Subgroups — C₂×C₄₃×#2455 #24954669

Order 11008.

3894 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₄₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₄₃	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2455	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#394	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₃×#392	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#389	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₃×#388	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₃×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
15	C₂×#123×C₄₃	—	2	16	no	—
16	C₂×#123×C₄₃	C₂²	1	16	yes	complemented
17	C₂×C₄×D₄×C₄₃	—	2	16	no	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	16	yes	complemented
19	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
32	C₄₃×#399	C₂²	1	8	yes	complemented
33	C₄₃×#394	C₂²	1	16	yes	complemented
34	C₄₃×#392	C₂²	1	8	yes	—
35	C₄₃×#389	C₂²	1	16	yes	complemented
36	C₄₃×#388	C₂²	1	16	yes	complemented
37	C₄₃×#385	C₂²	1	8	yes	complemented
38	C₄₃×#385	C₂²	1	16	yes	complemented
39	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#95×C₄₃	C₂²	1	2	yes	—
41	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#95×C₄₃	C₂²	1	2	yes	—
43	C₂⁵×C₄₃	C₂³	1	2	yes	—
44	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	—	2	8	no	—
46	C₂²×D₄×C₄₃	—	2	8	no	—
47	C₂²×D₄×C₄₃	—	2	8	no	—
48	C₂²×D₄×C₄₃	—	2	8	no	—
49	C₂²×D₄×C₄₃	—	4	2	no	—
50	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
51	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₄₃	—	2	8	no	—
53	C₂³×C₄×C₄₃	—	2	8	no	—
54	C₂³×C₄×C₄₃	—	2	8	no	—
55	C₂³×C₄×C₄₃	—	4	2	no	—
56	C₂³×C₄×C₄₃	—	4	4	no	—
57	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
66	#123×C₄₃	—	2	64	no	—
67	C₄×D₄×C₄₃	—	2	64	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
72	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₄₃	D₄	1	16	yes	complemented
85	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
92	C₂×C₄²×C₄₃	—	2	8	no	—
93	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
94	#95×C₄₃	C₂³	1	8	yes	—
95	#95×C₄₃	C₂³	1	8	yes	—
96	#95×C₄₃	C₂³	1	4	yes	—
97	#95×C₄₃	C₂³	1	4	yes	—
98	C₂⁴×C₄₃	—	2	4	no	—
99	C₂⁴×C₄₃	—	2	4	no	—
100	C₂⁴×C₄₃	—	2	4	no	—
101	C₂⁴×C₄₃	—	2	4	no	—
102	C₂⁴×C₄₃	—	2	4	no	—
103	C₂⁴×C₄₃	—	2	4	no	—
104	C₂⁴×C₄₃	—	2	2	no	—
105	C₂⁴×C₄₃	—	2	4	no	—
106	C₂⁴×C₄₃	—	2	2	no	—
107	C₂⁴×C₄₃	—	2	4	no	—
108	C₂⁴×C₄₃	C₂×D₄	1	8	yes	—
109	C₂⁴×C₄₃	#41	1	4	yes	—
110	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
111	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
112	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂×D₄×C₄₃	—	2	64	no	—
114	C₂×D₄×C₄₃	—	2	16	no	—
115	C₂×D₄×C₄₃	—	2	16	no	—
116	C₂×D₄×C₄₃	—	2	16	no	—
117	C₂×D₄×C₄₃	—	2	16	no	—
118	C₂×D₄×C₄₃	—	4	4	no	—
119	C₂×D₄×C₄₃	—	4	16	no	—
120	C₂²×C₄×C₄₃	—	2	16	no	—
121	C₂²×C₄×C₄₃	—	2	16	no	—
122	C₂²×C₄×C₄₃	—	2	4	no	—
123	C₂²×C₄×C₄₃	—	2	4	no	—
124	C₂²×C₄×C₄₃	—	2	4	no	—
125	C₂²×C₄×C₄₃	—	2	4	no	—
126	C₂²×C₄×C₄₃	—	2	4	no	—
127	C₂²×C₄×C₄₃	—	2	4	no	—
128	C₂²×C₄×C₄₃	—	2	16	no	—
129	C₂²×C₄×C₄₃	—	2	4	no	—
130	C₂²×C₄×C₄₃	—	2	4	no	—
131	C₂²×C₄×C₄₃	—	2	4	no	—
132	C₂²×C₄×C₄₃	—	2	4	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	4	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	4	no	—
138	C₂²×C₄×C₄₃	—	2	4	no	—
139	C₂²×C₄×C₄₃	—	4	4	no	—
140	C₂²×C₄×C₄₃	—	4	8	no	—
141	C₂²×C₄×C₄₃	—	4	32	no	—
142	C₂²×C₄×C₄₃	—	4	16	no	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
145	C₂²×C₄×C₄₃	#41	1	8	yes	—
146	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
153	C₄⋊C₄×C₄₃	—	2	16	no	—
154	C₄⋊C₄×C₄₃	—	2	16	no	—
155	C₄⋊C₄×C₄₃	—	2	16	no	—
156	C₄⋊C₄×C₄₃	—	2	16	no	—
157	C₄⋊C₄×C₄₃	—	4	4	no	—
158	C₂²⋊C₄×C₄₃	—	2	16	no	—
159	C₂²⋊C₄×C₄₃	—	2	16	no	—
160	C₂²⋊C₄×C₄₃	—	2	16	no	—
161	C₂²⋊C₄×C₄₃	—	2	16	no	—
162	C₂²⋊C₄×C₄₃	—	2	8	no	—
163	C₂²⋊C₄×C₄₃	—	4	4	no	—
164	C₂²⋊C₄×C₄₃	C₂×D₄	1	32	yes	complemented
165	C₄²×C₄₃	—	2	16	no	—
166	C₂³×C₄₃	—	2	16	no	—
167	C₂³×C₄₃	—	2	16	no	—
168	C₂³×C₄₃	—	2	8	no	—
169	C₂³×C₄₃	—	2	16	no	—
170	C₂³×C₄₃	—	2	16	no	—
171	C₂³×C₄₃	—	2	4	no	—
172	C₂³×C₄₃	—	2	4	no	—
173	C₂³×C₄₃	—	2	4	no	—
174	C₂³×C₄₃	—	2	4	no	—
175	C₂³×C₄₃	—	2	4	no	—
176	C₂³×C₄₃	—	2	4	no	—
177	C₂³×C₄₃	—	2	2	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	4	8	no	—
182	C₂³×C₄₃	—	4	8	no	—
183	C₂³×C₄₃	—	4	4	no	—
184	C₂³×C₄₃	—	4	8	no	—
185	C₂³×C₄₃	—	4	8	no	—
186	C₂³×C₄₃	—	4	8	no	—
187	C₂³×C₄₃	—	4	4	no	—
188	C₂³×C₄₃	C₂²×D₄	1	8	yes	—
189	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
190	C₂³×C₄₃	C₂×#41	1	4	yes	—
191	C₂³×C₄₃	C₂×#41	1	2	yes	—
192	C₂³×C₄₃	C₂×#41	1	4	yes	—
193	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
194	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
195	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
196	D₄×C₄₃	—	2	64	no	—
197	D₄×C₄₃	—	4	16	no	—
198	C₂×C₄×C₄₃	—	2	16	no	—
199	C₂×C₄×C₄₃	—	2	16	no	—
200	C₂×C₄×C₄₃	—	2	16	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	4	no	—
204	C₂×C₄×C₄₃	—	2	4	no	—
205	C₂×C₄×C₄₃	—	2	4	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	4	no	—
213	C₂×C₄×C₄₃	—	2	4	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	4	16	no	—
218	C₂×C₄×C₄₃	—	4	32	no	—
219	C₂×C₄×C₄₃	—	4	8	no	—
220	C₂×C₄×C₄₃	—	4	8	no	—
221	C₂×C₄×C₄₃	—	4	4	no	—
222	C₂×C₄×C₄₃	—	4	4	no	—
223	C₂×C₄×C₄₃	C₂²×D₄	1	8	yes	—
224	C₂×C₄×C₄₃	C₂²×D₄	1	8	yes	—
225	C₂×C₄×C₄₃	C₂×#41	1	8	yes	—
226	C₂×#2455	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₄₃	—	2	8	no	—
228	C₂²×C₄₃	—	2	8	no	—
229	C₂²×C₄₃	—	2	4	no	—
230	C₂²×C₄₃	—	2	8	no	—
231	C₂²×C₄₃	—	2	8	no	—
232	C₂²×C₄₃	—	4	4	no	—
233	C₂²×C₄₃	—	4	4	no	—
234	C₂²×C₄₃	—	4	2	no	—
235	C₂²×C₄₃	—	4	4	no	—
236	C₂²×C₄₃	—	4	4	no	—
237	C₂²×C₄₃	—	4	32	no	—
238	C₂²×C₄₃	—	4	16	no	—
239	C₂²×C₄₃	—	4	4	no	—
240	C₂²×C₄₃	—	4	2	no	—
241	C₂²×C₄₃	#525	1	8	yes	—
242	C₂²×C₄₃	#539	1	4	yes	—
243	C₂²×C₄₃	D₄²	1	4	yes	—
244	C₂²×C₄₃	#547	1	8	yes	—
245	C₂²×C₄₃	#559	1	4	yes	—
246	C₂²×C₄₃	C₂³×D₄	1	2	yes	—
247	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
248	C₂²×C₄₃	C₂²×#41	1	2	yes	—
249	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	C₄×C₄₃	—	2	8	no	—
252	C₄×C₄₃	—	2	8	no	—
253	C₄×C₄₃	—	2	8	no	—
254	C₄×C₄₃	—	4	4	no	—
255	C₄×C₄₃	—	4	4	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	—	4	2	no	—
258	C₂²×#123	C₂×C₄₃	1	2	yes	complemented
259	C₂²×C₄×D₄	C₂×C₄₃	1	2	yes	complemented
260	#2455	C₂×C₄₃	1	16	yes	direct product factor
261	C₂×#399	C₂×C₄₃	1	1	yes	characteristic, complemented
262	C₂×#394	C₂×C₄₃	1	2	yes	complemented
263	C₂×#392	C₂×C₄₃	1	1	yes	characteristic
264	C₂×#389	C₂×C₄₃	1	2	yes	complemented
265	C₂×#388	C₂×C₄₃	1	2	yes	complemented
266	C₂×#385	C₂×C₄₃	1	2	yes	complemented
267	C₂×#385	C₂×C₄₃	1	1	yes	characteristic, complemented
268	C₂×C₄₃	—	4	8	no	—
269	C₂×C₄₃	—	4	4	no	—
270	C₂×C₄₃	#2455	1	8	yes	direct product factor
271	C₂×C₄₃	C₂×#525	1	2	yes	—
272	C₂×C₄₃	C₂×#539	1	1	yes	characteristic
273	C₂×C₄₃	C₂×D₄²	1	1	yes	characteristic
274	C₂×C₄₃	C₂×#547	1	2	yes	—
275	C₂×C₄₃	C₂×#559	1	1	yes	characteristic
276	C₂³×D₄	C₂²×C₄₃	1	2	yes	—
277	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
278	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
279	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
280	C₂×#123	—	2	16	no	—
281	C₂×#123	C₂²×C₄₃	1	16	yes	complemented
282	C₂×C₄×D₄	—	2	16	no	—
283	C₂×C₄×D₄	C₂²×C₄₃	1	16	yes	complemented
284	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
285	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
286	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
290	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
291	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
292	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
293	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
295	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
296	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
297	#399	C₂²×C₄₃	1	8	yes	complemented
298	#394	C₂²×C₄₃	1	16	yes	complemented
299	#392	C₂²×C₄₃	1	8	yes	—
300	#389	C₂²×C₄₃	1	16	yes	complemented
301	#388	C₂²×C₄₃	1	16	yes	complemented
302	#385	C₂²×C₄₃	1	8	yes	complemented
303	#385	C₂²×C₄₃	1	16	yes	complemented
304	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
305	C₂×#95	C₂²×C₄₃	1	2	yes	—
306	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
307	C₂×#95	C₂²×C₄₃	1	2	yes	—
308	C₄₃	C₂×#2455	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁵	C₂³×C₄₃	1	2	yes	—
310	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
311	C₂²×D₄	—	2	8	no	—
312	C₂²×D₄	—	2	8	no	—
313	C₂²×D₄	—	2	8	no	—
314	C₂²×D₄	—	2	8	no	—
315	C₂²×D₄	—	4	2	no	—
316	C₂²×D₄	C₂³×C₄₃	1	8	yes	—
317	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
318	C₂³×C₄	—	2	8	no	—
319	C₂³×C₄	—	2	8	no	—
320	C₂³×C₄	—	2	8	no	—
321	C₂³×C₄	—	4	2	no	—
322	C₂³×C₄	—	4	4	no	—
323	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
324	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
326	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
328	C₂³×C₄	C₂³×C₄₃	1	8	yes	—
329	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
330	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
331	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
332	#123	—	2	64	no	—
333	C₄×D₄	—	2	64	no	—
334	C₂×C₄⋊C₄	—	2	8	no	—
335	C₂×C₄⋊C₄	—	2	8	no	—
336	C₂×C₄⋊C₄	—	2	8	no	—
337	C₂×C₄⋊C₄	—	2	8	no	—
338	C₂×C₄⋊C₄	—	4	2	no	—
339	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
342	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
344	C₂×C₂²⋊C₄	—	2	8	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	—	2	8	no	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	—	4	2	no	—
350	C₂×C₂²⋊C₄	D₄×C₄₃	1	16	yes	complemented
351	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
358	C₂×C₄²	—	2	8	no	—
359	C₂×C₄²	C₂³×C₄₃	1	8	yes	—
360	#95	C₂³×C₄₃	1	8	yes	—
361	#95	C₂³×C₄₃	1	8	yes	—
362	#95	C₂³×C₄₃	1	4	yes	—
363	#95	C₂³×C₄₃	1	4	yes	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	—	2	4	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	4	no	—
374	C₂⁴	C₂×D₄×C₄₃	1	8	yes	—
375	C₂⁴	#41×C₄₃	1	4	yes	—
376	C₂⁴	C₂⁴×C₄₃	1	4	yes	—
377	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
378	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
379	C₂×D₄	—	2	64	no	—
380	C₂×D₄	—	2	16	no	—
381	C₂×D₄	—	2	16	no	—
382	C₂×D₄	—	2	16	no	—
383	C₂×D₄	—	2	16	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	16	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	16	no	—
404	C₂²×C₄	—	2	16	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	8	no	—
407	C₂²×C₄	—	4	16	no	—
408	C₂²×C₄	—	4	32	no	—
409	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
410	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
411	C₂²×C₄	#41×C₄₃	1	8	yes	—
412	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
419	C₄⋊C₄	—	2	16	no	—
420	C₄⋊C₄	—	2	16	no	—
421	C₄⋊C₄	—	2	16	no	—
422	C₄⋊C₄	—	2	16	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	2	16	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	—	2	16	no	—
428	C₂²⋊C₄	—	2	16	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	C₂×D₄×C₄₃	1	32	yes	complemented
431	C₄²	—	2	16	no	—
432	C₂³	—	2	16	no	—
433	C₂³	—	2	16	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	16	no	—
436	C₂³	—	2	16	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	4	8	no	—
448	C₂³	—	4	8	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	4	no	—
454	C₂³	C₂²×D₄×C₄₃	1	8	yes	—
455	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
456	C₂³	C₂×#41×C₄₃	1	4	yes	—
457	C₂³	C₂×#41×C₄₃	1	2	yes	—
458	C₂³	C₂×#41×C₄₃	1	4	yes	—
459	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
460	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
461	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
462	D₄	—	2	64	no	—
463	D₄	—	4	16	no	—
464	C₂×C₄	—	2	16	no	—
465	C₂×C₄	—	2	16	no	—
466	C₂×C₄	—	2	16	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	4	16	no	—
484	C₂×C₄	—	4	32	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	C₂²×D₄×C₄₃	1	8	yes	—
490	C₂×C₄	C₂²×D₄×C₄₃	1	8	yes	—
491	C₂×C₄	C₂×#41×C₄₃	1	8	yes	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	8	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	8	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	4	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	32	no	—
503	C₂²	—	4	16	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	C₄₃×#525	1	8	yes	—
507	C₂²	C₄₃×#539	1	4	yes	—
508	C₂²	D₄²×C₄₃	1	4	yes	—
509	C₂²	C₄₃×#547	1	8	yes	—
510	C₂²	C₄₃×#559	1	4	yes	—
511	C₂²	C₂³×D₄×C₄₃	1	2	yes	—
512	C₂²	C₂²×#41×C₄₃	1	1	yes	characteristic
513	C₂²	C₂²×#41×C₄₃	1	2	yes	—
514	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
515	C₂²	C₂×2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
516	C₄	—	2	8	no	—
517	C₄	—	2	8	no	—
518	C₄	—	2	8	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₂	—	4	8	no	—
524	C₂	—	4	4	no	—
525	C₂	C₄₃×#2455	1	8	yes	direct product factor
526	C₂	C₂×C₄₃×#525	1	2	yes	—
527	C₂	C₂×C₄₃×#539	1	1	yes	characteristic
528	C₂	C₂×D₄²×C₄₃	1	1	yes	characteristic
529	C₂	C₂×C₄₃×#547	1	2	yes	—
530	C₂	C₂×C₄₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₃
prime radical	C₂×C₄₃×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#123×C₄₃	C₂	semidirect
2. C₂²×C₄×D₄×C₄₃	C₂	semidirect
3. C₄₃×#2455	C₂	direct (N × H)
4. C₂×C₄₃×#399	C₂	semidirect
5. C₂×C₄₃×#394	C₂	semidirect
7. C₂×C₄₃×#389	C₂	semidirect
8. C₂×C₄₃×#388	C₂	semidirect
9. C₂×C₄₃×#385	C₂	semidirect
10. C₂×C₄₃×#385	C₂	semidirect
16. C₂×#123×C₄₃	C₂²	semidirect
18. C₂×C₄×D₄×C₄₃	C₂²	semidirect
32. C₄₃×#399	C₂²	semidirect
33. C₄₃×#394	C₂²	semidirect
35. C₄₃×#389	C₂²	semidirect
36. C₄₃×#388	C₂²	semidirect
37. C₄₃×#385	C₂²	semidirect
38. C₄₃×#385	C₂²	semidirect
84. C₂×C₂²⋊C₄×C₄₃	D₄	semidirect
164. C₂²⋊C₄×C₄₃	C₂×D₄	semidirect
226. C₂×#2455	C₄₃	direct (N × H)
258. C₂²×#123	C₂×C₄₃	semidirect
259. C₂²×C₄×D₄	C₂×C₄₃	semidirect
260. #2455	C₂×C₄₃	direct (N × H)
261. C₂×#399	C₂×C₄₃	semidirect
262. C₂×#394	C₂×C₄₃	semidirect
264. C₂×#389	C₂×C₄₃	semidirect
265. C₂×#388	C₂×C₄₃	semidirect
266. C₂×#385	C₂×C₄₃	semidirect
267. C₂×#385	C₂×C₄₃	semidirect
270. C₂×C₄₃	#2455	direct (N × H)
281. C₂×#123	C₂²×C₄₃	semidirect
283. C₂×C₄×D₄	C₂²×C₄₃	semidirect
297. #399	C₂²×C₄₃	semidirect
298. #394	C₂²×C₄₃	semidirect
300. #389	C₂²×C₄₃	semidirect
301. #388	C₂²×C₄₃	semidirect
302. #385	C₂²×C₄₃	semidirect
303. #385	C₂²×C₄₃	semidirect
308. C₄₃	C₂×#2455	direct (N × H)
350. C₂×C₂²⋊C₄	D₄×C₄₃	semidirect
430. C₂²⋊C₄	C₂×D₄×C₄₃	semidirect
525. C₂	C₄₃×#2455	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#123×C₄₃	2
C₂²×C₄×D₄×C₄₃	2
C₄₃×#2455	2
C₂×C₄₃×#399	2
C₂×C₄₃×#394	2
C₂×C₄₃×#392	2
C₂×C₄₃×#389	2
C₂×C₄₃×#388	2
C₂×C₄₃×#385	2
C₂×#2455	43

Subgroups — C2×C43×#2455 #24954669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#2455 #24954669