Subgroups — #19149116

Order 5504.

1160 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583646	C₂	1	2	yes	maximal, complemented
2	#14583641	C₂	1	2	yes	maximal, complemented
3	#14583631	C₂	1	2	yes	maximal, complemented
4	#14583558	C₂	1	2	yes	maximal, complemented
5	#14583544	C₂	1	2	yes	maximal, complemented
6	#14583541	C₂	1	2	yes	maximal, complemented
7	#14583536	C₂	1	2	yes	maximal, complemented
8	#14583531	C₂	1	2	yes	maximal, complemented
9	#14583515	C₂	1	2	yes	maximal, complemented
10	#14583489	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583488	C₂	1	2	yes	maximal, complemented
12	#14583486	C₂	1	2	yes	maximal, complemented
13	#14583465	C₂	1	2	yes	maximal, complemented
14	#14583461	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583457	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583444	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063311	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621898	C₂²	1	2	yes	complemented
21	C₂×#10621900	C₂²	1	2	yes	complemented
22	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
25	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
26	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
27	#13063324	C₂²	1	1	yes	characteristic, complemented
28	#13063321	C₂²	1	2	yes	—
29	#13063321	C₂²	1	1	yes	characteristic, complemented
30	#13063320	C₂²	1	2	yes	complemented
31	#13063320	C₂²	1	2	yes	complemented
32	#13063316	C₂²	1	1	yes	characteristic, complemented
33	#13063314	C₂²	1	2	yes	complemented
34	#13063314	C₂²	1	1	yes	characteristic, complemented
35	#13063313	C₂²	1	2	yes	complemented
36	#13063313	C₂²	1	2	yes	complemented
37	#13063311	C₂²	1	2	yes	complemented
38	#13063311	C₂²	1	2	yes	complemented
39	#13063311	C₂²	1	2	yes	complemented
40	#13063311	C₂²	1	2	yes	complemented
41	#13063311	C₂²	1	2	yes	complemented
42	#13063311	C₂²	1	2	yes	complemented
43	#13063311	C₂²	1	2	yes	complemented
44	#13063311	C₂²	1	2	yes	complemented
45	#13063310	C₂²	1	2	yes	complemented
46	#13063310	C₂²	1	2	yes	complemented
47	#13063309	C₂²	1	2	yes	complemented
48	#13063309	C₂²	1	2	yes	complemented
49	#13063309	C₂²	1	2	yes	complemented
50	#13063309	C₂²	1	2	yes	complemented
51	#13063307	C₂²	1	2	yes	complemented
52	#13063307	C₂²	1	2	yes	complemented
53	#13063305	C₂²	1	2	yes	complemented
54	#13063304	C₂²	1	2	yes	complemented
55	#13063303	C₂²	1	2	yes	complemented
56	#13063303	C₂²	1	2	yes	complemented
57	#13063302	C₂²	1	2	yes	complemented
58	#13063300	C₂²	1	2	yes	complemented
59	#13063300	C₂²	1	2	yes	complemented
60	#13063299	C₂²	1	1	yes	characteristic
61	#13063299	C₂²	1	2	yes	complemented
62	#13063299	C₂²	1	2	yes	complemented
63	#13063299	C₂²	1	1	yes	characteristic, complemented
64	#13063298	C₂²	1	2	yes	—
65	#13063298	C₂²	1	2	yes	complemented
66	#13063297	C₂²	1	2	yes	complemented
67	#13063297	C₂²	1	2	yes	complemented
68	#13063297	C₂²	1	2	yes	complemented
69	#13063297	C₂²	1	2	yes	complemented
70	#13063296	C₂²	1	2	yes	complemented
71	#13063295	C₂²	1	2	yes	complemented
72	#13063295	C₂²	1	2	yes	complemented
73	#13063295	C₂²	1	2	yes	complemented
74	#13063295	C₂²	1	2	yes	complemented
75	#13063295	C₂²	1	2	yes	complemented
76	#13063295	C₂²	1	2	yes	complemented
77	#13063293	C₂²	1	2	yes	complemented
78	#13063293	C₂²	1	2	yes	complemented
79	#13063293	C₂²	1	2	yes	complemented
80	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₈₆	C₂²	1	2	yes	complemented
82	C₄×D₁₇₂	C₂²	1	2	yes	complemented
83	D₄×Dic₄₃	C₂²	1	2	yes	complemented
84	D₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
85	#13063287	C₂²	1	1	yes	characteristic, complemented
86	#13063287	C₂²	1	1	yes	characteristic, complemented
87	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
88	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
90	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
91	#13063283	C₂²	1	2	yes	complemented
92	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
97	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
98	#126×C₄₃	C₂²	1	2	yes	complemented
99	#124×C₄₃	C₂²	1	2	yes	complemented
100	#123×C₄₃	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
102	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
103	#121×C₄₃	C₂²	1	2	yes	complemented
104	#120×C₄₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
108	C₂³×D₄₃	C₂³	1	1	yes	characteristic
109	C₂³×D₄₃	C₂³	1	2	yes	—
110	C₂³×D₄₃	C₂³	1	2	yes	—
111	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₄₃	C₂³	1	2	yes	—
113	C₂×D₄×C₄₃	C₂³	1	2	yes	—
114	C₂×D₄×C₄₃	C₂³	1	2	yes	—
115	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₄₃	—	4	4	no	—
120	C₂×C₂²⋊D₄₃	—	4	2	no	—
121	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
131	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₄₃	C₂³	1	2	yes	—
135	C₂²×Dic₄₃	C₂³	1	2	yes	—
136	#10621900	—	4	4	no	—
137	D₄×D₄₃	—	4	4	no	—
138	D₄×D₄₃	—	4	4	no	—
139	#10621898	—	4	4	no	—
140	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
141	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
142	C₂×D₁₇₂	C₂³	1	2	yes	—
143	C₂×D₁₇₂	C₂³	1	2	yes	—
144	C₂×D₁₇₂	C₂³	1	2	yes	—
145	C₂×D₁₇₂	C₂³	1	2	yes	—
146	C₂×C₄×D₄₃	C₂³	1	2	yes	—
147	C₂×C₄×D₄₃	C₂³	1	2	yes	—
148	C₂×C₄×D₄₃	C₂³	1	2	yes	—
149	C₂×C₄×D₄₃	C₂³	1	2	yes	—
150	C₂×Dic₈₆	—	4	2	no	—
151	C₂×Dic₈₆	C₂³	1	2	yes	—
152	C₂×Dic₈₆	C₂³	1	2	yes	—
153	C₂×Dic₈₆	C₂³	1	2	yes	—
154	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
158	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
165	C₄²×C₄₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
170	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
186	C₄⋊Dic₄₃	C₂³	1	2	yes	—
187	C₄⋊Dic₄₃	C₂³	1	2	yes	—
188	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₄₃	C₂³	1	2	yes	—
190	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
191	Dic₄₃⋊C₄	C₂³	1	2	yes	—
192	Dic₄₃⋊C₄	C₂³	1	2	yes	—
193	Dic₄₃⋊C₄	C₂³	1	2	yes	—
194	Dic₄₃⋊C₄	C₂³	1	2	yes	—
195	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₄₃	C₂³	1	2	yes	—
200	C₄×Dic₄₃	C₂³	1	2	yes	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	4	1	no	—
203	C₂³×C₄₃	—	4	1	no	—
204	C₂³×C₄₃	C₂⁴	1	2	yes	—
205	C₂³×C₄₃	C₂⁴	1	2	yes	—
206	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
207	C₂²×D₄₃	—	2	2	no	—
208	C₂²×D₄₃	—	4	2	no	—
209	C₂²×D₄₃	—	4	2	no	—
210	C₂²×D₄₃	—	4	2	no	—
211	C₂²×D₄₃	—	4	1	no	—
212	C₂²×D₄₃	—	4	2	no	—
213	C₂²×D₄₃	—	4	1	no	—
214	C₂²×D₄₃	—	4	2	no	—
215	C₂²×D₄₃	—	4	2	no	—
216	C₂²×D₄₃	C₂⁴	1	2	yes	—
217	C₂²×D₄₃	C₂⁴	1	2	yes	—
218	C₂²×D₄₃	C₂⁴	1	2	yes	—
219	Q₈×C₄₃	—	4	1	no	—
220	D₄×C₄₃	—	2	4	no	—
221	D₄×C₄₃	—	4	2	no	—
222	D₄×C₄₃	—	4	1	no	—
223	D₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
228	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
233	C₂²⋊D₄₃	—	2	4	no	—
234	C₂²⋊D₄₃	—	2	4	no	—
235	C₂²⋊D₄₃	—	2	4	no	—
236	C₂²⋊D₄₃	—	2	4	no	—
237	C₂²⋊D₄₃	—	4	2	no	—
238	C₂²⋊D₄₃	—	4	2	no	—
239	C₂²⋊D₄₃	—	4	2	no	—
240	C₂²⋊D₄₃	—	4	2	no	—
241	C₂²⋊D₄₃	—	4	2	no	—
242	C₂²⋊D₄₃	—	4	2	no	—
243	C₂×Dic₄₃	—	2	2	no	—
244	C₂×Dic₄₃	—	2	2	no	—
245	C₂×Dic₄₃	—	4	1	no	—
246	C₂×Dic₄₃	—	4	2	no	—
247	C₂×Dic₄₃	—	4	2	no	—
248	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₄₃	C₂⁴	1	2	yes	—
252	C₂×Dic₄₃	C₂⁴	1	2	yes	—
253	C₂×Dic₄₃	C₂⁴	1	2	yes	—
254	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
255	D₁₇₂	—	4	1	no	—
256	D₁₇₂	—	4	1	no	—
257	D₁₇₂	—	4	2	no	—
258	D₁₇₂	—	4	2	no	—
259	D₁₇₂	—	4	2	no	—
260	D₁₇₂	—	4	2	no	—
261	C₄×D₄₃	—	2	4	no	—
262	C₄×D₄₃	—	4	2	no	—
263	C₄×D₄₃	—	4	2	no	—
264	C₄×D₄₃	—	4	2	no	—
265	Dic₈₆	—	2	4	no	—
266	Dic₈₆	—	4	2	no	—
267	Dic₈₆	—	4	2	no	—
268	C₂²×C₄₃	—	2	1	no	—
269	C₂²×C₄₃	—	2	1	no	—
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	—	2	2	no	—
272	C₂²×C₄₃	—	2	2	no	—
273	C₂²×C₄₃	—	2	2	no	—
274	C₂²×C₄₃	—	2	2	no	—
275	C₂²×C₄₃	—	2	2	no	—
276	C₂²×C₄₃	—	8	2	no	—
277	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
278	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
279	C₂×D₄₃	—	2	2	no	—
280	C₂×D₄₃	—	2	2	no	—
281	C₂×D₄₃	—	2	2	no	—
282	C₂×D₄₃	—	2	2	no	—
283	C₂×D₄₃	—	2	2	no	—
284	C₂×D₄₃	—	2	2	no	—
285	C₂×D₄₃	—	2	2	no	—
286	C₂×D₄₃	—	2	2	no	—
287	C₂×D₄₃	—	2	2	no	—
288	C₂×D₄₃	—	8	2	no	—
289	C₂×D₄₃	—	8	4	no	—
290	C₂×D₄₃	—	8	4	no	—
291	C₄×C₄₃	—	2	2	no	—
292	C₄×C₄₃	—	2	2	no	—
293	C₄×C₄₃	—	2	2	no	—
294	C₄×C₄₃	—	2	1	no	—
295	C₄×C₄₃	—	2	1	no	—
296	C₄×C₄₃	—	2	2	no	—
297	Dic₄₃	—	2	2	no	—
298	Dic₄₃	—	2	1	no	—
299	Dic₄₃	—	2	1	no	—
300	Dic₄₃	—	2	2	no	—
301	Dic₄₃	—	2	1	no	—
302	Dic₄₃	—	2	2	no	—
303	Dic₄₃	H(5,𝔽₂)	1	2	yes	—
304	#3558	—	43	1	no	maximal, Sylow
305	C₂×C₄₃	—	2	2	no	—
306	C₂×C₄₃	—	4	2	no	—
307	C₂×C₄₃	—	4	2	no	—
308	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₄₃	#585	1	1	yes	characteristic
311	D₄₃	—	4	2	no	—
312	D₄₃	—	4	2	no	—
313	D₄₃	—	4	2	no	—
314	#562	—	43	2	no	—
315	H(3,𝔽₄)	—	43	2	no	—
316	#559	—	43	2	no	—
317	#548	—	43	2	no	—
318	#546	—	43	2	no	—
319	#546	—	43	2	no	—
320	#546	—	43	2	no	—
321	D₄²	—	43	2	no	—
322	#542	—	43	2	no	—
323	#538	—	43	2	no	—
324	#538	—	43	1	no	—
325	#538	—	43	2	no	—
326	#538	D₄₃	1	1	yes	characteristic, complemented
327	#535	—	43	2	no	—
328	#534	—	43	1	no	—
329	#534	—	43	1	no	—
330	#532	—	43	1	no	—
331	#529	—	43	1	no	—
332	C₂×#124	—	43	1	no	—
333	C₄₃	#3558	1	1	yes	characteristic, complemented, Sylow
334	C₂×#41	—	43	2	no	—
335	C₂×#41	—	43	2	no	—
336	C₂²×Q₈	—	43	1	no	—
337	C₂²×D₄	—	43	1	no	—
338	C₂²×D₄	—	43	2	no	—
339	C₂²×D₄	—	43	2	no	—
340	C₂²×D₄	—	43	2	no	—
341	C₄⋊Q₈	—	43	1	no	—
342	#127	—	43	1	no	—
343	#127	—	43	2	no	—
344	#126	—	43	2	no	—
345	#126	—	43	2	no	—
346	#126	C₂×D₄₃	1	2	yes	complemented
347	#125	—	43	1	no	—
348	#124	—	43	1	no	—
349	#124	—	43	2	no	—
350	#124	—	43	2	no	—
351	#124	—	43	2	no	—
352	#124	—	43	2	no	—
353	#124	—	43	2	no	—
354	#124	—	43	2	no	—
355	#124	—	43	2	no	—
356	#124	—	43	2	no	—
357	#124	—	43	2	no	—
358	#124	—	43	2	no	—
359	#124	—	43	2	no	—
360	#124	C₂×D₄₃	1	2	yes	complemented
361	#123	—	43	2	no	—
362	#123	—	43	2	no	—
363	#123	—	43	2	no	—
364	#123	—	43	2	no	—
365	#123	—	43	2	no	—
366	#123	—	43	2	no	—
367	#123	—	43	2	no	—
368	#123	—	43	2	no	—
369	#123	C₂×D₄₃	1	2	yes	complemented
370	C₂²⋊Q₈	—	43	2	no	—
371	C₂²⋊Q₈	—	43	2	no	—
372	C₂²⋊Q₈	—	43	2	no	—
373	C₂²⋊Q₈	—	43	2	no	—
374	C₂²⋊Q₈	—	43	2	no	—
375	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
376	#121	—	43	2	no	—
377	#121	—	43	2	no	—
378	#121	—	43	2	no	—
379	#121	—	43	2	no	—
380	#121	—	43	2	no	—
381	#121	—	43	1	no	—
382	#121	—	43	1	no	—
383	#121	—	43	2	no	—
384	#121	—	43	2	no	—
385	#121	—	43	2	no	—
386	#121	—	43	2	no	—
387	#121	—	43	2	no	—
388	#121	—	43	2	no	—
389	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
390	#121	C₂×D₄₃	1	2	yes	complemented
391	#120	—	43	2	no	—
392	#120	—	43	2	no	—
393	#120	—	43	2	no	—
394	#120	—	43	2	no	—
395	#120	—	43	2	no	—
396	#120	—	43	2	no	—
397	#120	—	43	2	no	—
398	#120	—	43	2	no	—
399	#120	—	43	2	no	—
400	#120	C₂×D₄₃	1	2	yes	complemented
401	C₄×Q₈	—	43	1	no	—
402	C₄×Q₈	—	43	2	no	—
403	C₄×D₄	—	43	1	no	—
404	C₄×D₄	—	43	2	no	—
405	C₄×D₄	—	43	1	no	—
406	C₄×D₄	—	43	1	no	—
407	C₄×D₄	—	43	2	no	—
408	C₄×D₄	—	43	2	no	—
409	C₄×D₄	—	43	2	no	—
410	C₄×D₄	—	43	2	no	—
411	C₄×D₄	—	43	2	no	—
412	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
413	#117	—	43	2	no	—
414	C₂×C₂²⋊C₄	—	43	1	no	—
415	C₂×C₂²⋊C₄	—	43	1	no	—
416	C₂×C₂²⋊C₄	—	43	1	no	—
417	C₂×C₂²⋊C₄	—	43	2	no	—
418	C₂×C₂²⋊C₄	—	43	2	no	—
419	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
420	C₂×C₄²	—	43	1	no	—
421	C₂⁴	—	43	1	no	—
422	C₂⁴	—	43	2	no	—
423	C₂⁴	—	43	2	no	—
424	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
425	#41	—	172	4	no	—
426	#41	—	172	4	no	—
427	C₂×Q₈	—	43	2	no	—
428	C₂×Q₈	—	43	2	no	—
429	C₂×Q₈	—	43	2	no	—
430	C₂×Q₈	—	172	2	no	—
431	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
432	C₂×D₄	—	43	2	no	—
433	C₂×D₄	—	43	2	no	—
434	C₂×D₄	—	43	2	no	—
435	C₂×D₄	—	43	2	no	—
436	C₂×D₄	—	43	2	no	—
437	C₂×D₄	—	43	2	no	—
438	C₂×D₄	—	43	2	no	—
439	C₂×D₄	—	43	2	no	—
440	C₂×D₄	—	43	2	no	—
441	C₂×D₄	—	43	2	no	—
442	C₂×D₄	—	43	1	no	—
443	C₂×D₄	—	43	2	no	—
444	C₂×D₄	—	43	1	no	—
445	C₂×D₄	—	43	2	no	—
446	C₂×D₄	—	43	2	no	—
447	C₂×D₄	—	43	2	no	—
448	C₂×D₄	—	172	4	no	—
449	C₂×D₄	—	172	2	no	—
450	C₂×D₄	—	172	4	no	—
451	C₂×D₄	—	172	4	no	—
452	C₂×D₄	C₂²×D₄₃	1	2	yes	—
453	C₂×D₄	C₂²×D₄₃	1	2	yes	—
454	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₄₃	1	2	yes	—
456	C₂²×C₄	—	43	1	no	—
457	C₂²×C₄	—	43	1	no	—
458	C₂²×C₄	—	43	1	no	—
459	C₂²×C₄	—	43	2	no	—
460	C₂²×C₄	—	43	2	no	—
461	C₂²×C₄	—	43	2	no	—
462	C₂²×C₄	—	43	2	no	—
463	C₂²×C₄	—	43	2	no	—
464	C₂²×C₄	—	43	2	no	—
465	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
468	C₄⋊C₄	—	43	2	no	—
469	C₄⋊C₄	—	43	2	no	—
470	C₄⋊C₄	—	43	2	no	—
471	C₄⋊C₄	—	43	2	no	—
472	C₄⋊C₄	—	43	2	no	—
473	C₄⋊C₄	—	43	1	no	—
474	C₄⋊C₄	—	43	2	no	—
475	C₄⋊C₄	—	43	2	no	—
476	C₄⋊C₄	—	43	1	no	—
477	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
481	C₂²⋊C₄	—	43	2	no	—
482	C₂²⋊C₄	—	43	2	no	—
483	C₂²⋊C₄	—	43	2	no	—
484	C₂²⋊C₄	—	43	2	no	—
485	C₂²⋊C₄	—	43	2	no	—
486	C₂²⋊C₄	—	43	2	no	—
487	C₂²⋊C₄	—	43	2	no	—
488	C₂²⋊C₄	—	43	2	no	—
489	C₂²⋊C₄	—	43	2	no	—
490	C₂²⋊C₄	—	43	2	no	—
491	C₂²⋊C₄	—	43	2	no	—
492	C₂²⋊C₄	—	43	2	no	—
493	C₂²⋊C₄	—	43	2	no	—
494	C₂²⋊C₄	—	43	2	no	—
495	C₂²⋊C₄	—	43	2	no	—
496	C₂²⋊C₄	—	43	2	no	—
497	C₂²⋊C₄	—	43	2	no	—
498	C₂²⋊C₄	—	43	2	no	—
499	C₂²⋊C₄	—	43	2	no	—
500	C₂²⋊C₄	—	43	2	no	—
501	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
506	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
508	C₄²	—	43	1	no	—
509	C₄²	—	43	1	no	—
510	C₄²	—	43	1	no	—
511	C₄²	—	43	1	no	—
512	C₄²	—	43	2	no	—
513	C₄²	—	43	2	no	—
514	C₄²	C₂²×D₄₃	1	2	yes	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	43	2	no	—
519	C₂³	—	43	2	no	—
520	C₂³	—	43	2	no	—
521	C₂³	—	86	2	no	—
522	C₂³	—	172	1	no	—
523	C₂³	—	172	2	no	—
524	C₂³	—	172	2	no	—
525	C₂³	—	172	2	no	—
526	C₂³	—	172	2	no	—
527	C₂³	—	172	1	no	—
528	C₂³	—	172	2	no	—
529	C₂³	—	172	2	no	—
530	C₂³	C₂³×D₄₃	1	2	yes	—
531	C₂³	C₂³×D₄₃	1	2	yes	—
532	C₂³	C₂³×D₄₃	1	1	yes	characteristic
533	Q₈	—	4	1	no	—
534	Q₈	—	86	4	no	—
535	Q₈	—	172	2	no	—
536	Q₈	—	172	2	no	—
537	D₄	—	2	4	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	2	no	—
541	D₄	—	86	4	no	—
542	D₄	—	86	4	no	—
543	D₄	—	86	4	no	—
544	D₄	—	86	4	no	—
545	D₄	—	172	2	no	—
546	D₄	—	172	2	no	—
547	D₄	—	172	2	no	—
548	D₄	—	172	1	no	—
549	D₄	—	172	1	no	—
550	D₄	—	172	2	no	—
551	D₄	—	172	2	no	—
552	D₄	—	172	2	no	—
553	D₄	—	172	2	no	—
554	D₄	—	172	2	no	—
555	D₄	—	172	2	no	—
556	D₄	—	172	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	43	1	no	—
561	C₂×C₄	—	43	1	no	—
562	C₂×C₄	—	43	1	no	—
563	C₂×C₄	—	43	1	no	—
564	C₂×C₄	—	43	2	no	—
565	C₂×C₄	—	43	2	no	—
566	C₂×C₄	—	43	2	no	—
567	C₂×C₄	—	86	4	no	—
568	C₂×C₄	—	86	2	no	—
569	C₂×C₄	—	86	2	no	—
570	C₂×C₄	—	172	2	no	—
571	C₂×C₄	—	172	2	no	—
572	C₂×C₄	—	172	2	no	—
573	C₂×C₄	—	172	2	no	—
574	C₂×C₄	—	172	1	no	—
575	C₂×C₄	—	172	2	no	—
576	C₂×C₄	C₂³×D₄₃	1	2	yes	—
577	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
578	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₄₃	1	2	yes	—
580	C₂×C₄	C₂³×D₄₃	1	2	yes	—
581	C₂×C₄	C₂³×D₄₃	1	2	yes	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	8	2	no	—
591	C₂²	—	86	2	no	—
592	C₂²	—	86	2	no	—
593	C₂²	—	86	2	no	—
594	C₂²	—	86	2	no	—
595	C₂²	—	86	2	no	—
596	C₂²	—	86	2	no	—
597	C₂²	—	86	2	no	—
598	C₂²	—	86	2	no	—
599	C₂²	—	86	2	no	—
600	C₂²	—	344	2	no	—
601	C₂²	—	344	4	no	—
602	C₂²	—	344	4	no	—
603	C₂²	#13063371	1	2	yes	—
604	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	43	2	no	—
612	C₄	—	86	1	no	—
613	C₄	—	86	2	no	—
614	C₄	—	86	1	no	—
615	C₄	—	86	1	no	—
616	C₄	—	86	2	no	—
617	C₄	—	86	2	no	—
618	C₂	—	2	2	no	—
619	C₂	—	4	2	no	—
620	C₂	—	4	2	no	—
621	C₂	—	172	2	no	—
622	C₂	—	172	2	no	—
623	C₂	—	172	2	no	—
624	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
625	C₂	C₂×#13063371	1	1	yes	characteristic
626	C₂	#14583734	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#538	C₂
hypercenter	#538	D₄₃
hypocenter	C₄₃	#3558
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #14583646	C₂	semidirect
2. #14583641	C₂	semidirect
3. #14583631	C₂	semidirect
4. #14583558	C₂	semidirect
5. #14583544	C₂	semidirect
6. #14583541	C₂	semidirect
7. #14583536	C₂	semidirect
8. #14583531	C₂	semidirect
9. #14583515	C₂	semidirect
10. #14583489	C₂	semidirect
11. #14583488	C₂	semidirect
12. #14583486	C₂	semidirect
13. #14583465	C₂	semidirect
14. #14583461	C₂	semidirect
15. #14583457	C₂	semidirect
16. #14583444	C₂	semidirect
17. #14583435	C₂	semidirect
18. C₂×#13063311	C₂	semidirect
19. C₄₃×#538	C₂	semidirect
20. C₂×#10621898	C₂²	semidirect
21. C₂×#10621900	C₂²	semidirect
22. C₂²×Dic₈₆	C₂²	semidirect
24. C₂²×C₂²⋊D₄₃	C₂²	semidirect
25. C₂×D₄×D₄₃	C₂²	semidirect
26. C₂×D₄×D₄₃	C₂²	semidirect
27. #13063324	C₂²	semidirect
29. #13063321	C₂²	semidirect
30. #13063320	C₂²	semidirect
31. #13063320	C₂²	semidirect
32. #13063316	C₂²	semidirect
33. #13063314	C₂²	semidirect
34. #13063314	C₂²	semidirect
35. #13063313	C₂²	semidirect
36. #13063313	C₂²	semidirect
37. #13063311	C₂²	semidirect
38. #13063311	C₂²	semidirect
39. #13063311	C₂²	semidirect
40. #13063311	C₂²	semidirect
41. #13063311	C₂²	semidirect
42. #13063311	C₂²	semidirect
43. #13063311	C₂²	semidirect
44. #13063311	C₂²	semidirect
45. #13063310	C₂²	semidirect
46. #13063310	C₂²	semidirect
47. #13063309	C₂²	semidirect
48. #13063309	C₂²	semidirect
49. #13063309	C₂²	semidirect
50. #13063309	C₂²	semidirect
51. #13063307	C₂²	semidirect
52. #13063307	C₂²	semidirect
53. #13063305	C₂²	semidirect
54. #13063304	C₂²	semidirect
55. #13063303	C₂²	semidirect
56. #13063303	C₂²	semidirect
57. #13063302	C₂²	semidirect
58. #13063300	C₂²	semidirect
59. #13063300	C₂²	semidirect
61. #13063299	C₂²	semidirect
62. #13063299	C₂²	semidirect
63. #13063299	C₂²	semidirect
65. #13063298	C₂²	semidirect
66. #13063297	C₂²	semidirect
67. #13063297	C₂²	semidirect
68. #13063297	C₂²	semidirect
69. #13063297	C₂²	semidirect
70. #13063296	C₂²	semidirect
71. #13063295	C₂²	semidirect
72. #13063295	C₂²	semidirect
73. #13063295	C₂²	semidirect
74. #13063295	C₂²	semidirect
75. #13063295	C₂²	semidirect
76. #13063295	C₂²	semidirect
77. #13063293	C₂²	semidirect
78. #13063293	C₂²	semidirect
79. #13063293	C₂²	semidirect
80. Q₈×Dic₄₃	C₂²	semidirect
81. C₄×Dic₈₆	C₂²	semidirect
82. C₄×D₁₇₂	C₂²	semidirect
83. D₄×Dic₄₃	C₂²	semidirect
84. D₄×Dic₄₃	C₂²	semidirect
85. #13063287	C₂²	semidirect
86. #13063287	C₂²	semidirect
87. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
88. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
90. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
91. #13063283	C₂²	semidirect
92. C₂×C₂²⋊Dic₄₃	C₂²	semidirect
93. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
94. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
95. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
96. C₂²⋊C₄×D₄₃	C₂²	semidirect
97. C₂×C₄×Dic₄₃	C₂²	semidirect
98. #126×C₄₃	C₂²	semidirect
99. #124×C₄₃	C₂²	semidirect
100. #123×C₄₃	C₂²	semidirect
101. C₂²⋊Q₈×C₄₃	C₂²	semidirect
102. #121×C₄₃	C₂²	semidirect
103. #121×C₄₃	C₂²	semidirect
104. #120×C₄₃	C₂²	semidirect
105. C₄×D₄×C₄₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₄₃	C₂²	semidirect
326. #538	D₄₃	semidirect
333. C₄₃	#3558	semidirect
346. #126	C₂×D₄₃	semidirect
360. #124	C₂×D₄₃	semidirect
369. #123	C₂×D₄₃	semidirect
375. C₂²⋊Q₈	C₂×D₄₃	semidirect
389. #121	C₂×D₄₃	semidirect
390. #121	C₂×D₄₃	semidirect
400. #120	C₂×D₄₃	semidirect
412. C₄×D₄	C₂×D₄₃	semidirect
419. C₂×C₂²⋊C₄	C₂×D₄₃	semidirect