Subgroups — #19148332

Order 5504.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583614	C₂	1	2	yes	maximal, complemented
2	#14583595	C₂	1	2	yes	maximal, complemented
3	#14583595	C₂	1	2	yes	maximal, complemented
4	#14583572	C₂	1	4	yes	maximal, complemented
5	#14583553	C₂	1	2	yes	maximal, complemented
6	#14583536	C₂	1	4	yes	maximal, complemented
7	#14583527	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583522	C₂	1	2	yes	maximal, complemented
9	#14583502	C₂	1	2	yes	maximal, complemented
10	#14583463	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583444	C₂	1	2	yes	maximal, complemented
12	#14583435	C₂	1	2	yes	maximal, complemented
13	C₂×#13063299	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583382	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583373	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×#10621900	C₂²	1	4	yes	complemented
19	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	—
21	#13063325	C₂²	1	2	yes	complemented
22	#13063324	C₂²	1	2	yes	complemented
23	#13063321	C₂²	1	2	yes	complemented
24	#13063320	C₂²	1	4	yes	complemented
25	#13063320	C₂²	1	4	yes	complemented
26	#13063317	C₂²	1	2	yes	complemented
27	#13063316	C₂²	1	2	yes	complemented
28	#13063314	C₂²	1	2	yes	complemented
29	#13063311	C₂²	1	4	yes	complemented
30	#13063311	C₂²	1	4	yes	complemented
31	#13063309	C₂²	1	4	yes	complemented
32	#13063309	C₂²	1	4	yes	complemented
33	#13063307	C₂²	1	4	yes	complemented
34	#13063307	C₂²	1	4	yes	complemented
35	#13063305	C₂²	1	4	yes	complemented
36	#13063302	C₂²	1	4	yes	—
37	#13063299	C₂²	1	2	yes	—
38	#13063299	C₂²	1	2	yes	—
39	#13063299	C₂²	1	2	yes	—
40	#13063299	C₂²	1	2	yes	—
41	#13063299	C₂²	1	2	yes	complemented
42	#13063299	C₂²	1	2	yes	complemented
43	#13063297	C₂²	1	4	yes	complemented
44	#13063297	C₂²	1	4	yes	complemented
45	#13063296	C₂²	1	4	yes	complemented
46	#13063293	C₂²	1	4	yes	—
47	Q₈×Dic₄₃	C₂²	1	2	yes	complemented
48	C₄×D₁₇₂	C₂²	1	2	yes	complemented
49	C₄×D₁₇₂	C₂²	1	2	yes	complemented
50	D₄×Dic₄₃	C₂²	1	4	yes	—
51	D₄×Dic₄₃	C₂²	1	2	yes	complemented
52	#13063287	C₂²	1	2	yes	complemented
53	#13063287	C₂²	1	2	yes	complemented
54	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
55	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
56	#13063284	C₂²	1	2	yes	—
57	#13063284	C₂²	1	1	yes	characteristic
58	#13063284	C₂²	1	1	yes	characteristic
59	#13063284	C₂²	1	1	yes	characteristic, complemented
60	#13063284	C₂²	1	2	yes	complemented
61	#13063284	C₂²	1	1	yes	characteristic, complemented
62	#13063284	C₂²	1	2	yes	complemented
63	#13063283	C₂²	1	4	yes	complemented
64	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
67	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
69	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
70	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
71	C₂×C₄×Dic₄₃	C₂²	1	2	yes	complemented
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, complemented
76	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
77	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
78	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
79	#120×C₄₃	C₂²	1	2	yes	—
80	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
81	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
82	#117×C₄₃	C₂²	1	1	yes	characteristic
83	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
84	C₂³×D₄₃	C₂³	1	2	yes	—
85	#41×C₄₃	—	2	4	no	—
86	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₄₃	C₂³	1	2	yes	—
88	C₂×D₄×C₄₃	C₂³	1	2	yes	—
89	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₄₃	C₂³	1	2	yes	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊D₄₃	—	4	4	no	—
100	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
104	C₂²×Dic₄₃	C₂³	1	2	yes	—
105	C₂²×Dic₄₃	C₂³	1	2	yes	—
106	C₂²×Dic₄₃	C₂³	1	2	yes	—
107	C₂²×Dic₄₃	C₂³	1	4	yes	—
108	#10621900	—	4	8	no	—
109	C₂×D₁₇₂	—	2	4	no	—
110	C₂×D₁₇₂	C₂³	1	2	yes	—
111	C₂×D₁₇₂	C₂³	1	2	yes	—
112	C₂×C₄×D₄₃	C₂³	1	4	yes	—
113	C₂×C₄×D₄₃	C₂³	1	4	yes	—
114	C₂×Dic₈₆	C₂³	1	4	yes	—
115	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
118	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
119	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
123	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₄²×C₄₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
128	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
129	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
134	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₄₃)⋊C₄	C₂³	1	4	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	1	yes	characteristic
141	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₄₃	C₂³	1	2	yes	—
143	C₄⋊Dic₄₃	C₂³	1	2	yes	—
144	C₄⋊Dic₄₃	C₂³	1	4	yes	—
145	C₄⋊Dic₄₃	C₂³	1	4	yes	—
146	Dic₄₃⋊C₄	C₂³	1	4	yes	—
147	Dic₄₃⋊C₄	C₂³	1	4	yes	—
148	C₄×Dic₄₃	C₂³	1	2	yes	—
149	C₄×Dic₄₃	C₂³	1	2	yes	—
150	C₄×Dic₄₃	C₂³	1	2	yes	—
151	C₄×Dic₄₃	C₂³	1	2	yes	—
152	C₄×Dic₄₃	C₂³	1	4	yes	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₄₃	C₂⁴	1	2	yes	—
158	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
160	C₂²×D₄₃	—	2	4	no	—
161	C₂²×D₄₃	—	4	2	no	—
162	C₂²×D₄₃	—	4	2	no	—
163	C₂²×D₄₃	C₂⁴	1	4	yes	—
164	Q₈×C₄₃	—	2	2	no	—
165	D₄×C₄₃	—	2	4	no	—
166	D₄×C₄₃	—	2	4	no	—
167	D₄×C₄₃	—	2	2	no	—
168	D₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	#41	1	4	yes	complemented
176	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
180	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
183	C₂²⋊D₄₃	—	2	8	no	—
184	C₂²⋊D₄₃	—	4	4	no	—
185	C₂²⋊D₄₃	—	4	4	no	—
186	C₂²⋊D₄₃	—	4	4	no	—
187	C₂×Dic₄₃	—	2	4	no	—
188	C₂×Dic₄₃	—	4	4	no	—
189	C₂×Dic₄₃	—	4	2	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	C₂⁴	1	2	yes	—
192	C₂×Dic₄₃	C₂⁴	1	2	yes	—
193	C₂×Dic₄₃	C₂⁴	1	2	yes	—
194	C₂×Dic₄₃	C₂⁴	1	2	yes	—
195	C₂×Dic₄₃	C₂⁴	1	4	yes	—
196	D₁₇₂	—	2	4	no	—
197	D₁₇₂	—	2	4	no	—
198	C₄×D₄₃	—	4	4	no	—
199	C₄×D₄₃	—	4	4	no	—
200	Dic₈₆	—	4	4	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	—	2	1	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	4	4	no	—
212	C₂²×C₄₃	C₂×#41	1	2	yes	—
213	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
215	C₂×D₄₃	—	2	4	no	—
216	C₂×D₄₃	—	2	4	no	—
217	C₂×D₄₃	—	2	4	no	—
218	C₂×D₄₃	—	8	4	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	2	2	no	—
224	C₄×C₄₃	C₂×#41	1	2	yes	—
225	C₄×C₄₃	C₂×#41	1	2	yes	—
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	2	4	no	—
228	Dic₄₃	—	2	2	no	—
229	Dic₄₃	—	2	2	no	—
230	Dic₄₃	—	2	2	no	—
231	#3494	—	43	1	no	maximal, Sylow
232	C₂×C₄₃	—	2	2	no	—
233	C₂×C₄₃	—	2	2	no	—
234	C₂×C₄₃	—	4	2	no	—
235	C₂×C₄₃	—	4	1	no	—
236	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
237	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄₃	#585	1	1	yes	characteristic
239	D₄₃	—	4	4	no	—
240	#555	—	43	2	no	—
241	#553	—	43	2	no	—
242	#553	—	43	2	no	—
243	#551	—	43	4	no	—
244	#547	—	43	2	no	—
245	#546	—	43	4	no	—
246	#544	—	43	1	no	—
247	#542	—	43	2	no	—
248	#540	—	43	2	no	—
249	#535	—	43	1	no	—
250	#532	—	43	2	no	—
251	#529	—	43	2	no	—
252	#525	D₄₃	1	1	yes	characteristic, complemented
253	C₂×#121	—	43	1	no	—
254	#520	—	43	1	no	—
255	#518	—	43	1	no	—
256	C₂×#117	—	43	1	no	—
257	C₄₃	#3494	1	1	yes	characteristic, complemented, Sylow
258	C₂×#41	—	43	4	no	—
259	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
260	C₂²×D₄	—	43	2	no	—
261	C₂²×D₄	—	43	1	no	—
262	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
263	C₄⋊Q₈	—	43	2	no	—
264	C₄⋊Q₈	—	43	2	no	—
265	#127	—	43	2	no	—
266	#126	—	43	4	no	—
267	#126	—	43	4	no	—
268	#125	—	43	2	no	—
269	#125	—	43	2	no	—
270	#124	—	43	2	no	—
271	#124	—	43	4	no	—
272	#124	—	43	4	no	—
273	#123	—	43	4	no	—
274	#123	—	43	4	no	—
275	#123	—	43	4	no	—
276	#123	—	43	4	no	—
277	#123	C₂×D₄₃	1	2	yes	—
278	C₂²⋊Q₈	—	43	4	no	—
279	C₂²⋊Q₈	—	43	4	no	—
280	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
281	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
282	#121	—	43	4	no	—
283	#121	—	43	4	no	—
284	#121	—	43	4	no	—
285	#121	—	43	2	no	—
286	#121	—	43	2	no	—
287	#121	—	43	2	no	—
288	#121	—	43	2	no	—
289	#121	—	43	2	no	—
290	#121	—	43	2	no	—
291	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
292	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
293	#120	—	43	4	no	—
294	#120	C₂×D₄₃	1	2	yes	—
295	C₄×Q₈	—	43	2	no	—
296	C₄×D₄	—	43	2	no	—
297	C₄×D₄	—	43	4	no	—
298	C₄×D₄	—	43	2	no	—
299	C₄×D₄	—	43	2	no	—
300	C₄×D₄	—	43	4	no	—
301	C₄×D₄	—	43	4	no	—
302	C₄×D₄	—	43	2	no	—
303	C₄×D₄	—	43	2	no	—
304	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
305	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
306	#117	—	43	1	no	—
307	#117	—	43	1	no	—
308	#117	—	43	2	no	—
309	#117	—	43	2	no	—
310	#117	—	43	1	no	—
311	#117	—	43	1	no	—
312	#117	—	43	2	no	—
313	#117	—	43	4	no	—
314	#117	C₂×D₄₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	43	1	no	—
316	C₂×C₄⋊C₄	—	43	1	no	—
317	C₂×C₄⋊C₄	—	43	1	no	—
318	C₂×C₄⋊C₄	—	43	2	no	—
319	C₂×C₂²⋊C₄	—	43	2	no	—
320	C₂×C₂²⋊C₄	—	43	2	no	—
321	C₂×C₂²⋊C₄	—	43	4	no	—
322	C₂×C₄²	—	43	2	no	—
323	C₂⁴	—	43	2	no	—
324	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
325	#41	—	2	4	no	—
326	#41	—	172	8	no	—
327	C₂×Q₈	—	43	4	no	—
328	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
329	C₂×D₄	—	43	4	no	—
330	C₂×D₄	—	43	4	no	—
331	C₂×D₄	—	43	4	no	—
332	C₂×D₄	—	43	4	no	—
333	C₂×D₄	—	43	2	no	—
334	C₂×D₄	—	43	2	no	—
335	C₂×D₄	—	86	4	no	—
336	C₂×D₄	—	172	4	no	—
337	C₂×D₄	C₂²×D₄₃	1	2	yes	—
338	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
339	C₂×D₄	C₂²×D₄₃	1	2	yes	—
340	C₂×D₄	C₂²×D₄₃	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	43	2	no	—
343	C₂²×C₄	—	43	2	no	—
344	C₂²×C₄	—	43	2	no	—
345	C₂²×C₄	—	43	4	no	—
346	C₂²×C₄	—	43	4	no	—
347	C₂²×C₄	—	43	4	no	—
348	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
352	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
355	C₄⋊C₄	—	43	1	no	—
356	C₄⋊C₄	—	43	2	no	—
357	C₄⋊C₄	—	43	1	no	—
358	C₄⋊C₄	—	43	1	no	—
359	C₄⋊C₄	—	43	1	no	—
360	C₄⋊C₄	—	43	2	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	4	no	—
366	C₄⋊C₄	—	43	4	no	—
367	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
368	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
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	4	no	—
376	C₂²⋊C₄	—	43	4	no	—
377	C₂²⋊C₄	—	43	4	no	—
378	C₂²⋊C₄	—	43	4	no	—
379	C₂²⋊C₄	—	43	4	no	—
380	C₂²⋊C₄	—	43	4	no	—
381	C₂²⋊C₄	—	43	4	no	—
382	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
383	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
384	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
387	C₄²	—	43	2	no	—
388	C₄²	—	43	2	no	—
389	C₄²	—	43	2	no	—
390	C₄²	—	43	2	no	—
391	C₄²	—	43	4	no	—
392	C₄²	C₂²×D₄₃	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	43	4	no	—
397	C₂³	—	86	4	no	—
398	C₂³	—	172	2	no	—
399	C₂³	—	172	2	no	—
400	C₂³	C₂³×D₄₃	1	1	yes	characteristic
401	C₂³	C₂³×D₄₃	1	2	yes	—
402	C₂³	C₂³×D₄₃	1	1	yes	characteristic
403	C₂³	C₂³×D₄₃	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	172	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	86	8	no	—
411	D₄	—	86	4	no	—
412	D₄	—	86	4	no	—
413	D₄	—	172	4	no	—
414	D₄	—	172	4	no	—
415	D₄	—	172	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	43	2	no	—
423	C₂×C₄	—	43	2	no	—
424	C₂×C₄	—	43	2	no	—
425	C₂×C₄	—	43	2	no	—
426	C₂×C₄	—	43	4	no	—
427	C₂×C₄	—	86	4	no	—
428	C₂×C₄	—	172	4	no	—
429	C₂×C₄	—	172	4	no	—
430	C₂×C₄	—	172	2	no	—
431	C₂×C₄	—	172	4	no	—
432	C₂×C₄	—	172	2	no	—
433	C₂×C₄	#10621900	1	4	yes	complemented
434	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₄₃	1	2	yes	—
436	C₂×C₄	C₂³×D₄₃	1	2	yes	—
437	C₂×C₄	C₂³×D₄₃	1	2	yes	—
438	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	86	4	no	—
453	C₂²	—	86	4	no	—
454	C₂²	—	86	4	no	—
455	C₂²	—	344	4	no	—
456	C₂²	C₂×#10621900	1	2	yes	—
457	C₂²	#13063371	1	2	yes	—
458	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	86	2	no	—
465	C₄	—	86	2	no	—
466	C₄	—	86	4	no	—
467	C₄	—	86	2	no	—
468	C₄	—	86	2	no	—
469	C₄	C₂×#10621900	1	2	yes	—
470	C₄	C₂×#10621900	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	2	2	no	—
473	C₂	—	4	1	no	—
474	C₂	—	4	2	no	—
475	C₂	—	172	4	no	—
476	C₂	C₂²×#10621900	1	1	yes	characteristic
477	C₂	C₂×#13063371	1	1	yes	characteristic
478	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	#3494
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. #14583614	C₂	semidirect
2. #14583595	C₂	semidirect
3. #14583595	C₂	semidirect
4. #14583572	C₂	semidirect
5. #14583553	C₂	semidirect
6. #14583536	C₂	semidirect
7. #14583527	C₂	semidirect
8. #14583522	C₂	semidirect
9. #14583502	C₂	semidirect
10. #14583463	C₂	semidirect
11. #14583444	C₂	semidirect
12. #14583435	C₂	semidirect
13. C₂×#13063299	C₂	semidirect
14. #14583382	C₂	semidirect
15. #14583373	C₂	semidirect
16. C₂×#13063284	C₂	semidirect
17. C₄₃×#525	C₂	semidirect
18. C₂×#10621900	C₂²	semidirect
21. #13063325	C₂²	semidirect
22. #13063324	C₂²	semidirect
23. #13063321	C₂²	semidirect
24. #13063320	C₂²	semidirect
25. #13063320	C₂²	semidirect
26. #13063317	C₂²	semidirect
27. #13063316	C₂²	semidirect
28. #13063314	C₂²	semidirect
29. #13063311	C₂²	semidirect
30. #13063311	C₂²	semidirect
31. #13063309	C₂²	semidirect
32. #13063309	C₂²	semidirect
33. #13063307	C₂²	semidirect
34. #13063307	C₂²	semidirect
35. #13063305	C₂²	semidirect
41. #13063299	C₂²	semidirect
42. #13063299	C₂²	semidirect
43. #13063297	C₂²	semidirect
44. #13063297	C₂²	semidirect
45. #13063296	C₂²	semidirect
47. Q₈×Dic₄₃	C₂²	semidirect
48. C₄×D₁₇₂	C₂²	semidirect
49. C₄×D₁₇₂	C₂²	semidirect
51. D₄×Dic₄₃	C₂²	semidirect
52. #13063287	C₂²	semidirect
53. #13063287	C₂²	semidirect
54. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
55. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
59. #13063284	C₂²	semidirect
60. #13063284	C₂²	semidirect
61. #13063284	C₂²	semidirect
62. #13063284	C₂²	semidirect
63. #13063283	C₂²	semidirect
65. C₂×C₄⋊Dic₄₃	C₂²	semidirect
66. C₂×C₄⋊Dic₄₃	C₂²	semidirect
67. C₂×C₄⋊Dic₄₃	C₂²	semidirect
71. C₂×C₄×Dic₄₃	C₂²	semidirect
75. C₂²⋊Q₈×C₄₃	C₂²	semidirect
76. C₂²⋊Q₈×C₄₃	C₂²	semidirect
77. #121×C₄₃	C₂²	semidirect
78. #121×C₄₃	C₂²	semidirect
80. C₄×D₄×C₄₃	C₂²	semidirect
81. C₄×D₄×C₄₃	C₂²	semidirect
175. C₂×C₄×C₄₃	#41	semidirect
252. #525	D₄₃	semidirect
257. C₄₃	#3494	semidirect
280. C₂²⋊Q₈	C₂×D₄₃	semidirect
281. C₂²⋊Q₈	C₂×D₄₃	semidirect
291. #121	C₂×D₄₃	semidirect
292. #121	C₂×D₄₃	semidirect
304. C₄×D₄	C₂×D₄₃	semidirect
305. C₄×D₄	C₂×D₄₃	semidirect
433. C₂×C₄	#10621900	semidirect