Subgroups — #19148197

Order 5504.

1242 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583633	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583603	C₂	1	2	yes	maximal, complemented
3	#14583594	C₂	1	2	yes	maximal, complemented
4	#14583592	C₂	1	2	yes	maximal, complemented
5	#14583580	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583577	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583576	C₂	1	2	yes	maximal, complemented
8	#14583538	C₂	1	2	yes	maximal, complemented
9	#14583536	C₂	1	2	yes	maximal, complemented
10	#14583531	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583445	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583429	C₂	1	2	yes	maximal, complemented
13	#14583427	C₂	1	2	yes	maximal, complemented
14	#14583408	C₂	1	2	yes	maximal, complemented
15	#14583406	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#10621900	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₄₃	C₂	1	2	yes	maximal, complemented
19	C₄₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10621900	C₂²	1	2	yes	—
22	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	—
23	C₂×D₄×D₄₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₄₃	C₂²	1	2	yes	complemented
26	#13063323	C₂²	1	1	yes	characteristic, complemented
27	#13063321	C₂²	1	1	yes	characteristic
28	#13063320	C₂²	1	2	yes	complemented
29	#13063320	C₂²	1	2	yes	complemented
30	#13063318	C₂²	1	2	yes	complemented
31	#13063318	C₂²	1	2	yes	complemented
32	#13063315	C₂²	1	2	yes	complemented
33	#13063315	C₂²	1	2	yes	complemented
34	#13063314	C₂²	1	1	yes	characteristic, complemented
35	#13063312	C₂²	1	1	yes	characteristic, complemented
36	#13063311	C₂²	1	2	yes	complemented
37	#13063311	C₂²	1	2	yes	complemented
38	#13063310	C₂²	1	2	yes	complemented
39	#13063310	C₂²	1	2	yes	complemented
40	#13063309	C₂²	1	2	yes	complemented
41	#13063307	C₂²	1	2	yes	complemented
42	#13063307	C₂²	1	2	yes	complemented
43	#13063306	C₂²	1	1	yes	characteristic, complemented
44	#13063306	C₂²	1	2	yes	complemented
45	#13063306	C₂²	1	1	yes	characteristic, complemented
46	#13063303	C₂²	1	2	yes	complemented
47	#13063303	C₂²	1	2	yes	complemented
48	#13063302	C₂²	1	2	yes	complemented
49	#13063302	C₂²	1	2	yes	complemented
50	#13063301	C₂²	1	2	yes	complemented
51	#13063298	C₂²	1	2	yes	—
52	#13063298	C₂²	1	2	yes	complemented
53	#13063297	C₂²	1	2	yes	—
54	#13063297	C₂²	1	2	yes	complemented
55	#13063297	C₂²	1	2	yes	complemented
56	#13063297	C₂²	1	2	yes	complemented
57	#13063296	C₂²	1	2	yes	complemented
58	#13063295	C₂²	1	2	yes	—
59	#13063293	C₂²	1	1	yes	characteristic
60	#13063293	C₂²	1	1	yes	characteristic, complemented
61	#13063293	C₂²	1	2	yes	complemented
62	C₄×Dic₈₆	C₂²	1	2	yes	complemented
63	#13063290	C₂²	1	2	yes	complemented
64	C₄×D₁₇₂	C₂²	1	2	yes	complemented
65	D₄×Dic₄₃	C₂²	1	2	yes	complemented
66	D₄×Dic₄₃	C₂²	1	2	yes	complemented
67	#13063287	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
69	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
78	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
79	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
80	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
81	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
82	#13063284	C₂²	1	1	yes	characteristic, complemented
83	#13063283	C₂²	1	2	yes	complemented
84	#13063282	C₂²	1	2	yes	complemented
85	#13063281	C₂²	1	2	yes	complemented
86	#13063281	C₂²	1	2	yes	complemented
87	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	complemented
90	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₄₃	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
95	C₄²×D₄₃	C₂²	1	2	yes	complemented
96	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
98	#123×C₄₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₄₃	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
101	#121×C₄₃	C₂²	1	2	yes	complemented
102	#120×C₄₃	C₂²	1	1	yes	characteristic
103	#120×C₄₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
106	#117×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	#41×C₄₃	—	4	2	no	—
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	1	yes	characteristic
115	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₃	—	2	8	no	—
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	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
132	C₂²×Dic₄₃	C₂³	1	2	yes	—
133	C₂²×Dic₄₃	C₂³	1	2	yes	—
134	C₂²×Dic₄₃	C₂³	1	2	yes	—
135	C₂²×Dic₄₃	C₂³	1	2	yes	—
136	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
137	#10621900	—	2	8	no	—
138	D₄×D₄₃	—	2	8	no	—
139	#10621898	—	4	2	no	—
140	C₂×D₁₇₂	C₂³	1	2	yes	—
141	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₄₃	—	4	2	no	—
143	C₂×C₄×D₄₃	—	4	4	no	—
144	C₂×C₄×D₄₃	C₂³	1	2	yes	—
145	C₂×C₄×D₄₃	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×C₄×D₄₃	C₂³	1	2	yes	—
151	C₂×Dic₈₆	C₂³	1	2	yes	—
152	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
154	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
157	C₂²⋊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	C₄²×C₄₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₄₃	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	1	yes	characteristic
170	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₄₃	C₂³	1	2	yes	—
182	C₄⋊Dic₄₃	C₂³	1	2	yes	—
183	C₄⋊Dic₄₃	C₂³	1	2	yes	—
184	Dic₄₃⋊C₄	C₂³	1	2	yes	—
185	Dic₄₃⋊C₄	C₂³	1	2	yes	—
186	Dic₄₃⋊C₄	C₂³	1	2	yes	—
187	Dic₄₃⋊C₄	C₂³	1	2	yes	—
188	Dic₄₃⋊C₄	C₂³	1	2	yes	—
189	Dic₄₃⋊C₄	C₂³	1	2	yes	—
190	Dic₄₃⋊C₄	C₂³	1	2	yes	—
191	Dic₄₃⋊C₄	C₂³	1	2	yes	—
192	Dic₄₃⋊C₄	C₂³	1	2	yes	—
193	Dic₄₃⋊C₄	C₂³	1	2	yes	—
194	C₄×Dic₄₃	C₂³	1	2	yes	—
195	C₄×Dic₄₃	C₂³	1	2	yes	—
196	C₄×Dic₄₃	C₂³	1	2	yes	—
197	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₄₃	C₂³	1	2	yes	—
199	C₄×Dic₄₃	C₂³	1	2	yes	—
200	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₄₃	C₂³	1	2	yes	—
202	C₂³×C₄₃	—	2	4	no	—
203	C₂³×C₄₃	—	4	1	no	—
204	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₄₃	C₂⁴	1	2	yes	—
208	C₂²×D₄₃	—	2	4	no	—
209	C₂²×D₄₃	—	2	4	no	—
210	C₂²×D₄₃	—	2	4	no	—
211	C₂²×D₄₃	—	4	1	no	—
212	C₂²×D₄₃	—	4	2	no	—
213	C₂²×D₄₃	C₂⁴	1	2	yes	—
214	C₂²×D₄₃	C₂⁴	1	2	yes	—
215	Q₈×C₄₃	—	4	1	no	—
216	D₄×C₄₃	—	2	4	no	—
217	D₄×C₄₃	—	2	4	no	—
218	D₄×C₄₃	—	4	1	no	—
219	D₄×C₄₃	—	4	1	no	—
220	D₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	2	4	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
229	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
234	C₂²⋊D₄₃	—	2	4	no	—
235	C₂²⋊D₄₃	—	2	4	no	—
236	C₂²⋊D₄₃	—	2	4	no	—
237	C₂²⋊D₄₃	—	2	4	no	—
238	C₂²⋊D₄₃	—	2	4	no	—
239	C₂²⋊D₄₃	—	4	2	no	—
240	C₂²⋊D₄₃	#41	1	8	yes	complemented
241	C₂×Dic₄₃	—	2	4	no	—
242	C₂×Dic₄₃	—	2	4	no	—
243	C₂×Dic₄₃	—	2	4	no	—
244	C₂×Dic₄₃	—	4	2	no	—
245	C₂×Dic₄₃	—	4	1	no	—
246	C₂×Dic₄₃	C₂⁴	1	2	yes	—
247	C₂×Dic₄₃	C₂⁴	1	2	yes	—
248	C₂×Dic₄₃	C₂⁴	1	2	yes	—
249	C₂×Dic₄₃	C₂⁴	1	2	yes	—
250	C₂×Dic₄₃	C₂⁴	1	2	yes	—
251	C₂×Dic₄₃	C₂⁴	1	2	yes	—
252	D₁₇₂	—	2	4	no	—
253	D₁₇₂	—	4	1	no	—
254	C₄×D₄₃	—	2	4	no	—
255	C₄×D₄₃	—	2	4	no	—
256	C₄×D₄₃	—	2	4	no	—
257	C₄×D₄₃	—	2	4	no	—
258	C₄×D₄₃	—	4	2	no	—
259	C₄×D₄₃	—	4	2	no	—
260	C₄×D₄₃	—	4	2	no	—
261	Dic₈₆	—	2	4	no	—
262	Dic₈₆	—	4	1	no	—
263	C₂²×C₄₃	—	2	2	no	—
264	C₂²×C₄₃	—	2	2	no	—
265	C₂²×C₄₃	—	2	2	no	—
266	C₂²×C₄₃	—	2	2	no	—
267	C₂²×C₄₃	—	2	2	no	—
268	C₂²×C₄₃	—	2	1	no	—
269	C₂²×C₄₃	—	2	1	no	—
270	C₂²×C₄₃	—	2	1	no	—
271	C₂²×C₄₃	—	4	4	no	—
272	C₂²×C₄₃	C₂×#41	1	4	yes	—
273	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
274	C₂×D₄₃	—	2	2	no	—
275	C₂×D₄₃	—	2	2	no	—
276	C₂×D₄₃	—	2	2	no	—
277	C₂×D₄₃	—	2	2	no	—
278	C₂×D₄₃	—	2	2	no	—
279	C₂×D₄₃	—	4	4	no	—
280	C₂×D₄₃	—	4	8	no	—
281	C₂×D₄₃	C₂×#41	1	4	yes	—
282	C₄×C₄₃	—	2	2	no	—
283	C₄×C₄₃	—	2	2	no	—
284	C₄×C₄₃	—	2	1	no	—
285	C₄×C₄₃	—	2	2	no	—
286	C₄×C₄₃	—	2	1	no	—
287	C₄×C₄₃	—	2	1	no	—
288	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
289	Dic₄₃	—	2	2	no	—
290	Dic₄₃	—	2	2	no	—
291	Dic₄₃	—	2	2	no	—
292	Dic₄₃	—	2	2	no	—
293	Dic₄₃	—	2	2	no	—
294	Dic₄₃	C₂×#41	1	4	yes	—
295	#3481	—	43	1	no	maximal, Sylow
296	C₂×C₄₃	—	2	4	no	—
297	C₂×C₄₃	—	4	1	no	—
298	C₂×C₄₃	—	4	1	no	—
299	C₂×C₄₃	—	4	1	no	—
300	C₂×C₄₃	C₂²×#41	1	2	yes	—
301	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
302	D₄₃	—	2	4	no	—
303	D₄₃	—	4	2	no	—
304	#559	—	43	1	no	—
305	#554	—	43	2	no	—
306	#553	—	43	2	no	—
307	#553	—	43	2	no	—
308	#551	—	43	1	no	—
309	#551	—	43	2	no	—
310	#551	—	43	1	no	—
311	#546	—	43	2	no	—
312	#546	—	43	2	no	—
313	D₄²	—	43	1	no	—
314	#532	—	43	1	no	—
315	#529	—	43	2	no	—
316	#529	—	43	2	no	—
317	#525	—	43	1	no	—
318	#525	—	43	2	no	—
319	#525	D₄₃	1	1	yes	characteristic, complemented
320	C₄×#41	—	43	2	no	—
321	C₂×C₄×D₄	—	43	2	no	—
322	C₂×C₄×D₄	—	43	2	no	—
323	C₄₃	#3481	1	1	yes	characteristic, complemented, Sylow
324	C₂×#41	—	43	2	no	—
325	C₂×#41	—	43	1	no	—
326	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
327	C₂²×D₄	—	43	2	no	—
328	C₂²×D₄	—	43	2	no	—
329	C₂³×C₄	—	43	2	no	—
330	C₂³×C₄	—	43	1	no	—
331	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	—	43	1	no	—
333	#127	—	43	1	no	—
334	#126	—	43	2	no	—
335	#126	—	43	2	no	—
336	#126	—	43	2	no	—
337	#126	—	43	2	no	—
338	#125	—	43	2	no	—
339	#125	—	43	2	no	—
340	#124	—	43	1	no	—
341	#124	—	43	1	no	—
342	#124	—	43	2	no	—
343	#124	—	43	2	no	—
344	#123	—	43	1	no	—
345	#123	—	43	1	no	—
346	#123	—	43	2	no	—
347	#123	—	43	2	no	—
348	#123	—	43	2	no	—
349	#123	—	43	2	no	—
350	#123	—	43	2	no	—
351	#123	—	43	2	no	—
352	#123	C₂×D₄₃	1	1	yes	characteristic, complemented
353	#123	C₂×D₄₃	1	1	yes	characteristic, complemented
354	C₂²⋊Q₈	—	43	2	no	—
355	C₂²⋊Q₈	—	43	2	no	—
356	C₂²⋊Q₈	—	43	2	no	—
357	C₂²⋊Q₈	—	43	2	no	—
358	C₂²⋊Q₈	—	43	2	no	—
359	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
360	#121	—	43	2	no	—
361	#121	—	43	2	no	—
362	#121	—	43	2	no	—
363	#121	—	43	2	no	—
364	#121	—	43	2	no	—
365	#121	—	43	2	no	—
366	#121	—	43	2	no	—
367	#121	C₂×D₄₃	1	2	yes	complemented
368	#120	—	43	1	no	—
369	#120	—	43	2	no	—
370	#120	—	43	1	no	—
371	#120	—	43	2	no	—
372	#120	C₂×D₄₃	1	1	yes	characteristic
373	#120	C₂×D₄₃	1	1	yes	characteristic, complemented
374	C₄×Q₈	—	43	2	no	—
375	C₄×Q₈	—	43	2	no	—
376	C₄×D₄	—	43	2	no	—
377	C₄×D₄	—	43	2	no	—
378	C₄×D₄	—	43	2	no	—
379	C₄×D₄	—	43	2	no	—
380	C₄×D₄	—	43	2	no	—
381	C₄×D₄	—	43	2	no	—
382	C₄×D₄	—	43	2	no	—
383	C₄×D₄	—	43	2	no	—
384	C₄×D₄	—	43	2	no	—
385	C₄×D₄	—	43	2	no	—
386	C₄×D₄	—	43	2	no	—
387	C₄×D₄	—	43	2	no	—
388	C₄×D₄	—	43	2	no	—
389	C₄×D₄	—	43	2	no	—
390	C₄×D₄	—	43	2	no	—
391	C₄×D₄	—	43	2	no	—
392	C₄×D₄	—	43	2	no	—
393	C₄×D₄	—	43	2	no	—
394	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
395	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
396	#117	—	43	1	no	—
397	#117	—	43	2	no	—
398	#117	—	43	2	no	—
399	#117	—	43	2	no	—
400	#117	—	43	2	no	—
401	#117	C₂×D₄₃	1	1	yes	characteristic, complemented
402	C₂×C₄⋊C₄	—	43	2	no	—
403	C₂×C₄⋊C₄	—	43	2	no	—
404	C₂×C₂²⋊C₄	—	43	2	no	—
405	C₂×C₂²⋊C₄	—	43	2	no	—
406	C₂×C₂²⋊C₄	—	43	2	no	—
407	C₂×C₂²⋊C₄	—	43	2	no	—
408	C₂×C₄²	—	43	2	no	—
409	C₂×C₄²	—	43	1	no	—
410	C₂×C₄²	—	43	2	no	—
411	C₂⁴	—	43	1	no	—
412	C₂⁴	—	43	2	no	—
413	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
414	#41	—	4	2	no	—
415	#41	—	86	8	no	—
416	#41	—	172	2	no	—
417	C₂×Q₈	—	43	2	no	—
418	C₂×Q₈	—	43	1	no	—
419	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
420	C₂×D₄	—	43	2	no	—
421	C₂×D₄	—	43	2	no	—
422	C₂×D₄	—	43	2	no	—
423	C₂×D₄	—	43	2	no	—
424	C₂×D₄	—	43	2	no	—
425	C₂×D₄	—	43	2	no	—
426	C₂×D₄	—	43	2	no	—
427	C₂×D₄	—	43	2	no	—
428	C₂×D₄	—	43	1	no	—
429	C₂×D₄	—	86	8	no	—
430	C₂×D₄	—	86	8	no	—
431	C₂×D₄	C₂²×D₄₃	1	2	yes	—
432	C₂×D₄	C₂²×D₄₃	1	2	yes	—
433	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	43	2	no	—
438	C₂²×C₄	—	43	2	no	—
439	C₂²×C₄	—	43	2	no	—
440	C₂²×C₄	—	43	2	no	—
441	C₂²×C₄	—	43	1	no	—
442	C₂²×C₄	—	43	2	no	—
443	C₂²×C₄	—	43	2	no	—
444	C₂²×C₄	—	43	2	no	—
445	C₂²×C₄	—	43	2	no	—
446	C₂²×C₄	—	43	2	no	—
447	C₂²×C₄	—	43	2	no	—
448	C₂²×C₄	—	43	2	no	—
449	C₂²×C₄	—	172	4	no	—
450	C₂²×C₄	—	172	2	no	—
451	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
452	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
457	C₄⋊C₄	—	43	2	no	—
458	C₄⋊C₄	—	43	2	no	—
459	C₄⋊C₄	—	43	2	no	—
460	C₄⋊C₄	—	43	2	no	—
461	C₄⋊C₄	—	43	2	no	—
462	C₄⋊C₄	—	43	2	no	—
463	C₄⋊C₄	—	43	2	no	—
464	C₄⋊C₄	—	43	2	no	—
465	C₄⋊C₄	—	43	2	no	—
466	C₄⋊C₄	—	43	2	no	—
467	C₄⋊C₄	—	43	2	no	—
468	C₄⋊C₄	—	43	2	no	—
469	C₄⋊C₄	—	43	2	no	—
470	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
473	C₂²⋊C₄	—	43	2	no	—
474	C₂²⋊C₄	—	43	2	no	—
475	C₂²⋊C₄	—	43	2	no	—
476	C₂²⋊C₄	—	43	2	no	—
477	C₂²⋊C₄	—	43	2	no	—
478	C₂²⋊C₄	—	43	2	no	—
479	C₂²⋊C₄	—	43	1	no	—
480	C₂²⋊C₄	—	43	1	no	—
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	C₂²×D₄₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
496	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
497	C₄²	—	43	1	no	—
498	C₄²	—	43	2	no	—
499	C₄²	—	43	2	no	—
500	C₄²	—	43	2	no	—
501	C₄²	—	43	2	no	—
502	C₄²	—	43	1	no	—
503	C₄²	—	43	2	no	—
504	C₄²	—	43	2	no	—
505	C₄²	C₂²×D₄₃	1	2	yes	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	43	2	no	—
509	C₂³	—	43	2	no	—
510	C₂³	—	86	4	no	—
511	C₂³	—	86	4	no	—
512	C₂³	—	86	4	no	—
513	C₂³	—	172	2	no	—
514	C₂³	—	172	1	no	—
515	C₂³	C₂³×D₄₃	1	1	yes	characteristic
516	C₂³	C₂³×D₄₃	1	1	yes	characteristic
517	C₂³	C₂³×D₄₃	1	1	yes	characteristic
518	C₂³	C₂³×D₄₃	1	2	yes	—
519	Q₈	—	4	1	no	—
520	Q₈	—	86	4	no	—
521	Q₈	—	172	1	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	43	8	no	—
528	D₄	—	86	4	no	—
529	D₄	—	86	4	no	—
530	D₄	—	86	4	no	—
531	D₄	—	86	4	no	—
532	D₄	—	86	4	no	—
533	D₄	—	86	4	no	—
534	D₄	—	172	1	no	—
535	D₄	—	172	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	43	2	no	—
543	C₂×C₄	—	43	2	no	—
544	C₂×C₄	—	43	2	no	—
545	C₂×C₄	—	43	2	no	—
546	C₂×C₄	—	43	2	no	—
547	C₂×C₄	—	43	2	no	—
548	C₂×C₄	—	86	4	no	—
549	C₂×C₄	—	86	4	no	—
550	C₂×C₄	—	86	4	no	—
551	C₂×C₄	—	86	4	no	—
552	C₂×C₄	—	86	4	no	—
553	C₂×C₄	—	86	4	no	—
554	C₂×C₄	—	86	4	no	—
555	C₂×C₄	—	172	2	no	—
556	C₂×C₄	—	172	2	no	—
557	C₂×C₄	—	172	2	no	—
558	C₂×C₄	—	172	1	no	—
559	C₂×C₄	—	172	2	no	—
560	C₂×C₄	C₂³×D₄₃	1	2	yes	—
561	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₄₃	1	2	yes	—
563	C₂×C₄	C₂³×D₄₃	1	2	yes	—
564	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	43	4	no	—
577	C₂²	—	86	2	no	—
578	C₂²	—	86	2	no	—
579	C₂²	—	86	2	no	—
580	C₂²	—	86	2	no	—
581	C₂²	—	86	2	no	—
582	C₂²	—	172	8	no	—
583	C₂²	—	172	4	no	—
584	C₂²	#41×D₄₃	1	4	yes	—
585	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	43	4	no	—
593	C₄	—	86	2	no	—
594	C₄	—	86	2	no	—
595	C₄	—	86	2	no	—
596	C₄	—	86	2	no	—
597	C₄	—	86	2	no	—
598	C₄	#13063370	1	2	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	86	4	no	—
604	C₂	—	172	2	no	—
605	C₂	C₂×#41×D₄₃	1	2	yes	—
606	C₂	C₂×#13063370	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₄₃×#525	C₂
hypercenter	#525	D₄₃
hypocenter	C₄₃	#3481
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #14583633	C₂	semidirect
2. #14583603	C₂	semidirect
3. #14583594	C₂	semidirect
4. #14583592	C₂	semidirect
5. #14583580	C₂	semidirect
6. #14583577	C₂	semidirect
7. #14583576	C₂	semidirect
8. #14583538	C₂	semidirect
9. #14583536	C₂	semidirect
10. #14583531	C₂	semidirect
11. #14583445	C₂	semidirect
12. #14583429	C₂	semidirect
13. #14583427	C₂	semidirect
14. #14583408	C₂	semidirect
15. #14583406	C₂	semidirect
16. C₄×#10621900	C₂	semidirect
17. C₂×C₄×C₂²⋊D₄₃	C₂	semidirect
18. C₄×D₄×D₄₃	C₂	semidirect
19. C₄₃×#525	C₂	semidirect
20. C₂×#10621898	C₂²	semidirect
24. C₂²×C₄×D₄₃	C₂²	semidirect
25. C₂²×C₄×D₄₃	C₂²	semidirect
26. #13063323	C₂²	semidirect
28. #13063320	C₂²	semidirect
29. #13063320	C₂²	semidirect
30. #13063318	C₂²	semidirect
31. #13063318	C₂²	semidirect
32. #13063315	C₂²	semidirect
33. #13063315	C₂²	semidirect
34. #13063314	C₂²	semidirect
35. #13063312	C₂²	semidirect
36. #13063311	C₂²	semidirect
37. #13063311	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063310	C₂²	semidirect
40. #13063309	C₂²	semidirect
41. #13063307	C₂²	semidirect
42. #13063307	C₂²	semidirect
43. #13063306	C₂²	semidirect
44. #13063306	C₂²	semidirect
45. #13063306	C₂²	semidirect
46. #13063303	C₂²	semidirect
47. #13063303	C₂²	semidirect
48. #13063302	C₂²	semidirect
49. #13063302	C₂²	semidirect
50. #13063301	C₂²	semidirect
52. #13063298	C₂²	semidirect
54. #13063297	C₂²	semidirect
55. #13063297	C₂²	semidirect
56. #13063297	C₂²	semidirect
57. #13063296	C₂²	semidirect
60. #13063293	C₂²	semidirect
61. #13063293	C₂²	semidirect
62. C₄×Dic₈₆	C₂²	semidirect
63. #13063290	C₂²	semidirect
64. C₄×D₁₇₂	C₂²	semidirect
65. D₄×Dic₄₃	C₂²	semidirect
66. D₄×Dic₄₃	C₂²	semidirect
67. #13063287	C₂²	semidirect
70. C₄×C₂²⋊D₄₃	C₂²	semidirect
71. C₄×C₂²⋊D₄₃	C₂²	semidirect
72. C₄×C₂²⋊D₄₃	C₂²	semidirect
73. C₄×C₂²⋊D₄₃	C₂²	semidirect
74. C₄×C₂²⋊D₄₃	C₂²	semidirect
75. C₄×C₂²⋊D₄₃	C₂²	semidirect
76. C₄×C₂²⋊D₄₃	C₂²	semidirect
77. C₄×C₂²⋊D₄₃	C₂²	semidirect
80. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
81. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
82. #13063284	C₂²	semidirect
83. #13063283	C₂²	semidirect
84. #13063282	C₂²	semidirect
85. #13063281	C₂²	semidirect
86. #13063281	C₂²	semidirect
87. C₂×Dic₄₃⋊C₄	C₂²	semidirect
88. C₄⋊C₄×D₄₃	C₂²	semidirect
89. C₂×C₂²⋊Dic₄₃	C₂²	semidirect
90. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
91. C₂²⋊C₄×D₄₃	C₂²	semidirect
92. C₂²⋊C₄×D₄₃	C₂²	semidirect
93. C₂×C₄×Dic₄₃	C₂²	semidirect
94. C₂×C₄×Dic₄₃	C₂²	semidirect
95. C₄²×D₄₃	C₂²	semidirect
96. C₂×#41×C₄₃	C₂²	semidirect
97. C₂³×C₄×C₄₃	C₂²	semidirect
98. #123×C₄₃	C₂²	semidirect
99. #123×C₄₃	C₂²	semidirect
100. C₂²⋊Q₈×C₄₃	C₂²	semidirect
101. #121×C₄₃	C₂²	semidirect
103. #120×C₄₃	C₂²	semidirect
104. C₄×D₄×C₄₃	C₂²	semidirect
105. C₄×D₄×C₄₃	C₂²	semidirect
106. #117×C₄₃	C₂²	semidirect
240. C₂²⋊D₄₃	#41	semidirect
319. #525	D₄₃	semidirect
323. C₄₃	#3481	semidirect
326. C₂×#41	C₂×D₄₃	semidirect
331. C₂³×C₄	C₂×D₄₃	semidirect
352. #123	C₂×D₄₃	semidirect
353. #123	C₂×D₄₃	semidirect
359. C₂²⋊Q₈	C₂×D₄₃	semidirect
367. #121	C₂×D₄₃	semidirect
373. #120	C₂×D₄₃	semidirect
394. C₄×D₄	C₂×D₄₃	semidirect
395. C₄×D₄	C₂×D₄₃	semidirect
401. #117	C₂×D₄₃	semidirect