Subgroups — #19148308

Order 5504.

1040 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583622	C₂	1	2	yes	maximal, complemented
2	#14583617	C₂	1	2	yes	maximal, complemented
3	#14583614	C₂	1	2	yes	maximal, complemented
4	#14583612	C₂	1	2	yes	maximal, complemented
5	#14583599	C₂	1	2	yes	maximal, complemented
6	#14583597	C₂	1	2	yes	maximal, complemented
7	#14583590	C₂	1	2	yes	maximal, complemented
8	#14583584	C₂	1	2	yes	maximal, complemented
9	#14583527	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583482	C₂	1	4	yes	maximal, complemented
11	#14583477	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583429	C₂	1	4	yes	maximal, complemented
13	#14583411	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583406	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063283	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621898	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
20	#13063325	C₂²	1	2	yes	complemented
21	#13063324	C₂²	1	2	yes	complemented
22	#13063320	C₂²	1	4	yes	—
23	#13063320	C₂²	1	4	yes	complemented
24	#13063319	C₂²	1	4	yes	—
25	#13063318	C₂²	1	4	yes	complemented
26	#13063317	C₂²	1	2	yes	complemented
27	#13063316	C₂²	1	2	yes	complemented
28	#13063315	C₂²	1	4	yes	complemented
29	#13063313	C₂²	1	4	yes	—
30	#13063311	C₂²	1	4	yes	—
31	#13063311	C₂²	1	4	yes	complemented
32	#13063310	C₂²	1	4	yes	—
33	#13063309	C₂²	1	2	yes	—
34	#13063308	C₂²	1	4	yes	—
35	#13063306	C₂²	1	2	yes	—
36	#13063305	C₂²	1	1	yes	characteristic
37	#13063305	C₂²	1	1	yes	characteristic
38	#13063304	C₂²	1	2	yes	complemented
39	#13063302	C₂²	1	4	yes	—
40	#13063301	C₂²	1	1	yes	characteristic
41	#13063301	C₂²	1	1	yes	characteristic
42	#13063301	C₂²	1	2	yes	complemented
43	#13063300	C₂²	1	1	yes	characteristic
44	#13063300	C₂²	1	1	yes	characteristic
45	#13063299	C₂²	1	4	yes	—
46	#13063299	C₂²	1	2	yes	complemented
47	#13063298	C₂²	1	4	yes	—
48	#13063297	C₂²	1	4	yes	—
49	#13063296	C₂²	1	1	yes	characteristic
50	#13063296	C₂²	1	1	yes	characteristic
51	#13063296	C₂²	1	2	yes	complemented
52	#13063295	C₂²	1	2	yes	—
53	#13063293	C₂²	1	2	yes	—
54	C₄×Dic₈₆	C₂²	1	4	yes	complemented
55	#13063290	C₂²	1	2	yes	complemented
56	C₄×D₁₇₂	C₂²	1	2	yes	—
57	C₄×D₁₇₂	C₂²	1	2	yes	—
58	#13063287	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
62	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
63	#13063284	C₂²	1	1	yes	characteristic
64	#13063284	C₂²	1	4	yes	complemented
65	#13063283	C₂²	1	2	yes	—
66	#13063283	C₂²	1	2	yes	—
67	#13063283	C₂²	1	2	yes	—
68	#13063283	C₂²	1	2	yes	—
69	#13063283	C₂²	1	2	yes	complemented
70	#13063282	C₂²	1	4	yes	complemented
71	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
73	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
74	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
75	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
76	C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
77	C₄×D₄×C₄₃	C₂²	1	4	yes	—
78	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
79	#117×C₄₃	C₂²	1	1	yes	characteristic
80	#117×C₄₃	C₂²	1	2	yes	complemented
81	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
83	C₂³×D₄₃	C₂³	1	1	yes	characteristic
84	#41×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₄₃	C₂³	1	2	yes	—
87	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
91	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
96	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
97	C₂²×Dic₄₃	C₂³	1	2	yes	—
98	#10621898	—	2	4	no	—
99	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
100	C₂×D₁₇₂	C₂³	1	2	yes	—
101	C₂×D₁₇₂	C₂³	1	2	yes	—
102	C₂×C₄×D₄₃	—	2	4	no	—
103	C₂×C₄×D₄₃	C₂³	1	2	yes	—
104	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₄₃	C₂³	1	4	yes	—
109	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
110	C₂×Dic₈₆	C₂³	1	4	yes	—
111	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
113	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
118	C₄²×C₄₃	C₂³	1	2	yes	—
119	C₄²×C₄₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
124	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
134	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₄₃	C₂³	1	2	yes	—
136	C₄⋊Dic₄₃	C₂³	1	2	yes	—
137	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₄₃	C₂³	1	2	yes	—
139	C₄⋊Dic₄₃	C₂³	1	4	yes	—
140	C₄⋊Dic₄₃	C₂³	1	2	yes	—
141	Dic₄₃⋊C₄	C₂³	1	4	yes	—
142	Dic₄₃⋊C₄	C₂³	1	2	yes	—
143	Dic₄₃⋊C₄	C₂³	1	4	yes	—
144	Dic₄₃⋊C₄	C₂³	1	2	yes	—
145	Dic₄₃⋊C₄	C₂³	1	4	yes	—
146	Dic₄₃⋊C₄	C₂³	1	4	yes	—
147	C₄×Dic₄₃	C₂³	1	4	yes	—
148	C₄×Dic₄₃	C₂³	1	4	yes	—
149	C₄×Dic₄₃	C₂³	1	4	yes	—
150	C₄×Dic₄₃	C₂³	1	2	yes	—
151	C₂³×C₄₃	C₂⁴	1	2	yes	—
152	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	2	no	—
154	C₂²×D₄₃	—	4	1	no	—
155	C₂²×D₄₃	—	4	1	no	—
156	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
158	C₂²×D₄₃	C₂⁴	1	2	yes	—
159	Q₈×C₄₃	—	2	2	no	—
160	D₄×C₄₃	—	2	4	no	—
161	D₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	#41	1	4	yes	—
166	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
167	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₄₃	—	2	4	no	—
173	C₂²⋊D₄₃	—	4	2	no	—
174	C₂²⋊D₄₃	—	4	4	no	—
175	C₂²⋊D₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₄₃	C₂⁴	1	2	yes	—
181	C₂×Dic₄₃	C₂⁴	1	2	yes	—
182	C₂×Dic₄₃	C₂⁴	1	4	yes	—
183	C₂×Dic₄₃	C₂⁴	1	2	yes	—
184	D₁₇₂	—	2	2	no	—
185	D₁₇₂	—	4	2	no	—
186	D₁₇₂	—	4	2	no	—
187	C₄×D₄₃	—	2	2	no	—
188	C₄×D₄₃	—	2	2	no	—
189	C₄×D₄₃	—	2	2	no	—
190	C₄×D₄₃	—	2	2	no	—
191	C₄×D₄₃	—	2	4	no	—
192	C₄×D₄₃	—	4	4	no	—
193	Dic₈₆	—	2	2	no	—
194	Dic₈₆	—	4	4	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	2	2	no	—
199	C₂²×C₄₃	—	2	2	no	—
200	C₂²×C₄₃	C₂×#41	1	2	yes	—
201	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₄₃	—	2	1	no	—
203	C₂×D₄₃	—	2	1	no	—
204	C₂×D₄₃	—	2	2	no	—
205	C₂×D₄₃	—	2	1	no	—
206	C₂×D₄₃	—	2	1	no	—
207	C₂×D₄₃	—	2	1	no	—
208	C₂×D₄₃	—	2	1	no	—
209	C₂×D₄₃	—	2	2	no	—
210	C₂×D₄₃	—	2	2	no	—
211	C₂×D₄₃	—	4	4	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	—	2	2	no	—
214	C₄×C₄₃	—	2	4	no	—
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	C₂×#41	1	2	yes	—
217	C₄×C₄₃	C₂×#41	1	2	yes	—
218	Dic₄₃	—	2	2	no	—
219	Dic₄₃	—	2	1	no	—
220	Dic₄₃	—	2	1	no	—
221	Dic₄₃	—	2	2	no	—
222	Dic₄₃	—	2	4	no	—
223	Dic₄₃	—	2	2	no	—
224	#3493	—	43	1	no	maximal, Sylow
225	C₂×C₄₃	—	2	2	no	—
226	C₂×C₄₃	—	4	2	no	—
227	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
228	C₂×C₄₃	#585	1	1	yes	characteristic
229	C₂×C₄₃	#585	1	1	yes	characteristic
230	D₄₃	—	4	2	no	—
231	D₄₃	—	4	1	no	—
232	D₄₃	—	4	1	no	—
233	#556	—	43	2	no	—
234	#556	—	43	2	no	—
235	#555	—	43	2	no	—
236	#555	—	43	2	no	—
237	#553	—	43	2	no	—
238	#553	—	43	2	no	—
239	#552	—	43	2	no	—
240	#552	—	43	2	no	—
241	#544	—	43	1	no	—
242	#538	—	43	4	no	—
243	#537	—	43	1	no	—
244	#529	—	43	4	no	—
245	#525	—	43	1	no	—
246	#525	—	43	1	no	—
247	#520	—	43	1	no	—
248	#520	D₄₃	1	1	yes	characteristic, complemented
249	C₂×#117	—	43	1	no	—
250	C₄₃	#3493	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	43	1	no	—
252	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
253	C₂³×C₄	—	43	1	no	—
254	C₄⋊Q₈	—	43	2	no	—
255	C₄⋊Q₈	—	43	2	no	—
256	#126	—	43	4	no	—
257	#126	—	43	4	no	—
258	#126	—	43	4	no	—
259	#126	—	43	4	no	—
260	#125	—	43	4	no	—
261	#125	—	43	2	no	—
262	#125	—	43	2	no	—
263	#124	—	43	4	no	—
264	#124	—	43	4	no	—
265	#124	—	43	4	no	—
266	#123	—	43	2	no	—
267	#123	—	43	4	no	—
268	#123	—	43	4	no	—
269	#123	—	43	2	no	—
270	C₂²⋊Q₈	—	43	1	no	—
271	C₂²⋊Q₈	—	43	1	no	—
272	C₂²⋊Q₈	—	43	2	no	—
273	C₂²⋊Q₈	—	43	2	no	—
274	C₂²⋊Q₈	—	43	1	no	—
275	C₂²⋊Q₈	—	43	1	no	—
276	C₂²⋊Q₈	—	43	4	no	—
277	#121	—	43	1	no	—
278	#121	—	43	1	no	—
279	#121	—	43	4	no	—
280	#121	—	43	2	no	—
281	#121	—	43	2	no	—
282	#121	—	43	4	no	—
283	#121	—	43	1	no	—
284	#121	—	43	1	no	—
285	#121	—	43	4	no	—
286	#120	—	43	2	no	—
287	#120	—	43	2	no	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	—	43	4	no	—
290	C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
291	C₄×D₄	—	43	4	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	2	no	—
294	C₄×D₄	—	43	4	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	—	43	2	no	—
297	C₄×D₄	—	43	2	no	—
298	C₄×D₄	C₂×D₄₃	1	4	yes	—
299	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
300	#117	—	43	1	no	—
301	#117	—	43	4	no	—
302	#117	—	43	2	no	—
303	#117	—	43	2	no	—
304	#117	—	43	2	no	—
305	#117	—	43	2	no	—
306	#117	—	43	2	no	—
307	#117	—	43	4	no	—
308	#117	C₂×D₄₃	1	1	yes	characteristic
309	#117	C₂×D₄₃	1	2	yes	complemented
310	C₂×C₄⋊C₄	—	43	1	no	—
311	C₂×C₄⋊C₄	—	43	2	no	—
312	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	complemented
314	C₂×C₂²⋊C₄	—	43	2	no	—
315	C₂×C₄²	—	43	2	no	—
316	C₂⁴	—	43	1	no	—
317	#41	—	2	4	no	—
318	#41	—	86	4	no	—
319	C₂×Q₈	—	43	1	no	—
320	C₂×Q₈	—	43	4	no	—
321	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₂×D₄	—	43	2	no	—
323	C₂×D₄	—	43	2	no	—
324	C₂×D₄	—	43	2	no	—
325	C₂×D₄	—	43	4	no	—
326	C₂×D₄	—	43	1	no	—
327	C₂×D₄	—	43	2	no	—
328	C₂×D₄	—	43	2	no	—
329	C₂×D₄	C₂²×D₄₃	1	2	yes	—
330	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
331	C₂²×C₄	—	43	1	no	—
332	C₂²×C₄	—	43	2	no	—
333	C₂²×C₄	—	43	2	no	—
334	C₂²×C₄	—	43	1	no	—
335	C₂²×C₄	—	43	1	no	—
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	43	1	no	—
338	C₂²×C₄	—	43	4	no	—
339	C₂²×C₄	—	86	4	no	—
340	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
341	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
342	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
343	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
344	C₄⋊C₄	—	43	1	no	—
345	C₄⋊C₄	—	43	2	no	—
346	C₄⋊C₄	—	43	2	no	—
347	C₄⋊C₄	—	43	4	no	—
348	C₄⋊C₄	—	43	1	no	—
349	C₄⋊C₄	—	43	2	no	—
350	C₄⋊C₄	—	43	2	no	—
351	C₄⋊C₄	—	43	4	no	—
352	C₄⋊C₄	—	43	4	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	—	43	2	no	—
355	C₄⋊C₄	—	43	4	no	—
356	C₄⋊C₄	—	43	4	no	—
357	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
359	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
361	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
362	C₂²⋊C₄	—	43	2	no	—
363	C₂²⋊C₄	—	43	2	no	—
364	C₂²⋊C₄	—	43	4	no	—
365	C₂²⋊C₄	—	43	2	no	—
366	C₂²⋊C₄	—	43	4	no	—
367	C₂²⋊C₄	—	43	4	no	—
368	C₂²⋊C₄	—	43	2	no	—
369	C₂²⋊C₄	—	43	4	no	—
370	C₂²⋊C₄	—	43	4	no	—
371	C₂²⋊C₄	—	43	2	no	—
372	C₂²⋊C₄	—	43	2	no	—
373	C₂²⋊C₄	—	43	2	no	—
374	C₂²⋊C₄	—	43	2	no	—
375	C₂²⋊C₄	—	43	2	no	—
376	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
378	C₄²	—	43	4	no	—
379	C₄²	—	43	4	no	—
380	C₄²	—	43	4	no	—
381	C₄²	—	43	2	no	—
382	C₄²	C₂²×D₄₃	1	4	yes	—
383	C₄²	C₂²×D₄₃	1	2	yes	—
384	C₂³	—	43	1	no	—
385	C₂³	—	43	1	no	—
386	C₂³	—	43	2	no	—
387	C₂³	—	86	2	no	—
388	C₂³	—	172	1	no	—
389	C₂³	—	172	1	no	—
390	C₂³	C₂³×D₄₃	1	2	yes	—
391	C₂³	C₂³×D₄₃	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	86	2	no	—
394	Q₈	—	172	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	86	4	no	—
398	D₄	—	86	2	no	—
399	D₄	—	172	2	no	—
400	D₄	—	172	2	no	—
401	D₄	—	172	2	no	—
402	D₄	—	172	4	no	—
403	D₄	—	172	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	43	1	no	—
408	C₂×C₄	—	43	1	no	—
409	C₂×C₄	—	43	2	no	—
410	C₂×C₄	—	43	2	no	—
411	C₂×C₄	—	43	4	no	—
412	C₂×C₄	—	43	2	no	—
413	C₂×C₄	—	86	2	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	86	2	no	—
417	C₂×C₄	—	86	2	no	—
418	C₂×C₄	—	86	4	no	—
419	C₂×C₄	—	172	4	no	—
420	C₂×C₄	—	172	2	no	—
421	C₂×C₄	#10621898	1	4	yes	—
422	C₂×C₄	C₂³×D₄₃	1	4	yes	—
423	C₂×C₄	C₂³×D₄₃	1	2	yes	—
424	C₂×C₄	C₂³×D₄₃	1	2	yes	—
425	C₂×C₄	C₂³×D₄₃	1	2	yes	—
426	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	86	1	no	—
434	C₂²	—	86	1	no	—
435	C₂²	—	86	2	no	—
436	C₂²	—	86	2	no	—
437	C₂²	—	86	1	no	—
438	C₂²	—	86	1	no	—
439	C₂²	—	86	2	no	—
440	C₂²	—	86	1	no	—
441	C₂²	—	86	1	no	—
442	C₂²	—	172	4	no	—
443	C₂²	C₂×#10621898	1	2	yes	—
444	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	86	1	no	—
450	C₄	—	86	1	no	—
451	C₄	—	86	2	no	—
452	C₄	—	86	2	no	—
453	C₄	—	86	4	no	—
454	C₄	—	86	2	no	—
455	C₄	C₂×#10621898	1	2	yes	—
456	C₄	C₂×#10621898	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	172	1	no	—
460	C₂	—	172	1	no	—
461	C₂	—	172	2	no	—
462	C₂	C₂²×#10621898	1	1	yes	characteristic
463	C₂	#14583734	1	1	yes	characteristic
464	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#520	C₂
hypercenter	#520	D₄₃
hypocenter	C₄₃	#3493
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #14583622	C₂	semidirect
2. #14583617	C₂	semidirect
3. #14583614	C₂	semidirect
4. #14583612	C₂	semidirect
5. #14583599	C₂	semidirect
6. #14583597	C₂	semidirect
7. #14583590	C₂	semidirect
8. #14583584	C₂	semidirect
9. #14583527	C₂	semidirect
10. #14583482	C₂	semidirect
11. #14583477	C₂	semidirect
12. #14583429	C₂	semidirect
13. #14583411	C₂	semidirect
14. #14583406	C₂	semidirect
15. #14583380	C₂	semidirect
16. C₂×#13063283	C₂	semidirect
17. C₄₃×#520	C₂	semidirect
20. #13063325	C₂²	semidirect
21. #13063324	C₂²	semidirect
23. #13063320	C₂²	semidirect
25. #13063318	C₂²	semidirect
26. #13063317	C₂²	semidirect
27. #13063316	C₂²	semidirect
28. #13063315	C₂²	semidirect
31. #13063311	C₂²	semidirect
38. #13063304	C₂²	semidirect
42. #13063301	C₂²	semidirect
46. #13063299	C₂²	semidirect
51. #13063296	C₂²	semidirect
54. C₄×Dic₈₆	C₂²	semidirect
55. #13063290	C₂²	semidirect
58. #13063287	C₂²	semidirect
62. C₄×C₂²⋊D₄₃	C₂²	semidirect
64. #13063284	C₂²	semidirect
69. #13063283	C₂²	semidirect
70. #13063282	C₂²	semidirect
72. C₄⋊C₄×D₄₃	C₂²	semidirect
76. C₄×Q₈×C₄₃	C₂²	semidirect
78. C₄×D₄×C₄₃	C₂²	semidirect
80. #117×C₄₃	C₂²	semidirect
82. C₂×C₄⋊C₄×C₄₃	C₂²	semidirect
248. #520	D₄₃	semidirect
250. C₄₃	#3493	semidirect
290. C₄×Q₈	C₂×D₄₃	semidirect
299. C₄×D₄	C₂×D₄₃	semidirect
309. #117	C₂×D₄₃	semidirect
313. C₂×C₄⋊C₄	C₂×D₄₃	semidirect