Subgroups — #19148429

Order 5504.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583601	C₂	1	2	yes	maximal, complemented
2	#14583592	C₂	1	4	yes	maximal, complemented
3	#14583584	C₂	1	2	yes	maximal, complemented
4	#14583575	C₂	1	4	yes	maximal, complemented
5	#14583555	C₂	1	2	yes	maximal, complemented
6	#14583543	C₂	1	2	yes	maximal, complemented
7	#14583494	C₂	1	2	yes	maximal, complemented
8	#14583486	C₂	1	2	yes	maximal, complemented
9	#14583458	C₂	1	2	yes	maximal, complemented
10	#14583430	C₂	1	2	yes	maximal, complemented
11	#14583409	C₂	1	2	yes	maximal, complemented
12	C₂×#13063304	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583374	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621900	C₂²	1	2	yes	complemented
17	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
20	#13063320	C₂²	1	4	yes	complemented
21	#13063318	C₂²	1	4	yes	complemented
22	#13063318	C₂²	1	4	yes	complemented
23	#13063316	C₂²	1	2	yes	complemented
24	#13063315	C₂²	1	4	yes	complemented
25	#13063312	C₂²	1	2	yes	complemented
26	#13063311	C₂²	1	4	yes	complemented
27	#13063309	C₂²	1	4	yes	complemented
28	#13063308	C₂²	1	4	yes	—
29	#13063307	C₂²	1	4	yes	complemented
30	#13063306	C₂²	1	4	yes	complemented
31	#13063306	C₂²	1	4	yes	complemented
32	#13063305	C₂²	1	2	yes	complemented
33	#13063304	C₂²	1	2	yes	complemented
34	#13063304	C₂²	1	2	yes	complemented
35	#13063304	C₂²	1	2	yes	complemented
36	#13063304	C₂²	1	2	yes	complemented
37	#13063302	C₂²	1	4	yes	complemented
38	#13063297	C₂²	1	4	yes	complemented
39	#13063297	C₂²	1	4	yes	complemented
40	#13063297	C₂²	1	4	yes	complemented
41	#13063296	C₂²	1	2	yes	complemented
42	#13063294	C₂²	1	4	yes	—
43	#13063293	C₂²	1	4	yes	complemented
44	#13063290	C₂²	1	2	yes	complemented
45	D₄×Dic₄₃	C₂²	1	4	yes	complemented
46	D₄×Dic₄₃	C₂²	1	4	yes	complemented
47	D₄×Dic₄₃	C₂²	1	2	yes	complemented
48	D₄×Dic₄₃	C₂²	1	4	yes	complemented
49	D₄×Dic₄₃	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
54	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
55	#13063284	C₂²	1	4	yes	complemented
56	#13063283	C₂²	1	2	yes	complemented
57	#13063281	C₂²	1	4	yes	complemented
58	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	complemented
60	C₂×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
63	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	complemented
64	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
66	C₂²×D₄×C₄₃	C₂²	1	2	yes	—
67	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
68	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
69	#121×C₄₃	C₂²	1	2	yes	—
70	#121×C₄₃	C₂²	1	2	yes	—
71	#121×C₄₃	C₂²	1	2	yes	complemented
72	#121×C₄₃	C₂²	1	2	yes	complemented
73	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	complemented
75	C₂⁴×C₄₃	C₂³	1	2	yes	—
76	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
77	C₂³×D₄₃	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₄₃	—	2	8	no	—
79	C₂×D₄×C₄₃	—	4	2	no	—
80	C₂×D₄×C₄₃	C₂³	1	4	yes	—
81	C₂×D₄×C₄₃	C₂³	1	2	yes	—
82	C₂×D₄×C₄₃	C₂³	1	4	yes	—
83	C₂×D₄×C₄₃	C₂³	1	2	yes	—
84	C₂²×C₄×C₄₃	—	4	2	no	—
85	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₄₃	—	2	4	no	—
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	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
97	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
98	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
99	C₂²×Dic₄₃	C₂³	1	2	yes	—
100	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
101	C₂²×Dic₄₃	C₂³	1	2	yes	—
102	C₂²×Dic₄₃	C₂³	1	4	yes	—
103	C₂²×Dic₄₃	C₂³	1	4	yes	—
104	#10621900	—	4	4	no	—
105	C₂×C₄×D₄₃	—	4	2	no	—
106	C₂×C₄×D₄₃	C₂³	1	2	yes	—
107	C₂×C₄×D₄₃	C₂³	1	2	yes	—
108	C₂×Dic₈₆	—	4	2	no	—
109	C₂×Dic₈₆	C₂³	1	2	yes	—
110	C₂×Dic₈₆	C₂³	1	2	yes	—
111	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
112	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
114	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
116	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
117	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
119	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
120	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
122	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
123	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
127	C₄⋊Dic₄₃	C₂³	1	2	yes	—
128	C₄⋊Dic₄₃	C₂³	1	2	yes	—
129	C₄⋊Dic₄₃	C₂³	1	4	yes	—
130	C₄⋊Dic₄₃	C₂³	1	4	yes	—
131	Dic₄₃⋊C₄	C₂³	1	4	yes	—
132	Dic₄₃⋊C₄	C₂³	1	2	yes	—
133	Dic₄₃⋊C₄	C₂³	1	2	yes	—
134	Dic₄₃⋊C₄	C₂³	1	4	yes	—
135	Dic₄₃⋊C₄	C₂³	1	4	yes	—
136	Dic₄₃⋊C₄	C₂³	1	4	yes	—
137	C₄×Dic₄₃	C₂³	1	2	yes	—
138	C₄×Dic₄₃	C₂³	1	2	yes	—
139	C₄×Dic₄₃	C₂³	1	4	yes	—
140	C₄×Dic₄₃	C₂³	1	4	yes	—
141	C₂³×C₄₃	—	2	4	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	#41	1	4	yes	complemented
147	C₂³×C₄₃	C₂⁴	1	4	yes	—
148	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
150	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂²×D₄₃	—	2	2	no	—
152	C₂²×D₄₃	—	4	1	no	—
153	C₂²×D₄₃	—	4	1	no	—
154	C₂²×D₄₃	C₂⁴	1	2	yes	—
155	D₄×C₄₃	—	2	8	no	—
156	D₄×C₄₃	—	2	8	no	—
157	D₄×C₄₃	—	2	4	no	—
158	D₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
168	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₄₃	—	2	4	no	—
172	C₂²⋊D₄₃	—	2	4	no	—
173	C₂²⋊D₄₃	—	4	4	no	—
174	C₂²⋊D₄₃	—	4	4	no	—
175	C₂×Dic₄₃	—	2	2	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	4	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	4	no	—
181	C₂×Dic₄₃	—	4	2	no	—
182	C₂×Dic₄₃	C₂⁴	1	2	yes	—
183	C₂×Dic₄₃	C₂⁴	1	2	yes	—
184	C₂×Dic₄₃	C₂⁴	1	2	yes	—
185	C₂×Dic₄₃	C₂⁴	1	4	yes	—
186	C₂×Dic₄₃	C₂⁴	1	4	yes	—
187	C₄×D₄₃	—	2	4	no	—
188	C₄×D₄₃	—	4	2	no	—
189	Dic₈₆	—	2	4	no	—
190	Dic₈₆	—	4	2	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	4	no	—
198	C₂²×C₄₃	—	2	4	no	—
199	C₂²×C₄₃	—	2	4	no	—
200	C₂²×C₄₃	—	4	4	no	—
201	C₂²×C₄₃	—	8	4	no	—
202	C₂²×C₄₃	C₂×#41	1	2	yes	—
203	C₂²×C₄₃	C₂×#41	1	2	yes	—
204	C₂²×C₄₃	C₂×#41	1	2	yes	—
205	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₄₃	—	2	2	no	—
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	2	2	no	—
209	C₂×D₄₃	—	4	4	no	—
210	C₄×C₄₃	—	2	4	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
215	Dic₄₃	—	2	2	no	—
216	Dic₄₃	—	2	4	no	—
217	Dic₄₃	—	2	2	no	—
218	Dic₄₃	—	2	2	no	—
219	Dic₄₃	—	2	4	no	—
220	#3505	—	43	1	no	maximal, Sylow
221	C₂×C₄₃	—	2	2	no	—
222	C₂×C₄₃	—	2	2	no	—
223	C₂×C₄₃	—	2	2	no	—
224	C₂×C₄₃	—	4	4	no	—
225	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄₃	#585	1	1	yes	characteristic
228	D₄₃	—	4	2	no	—
229	#553	—	43	4	no	—
230	#553	—	43	2	no	—
231	#552	—	43	2	no	—
232	#551	—	43	4	no	—
233	#548	—	43	2	no	—
234	#546	—	43	2	no	—
235	#539	—	43	2	no	—
236	#538	—	43	2	no	—
237	#534	—	43	2	no	—
238	#529	—	43	2	no	—
239	#525	—	43	2	no	—
240	C₂×C₂²⋊Q₈	—	43	1	no	—
241	C₂×#121	D₄₃	1	1	yes	characteristic, complemented
242	#518	—	43	2	no	—
243	C₂×C₄×D₄	—	43	1	no	—
244	C₄₃	#3505	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	—	43	2	no	—
246	C₂²×Q₈	—	43	1	no	—
247	C₂²×D₄	—	43	1	no	—
248	C₂²×D₄	C₂×D₄₃	1	2	yes	—
249	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
250	C₂³×C₄	—	43	1	no	—
251	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
252	#126	—	43	4	no	—
253	#126	—	43	4	no	—
254	#126	—	43	4	no	—
255	#125	—	43	2	no	—
256	#125	—	43	4	no	—
257	#124	—	43	2	no	—
258	#124	—	43	4	no	—
259	#123	—	43	4	no	—
260	#123	—	43	4	no	—
261	#123	—	43	4	no	—
262	#123	—	43	4	no	—
263	#123	—	43	4	no	—
264	C₂²⋊Q₈	—	43	2	no	—
265	C₂²⋊Q₈	—	43	2	no	—
266	C₂²⋊Q₈	—	43	2	no	—
267	C₂²⋊Q₈	—	43	2	no	—
268	C₂²⋊Q₈	—	43	2	no	—
269	C₂²⋊Q₈	—	43	4	no	—
270	#121	—	43	2	no	—
271	#121	—	43	4	no	—
272	#121	—	43	4	no	—
273	#121	—	43	4	no	—
274	#121	C₂×D₄₃	1	2	yes	—
275	#121	C₂×D₄₃	1	2	yes	—
276	#121	C₂×D₄₃	1	2	yes	complemented
277	#121	C₂×D₄₃	1	2	yes	complemented
278	#120	—	43	4	no	—
279	#120	—	43	4	no	—
280	C₄×Q₈	—	43	2	no	—
281	C₄×D₄	—	43	4	no	—
282	C₄×D₄	—	43	4	no	—
283	C₄×D₄	—	43	4	no	—
284	C₄×D₄	—	43	4	no	—
285	C₄×D₄	—	43	2	no	—
286	C₄×D₄	—	43	2	no	—
287	C₄×D₄	—	43	2	no	—
288	C₄×D₄	—	43	2	no	—
289	C₄×D₄	—	43	2	no	—
290	C₄×D₄	—	43	4	no	—
291	#117	—	43	4	no	—
292	#117	—	43	2	no	—
293	#117	—	43	4	no	—
294	C₂×C₄⋊C₄	—	43	1	no	—
295	C₂×C₄⋊C₄	—	43	2	no	—
296	C₂×C₄⋊C₄	—	43	1	no	—
297	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
298	C₂×C₂²⋊C₄	—	43	1	no	—
299	C₂×C₂²⋊C₄	—	43	2	no	—
300	C₂×C₂²⋊C₄	—	43	4	no	—
301	C₂×C₂²⋊C₄	—	43	1	no	—
302	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	complemented
303	C₂×C₄²	—	43	1	no	—
304	C₂⁴	—	43	1	no	—
305	C₂⁴	C₂²×D₄₃	1	2	yes	—
306	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
307	#41	—	172	4	no	—
308	C₂×Q₈	—	43	2	no	—
309	C₂×Q₈	—	43	2	no	—
310	C₂×Q₈	—	172	2	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	43	2	no	—
314	C₂×D₄	—	43	2	no	—
315	C₂×D₄	—	43	4	no	—
316	C₂×D₄	—	43	4	no	—
317	C₂×D₄	—	86	4	no	—
318	C₂×D₄	C₂²×D₄₃	1	4	yes	—
319	C₂×D₄	C₂²×D₄₃	1	4	yes	—
320	C₂×D₄	C₂²×D₄₃	1	2	yes	—
321	C₂×D₄	C₂²×D₄₃	1	2	yes	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	43	1	no	—
324	C₂²×C₄	—	43	1	no	—
325	C₂²×C₄	—	43	2	no	—
326	C₂²×C₄	—	43	1	no	—
327	C₂²×C₄	—	43	2	no	—
328	C₂²×C₄	—	43	4	no	—
329	C₂²×C₄	—	43	4	no	—
330	C₂²×C₄	—	43	2	no	—
331	C₂²×C₄	—	43	2	no	—
332	C₂²×C₄	—	172	2	no	—
333	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
335	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
340	C₄⋊C₄	—	43	2	no	—
341	C₄⋊C₄	—	43	4	no	—
342	C₄⋊C₄	—	43	2	no	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	43	2	no	—
346	C₄⋊C₄	—	43	4	no	—
347	C₄⋊C₄	—	43	4	no	—
348	C₄⋊C₄	—	43	4	no	—
349	C₄⋊C₄	—	43	4	no	—
350	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
351	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
352	C₂²⋊C₄	—	43	2	no	—
353	C₂²⋊C₄	—	43	4	no	—
354	C₂²⋊C₄	—	43	2	no	—
355	C₂²⋊C₄	—	43	4	no	—
356	C₂²⋊C₄	—	43	4	no	—
357	C₂²⋊C₄	—	43	4	no	—
358	C₂²⋊C₄	—	43	4	no	—
359	C₂²⋊C₄	—	43	4	no	—
360	C₂²⋊C₄	—	43	2	no	—
361	C₂²⋊C₄	—	43	2	no	—
362	C₂²⋊C₄	—	43	4	no	—
363	C₂²⋊C₄	—	43	4	no	—
364	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
365	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
366	C₄²	—	43	2	no	—
367	C₄²	—	43	2	no	—
368	C₄²	—	43	4	no	—
369	C₄²	—	43	4	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	43	2	no	—
376	C₂³	—	86	2	no	—
377	C₂³	—	172	1	no	—
378	C₂³	—	172	1	no	—
379	C₂³	#10621900	1	4	yes	complemented
380	C₂³	C₂³×D₄₃	1	4	yes	—
381	C₂³	C₂³×D₄₃	1	1	yes	characteristic
382	C₂³	C₂³×D₄₃	1	1	yes	characteristic
383	C₂³	C₂³×D₄₃	1	1	yes	characteristic
384	Q₈	—	86	4	no	—
385	Q₈	—	172	2	no	—
386	D₄	—	2	8	no	—
387	D₄	—	2	8	no	—
388	D₄	—	2	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	86	4	no	—
391	D₄	—	86	4	no	—
392	D₄	—	172	4	no	—
393	D₄	—	172	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	43	2	no	—
402	C₂×C₄	—	43	2	no	—
403	C₂×C₄	—	43	2	no	—
404	C₂×C₄	—	43	4	no	—
405	C₂×C₄	—	43	4	no	—
406	C₂×C₄	—	86	2	no	—
407	C₂×C₄	—	86	4	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	172	1	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	4	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	4	no	—
414	C₂×C₄	—	172	2	no	—
415	C₂×C₄	C₂³×D₄₃	1	4	yes	—
416	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
418	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	86	2	no	—
432	C₂²	—	86	2	no	—
433	C₂²	—	86	2	no	—
434	C₂²	—	172	4	no	—
435	C₂²	C₂×#10621900	1	2	yes	—
436	C₂²	C₂×#10621900	1	2	yes	—
437	C₂²	C₂×#10621900	1	2	yes	—
438	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	86	2	no	—
444	C₄	—	86	2	no	—
445	C₄	—	86	4	no	—
446	C₄	—	86	2	no	—
447	C₄	—	86	4	no	—
448	C₄	#13063370	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	4	4	no	—
453	C₂	—	172	2	no	—
454	C₂	C₂²×#10621900	1	1	yes	characteristic
455	C₂	C₂×#13063370	1	1	yes	characteristic
456	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₂×#121×C₄₃	C₂
hypercenter	C₂×#121	D₄₃
hypocenter	C₄₃	#3505
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #14583601	C₂	semidirect
2. #14583592	C₂	semidirect
3. #14583584	C₂	semidirect
4. #14583575	C₂	semidirect
5. #14583555	C₂	semidirect
6. #14583543	C₂	semidirect
7. #14583494	C₂	semidirect
8. #14583486	C₂	semidirect
9. #14583458	C₂	semidirect
10. #14583430	C₂	semidirect
11. #14583409	C₂	semidirect
12. C₂×#13063304	C₂	semidirect
13. #14583374	C₂	semidirect
14. C₂×C₄×C₂²⋊D₄₃	C₂	semidirect
15. C₂×#121×C₄₃	C₂	semidirect
16. C₂×#10621900	C₂²	semidirect
17. C₂²×Dic₈₆	C₂²	semidirect
19. C₂²×C₄×D₄₃	C₂²	semidirect
20. #13063320	C₂²	semidirect
21. #13063318	C₂²	semidirect
22. #13063318	C₂²	semidirect
23. #13063316	C₂²	semidirect
24. #13063315	C₂²	semidirect
25. #13063312	C₂²	semidirect
26. #13063311	C₂²	semidirect
27. #13063309	C₂²	semidirect
29. #13063307	C₂²	semidirect
30. #13063306	C₂²	semidirect
31. #13063306	C₂²	semidirect
32. #13063305	C₂²	semidirect
33. #13063304	C₂²	semidirect
34. #13063304	C₂²	semidirect
35. #13063304	C₂²	semidirect
36. #13063304	C₂²	semidirect
37. #13063302	C₂²	semidirect
38. #13063297	C₂²	semidirect
39. #13063297	C₂²	semidirect
40. #13063297	C₂²	semidirect
41. #13063296	C₂²	semidirect
43. #13063293	C₂²	semidirect
44. #13063290	C₂²	semidirect
45. D₄×Dic₄₃	C₂²	semidirect
46. D₄×Dic₄₃	C₂²	semidirect
47. D₄×Dic₄₃	C₂²	semidirect
48. D₄×Dic₄₃	C₂²	semidirect
49. D₄×Dic₄₃	C₂²	semidirect
52. C₄×C₂²⋊D₄₃	C₂²	semidirect
53. C₄×C₂²⋊D₄₃	C₂²	semidirect
54. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
55. #13063284	C₂²	semidirect
56. #13063283	C₂²	semidirect
57. #13063281	C₂²	semidirect
58. C₂×C₄⋊Dic₄₃	C₂²	semidirect
59. C₂×Dic₄₃⋊C₄	C₂²	semidirect
60. C₂×Dic₄₃⋊C₄	C₂²	semidirect
63. C₂×C₂²⋊Dic₄₃	C₂²	semidirect
64. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
65. C₂×C₄×Dic₄₃	C₂²	semidirect
67. C₂²×D₄×C₄₃	C₂²	semidirect
71. #121×C₄₃	C₂²	semidirect
72. #121×C₄₃	C₂²	semidirect
73. C₂×C₄⋊C₄×C₄₃	C₂²	semidirect
74. C₂×C₂²⋊C₄×C₄₃	C₂²	semidirect
146. C₂³×C₄₃	#41	semidirect
241. C₂×#121	D₄₃	semidirect
244. C₄₃	#3505	semidirect
249. C₂²×D₄	C₂×D₄₃	semidirect
276. #121	C₂×D₄₃	semidirect
277. #121	C₂×D₄₃	semidirect
297. C₂×C₄⋊C₄	C₂×D₄₃	semidirect
302. C₂×C₂²⋊C₄	C₂×D₄₃	semidirect
379. C₂³	#10621900	semidirect