²×SD₁₆	C₂×D₄₃	semidirect
530. C₂²×D₈	C₂×D₄₃	semidirect
539. C₂³×C₈	C₂×D₄₃	semidirect
540. C₄₃	C₂×#3584	semidirect
583. C₂×#41	C₂²×D₄₃	semidirect
623. #135	C₂²×D₄₃	semidirect
624. #135	C₂²×D₄₃	semidirect
625. #135	C₂²×D₄₃	semidirect
626. #135	C₂²×D₄₃	semidirect
634. C₂×Q₁₆	C₂²×D₄₃	semidirect
643. C₂×SD₁₆	C₂²×D₄₃	semidirect
651. C₂×D₈	C₂²×D₄₃	semidirect
672. C₂²×C₈	C₂²×D₄₃	semidirect
921. C₂	#19149364	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14583735	2
#19149364	2
C₂×#14583713	2
C₂×#14583712	2
C₂×#14583706	2
C₂×#14583705	2
C₂×#14583701	2
C₂×#14583700	2
C₂×#14583697	2
C₂×#14583696	2
C₂²×#13063347	2
C₂×#135×D₄₃	2
C₂²×#13063331	2
C₂²×#135×C₄₃	2
C₂×#3584	43

Subgroups — C2×#19149364 #26010426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19149364 #26010426