Subgroups — #25966818

Order 11008.

1980 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148330	C₂	1	2	yes	maximal, complemented
2	#19145293	C₂	1	4	yes	maximal, complemented
3	#19145278	C₂	1	4	yes	maximal, complemented
4	#19145245	C₂	1	2	yes	maximal, complemented
5	#19145234	C₂	1	2	yes	maximal, complemented
6	#19145174	C₂	1	2	yes	maximal, complemented
7	#19145165	C₂	1	2	yes	maximal, complemented
8	#19145134	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145081	C₂	1	1	yes	maximal, characteristic, complemented
10	#19144951	C₂	1	2	yes	maximal, complemented
11	#19144214	C₂	1	2	yes	maximal, complemented
12	#19144176	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14583135	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143472	C₂	1	1	yes	maximal, characteristic, complemented
15	#19143448	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143429	C₂	1	2	yes	maximal, complemented
17	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063353	C₂²	1	2	yes	—
19	C₂×#13063347	C₂²	1	1	yes	characteristic
20	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
21	#14583612	—	2	2	no	—
22	#14583597	—	2	2	no	—
23	#14583593	—	2	2	no	—
24	#14583573	—	2	4	no	—
25	#14583550	—	2	2	no	—
26	#14583539	—	2	4	no	—
27	#14583527	C₂²	1	2	yes	—
28	#14583520	C₂²	1	4	yes	complemented
29	#14583504	C₂²	1	4	yes	complemented
30	#14583468	C₂²	1	2	yes	—
31	#14583449	C₂²	1	4	yes	complemented
32	#14583433	C₂²	1	4	yes	complemented
33	#14583410	C₂²	1	2	yes	—
34	C₂×#13063299	C₂²	1	2	yes	—
35	#14583379	C₂²	1	2	yes	—
36	#14583373	C₂²	1	2	yes	—
37	#14583308	C₂²	1	4	yes	complemented
38	#14583304	C₂²	1	2	yes	complemented
39	#14583301	C₂²	1	2	yes	complemented
40	#14583288	C₂²	1	4	yes	complemented
41	#14583283	C₂²	1	2	yes	complemented
42	#14583276	C₂²	1	2	yes	complemented
43	#14583264	C₂²	1	4	yes	complemented
44	#14583259	C₂²	1	4	yes	complemented
45	#14583254	C₂²	1	4	yes	complemented
46	#14583246	C₂²	1	4	yes	complemented
47	#14583152	C₂²	1	4	yes	complemented
48	#14583145	C₂²	1	4	yes	complemented
49	#14583140	C₂²	1	1	yes	characteristic, complemented
50	#14583140	C₂²	1	1	yes	characteristic, complemented
51	#14583135	C₂²	1	2	yes	—
52	#14583135	C₂²	1	2	yes	—
53	#14583135	C₂²	1	2	yes	—
54	#14583135	C₂²	1	2	yes	—
55	#14583135	C₂²	1	4	yes	complemented
56	#14583135	C₂²	1	1	yes	characteristic, complemented
57	#14583135	C₂²	1	1	yes	characteristic, complemented
58	#14583128	C₂²	1	4	yes	complemented
59	#14583128	C₂²	1	2	yes	complemented
60	#14583128	C₂²	1	2	yes	complemented
61	#14583012	C₂²	1	4	yes	complemented
62	#14583012	C₂²	1	4	yes	complemented
63	#14583001	C₂²	1	4	yes	complemented
64	#14583001	C₂²	1	4	yes	complemented
65	C₄×Dic₁₇₂	C₂²	1	2	yes	complemented
66	C₄×#10621873	C₂²	1	4	yes	complemented
67	C₄×D₃₄₄	C₂²	1	4	yes	complemented
68	C₄×D₃₄₄	C₂²	1	2	yes	complemented
69	C₄×D₃₄₄	C₂²	1	2	yes	complemented
70	C₄×D₃₄₄	C₂²	1	2	yes	complemented
71	#14582941	C₂²	1	2	yes	—
72	#14582937	C₂²	1	1	yes	characteristic
73	C₂×#13063259	C₂²	1	1	yes	characteristic
74	#14582905	C₂²	1	2	yes	—
75	#14582901	C₂²	1	2	yes	—
76	#14582896	C₂²	1	2	yes	—
77	C₂×#13063247	C₂²	1	2	yes	—
78	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
79	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
80	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
81	C₄₃×#405	C₂²	1	1	yes	characteristic
82	C₄₃×#405	C₂²	1	1	yes	characteristic
83	C₄₃×#405	C₂²	1	1	yes	characteristic
84	C₄₃×#405	C₂²	1	1	yes	characteristic
85	C₄₃×#405	C₂²	1	2	yes	complemented
86	C₄₃×#405	C₂²	1	2	yes	complemented
87	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
89	C₂×#10621898	—	2	4	no	—
90	C₂×#10621898	C₂³	1	2	yes	—
91	C₂²×D₁₇₂	C₂³	1	2	yes	—
92	C₂²×C₂²⋊D₄₃	—	2	2	no	—
93	#13063353	—	2	8	no	—
94	#13063347	—	2	4	no	—
95	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
96	C₂×#10621873	C₂³	1	2	yes	—
97	C₂×#10621873	C₂³	1	4	yes	—
98	C₂×D₃₄₄	—	2	4	no	—
99	C₂×D₃₄₄	C₂³	1	2	yes	—
100	C₂×D₃₄₄	C₂³	1	2	yes	—
101	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
102	C₂×D₃₄₄	C₂³	1	4	yes	—
103	#13063325	C₂³	1	4	yes	—
104	#13063324	—	2	2	no	—
105	#13063322	C₂³	1	4	yes	—
106	#13063320	—	2	4	no	—
107	#13063319	—	2	4	no	—
108	#13063317	C₂³	1	4	yes	—
109	#13063316	—	2	2	no	—
110	#13063313	—	2	4	no	—
111	#13063313	C₂³	1	4	yes	—
112	#13063311	—	2	4	no	—
113	#13063310	—	2	4	no	—
114	#13063310	—	2	4	no	—
115	#13063308	—	2	2	no	—
116	#13063308	—	2	4	no	—
117	#13063307	—	2	4	no	—
118	#13063304	C₂³	1	2	yes	—
119	#13063304	C₂³	1	2	yes	—
120	#13063303	—	2	4	no	—
121	#13063302	—	2	4	no	—
122	#13063300	—	2	2	no	—
123	#13063300	—	2	2	no	—
124	#13063299	—	2	2	no	—
125	#13063299	—	2	2	no	—
126	#13063299	—	2	4	no	—
127	#13063299	C₂³	1	4	yes	—
128	#13063299	C₂³	1	2	yes	—
129	#13063299	C₂³	1	2	yes	—
130	#13063299	C₂³	1	4	yes	—
131	#13063298	—	2	4	no	—
132	#13063298	—	2	4	no	—
133	#13063295	—	2	4	no	—
134	#13063294	—	2	2	no	—
135	C₄×Dic₈₆	C₂³	1	4	yes	—
136	C₄×D₁₇₂	—	2	4	no	—
137	C₄×D₁₇₂	C₂³	1	4	yes	—
138	C₄×D₁₇₂	C₂³	1	4	yes	—
139	C₄×D₁₇₂	C₂³	1	4	yes	—
140	#13063287	—	2	2	no	—
141	#13063287	—	2	2	no	—
142	C₄×C₂²⋊D₄₃	—	2	2	no	—
143	C₄×C₂²⋊D₄₃	—	2	2	no	—
144	C₄×C₂²⋊D₄₃	—	2	4	no	—
145	(C₂²⋊D₄₃)⋊C₄	—	2	4	no	—
146	#13063284	C₂³	1	2	yes	—
147	#13063283	—	2	2	no	—
148	#13063282	—	2	4	no	—
149	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
150	C₄⋊C₄×D₄₃	—	2	2	no	—
151	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
152	C₂²⋊C₄×D₄₃	—	2	4	no	—
153	#13063259	C₂³	1	1	yes	characteristic
154	#13063259	C₂³	1	2	yes	—
155	#13063259	C₂³	1	1	yes	characteristic
156	#13063259	C₂³	1	4	yes	—
157	#13063259	C₂³	1	2	yes	—
158	#13063257	C₂³	1	4	yes	—
159	#13063257	C₂³	1	2	yes	—
160	#13063250	C₂³	1	2	yes	—
161	#13063250	C₂³	1	2	yes	—
162	#13063250	C₂³	1	4	yes	—
163	#13063247	C₂³	1	2	yes	—
164	#13063247	C₂³	1	2	yes	—
165	#13063247	C₂³	1	4	yes	—
166	#13063247	C₂³	1	4	yes	—
167	#13063247	C₂³	1	4	yes	—
168	#13063247	C₂³	1	4	yes	—
169	#13063247	C₂³	1	4	yes	—
170	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₄₃	—	2	4	no	—
172	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
173	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₄₃	—	2	4	no	—
176	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
179	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
182	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
183	#117×C₄₃	D₄	1	2	yes	—
184	#117×C₄₃	D₄	1	1	yes	characteristic
185	#117×C₄₃	D₄	1	1	yes	characteristic
186	#117×C₄₃	C₂³	1	1	yes	characteristic
187	#117×C₄₃	C₂³	1	1	yes	characteristic
188	#117×C₄₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
192	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
193	#97×C₄₃	C₂³	1	2	yes	—
194	#97×C₄₃	C₂³	1	2	yes	—
195	#97×C₄₃	C₂³	1	2	yes	—
196	#97×C₄₃	C₂³	1	2	yes	—
197	C₄×C₈×C₄₃	C₂³	1	2	yes	—
198	C₄×C₈×C₄₃	C₂³	1	2	yes	—
199	C₄×C₈×C₄₃	C₂³	1	2	yes	—
200	C₄×C₈×C₄₃	C₂³	1	2	yes	—
201	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
202	C₂³×D₄₃	—	2	2	no	—
203	C₂²×C₄×C₄₃	—	2	2	no	—
204	C₂²×C₄×C₄₃	—	2	2	no	—
205	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₂²⋊D₄₃	—	2	2	no	—
214	C₂×C₂²⋊D₄₃	—	2	2	no	—
215	C₂×C₂²⋊D₄₃	—	2	4	no	—
216	C₂×C₂²⋊D₄₃	—	2	2	no	—
217	C₂×C₂²⋊D₄₃	—	2	4	no	—
218	C₂×C₂²⋊D₄₃	—	8	4	no	—
219	C₂²×Dic₄₃	—	2	2	no	—
220	#10621898	—	2	4	no	—
221	#10621898	—	2	4	no	—
222	#10621898	—	8	8	no	—
223	C₂×D₁₇₂	—	2	2	no	—
224	C₂×D₁₇₂	—	2	4	no	—
225	C₂×D₁₇₂	—	2	4	no	—
226	C₂×D₁₇₂	—	2	4	no	—
227	C₂×D₁₇₂	—	2	4	no	—
228	C₂×D₁₇₂	C₂⁴	1	4	yes	—
229	C₂×D₁₇₂	C₂⁴	1	2	yes	—
230	C₂×C₄×D₄₃	—	2	2	no	—
231	C₂×C₄×D₄₃	—	2	4	no	—
232	C₂×C₄×D₄₃	—	2	4	no	—
233	C₂×C₄×D₄₃	—	2	4	no	—
234	C₂×Dic₈₆	—	2	4	no	—
235	C₂×Dic₈₆	C₂⁴	1	2	yes	—
236	M₁₆×C₄₃	—	2	2	no	—
237	M₁₆×C₄₃	—	2	4	no	—
238	M₁₆×C₄₃	#41	1	4	yes	complemented
239	C₂×C₈×C₄₃	—	2	2	no	—
240	C₂×C₈×C₄₃	—	2	2	no	—
241	C₂×C₈×C₄₃	—	2	2	no	—
242	C₂×C₈×C₄₃	—	2	2	no	—
243	C₂×C₈×C₄₃	—	2	2	no	—
244	C₂×C₈×C₄₃	—	2	4	no	—
245	C₂×C₈×C₄₃	#41	1	4	yes	complemented
246	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
252	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
253	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
254	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
255	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
258	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
259	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
260	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
261	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
262	C₄²×C₄₃	C₂×D₄	1	2	yes	—
263	C₄²×C₄₃	C₂×D₄	1	2	yes	—
264	C₄²×C₄₃	C₂⁴	1	2	yes	—
265	C₄²×C₄₃	C₂⁴	1	2	yes	—
266	C₂²⋊Dic₄₃	—	2	2	no	—
267	C₂²⋊Dic₄₃	—	2	2	no	—
268	C₂²⋊Dic₄₃	—	2	2	no	—
269	(C₂×D₄₃)⋊C₄	—	2	4	no	—
270	(C₂×D₄₃)⋊C₄	—	2	4	no	—
271	(C₂×D₄₃)⋊C₄	—	2	4	no	—
272	(C₂×D₄₃)⋊C₄	—	2	4	no	—
273	(C₂×D₄₃)⋊C₄	—	2	4	no	—
274	(C₂×D₄₃)⋊C₄	—	2	4	no	—
275	(C₂×D₄₃)⋊C₄	—	2	2	no	—
276	(C₂×D₄₃)⋊C₄	—	2	4	no	—
277	(C₂×D₄₃)⋊C₄	—	2	2	no	—
278	C₄⋊Dic₄₃	—	2	2	no	—
279	C₄⋊Dic₄₃	—	2	4	no	—
280	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
281	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
282	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
283	Dic₄₃⋊C₄	—	2	4	no	—
284	Dic₄₃⋊C₄	—	2	2	no	—
285	Dic₄₃⋊C₄	—	2	4	no	—
286	Dic₄₃⋊C₄	—	2	4	no	—
287	Dic₄₃⋊C₄	—	2	2	no	—
288	C₄×Dic₄₃	—	2	4	no	—
289	C₄×Dic₄₃	—	2	2	no	—
290	Dic₁₇₂	—	2	2	no	—
291	D₃₄₄	—	2	4	no	—
292	D₃₄₄	—	2	4	no	—
293	D₃₄₄	—	2	2	no	—
294	D₃₄₄	—	2	8	no	—
295	#10621873	—	2	4	no	—
296	#10621873	—	2	8	no	—
297	C₂³×C₄₃	—	2	2	no	—
298	C₂³×C₄₃	—	2	2	no	—
299	C₂³×C₄₃	—	4	1	no	—
300	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
302	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
303	C₂²×D₄₃	—	2	4	no	—
304	C₂²×D₄₃	—	2	2	no	—
305	C₂²×D₄₃	—	4	4	no	—
306	C₂²×D₄₃	—	8	2	no	—
307	C₂²×D₄₃	—	8	2	no	—
308	C₂×C₄×C₄₃	—	2	2	no	—
309	C₂×C₄×C₄₃	—	2	4	no	—
310	C₂×C₄×C₄₃	—	2	2	no	—
311	C₂×C₄×C₄₃	—	2	2	no	—
312	C₂×C₄×C₄₃	—	2	1	no	—
313	C₂×C₄×C₄₃	—	2	1	no	—
314	C₂×C₄×C₄₃	—	2	1	no	—
315	C₂×C₄×C₄₃	—	2	1	no	—
316	C₂×C₄×C₄₃	—	4	2	no	—
317	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
325	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
326	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
327	C₂²⋊D₄₃	—	4	4	no	—
328	C₂²⋊D₄₃	—	4	4	no	—
329	C₂²⋊D₄₃	—	4	8	no	—
330	C₂²⋊D₄₃	—	8	2	no	—
331	C₂²⋊D₄₃	—	8	4	no	—
332	C₂×Dic₄₃	—	2	2	no	—
333	C₂×Dic₄₃	—	2	2	no	—
334	C₂×Dic₄₃	—	2	4	no	—
335	C₂×Dic₄₃	—	2	2	no	—
336	C₂×Dic₄₃	—	8	2	no	—
337	D₁₇₂	—	2	4	no	—
338	D₁₇₂	—	2	2	no	—
339	D₁₇₂	—	2	4	no	—
340	D₁₇₂	—	2	2	no	—
341	D₁₇₂	—	4	4	no	—
342	D₁₇₂	—	8	4	no	—
343	D₁₇₂	—	8	4	no	—
344	C₄×D₄₃	—	4	4	no	—
345	C₄×D₄₃	—	8	4	no	—
346	C₄×D₄₃	—	8	4	no	—
347	C₄×D₄₃	—	8	4	no	—
348	Dic₈₆	—	2	2	no	—
349	Dic₈₆	—	2	2	no	—
350	Dic₈₆	—	8	4	no	—
351	C₈×C₄₃	—	2	1	no	—
352	C₈×C₄₃	—	2	1	no	—
353	C₈×C₄₃	—	2	2	no	—
354	C₈×C₄₃	C₂×#41	1	2	yes	—
355	C₈×C₄₃	C₂×#41	1	4	yes	—
356	C₈×C₄₃	C₂×#41	1	2	yes	—
357	#60707	—	43	1	no	maximal, Sylow
358	C₂²×C₄₃	—	2	1	no	—
359	C₂²×C₄₃	—	2	1	no	—
360	C₂²×C₄₃	—	2	1	no	—
361	C₂²×C₄₃	—	2	1	no	—
362	C₂²×C₄₃	—	2	1	no	—
363	C₂²×C₄₃	—	2	1	no	—
364	C₂²×C₄₃	—	2	1	no	—
365	C₂²×C₄₃	—	4	4	no	—
366	C₂²×C₄₃	#532	1	2	yes	—
367	C₂²×C₄₃	#576	1	2	yes	—
368	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
369	C₂×D₄₃	—	4	4	no	—
370	C₂×D₄₃	—	4	2	no	—
371	C₂×D₄₃	—	4	4	no	—
372	C₂×D₄₃	—	4	2	no	—
373	C₂×D₄₃	—	4	4	no	—
374	C₂×D₄₃	—	4	2	no	—
375	C₂×D₄₃	—	16	4	no	—
376	C₄×C₄₃	—	2	2	no	—
377	C₄×C₄₃	—	2	2	no	—
378	C₄×C₄₃	—	2	1	no	—
379	C₄×C₄₃	—	2	1	no	—
380	C₄×C₄₃	—	2	2	no	—
381	C₄×C₄₃	—	2	2	no	—
382	C₄×C₄₃	#532	1	2	yes	—
383	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
384	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
385	Dic₄₃	—	4	2	no	—
386	Dic₄₃	—	4	2	no	—
387	Dic₄₃	—	4	2	no	—
388	Dic₄₃	—	4	4	no	—
389	#3494	—	43	2	no	—
390	#3180	—	43	4	no	—
391	#3179	—	43	4	no	—
392	#3176	—	43	2	no	—
393	#3175	—	43	2	no	—
394	#3169	—	43	2	no	—
395	#3168	—	43	2	no	—
396	#3164	—	43	1	no	—
397	#3155	—	43	1	no	—
398	#3136	—	43	2	no	—
399	#3055	—	43	2	no	—
400	#3050	—	43	1	no	—
401	C₂×#466	—	43	1	no	—
402	#2951	—	43	1	no	—
403	#2948	—	43	1	no	—
404	#2946	—	43	2	no	—
405	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
406	C₂×C₄₃	—	2	2	no	—
407	C₂×C₄₃	—	2	2	no	—
408	C₂×C₄₃	—	4	1	no	—
409	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
410	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
411	C₂×C₄₃	#3584	1	1	yes	characteristic
412	D₄₃	—	8	2	no	—
413	D₄₃	—	8	4	no	—
414	C₂×AGL(1,ℤ/8)	—	43	2	no	—
415	C₂×#135	—	43	1	no	—
416	C₂²×D₈	—	43	1	no	—
417	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
418	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
419	#555	—	86	2	no	—
420	#553	—	86	2	no	—
421	#553	—	86	2	no	—
422	#551	—	86	4	no	—
423	#547	—	86	2	no	—
424	#546	—	86	4	no	—
425	#544	—	43	2	no	—
426	#542	—	43	4	no	—
427	#540	—	43	4	no	—
428	#535	—	43	2	no	—
429	#532	—	43	4	no	—
430	#529	—	43	4	no	—
431	#525	—	43	2	no	—
432	C₂×#121	—	43	2	no	—
433	#520	—	43	2	no	—
434	#518	—	43	2	no	—
435	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
436	#501	—	43	4	no	—
437	#500	—	43	2	no	—
438	#499	—	43	2	no	—
439	#496	—	43	4	no	—
440	#495	—	43	2	no	—
441	#493	—	43	2	no	—
442	#490	—	43	4	no	—
443	#489	—	43	4	no	—
444	#488	—	43	4	no	—
445	#486	—	43	4	no	—
446	#469	—	43	4	no	—
447	#468	—	43	4	no	—
448	#467	—	43	1	no	—
449	#467	—	43	1	no	—
450	#466	—	43	2	no	—
451	#466	—	43	2	no	—
452	#466	—	43	2	no	—
453	#466	—	43	2	no	—
454	#466	—	43	1	no	—
455	#466	—	43	4	no	—
456	#466	—	43	1	no	—
457	#465	—	43	4	no	—
458	#465	—	43	2	no	—
459	#465	—	43	2	no	—
460	#442	—	43	4	no	—
461	#442	—	43	4	no	—
462	#440	—	43	4	no	—
463	#440	—	43	4	no	—
464	C₄×Q₁₆	—	43	2	no	—
465	C₄×SD₁₆	—	43	4	no	—
466	C₄×D₈	—	43	2	no	—
467	C₄×D₈	—	43	2	no	—
468	C₄×D₈	—	43	2	no	—
469	C₄×D₈	—	43	4	no	—
470	#428	—	43	2	no	—
471	#427	—	43	1	no	—
472	C₂×#107	—	43	1	no	—
473	#418	—	43	2	no	—
474	#417	—	43	2	no	—
475	#416	—	43	2	no	—
476	C₂×#102	—	43	2	no	—
477	#405	C₂×D₄₃	1	1	yes	characteristic
478	#405	C₂×D₄₃	1	1	yes	characteristic
479	#405	C₂×D₄₃	1	1	yes	characteristic
480	#405	C₂×D₄₃	1	1	yes	characteristic
481	#405	C₂×D₄₃	1	2	yes	complemented
482	#405	C₂×D₄₃	1	2	yes	complemented
483	C₂×#97	C₂×D₄₃	1	2	yes	complemented
484	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	complemented
485	C₄₃	#60707	1	1	yes	characteristic, complemented, Sylow
486	C₂×#41	—	43	2	no	—
487	C₂×#41	—	86	4	no	—
488	C₂²×D₄	—	43	2	no	—
489	C₂²×D₄	—	86	2	no	—
490	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
491	AGL(1,ℤ/8)	—	86	8	no	—
492	#135	—	86	4	no	—
493	C₂×Q₁₆	—	43	1	no	—
494	C₂×SD₁₆	—	43	2	no	—
495	C₂×SD₁₆	—	43	4	no	—
496	C₂×D₈	—	43	2	no	—
497	C₂×D₈	—	43	2	no	—
498	C₂×D₈	—	43	1	no	—
499	C₂×D₈	—	43	4	no	—
500	C₂×D₈	—	86	4	no	—
501	C₂×M₁₆	—	2	4	no	—
502	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
503	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
504	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
505	C₂²×C₈	—	2	4	no	—
506	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
507	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
508	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
509	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
510	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
511	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
512	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
513	C₄⋊Q₈	—	43	4	no	—
514	C₄⋊Q₈	—	86	2	no	—
515	#127	—	43	4	no	—
516	#126	—	86	4	no	—
517	#126	—	86	4	no	—
518	#125	—	43	4	no	—
519	#125	—	86	2	no	—
520	#124	—	43	4	no	—
521	#124	—	86	4	no	—
522	#124	—	86	4	no	—
523	#123	—	86	2	no	—
524	#123	—	86	4	no	—
525	#123	—	86	4	no	—
526	#123	—	86	4	no	—
527	#123	—	86	4	no	—
528	C₂²⋊Q₈	—	43	2	no	—
529	C₂²⋊Q₈	—	43	2	no	—
530	C₂²⋊Q₈	—	86	4	no	—
531	C₂²⋊Q₈	—	86	4	no	—
532	#121	—	43	4	no	—
533	#121	—	43	4	no	—
534	#121	—	43	2	no	—
535	#121	—	43	2	no	—
536	#121	—	86	2	no	—
537	#121	—	86	2	no	—
538	#121	—	86	4	no	—
539	#121	—	86	2	no	—
540	#121	—	86	2	no	—
541	#121	—	86	4	no	—
542	#121	—	86	4	no	—
543	#120	—	86	2	no	—
544	#120	—	86	4	no	—
545	C₄×Q₈	—	43	4	no	—
546	C₄×D₄	—	43	4	no	—
547	C₄×D₄	—	43	4	no	—
548	C₄×D₄	—	43	4	no	—
549	C₄×D₄	—	86	2	no	—
550	C₄×D₄	—	86	2	no	—
551	C₄×D₄	—	86	4	no	—
552	C₄×D₄	—	86	2	no	—
553	C₄×D₄	—	86	2	no	—
554	C₄×D₄	—	86	4	no	—
555	C₄×D₄	—	86	4	no	—
556	#117	—	43	2	no	—
557	#117	—	86	2	no	—
558	#117	—	86	4	no	—
559	#117	D₁₇₂	1	2	yes	—
560	#117	D₁₇₂	1	1	yes	characteristic
561	#117	D₁₇₂	1	1	yes	characteristic
562	#117	C₂²×D₄₃	1	1	yes	characteristic
563	#117	C₂²×D₄₃	1	1	yes	characteristic
564	#117	C₂²×D₄₃	1	2	yes	—
565	C₂×C₄⋊C₄	—	43	2	no	—
566	C₂×C₄⋊C₄	—	86	2	no	—
567	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
568	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
569	C₂×C₂²⋊C₄	—	86	2	no	—
570	C₂×C₂²⋊C₄	—	86	4	no	—
571	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
572	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
573	#107	—	43	2	no	—
574	#107	—	43	2	no	—
575	#107	—	43	1	no	—
576	#107	—	43	1	no	—
577	#107	—	43	4	no	—
578	#106	—	43	2	no	—
579	#106	—	43	4	no	—
580	#103	—	43	2	no	—
581	#103	—	43	2	no	—
582	#103	—	43	4	no	—
583	#102	—	43	4	no	—
584	#102	—	43	4	no	—
585	#102	—	43	2	no	—
586	#102	—	43	2	no	—
587	#102	—	43	4	no	—
588	#102	—	43	4	no	—
589	#102	—	43	4	no	—
590	#97	C₂²×D₄₃	1	2	yes	—
591	#97	C₂²×D₄₃	1	2	yes	—
592	#97	C₂²×D₄₃	1	2	yes	—
593	#97	C₂²×D₄₃	1	2	yes	—
594	C₄×C₈	C₂²×D₄₃	1	2	yes	—
595	C₄×C₈	C₂²×D₄₃	1	2	yes	—
596	C₄×C₈	C₂²×D₄₃	1	2	yes	—
597	C₄×C₈	C₂²×D₄₃	1	2	yes	—
598	C₂⁴	—	86	2	no	—
599	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
600	#41	—	86	4	no	—
601	#41	—	86	4	no	—
602	#41	—	344	8	no	—
603	C₂×Q₈	—	43	2	no	—
604	C₂×Q₈	—	86	4	no	—
605	C₂×D₄	—	43	4	no	—
606	C₂×D₄	—	43	2	no	—
607	C₂×D₄	—	86	2	no	—
608	C₂×D₄	—	86	4	no	—
609	C₂×D₄	—	86	2	no	—
610	C₂×D₄	—	86	2	no	—
611	C₂×D₄	—	86	4	no	—
612	C₂×D₄	—	86	4	no	—
613	C₂×D₄	—	86	4	no	—
614	C₂×D₄	—	86	2	no	—
615	C₂×D₄	—	86	4	no	—
616	C₂×D₄	—	86	4	no	—
617	C₂×D₄	—	344	4	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	86	2	no	—
621	C₂²×C₄	—	86	4	no	—
622	C₂²×C₄	—	86	4	no	—
623	C₂²×C₄	—	86	4	no	—
624	C₂²×C₄	—	86	2	no	—
625	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
626	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
630	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
631	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
632	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
633	Q₁₆	—	86	2	no	—
634	SD₁₆	—	86	4	no	—
635	SD₁₆	—	86	8	no	—
636	D₈	—	86	4	no	—
637	D₈	—	86	4	no	—
638	D₈	—	86	2	no	—
639	D₈	—	86	8	no	—
640	M₁₆	—	2	2	no	—
641	M₁₆	—	2	4	no	—
642	M₁₆	#10621898	1	4	yes	complemented
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	#10621898	1	4	yes	complemented
650	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
651	C₂×C₈	C₂³×D₄₃	1	2	yes	—
652	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
653	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
654	C₂×C₈	C₂³×D₄₃	1	2	yes	—
655	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
656	C₄⋊C₄	—	43	2	no	—
657	C₄⋊C₄	—	43	4	no	—
658	C₄⋊C₄	—	43	2	no	—
659	C₄⋊C₄	—	86	2	no	—
660	C₄⋊C₄	—	86	4	no	—
661	C₄⋊C₄	—	86	2	no	—
662	C₄⋊C₄	—	86	4	no	—
663	C₄⋊C₄	—	86	4	no	—
664	C₄⋊C₄	—	86	4	no	—
665	C₄⋊C₄	—	86	2	no	—
666	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
667	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
668	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
669	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
670	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
671	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
672	C₂²⋊C₄	—	86	2	no	—
673	C₂²⋊C₄	—	86	2	no	—
674	C₂²⋊C₄	—	86	2	no	—
675	C₂²⋊C₄	—	86	4	no	—
676	C₂²⋊C₄	—	86	4	no	—
677	C₂²⋊C₄	—	86	4	no	—
678	C₂²⋊C₄	—	86	4	no	—
679	C₂²⋊C₄	—	86	4	no	—
680	C₂²⋊C₄	—	86	4	no	—
681	C₂²⋊C₄	—	86	2	no	—
682	C₂²⋊C₄	—	86	4	no	—
683	C₂²⋊C₄	—	86	2	no	—
684	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
685	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
686	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
687	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
688	C₄²	—	86	2	no	—
689	C₄²	—	86	4	no	—
690	C₄²	C₂×D₁₇₂	1	2	yes	—
691	C₄²	C₂×D₁₇₂	1	2	yes	—
692	C₄²	C₂³×D₄₃	1	2	yes	—
693	C₄²	C₂³×D₄₃	1	2	yes	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	86	4	no	—
698	C₂³	—	86	2	no	—
699	C₂³	—	344	2	no	—
700	C₂³	—	344	2	no	—
701	C₂³	—	172	4	no	—
702	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
703	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
704	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
705	Q₈	—	86	2	no	—
706	Q₈	—	86	2	no	—
707	Q₈	—	344	4	no	—
708	D₄	—	86	4	no	—
709	D₄	—	86	2	no	—
710	D₄	—	86	4	no	—
711	D₄	—	86	2	no	—
712	D₄	—	344	4	no	—
713	D₄	—	344	4	no	—
714	D₄	—	344	4	no	—
715	D₄	—	344	2	no	—
716	D₄	—	172	8	no	—
717	D₄	—	172	4	no	—
718	D₄	—	172	4	no	—
719	D₄	—	172	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	86	2	no	—
730	C₂×C₄	—	86	2	no	—
731	C₂×C₄	—	86	2	no	—
732	C₂×C₄	—	86	4	no	—
733	C₂×C₄	—	344	4	no	—
734	C₂×C₄	—	344	4	no	—
735	C₂×C₄	—	344	4	no	—
736	C₂×C₄	—	344	2	no	—
737	C₂×C₄	—	172	4	no	—
738	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
739	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
741	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
742	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
743	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
745	C₂×C₄	C₂×#10621898	1	2	yes	—
746	C₂×C₄	C₂×#10621898	1	2	yes	—
747	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
748	C₈	—	2	1	no	—
749	C₈	—	2	1	no	—
750	C₈	—	2	2	no	—
751	C₈	C₂×#10621898	1	2	yes	—
752	C₈	C₂×#10621898	1	2	yes	—
753	C₈	C₂×#10621898	1	4	yes	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	172	2	no	—
763	C₂²	—	172	4	no	—
764	C₂²	—	172	4	no	—
765	C₂²	—	172	2	no	—
766	C₂²	—	172	2	no	—
767	C₂²	—	172	4	no	—
768	C₂²	—	688	4	no	—
769	C₂²	#14583449	1	2	yes	—
770	C₂²	#14583704	1	2	yes	—
771	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	172	4	no	—
779	C₄	—	172	2	no	—
780	C₄	—	172	2	no	—
781	C₄	—	172	2	no	—
782	C₄	#14583449	1	2	yes	—
783	C₄	C₂²×#10621898	1	1	yes	characteristic
784	C₄	C₂²×#10621898	1	1	yes	characteristic
785	C₂	—	2	2	no	—
786	C₂	—	2	2	no	—
787	C₂	—	4	1	no	—
788	C₂	—	344	4	no	—
789	C₂	—	344	2	no	—
790	C₂	C₂×#14583449	1	1	yes	characteristic
791	C₂	C₂×#14583704	1	1	yes	characteristic
792	C₂	#19149369	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#60707
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
1. #19148330	C₂	semidirect
2. #19145293	C₂	semidirect
3. #19145278	C₂	semidirect
4. #19145245	C₂	semidirect
5. #19145234	C₂	semidirect
6. #19145174	C₂	semidirect
7. #19145165	C₂	semidirect
8. #19145134	C₂	semidirect
9. #19145081	C₂	semidirect
10. #19144951	C₂	semidirect
11. #19144214	C₂	semidirect
12. #19144176	C₂	semidirect
13. C₂×#14583135	C₂	semidirect
14. #19143472	C₂	semidirect
15. #19143448	C₂	semidirect
16. #19143429	C₂	semidirect
17. C₂×C₄₃×#405	C₂	semidirect
28. #14583520	C₂²	semidirect
29. #14583504	C₂²	semidirect
31. #14583449	C₂²	semidirect
32. #14583433	C₂²	semidirect
37. #14583308	C₂²	semidirect
38. #14583304	C₂²	semidirect
39. #14583301	C₂²	semidirect
40. #14583288	C₂²	semidirect
41. #14583283	C₂²	semidirect
42. #14583276	C₂²	semidirect
43. #14583264	C₂²	semidirect
44. #14583259	C₂²	semidirect
45. #14583254	C₂²	semidirect
46. #14583246	C₂²	semidirect
47. #14583152	C₂²	semidirect
48. #14583145	C₂²	semidirect
49. #14583140	C₂²	semidirect
50. #14583140	C₂²	semidirect
55. #14583135	C₂²	semidirect
56. #14583135	C₂²	semidirect
57. #14583135	C₂²	semidirect
58. #14583128	C₂²	semidirect
59. #14583128	C₂²	semidirect
60. #14583128	C₂²	semidirect
61. #14583012	C₂²	semidirect
62. #14583012	C₂²	semidirect
63. #14583001	C₂²	semidirect
64. #14583001	C₂²	semidirect
65. C₄×Dic₁₇₂	C₂²	semidirect
66. C₄×#10621873	C₂²	semidirect
67. C₄×D₃₄₄	C₂²	semidirect
68. C₄×D₃₄₄	C₂²	semidirect
69. C₄×D₃₄₄	C₂²	semidirect
70. C₄×D₃₄₄	C₂²	semidirect
85. C₄₃×#405	C₂²	semidirect
86. C₄₃×#405	C₂²	semidirect
87. C₂×#97×C₄₃	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
238. M₁₆×C₄₃	#41	semidirect
245. C₂×C₈×C₄₃	#41	semidirect
405. C₂×#405	D₄₃	semidirect
481. #405	C₂×D₄₃	semidirect
482. #405	C₂×D₄₃	semidirect
483. C₂×#97	C₂×D₄₃	semidirect
484. C₂×C₄×C₈	C₂×D₄₃	semidirect
485. C₄₃	#60707	semidirect
642. M₁₆	#10621898	semidirect
649. C₂×C₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148330	2
#19145293	2
#19145278	2
#19145245	2
#19145234	2
#19145174	2
#19145165	2
#19145134	2
#19145081	2
#19144951	2
#19144214	2
#19144176	2
C₂×#14583135	2
#19143472	2
#19143448	2
#19143429	2
C₂×C₄₃×#405	2
#60707	43