Subgroups — #19148298

Order 5504.

1124 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583609	C₂	1	2	yes	maximal, complemented
2	#14583604	C₂	1	2	yes	maximal, complemented
3	#14583599	C₂	1	2	yes	maximal, complemented
4	#14583593	C₂	1	2	yes	maximal, complemented
5	#14583590	C₂	1	2	yes	maximal, complemented
6	#14583588	C₂	1	2	yes	maximal, complemented
7	#14583554	C₂	1	2	yes	maximal, complemented
8	#14583550	C₂	1	2	yes	maximal, complemented
9	#14583527	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583491	C₂	1	4	yes	maximal, complemented
11	#14583477	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583411	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583408	C₂	1	4	yes	maximal, complemented
14	#14583406	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₄₃	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	C₂×#10621898	C₂²	1	4	yes	—
20	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
22	#13063325	C₂²	1	2	yes	complemented
23	#13063324	C₂²	1	2	yes	complemented
24	#13063319	C₂²	1	4	yes	complemented
25	#13063318	C₂²	1	4	yes	complemented
26	#13063317	C₂²	1	4	yes	complemented
27	#13063317	C₂²	1	2	yes	complemented
28	#13063316	C₂²	1	2	yes	complemented
29	#13063315	C₂²	1	4	yes	complemented
30	#13063310	C₂²	1	4	yes	—
31	#13063309	C₂²	1	2	yes	—
32	#13063308	C₂²	1	4	yes	complemented
33	#13063307	C₂²	1	4	yes	—
34	#13063307	C₂²	1	4	yes	complemented
35	#13063306	C₂²	1	2	yes	—
36	#13063305	C₂²	1	1	yes	characteristic
37	#13063305	C₂²	1	1	yes	characteristic
38	#13063304	C₂²	1	4	yes	complemented
39	#13063304	C₂²	1	2	yes	complemented
40	#13063303	C₂²	1	4	yes	—
41	#13063303	C₂²	1	4	yes	complemented
42	#13063302	C₂²	1	4	yes	—
43	#13063301	C₂²	1	1	yes	characteristic
44	#13063301	C₂²	1	1	yes	characteristic
45	#13063301	C₂²	1	2	yes	complemented
46	#13063300	C₂²	1	1	yes	characteristic
47	#13063300	C₂²	1	1	yes	characteristic
48	#13063299	C₂²	1	2	yes	complemented
49	#13063298	C₂²	1	4	yes	—
50	#13063297	C₂²	1	4	yes	—
51	#13063296	C₂²	1	1	yes	characteristic
52	#13063296	C₂²	1	1	yes	characteristic
53	#13063296	C₂²	1	2	yes	complemented
54	#13063295	C₂²	1	2	yes	—
55	#13063293	C₂²	1	2	yes	—
56	#13063290	C₂²	1	2	yes	complemented
57	C₄×D₁₇₂	C₂²	1	2	yes	—
58	C₄×D₁₇₂	C₂²	1	4	yes	—
59	C₄×D₁₇₂	C₂²	1	2	yes	—
60	#13063287	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
64	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
65	#13063284	C₂²	1	1	yes	characteristic
66	#13063283	C₂²	1	2	yes	complemented
67	#13063282	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
69	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
70	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
71	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
72	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
73	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
74	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
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	#10621898	—	4	8	no	—
100	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
101	C₂×D₁₇₂	C₂³	1	2	yes	—
102	C₂×D₁₇₂	C₂³	1	2	yes	—
103	C₂×C₄×D₄₃	—	2	4	no	—
104	C₂×C₄×D₄₃	—	4	4	no	—
105	C₂×C₄×D₄₃	C₂³	1	4	yes	—
106	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₄₃	C₂³	1	2	yes	—
111	C₂×C₄×D₄₃	C₂³	1	4	yes	—
112	C₂×C₄×D₄₃	C₂³	1	4	yes	—
113	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
114	C₂×Dic₈₆	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
119	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
120	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
122	C₄²×C₄₃	C₂³	1	2	yes	—
123	C₄²×C₄₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
136	C₄⋊Dic₄₃	C₂³	1	2	yes	—
137	C₄⋊Dic₄₃	C₂³	1	2	yes	—
138	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₄₃	C₂³	1	4	yes	—
141	C₄⋊Dic₄₃	C₂³	1	2	yes	—
142	C₄⋊Dic₄₃	C₂³	1	2	yes	—
143	Dic₄₃⋊C₄	C₂³	1	4	yes	—
144	Dic₄₃⋊C₄	C₂³	1	4	yes	—
145	Dic₄₃⋊C₄	C₂³	1	4	yes	—
146	Dic₄₃⋊C₄	C₂³	1	4	yes	—
147	Dic₄₃⋊C₄	C₂³	1	4	yes	—
148	Dic₄₃⋊C₄	C₂³	1	2	yes	—
149	Dic₄₃⋊C₄	C₂³	1	2	yes	—
150	Dic₄₃⋊C₄	C₂³	1	4	yes	—
151	C₄×Dic₄₃	C₂³	1	4	yes	—
152	C₄×Dic₄₃	C₂³	1	2	yes	—
153	C₂³×C₄₃	C₂⁴	1	2	yes	—
154	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	2	no	—
156	C₂²×D₄₃	—	2	2	no	—
157	C₂²×D₄₃	—	2	2	no	—
158	C₂²×D₄₃	C₂⁴	1	2	yes	—
159	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
160	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	2	4	no	—
163	D₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	4	no	—
167	C₂×C₄×C₄₃	#41	1	4	yes	complemented
168	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
169	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₄₃	—	2	4	no	—
175	C₂²⋊D₄₃	—	2	4	no	—
176	C₂²⋊D₄₃	—	2	4	no	—
177	C₂²⋊D₄₃	—	4	4	no	—
178	C₂×Dic₄₃	—	2	2	no	—
179	C₂×Dic₄₃	—	4	2	no	—
180	C₂×Dic₄₃	C₂⁴	1	2	yes	—
181	C₂×Dic₄₃	C₂⁴	1	2	yes	—
182	C₂×Dic₄₃	C₂⁴	1	2	yes	—
183	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₄₃	C₂⁴	1	4	yes	—
186	D₁₇₂	—	2	4	no	—
187	D₁₇₂	—	2	4	no	—
188	D₁₇₂	—	2	2	no	—
189	C₄×D₄₃	—	2	8	no	—
190	C₄×D₄₃	—	2	2	no	—
191	C₄×D₄₃	—	2	2	no	—
192	C₄×D₄₃	—	2	2	no	—
193	C₄×D₄₃	—	2	2	no	—
194	C₄×D₄₃	—	2	4	no	—
195	C₄×D₄₃	—	4	4	no	—
196	C₄×D₄₃	—	4	4	no	—
197	Dic₈₆	—	2	2	no	—
198	Dic₈₆	—	4	4	no	—
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	C₂×#41	1	2	yes	—
205	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₄₃	—	2	8	no	—
207	C₂×D₄₃	—	2	1	no	—
208	C₂×D₄₃	—	2	1	no	—
209	C₂×D₄₃	—	2	1	no	—
210	C₂×D₄₃	—	2	1	no	—
211	C₂×D₄₃	—	2	2	no	—
212	C₂×D₄₃	—	2	2	no	—
213	C₂×D₄₃	—	2	2	no	—
214	C₂×D₄₃	H(5,𝔽₂)	1	2	yes	—
215	C₂×D₄₃	2₋¹⁺⁴	1	2	yes	—
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	4	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	C₂×#41	1	2	yes	—
221	C₄×C₄₃	C₂×#41	1	2	yes	—
222	Dic₄₃	—	2	2	no	—
223	Dic₄₃	—	2	1	no	—
224	Dic₄₃	—	2	1	no	—
225	Dic₄₃	—	2	2	no	—
226	Dic₄₃	—	2	4	no	—
227	Dic₄₃	—	2	2	no	—
228	#3492	—	43	1	no	maximal, Sylow
229	C₂×C₄₃	—	2	2	no	—
230	C₂×C₄₃	—	4	2	no	—
231	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
232	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
234	D₄₃	—	2	2	no	—
235	D₄₃	—	2	2	no	—
236	D₄₃	—	4	2	no	—
237	#554	—	43	2	no	—
238	#554	—	43	2	no	—
239	#553	—	43	2	no	—
240	#553	—	43	2	no	—
241	#552	—	43	2	no	—
242	#552	—	43	2	no	—
243	#547	—	43	2	no	—
244	#547	—	43	2	no	—
245	#544	—	43	1	no	—
246	#539	—	43	4	no	—
247	#537	—	43	1	no	—
248	#525	—	43	1	no	—
249	#525	—	43	4	no	—
250	#525	—	43	1	no	—
251	#520	—	43	1	no	—
252	#520	D₄₃	1	1	yes	characteristic, complemented
253	C₂²×C₄⋊C₄	—	43	1	no	—
254	C₄₃	#3492	1	1	yes	characteristic, complemented, Sylow
255	C₂×#41	—	43	1	no	—
256	C₂×#41	—	43	4	no	—
257	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
258	C₂³×C₄	—	43	1	no	—
259	C₂³×C₄	—	43	2	no	—
260	C₄⋊Q₈	—	43	2	no	—
261	C₄⋊Q₈	—	43	2	no	—
262	#126	—	43	4	no	—
263	#126	—	43	4	no	—
264	#125	—	43	4	no	—
265	#125	—	43	2	no	—
266	#125	—	43	4	no	—
267	#125	—	43	2	no	—
268	#123	—	43	2	no	—
269	#123	—	43	4	no	—
270	#123	—	43	4	no	—
271	#123	—	43	2	no	—
272	#123	—	43	4	no	—
273	#123	—	43	4	no	—
274	C₂²⋊Q₈	—	43	1	no	—
275	C₂²⋊Q₈	—	43	1	no	—
276	C₂²⋊Q₈	—	43	2	no	—
277	C₂²⋊Q₈	—	43	2	no	—
278	C₂²⋊Q₈	—	43	4	no	—
279	C₂²⋊Q₈	—	43	1	no	—
280	C₂²⋊Q₈	—	43	4	no	—
281	C₂²⋊Q₈	—	43	1	no	—
282	C₂²⋊Q₈	—	43	4	no	—
283	C₂²⋊Q₈	—	43	4	no	—
284	#121	—	43	4	no	—
285	#121	—	43	1	no	—
286	#121	—	43	1	no	—
287	#121	—	43	2	no	—
288	#121	—	43	2	no	—
289	#121	—	43	1	no	—
290	#121	—	43	1	no	—
291	#121	—	43	4	no	—
292	#120	—	43	2	no	—
293	#120	—	43	2	no	—
294	C₄×Q₈	—	43	2	no	—
295	C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
296	C₄×D₄	—	43	4	no	—
297	C₄×D₄	—	43	2	no	—
298	C₄×D₄	—	43	4	no	—
299	C₄×D₄	—	43	2	no	—
300	C₄×D₄	—	43	2	no	—
301	C₄×D₄	—	43	2	no	—
302	C₄×D₄	—	43	4	no	—
303	C₄×D₄	—	43	2	no	—
304	C₄×D₄	C₂×D₄₃	1	4	yes	—
305	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
306	#117	—	43	1	no	—
307	#117	—	43	2	no	—
308	#117	—	43	4	no	—
309	#117	C₂×D₄₃	1	1	yes	characteristic
310	#117	C₂×D₄₃	1	2	yes	complemented
311	C₂×C₄⋊C₄	—	43	1	no	—
312	C₂×C₄⋊C₄	—	43	2	no	—
313	C₂×C₄⋊C₄	—	43	2	no	—
314	C₂×C₄⋊C₄	—	43	2	no	—
315	C₂×C₄⋊C₄	—	43	2	no	—
316	C₂×C₄⋊C₄	—	43	2	no	—
317	C₂×C₄⋊C₄	—	43	2	no	—
318	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	complemented
320	C₂⁴	—	43	1	no	—
321	#41	—	2	4	no	—
322	#41	—	86	4	no	—
323	#41	—	172	8	no	—
324	C₂×Q₈	—	43	1	no	—
325	C₂×Q₈	—	43	4	no	—
326	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
327	C₂×D₄	—	43	2	no	—
328	C₂×D₄	—	43	2	no	—
329	C₂×D₄	—	43	2	no	—
330	C₂×D₄	—	43	4	no	—
331	C₂×D₄	—	43	2	no	—
332	C₂×D₄	—	43	1	no	—
333	C₂×D₄	—	43	2	no	—
334	C₂×D₄	C₂²×D₄₃	1	2	yes	—
335	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	43	2	no	—
338	C₂²×C₄	—	43	4	no	—
339	C₂²×C₄	—	43	1	no	—
340	C₂²×C₄	—	43	1	no	—
341	C₂²×C₄	—	43	1	no	—
342	C₂²×C₄	—	43	1	no	—
343	C₂²×C₄	—	43	2	no	—
344	C₂²×C₄	—	43	4	no	—
345	C₂²×C₄	—	43	4	no	—
346	C₂²×C₄	—	86	4	no	—
347	C₂²×C₄	—	172	4	no	—
348	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
349	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
350	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
351	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
352	C₄⋊C₄	—	43	2	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	—	43	4	no	—
355	C₄⋊C₄	—	43	4	no	—
356	C₄⋊C₄	—	43	1	no	—
357	C₄⋊C₄	—	43	4	no	—
358	C₄⋊C₄	—	43	1	no	—
359	C₄⋊C₄	—	43	4	no	—
360	C₄⋊C₄	—	43	4	no	—
361	C₄⋊C₄	—	43	2	no	—
362	C₄⋊C₄	—	43	2	no	—
363	C₄⋊C₄	—	43	4	no	—
364	C₄⋊C₄	—	43	4	no	—
365	C₄⋊C₄	—	43	2	no	—
366	C₄⋊C₄	—	43	2	no	—
367	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
368	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
369	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
371	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
372	C₂²⋊C₄	—	43	2	no	—
373	C₂²⋊C₄	—	43	4	no	—
374	C₂²⋊C₄	—	43	2	no	—
375	C₂²⋊C₄	—	43	2	no	—
376	C₂²⋊C₄	—	43	2	no	—
377	C₂²⋊C₄	—	43	2	no	—
378	C₂²⋊C₄	—	43	4	no	—
379	C₂²⋊C₄	—	43	2	no	—
380	C₂²⋊C₄	—	43	2	no	—
381	C₂²⋊C₄	—	43	4	no	—
382	C₂²⋊C₄	—	43	2	no	—
383	C₂²⋊C₄	—	43	2	no	—
384	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
386	C₄²	—	43	4	no	—
387	C₄²	—	43	2	no	—
388	C₄²	C₂²×D₄₃	1	4	yes	—
389	C₄²	C₂²×D₄₃	1	2	yes	—
390	C₂³	—	43	1	no	—
391	C₂³	—	43	1	no	—
392	C₂³	—	43	2	no	—
393	C₂³	—	86	2	no	—
394	C₂³	—	86	2	no	—
395	C₂³	—	86	2	no	—
396	C₂³	C₂³×D₄₃	1	2	yes	—
397	C₂³	C₂³×D₄₃	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	86	2	no	—
400	Q₈	—	172	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	2	no	—
403	D₄	—	86	4	no	—
404	D₄	—	86	4	no	—
405	D₄	—	86	4	no	—
406	D₄	—	86	4	no	—
407	D₄	—	86	4	no	—
408	D₄	—	86	2	no	—
409	D₄	—	172	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	43	2	no	—
414	C₂×C₄	—	43	2	no	—
415	C₂×C₄	—	43	2	no	—
416	C₂×C₄	—	43	1	no	—
417	C₂×C₄	—	43	1	no	—
418	C₂×C₄	—	43	4	no	—
419	C₂×C₄	—	86	8	no	—
420	C₂×C₄	—	86	2	no	—
421	C₂×C₄	—	86	2	no	—
422	C₂×C₄	—	86	2	no	—
423	C₂×C₄	—	86	2	no	—
424	C₂×C₄	—	86	2	no	—
425	C₂×C₄	—	86	4	no	—
426	C₂×C₄	—	172	4	no	—
427	C₂×C₄	—	172	4	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	#10621898	1	4	yes	complemented
430	C₂×C₄	C₂³×D₄₃	1	4	yes	—
431	C₂×C₄	C₂³×D₄₃	1	2	yes	—
432	C₂×C₄	C₂³×D₄₃	1	2	yes	—
433	C₂×C₄	C₂³×D₄₃	1	2	yes	—
434	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	43	2	no	—
442	C₂²	—	43	2	no	—
443	C₂²	—	86	8	no	—
444	C₂²	—	86	1	no	—
445	C₂²	—	86	1	no	—
446	C₂²	—	86	1	no	—
447	C₂²	—	86	1	no	—
448	C₂²	—	86	2	no	—
449	C₂²	—	86	2	no	—
450	C₂²	—	86	2	no	—
451	C₂²	C₂×#10621898	1	2	yes	—
452	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	86	1	no	—
458	C₄	—	86	1	no	—
459	C₄	—	86	2	no	—
460	C₄	—	86	4	no	—
461	C₄	—	86	2	no	—
462	C₄	—	86	2	no	—
463	C₄	C₂×#10621898	1	2	yes	—
464	C₄	C₂×#10621898	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	4	2	no	—
467	C₂	—	86	2	no	—
468	C₂	—	86	2	no	—
469	C₂	—	172	2	no	—
470	C₂	C₂²×#10621898	1	1	yes	characteristic
471	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
472	C₂	2₋¹⁺⁴×D₄₃	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	#3492
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. #14583609	C₂	semidirect
2. #14583604	C₂	semidirect
3. #14583599	C₂	semidirect
4. #14583593	C₂	semidirect
5. #14583590	C₂	semidirect
6. #14583588	C₂	semidirect
7. #14583554	C₂	semidirect
8. #14583550	C₂	semidirect
9. #14583527	C₂	semidirect
10. #14583491	C₂	semidirect
11. #14583477	C₂	semidirect
12. #14583411	C₂	semidirect
13. #14583408	C₂	semidirect
14. #14583406	C₂	semidirect
15. #14583380	C₂	semidirect
16. C₂×C₄⋊C₄×D₄₃	C₂	semidirect
17. C₄₃×#520	C₂	semidirect
22. #13063325	C₂²	semidirect
23. #13063324	C₂²	semidirect
24. #13063319	C₂²	semidirect
25. #13063318	C₂²	semidirect
26. #13063317	C₂²	semidirect
27. #13063317	C₂²	semidirect
28. #13063316	C₂²	semidirect
29. #13063315	C₂²	semidirect
32. #13063308	C₂²	semidirect
34. #13063307	C₂²	semidirect
38. #13063304	C₂²	semidirect
39. #13063304	C₂²	semidirect
41. #13063303	C₂²	semidirect
45. #13063301	C₂²	semidirect
48. #13063299	C₂²	semidirect
53. #13063296	C₂²	semidirect
56. #13063290	C₂²	semidirect
60. #13063287	C₂²	semidirect
66. #13063283	C₂²	semidirect
74. 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
167. C₂×C₄×C₄₃	#41	semidirect
252. #520	D₄₃	semidirect
254. C₄₃	#3492	semidirect
295. C₄×Q₈	C₂×D₄₃	semidirect
305. C₄×D₄	C₂×D₄₃	semidirect
310. #117	C₂×D₄₃	semidirect
319. C₂×C₄⋊C₄	C₂×D₄₃	semidirect
429. C₂×C₄	#10621898	semidirect