Subgroups — #19148312

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	#14583620	C₂	1	2	yes	maximal, complemented
2	#14583619	C₂	1	2	yes	maximal, complemented
3	#14583614	C₂	1	2	yes	maximal, complemented
4	#14583613	C₂	1	2	yes	maximal, complemented
5	#14583596	C₂	1	2	yes	maximal, complemented
6	#14583595	C₂	1	2	yes	maximal, complemented
7	#14583589	C₂	1	2	yes	maximal, complemented
8	#14583583	C₂	1	2	yes	maximal, complemented
9	#14583527	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583484	C₂	1	4	yes	maximal, complemented
11	#14583477	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583426	C₂	1	4	yes	maximal, complemented
13	#14583410	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583382	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583379	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063284	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10621898	C₂²	1	1	yes	characteristic
19	#13063325	C₂²	1	2	yes	complemented
20	#13063324	C₂²	1	2	yes	complemented
21	#13063320	C₂²	1	4	yes	complemented
22	#13063318	C₂²	1	4	yes	—
23	#13063318	C₂²	1	4	yes	—
24	#13063318	C₂²	1	4	yes	complemented
25	#13063317	C₂²	1	2	yes	complemented
26	#13063316	C₂²	1	2	yes	complemented
27	#13063315	C₂²	1	4	yes	complemented
28	#13063312	C₂²	1	4	yes	—
29	#13063311	C₂²	1	4	yes	—
30	#13063311	C₂²	1	4	yes	complemented
31	#13063308	C₂²	1	2	yes	—
32	#13063307	C₂²	1	4	yes	—
33	#13063306	C₂²	1	4	yes	—
34	#13063304	C₂²	1	1	yes	characteristic
35	#13063304	C₂²	1	1	yes	characteristic
36	#13063304	C₂²	1	2	yes	complemented
37	#13063302	C₂²	1	4	yes	—
38	#13063301	C₂²	1	2	yes	complemented
39	#13063299	C₂²	1	1	yes	characteristic
40	#13063299	C₂²	1	1	yes	characteristic
41	#13063299	C₂²	1	2	yes	complemented
42	#13063297	C₂²	1	4	yes	—
43	#13063297	C₂²	1	4	yes	—
44	#13063296	C₂²	1	4	yes	—
45	#13063296	C₂²	1	2	yes	complemented
46	#13063294	C₂²	1	2	yes	—
47	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
48	C₄×Dic₈₆	C₂²	1	2	yes	complemented
49	#13063290	C₂²	1	4	yes	complemented
50	C₄×D₁₇₂	C₂²	1	2	yes	complemented
51	D₄×Dic₄₃	C₂²	1	4	yes	—
52	D₄×Dic₄₃	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
55	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
56	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
57	#13063284	C₂²	1	2	yes	—
58	#13063284	C₂²	1	2	yes	—
59	#13063284	C₂²	1	2	yes	—
60	#13063284	C₂²	1	2	yes	—
61	#13063284	C₂²	1	1	yes	characteristic
62	#13063284	C₂²	1	2	yes	complemented
63	#13063283	C₂²	1	4	yes	complemented
64	#13063283	C₂²	1	2	yes	complemented
65	#13063281	C₂²	1	4	yes	complemented
66	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
72	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
74	#123×C₄₃	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
77	#121×C₄₃	C₂²	1	1	yes	characteristic
78	#121×C₄₃	C₂²	1	1	yes	characteristic
79	#120×C₄₃	C₂²	1	2	yes	—
80	C₄×D₄×C₄₃	C₂²	1	2	yes	—
81	C₄×D₄×C₄₃	C₂²	1	2	yes	—
82	#117×C₄₃	C₂²	1	1	yes	characteristic
83	C₂⁴×C₄₃	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	C₂×D₄×C₄₃	C₂³	1	2	yes	—
89	C₂×D₄×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
101	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
102	C₂²×Dic₄₃	C₂³	1	2	yes	—
103	C₂²×Dic₄₃	C₂³	1	2	yes	—
104	C₂²×Dic₄₃	C₂³	1	4	yes	—
105	#10621898	—	2	4	no	—
106	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₄₃	C₂³	1	2	yes	—
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	1	yes	characteristic
112	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
120	C₄²×C₄₃	C₂³	1	2	yes	—
121	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
126	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	C₄⋊Dic₄₃	C₂³	1	2	yes	—
133	C₄⋊Dic₄₃	C₂³	1	2	yes	—
134	C₄⋊Dic₄₃	C₂³	1	2	yes	—
135	C₄⋊Dic₄₃	C₂³	1	2	yes	—
136	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₄₃	C₂³	1	4	yes	—
138	C₄⋊Dic₄₃	C₂³	1	4	yes	—
139	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
140	Dic₄₃⋊C₄	C₂³	1	4	yes	—
141	Dic₄₃⋊C₄	C₂³	1	2	yes	—
142	Dic₄₃⋊C₄	C₂³	1	4	yes	—
143	Dic₄₃⋊C₄	C₂³	1	4	yes	—
144	Dic₄₃⋊C₄	C₂³	1	2	yes	—
145	Dic₄₃⋊C₄	C₂³	1	4	yes	—
146	C₄×Dic₄₃	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	—	2	2	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	—	4	1	no	—
154	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
156	C₂³×C₄₃	C₂⁴	1	2	yes	—
157	C₂³×C₄₃	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	D₄×C₄₃	—	4	2	no	—
163	D₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	#41	1	4	yes	—
171	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₄₃	—	2	4	no	—
179	C₂²⋊D₄₃	—	4	2	no	—
180	C₂²⋊D₄₃	—	4	4	no	—
181	C₂²⋊D₄₃	—	4	2	no	—
182	C₂×Dic₄₃	—	4	2	no	—
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	4	4	no	—
185	C₂×Dic₄₃	C₂⁴	1	4	yes	—
186	C₂×Dic₄₃	C₂⁴	1	2	yes	—
187	C₂×Dic₄₃	C₂⁴	1	2	yes	—
188	C₂×Dic₄₃	C₂⁴	1	4	yes	—
189	C₂×Dic₄₃	C₂⁴	1	2	yes	—
190	D₁₇₂	—	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	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	—	2	2	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	4	4	no	—
207	C₂²×C₄₃	C₂×#41	1	2	yes	—
208	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
209	C₂×D₄₃	—	2	2	no	—
210	C₂×D₄₃	—	2	2	no	—
211	C₂×D₄₃	—	2	2	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	C₂×#41	1	2	yes	—
218	C₄×C₄₃	C₂×#41	1	2	yes	—
219	Dic₄₃	—	2	2	no	—
220	Dic₄₃	—	2	2	no	—
221	Dic₄₃	—	2	4	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	—	4	1	no	—
228	C₂×C₄₃	—	4	1	no	—
229	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
230	C₂×C₄₃	#585	1	1	yes	characteristic
231	C₂×C₄₃	#585	1	1	yes	characteristic
232	D₄₃	—	4	2	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	D₄₃	1	1	yes	characteristic, complemented
247	#520	—	43	1	no	—
248	#520	—	43	1	no	—
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	C₂×D₄₃	1	1	yes	characteristic
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	4	no	—
267	#123	—	43	2	no	—
268	#123	—	43	4	no	—
269	#123	C₂×D₄₃	1	2	yes	—
270	C₂²⋊Q₈	—	43	2	no	—
271	C₂²⋊Q₈	—	43	1	no	—
272	C₂²⋊Q₈	—	43	1	no	—
273	C₂²⋊Q₈	—	43	2	no	—
274	C₂²⋊Q₈	—	43	4	no	—
275	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
276	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
277	#121	—	43	4	no	—
278	#121	—	43	2	no	—
279	#121	—	43	4	no	—
280	#121	—	43	4	no	—
281	#121	—	43	1	no	—
282	#121	—	43	1	no	—
283	#121	—	43	2	no	—
284	#121	C₂×D₄₃	1	1	yes	characteristic
285	#121	C₂×D₄₃	1	1	yes	characteristic
286	#120	—	43	2	no	—
287	#120	C₂×D₄₃	1	2	yes	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	—	43	4	no	—
290	C₄×Q₈	—	43	2	no	—
291	C₄×D₄	—	43	4	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	43	2	no	—
294	C₄×D₄	—	43	2	no	—
295	C₄×D₄	—	43	4	no	—
296	C₄×D₄	—	43	4	no	—
297	C₄×D₄	—	43	2	no	—
298	C₄×D₄	C₂×D₄₃	1	2	yes	—
299	C₄×D₄	C₂×D₄₃	1	2	yes	—
300	#117	—	43	2	no	—
301	#117	—	43	2	no	—
302	#117	—	43	2	no	—
303	#117	—	43	2	no	—
304	#117	—	43	1	no	—
305	#117	—	43	2	no	—
306	#117	—	43	2	no	—
307	#117	—	43	4	no	—
308	#117	—	43	4	no	—
309	#117	C₂×D₄₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	43	1	no	—
311	C₂×C₄⋊C₄	—	43	1	no	—
312	C₂×C₄⋊C₄	—	43	2	no	—
313	C₂×C₄⋊C₄	—	43	2	no	—
314	C₂×C₂²⋊C₄	—	43	2	no	—
315	C₂×C₄²	—	43	2	no	—
316	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
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	C₂²×D₄₃	1	2	yes	—
328	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
329	C₂×D₄	C₂²×D₄₃	1	2	yes	—
330	C₂×D₄	C₂²×D₄₃	1	2	yes	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	43	2	no	—
333	C₂²×C₄	—	43	2	no	—
334	C₂²×C₄	—	43	4	no	—
335	C₂²×C₄	—	43	2	no	—
336	C₂²×C₄	—	43	4	no	—
337	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
344	C₄⋊C₄	—	43	2	no	—
345	C₄⋊C₄	—	43	2	no	—
346	C₄⋊C₄	—	43	1	no	—
347	C₄⋊C₄	—	43	2	no	—
348	C₄⋊C₄	—	43	2	no	—
349	C₄⋊C₄	—	43	4	no	—
350	C₄⋊C₄	—	43	4	no	—
351	C₄⋊C₄	—	43	1	no	—
352	C₄⋊C₄	—	43	2	no	—
353	C₄⋊C₄	—	43	4	no	—
354	C₄⋊C₄	—	43	4	no	—
355	C₄⋊C₄	—	43	2	no	—
356	C₄⋊C₄	—	43	4	no	—
357	C₄⋊C₄	—	43	4	no	—
358	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
362	C₂²⋊C₄	—	43	4	no	—
363	C₂²⋊C₄	—	43	4	no	—
364	C₂²⋊C₄	—	43	2	no	—
365	C₂²⋊C₄	—	43	4	no	—
366	C₂²⋊C₄	—	43	4	no	—
367	C₂²⋊C₄	—	43	2	no	—
368	C₂²⋊C₄	—	43	2	no	—
369	C₂²⋊C₄	—	43	2	no	—
370	C₂²⋊C₄	—	43	4	no	—
371	C₂²⋊C₄	—	43	4	no	—
372	C₂²⋊C₄	—	43	2	no	—
373	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
375	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
378	C₄²	—	43	4	no	—
379	C₄²	—	43	4	no	—
380	C₄²	—	43	4	no	—
381	C₄²	—	43	4	no	—
382	C₄²	—	43	2	no	—
383	C₄²	C₂²×D₄₃	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	43	2	no	—
388	C₂³	C₂³×D₄₃	1	1	yes	characteristic
389	C₂³	C₂³×D₄₃	1	1	yes	characteristic
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	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	86	4	no	—
400	D₄	—	86	2	no	—
401	D₄	—	172	2	no	—
402	D₄	—	172	4	no	—
403	D₄	—	172	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	43	4	no	—
411	C₂×C₄	—	43	2	no	—
412	C₂×C₄	—	43	2	no	—
413	C₂×C₄	—	43	4	no	—
414	C₂×C₄	—	43	2	no	—
415	C₂×C₄	—	86	4	no	—
416	C₂×C₄	—	172	4	no	—
417	C₂×C₄	—	172	2	no	—
418	C₂×C₄	—	172	4	no	—
419	C₂×C₄	—	172	2	no	—
420	C₂×C₄	#10621900	1	4	yes	—
421	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
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	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	86	2	no	—
441	C₂²	—	86	2	no	—
442	C₂²	—	86	2	no	—
443	C₂²	C₂×#10621900	1	2	yes	—
444	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	86	2	no	—
451	C₄	—	86	4	no	—
452	C₄	—	86	2	no	—
453	C₄	—	86	4	no	—
454	C₄	—	86	2	no	—
455	C₄	C₂×#10621900	1	2	yes	—
456	C₄	C₂×#10621900	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	4	1	no	—
459	C₂	—	4	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	172	2	no	—
462	C₂	C₂²×#10621900	1	1	yes	characteristic
463	C₂	#14583735	1	1	yes	characteristic
464	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#525	C₂
hypercenter	#525	D₄₃
hypocenter	C₄₃	#3493
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #14583620	C₂	semidirect
2. #14583619	C₂	semidirect
3. #14583614	C₂	semidirect
4. #14583613	C₂	semidirect
5. #14583596	C₂	semidirect
6. #14583595	C₂	semidirect
7. #14583589	C₂	semidirect
8. #14583583	C₂	semidirect
9. #14583527	C₂	semidirect
10. #14583484	C₂	semidirect
11. #14583477	C₂	semidirect
12. #14583426	C₂	semidirect
13. #14583410	C₂	semidirect
14. #14583382	C₂	semidirect
15. #14583379	C₂	semidirect
16. C₂×#13063284	C₂	semidirect
17. C₄₃×#525	C₂	semidirect
19. #13063325	C₂²	semidirect
20. #13063324	C₂²	semidirect
21. #13063320	C₂²	semidirect
24. #13063318	C₂²	semidirect
25. #13063317	C₂²	semidirect
26. #13063316	C₂²	semidirect
27. #13063315	C₂²	semidirect
30. #13063311	C₂²	semidirect
36. #13063304	C₂²	semidirect
38. #13063301	C₂²	semidirect
41. #13063299	C₂²	semidirect
45. #13063296	C₂²	semidirect
47. Q₈×Dic₄₃	C₂²	semidirect
48. C₄×Dic₈₆	C₂²	semidirect
49. #13063290	C₂²	semidirect
50. C₄×D₁₇₂	C₂²	semidirect
52. D₄×Dic₄₃	C₂²	semidirect
56. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
62. #13063284	C₂²	semidirect
63. #13063283	C₂²	semidirect
64. #13063283	C₂²	semidirect
65. #13063281	C₂²	semidirect
68. C₂×C₄⋊Dic₄₃	C₂²	semidirect
69. C₄⋊C₄×D₄₃	C₂²	semidirect
246. #525	D₄₃	semidirect
250. C₄₃	#3493	semidirect