Subgroups — #19148830

Order 5504.

1270 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583637	C₂	1	4	yes	maximal, complemented
2	#14583601	C₂	1	2	yes	maximal, complemented
3	#14583597	C₂	1	2	yes	maximal, complemented
4	#14583533	C₂	1	2	yes	maximal, complemented
5	D₄×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
6	D₄×C₂²⋊D₄₃	C₂	1	4	yes	maximal, complemented
7	#14583502	C₂	1	2	yes	maximal, complemented
8	#14583487	C₂	1	2	yes	maximal, complemented
9	#14583486	C₂	1	2	yes	maximal, complemented
10	#14583465	C₂	1	2	yes	maximal, complemented
11	#14583461	C₂	1	2	yes	maximal, complemented
12	#14583457	C₂	1	2	yes	maximal, complemented
13	#14583410	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13063299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
20	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
22	#13063321	C₂²	1	4	yes	complemented
23	#13063321	C₂²	1	2	yes	complemented
24	#13063320	C₂²	1	4	yes	complemented
25	#13063318	C₂²	1	4	yes	complemented
26	#13063316	C₂²	1	2	yes	complemented
27	#13063311	C₂²	1	4	yes	complemented
28	#13063310	C₂²	1	4	yes	complemented
29	#13063309	C₂²	1	4	yes	complemented
30	#13063309	C₂²	1	4	yes	complemented
31	#13063308	C₂²	1	2	yes	complemented
32	#13063307	C₂²	1	4	yes	complemented
33	#13063304	C₂²	1	1	yes	characteristic, complemented
34	#13063304	C₂²	1	1	yes	characteristic, complemented
35	#13063300	C₂²	1	2	yes	complemented
36	#13063299	C₂²	1	2	yes	complemented
37	#13063299	C₂²	1	4	yes	complemented
38	#13063299	C₂²	1	2	yes	complemented
39	#13063299	C₂²	1	2	yes	complemented
40	#13063299	C₂²	1	2	yes	complemented
41	#13063299	C₂²	1	1	yes	characteristic, complemented
42	#13063299	C₂²	1	1	yes	characteristic, complemented
43	#13063298	C₂²	1	4	yes	complemented
44	#13063297	C₂²	1	4	yes	complemented
45	#13063297	C₂²	1	4	yes	complemented
46	#13063297	C₂²	1	4	yes	complemented
47	#13063296	C₂²	1	2	yes	complemented
48	#13063296	C₂²	1	4	yes	complemented
49	#13063295	C₂²	1	4	yes	complemented
50	#13063295	C₂²	1	4	yes	complemented
51	#13063294	C₂²	1	2	yes	complemented
52	#13063294	C₂²	1	4	yes	complemented
53	#13063293	C₂²	1	4	yes	complemented
54	#13063293	C₂²	1	4	yes	complemented
55	#13063293	C₂²	1	4	yes	complemented
56	D₄×Dic₄₃	C₂²	1	4	yes	complemented
57	D₄×Dic₄₃	C₂²	1	2	yes	complemented
58	#13063287	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
62	#13063284	C₂²	1	1	yes	characteristic, complemented
63	#13063283	C₂²	1	2	yes	complemented
64	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
66	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₄₃	C₂²	1	2	yes	complemented
68	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	#121×C₄₃	C₂²	1	2	yes	complemented
70	#121×C₄₃	C₂²	1	2	yes	complemented
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	1	yes	characteristic
76	C₂⁴×C₄₃	C₂³	1	2	yes	—
77	C₂³×D₄₃	C₂³	1	2	yes	—
78	C₂³×D₄₃	C₂³	1	4	yes	—
79	C₂×D₄×C₄₃	—	4	4	no	—
80	C₂×D₄×C₄₃	—	4	2	no	—
81	C₂×D₄×C₄₃	C₂³	1	4	yes	—
82	C₂×D₄×C₄₃	C₂³	1	2	yes	—
83	C₂×D₄×C₄₃	C₂³	1	2	yes	—
84	C₂×D₄×C₄₃	C₂³	1	4	yes	—
85	C₂²×C₄×C₄₃	—	4	2	no	—
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	2	yes	—
91	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊D₄₃	—	4	4	no	—
94	C₂×C₂²⋊D₄₃	—	4	8	no	—
95	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
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	4	yes	—
106	D₄×D₄₃	—	4	8	no	—
107	D₄×D₄₃	—	4	4	no	—
108	#10621898	—	4	2	no	—
109	C₂×D₁₇₂	—	4	2	no	—
110	C₂×D₁₇₂	C₂³	1	2	yes	—
111	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
112	C₂×D₁₇₂	C₂³	1	2	yes	—
113	C₂×D₁₇₂	C₂³	1	4	yes	—
114	C₂×C₄×D₄₃	C₂³	1	2	yes	—
115	C₂×C₄×D₄₃	C₂³	1	4	yes	—
116	C₂×Dic₈₆	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	4	yes	—
120	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
121	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
122	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
123	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
133	C₄⋊Dic₄₃	C₂³	1	2	yes	—
134	C₄⋊Dic₄₃	C₂³	1	2	yes	—
135	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₄₃	C₂³	1	4	yes	—
138	Dic₄₃⋊C₄	C₂³	1	2	yes	—
139	Dic₄₃⋊C₄	C₂³	1	4	yes	—
140	Dic₄₃⋊C₄	C₂³	1	2	yes	—
141	C₄×Dic₄₃	C₂³	1	4	yes	—
142	C₄×Dic₄₃	C₂³	1	2	yes	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	4	no	—
146	C₂³×C₄₃	—	4	1	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	C₂⁴	1	4	yes	—
150	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	4	no	—
154	C₂²×D₄₃	—	4	2	no	—
155	C₂²×D₄₃	—	4	4	no	—
156	C₂²×D₄₃	—	4	4	no	—
157	C₂²×D₄₃	—	4	2	no	—
158	C₂²×D₄₃	—	4	4	no	—
159	C₂²×D₄₃	C₂⁴	1	4	yes	—
160	C₂²×D₄₃	C₂⁴	1	2	yes	—
161	D₄×C₄₃	—	2	8	no	—
162	D₄×C₄₃	—	2	4	no	—
163	D₄×C₄₃	—	4	4	no	—
164	D₄×C₄₃	—	4	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	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
173	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂²⋊D₄₃	—	2	4	no	—
178	C₂²⋊D₄₃	—	2	8	no	—
179	C₂²⋊D₄₃	—	2	4	no	—
180	C₂²⋊D₄₃	—	4	2	no	—
181	C₂²⋊D₄₃	—	4	4	no	—
182	C₂²⋊D₄₃	—	4	4	no	—
183	C₂²⋊D₄₃	—	4	4	no	—
184	C₂²⋊D₄₃	—	4	4	no	—
185	C₂²⋊D₄₃	—	4	4	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	4	4	no	—
188	C₂×Dic₄₃	C₂⁴	1	2	yes	—
189	C₂×Dic₄₃	C₂⁴	1	2	yes	—
190	C₂×Dic₄₃	C₂⁴	1	4	yes	—
191	C₂×Dic₄₃	C₂⁴	1	2	yes	—
192	D₁₇₂	—	2	4	no	—
193	D₁₇₂	—	4	2	no	—
194	D₁₇₂	—	4	1	no	—
195	D₁₇₂	—	4	4	no	—
196	C₄×D₄₃	—	2	4	no	—
197	C₄×D₄₃	—	4	4	no	—
198	Dic₈₆	—	4	1	no	—
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	4	no	—
204	C₂²×C₄₃	—	2	4	no	—
205	C₂²×C₄₃	—	2	4	no	—
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	4	4	no	—
210	C₂²×C₄₃	—	8	4	no	—
211	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
212	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
213	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
214	C₂×D₄₃	—	2	4	no	—
215	C₂×D₄₃	—	2	2	no	—
216	C₂×D₄₃	—	2	4	no	—
217	C₂×D₄₃	—	2	2	no	—
218	C₂×D₄₃	—	2	4	no	—
219	C₂×D₄₃	—	2	2	no	—
220	C₂×D₄₃	—	8	4	no	—
221	C₂×D₄₃	—	8	8	no	—
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	2	4	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	2	1	no	—
226	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
227	Dic₄₃	—	2	2	no	—
228	Dic₄₃	—	2	2	no	—
229	Dic₄₃	—	2	4	no	—
230	Dic₄₃	—	2	2	no	—
231	#3537	—	43	1	no	maximal, Sylow
232	C₂×C₄₃	—	2	2	no	—
233	C₂×C₄₃	—	2	2	no	—
234	C₂×C₄₃	—	4	4	no	—
235	C₂×C₄₃	—	4	1	no	—
236	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
239	D₄₃	—	4	4	no	—
240	D₄₃	—	4	2	no	—
241	#560	—	43	4	no	—
242	#553	—	43	2	no	—
243	#553	—	43	2	no	—
244	D₄²	—	43	4	no	—
245	D₄²	—	43	2	no	—
246	D₄²	—	43	2	no	—
247	#540	—	43	2	no	—
248	#538	—	43	2	no	—
249	#538	—	43	2	no	—
250	#535	—	43	2	no	—
251	#534	—	43	2	no	—
252	#534	—	43	2	no	—
253	#525	—	43	1	no	—
254	C₂×#121	—	43	1	no	—
255	C₂×#121	D₄₃	1	1	yes	characteristic, complemented
256	C₄₃	#3537	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	43	1	no	—
258	C₂²×D₄	—	43	2	no	—
259	C₂²×D₄	—	43	4	no	—
260	C₂²×D₄	—	43	4	no	—
261	C₂²×D₄	—	43	2	no	—
262	C₂²×D₄	—	43	1	no	—
263	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
264	C₂²×D₄	C₂×D₄₃	1	2	yes	complemented
265	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
266	#127	—	43	4	no	—
267	#127	—	43	2	no	—
268	#126	—	43	4	no	—
269	#126	—	43	4	no	—
270	#125	—	43	2	no	—
271	#124	—	43	4	no	—
272	#123	—	43	2	no	—
273	#123	—	43	4	no	—
274	#123	—	43	4	no	—
275	#123	—	43	4	no	—
276	#123	—	43	4	no	—
277	C₂²⋊Q₈	—	43	1	no	—
278	C₂²⋊Q₈	—	43	1	no	—
279	#121	—	43	4	no	—
280	#121	—	43	2	no	—
281	#121	—	43	4	no	—
282	#121	—	43	4	no	—
283	#121	—	43	4	no	—
284	#121	—	43	2	no	—
285	#121	—	43	2	no	—
286	#121	—	43	2	no	—
287	#121	—	43	2	no	—
288	#121	—	43	1	no	—
289	#121	—	43	1	no	—
290	#121	—	43	4	no	—
291	#121	—	43	2	no	—
292	#121	—	43	4	no	—
293	#121	C₂×D₄₃	1	2	yes	complemented
294	#121	C₂×D₄₃	1	2	yes	complemented
295	#121	C₂×D₄₃	1	2	yes	complemented
296	#121	C₂×D₄₃	1	2	yes	complemented
297	#120	—	43	2	no	—
298	#120	—	43	4	no	—
299	#120	—	43	4	no	—
300	#120	—	43	4	no	—
301	#120	—	43	4	no	—
302	#120	—	43	4	no	—
303	#120	—	43	4	no	—
304	C₄×D₄	—	43	4	no	—
305	C₄×D₄	—	43	2	no	—
306	C₄×D₄	—	43	2	no	—
307	C₄×D₄	—	43	2	no	—
308	C₄×D₄	—	43	4	no	—
309	C₄×D₄	—	43	2	no	—
310	#117	—	43	1	no	—
311	#117	—	43	2	no	—
312	C₂×C₄⋊C₄	—	43	1	no	—
313	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
314	C₂×C₂²⋊C₄	—	43	2	no	—
315	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	complemented
316	C₂⁴	—	43	2	no	—
317	C₂⁴	—	43	4	no	—
318	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
319	C₂⁴	C₂²×D₄₃	1	2	yes	—
320	#41	—	172	2	no	—
321	C₂×Q₈	—	43	1	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	43	2	no	—
325	C₂×D₄	—	43	2	no	—
326	C₂×D₄	—	43	4	no	—
327	C₂×D₄	—	43	2	no	—
328	C₂×D₄	—	43	4	no	—
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	1	no	—
335	C₂×D₄	—	43	2	no	—
336	C₂×D₄	—	43	4	no	—
337	C₂×D₄	—	172	2	no	—
338	C₂×D₄	—	172	4	no	—
339	C₂×D₄	—	172	8	no	—
340	C₂×D₄	—	172	4	no	—
341	C₂×D₄	—	172	8	no	—
342	C₂×D₄	C₂²×D₄₃	1	4	yes	—
343	C₂×D₄	C₂²×D₄₃	1	2	yes	—
344	C₂×D₄	C₂²×D₄₃	1	2	yes	—
345	C₂×D₄	C₂²×D₄₃	1	4	yes	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	43	2	no	—
348	C₂²×C₄	—	43	4	no	—
349	C₂²×C₄	—	43	2	no	—
350	C₂²×C₄	—	43	4	no	—
351	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
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	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
356	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
357	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
358	C₄⋊C₄	—	43	2	no	—
359	C₄⋊C₄	—	43	2	no	—
360	C₄⋊C₄	—	43	1	no	—
361	C₄⋊C₄	—	43	1	no	—
362	C₄⋊C₄	—	43	2	no	—
363	C₄⋊C₄	—	43	2	no	—
364	C₄⋊C₄	—	43	4	no	—
365	C₄⋊C₄	—	43	4	no	—
366	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
367	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
368	C₂²⋊C₄	—	43	2	no	—
369	C₂²⋊C₄	—	43	2	no	—
370	C₂²⋊C₄	—	43	2	no	—
371	C₂²⋊C₄	—	43	4	no	—
372	C₂²⋊C₄	—	43	4	no	—
373	C₂²⋊C₄	—	43	4	no	—
374	C₂²⋊C₄	—	43	4	no	—
375	C₂²⋊C₄	—	43	4	no	—
376	C₂²⋊C₄	—	43	4	no	—
377	C₂²⋊C₄	—	43	4	no	—
378	C₂²⋊C₄	—	43	2	no	—
379	C₂²⋊C₄	—	43	2	no	—
380	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
381	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
382	C₄²	—	43	2	no	—
383	C₄²	—	43	4	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	43	2	no	—
391	C₂³	—	43	4	no	—
392	C₂³	—	86	4	no	—
393	C₂³	—	172	2	no	—
394	C₂³	—	172	2	no	—
395	C₂³	—	172	4	no	—
396	C₂³	—	172	4	no	—
397	C₂³	—	172	4	no	—
398	C₂³	C₂³×D₄₃	1	4	yes	—
399	C₂³	C₂³×D₄₃	1	1	yes	characteristic
400	C₂³	C₂³×D₄₃	1	1	yes	characteristic
401	C₂³	C₂³×D₄₃	1	1	yes	characteristic
402	Q₈	—	172	1	no	—
403	D₄	—	2	8	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	86	4	no	—
408	D₄	—	86	4	no	—
409	D₄	—	86	8	no	—
410	D₄	—	86	4	no	—
411	D₄	—	172	2	no	—
412	D₄	—	172	4	no	—
413	D₄	—	172	1	no	—
414	D₄	—	172	4	no	—
415	D₄	—	172	4	no	—
416	D₄	—	172	4	no	—
417	D₄	—	172	4	no	—
418	D₄	—	172	4	no	—
419	D₄	—	172	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	43	2	no	—
428	C₂×C₄	—	43	2	no	—
429	C₂×C₄	—	43	2	no	—
430	C₂×C₄	—	43	4	no	—
431	C₂×C₄	—	86	4	no	—
432	C₂×C₄	—	172	4	no	—
433	C₂×C₄	—	172	2	no	—
434	C₂×C₄	—	172	4	no	—
435	C₂×C₄	C₂³×D₄₃	1	4	yes	—
436	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	—	86	2	no	—
453	C₂²	—	86	4	no	—
454	C₂²	—	86	2	no	—
455	C₂²	—	86	4	no	—
456	C₂²	—	86	2	no	—
457	C₂²	—	86	4	no	—
458	C₂²	—	344	4	no	—
459	C₂²	—	344	8	no	—
460	C₂²	#13063370	1	2	yes	—
461	C₂²	#13063371	1	2	yes	—
462	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	4	no	—
467	C₄	—	86	2	no	—
468	C₄	—	86	2	no	—
469	C₄	—	86	2	no	—
470	C₄	—	86	4	no	—
471	C₄	#13063370	1	2	yes	—
472	C₂	—	2	2	no	—
473	C₂	—	2	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	4	4	no	—
476	C₂	—	172	2	no	—
477	C₂	—	172	4	no	—
478	C₂	C₂×#13063370	1	1	yes	characteristic
479	C₂	C₂×#13063370	1	1	yes	characteristic
480	C₂	C₂×#13063371	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	#3537
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. #14583637	C₂	semidirect
2. #14583601	C₂	semidirect
3. #14583597	C₂	semidirect
4. #14583533	C₂	semidirect
5. D₄×C₂²⋊D₄₃	C₂	semidirect
6. D₄×C₂²⋊D₄₃	C₂	semidirect
7. #14583502	C₂	semidirect
8. #14583487	C₂	semidirect
9. #14583486	C₂	semidirect
10. #14583465	C₂	semidirect
11. #14583461	C₂	semidirect
12. #14583457	C₂	semidirect
13. #14583410	C₂	semidirect
14. C₂×#13063299	C₂	semidirect
15. C₂×#121×C₄₃	C₂	semidirect
16. C₂×#10621898	C₂²	semidirect
17. C₂²×D₁₇₂	C₂²	semidirect
18. C₂²×C₂²⋊D₄₃	C₂²	semidirect
19. C₂²×C₂²⋊D₄₃	C₂²	semidirect
20. C₂×D₄×D₄₃	C₂²	semidirect
21. C₂×D₄×D₄₃	C₂²	semidirect
22. #13063321	C₂²	semidirect
23. #13063321	C₂²	semidirect
24. #13063320	C₂²	semidirect
25. #13063318	C₂²	semidirect
26. #13063316	C₂²	semidirect
27. #13063311	C₂²	semidirect
28. #13063310	C₂²	semidirect
29. #13063309	C₂²	semidirect
30. #13063309	C₂²	semidirect
31. #13063308	C₂²	semidirect
32. #13063307	C₂²	semidirect
33. #13063304	C₂²	semidirect
34. #13063304	C₂²	semidirect
35. #13063300	C₂²	semidirect
36. #13063299	C₂²	semidirect
37. #13063299	C₂²	semidirect
38. #13063299	C₂²	semidirect
39. #13063299	C₂²	semidirect
40. #13063299	C₂²	semidirect
41. #13063299	C₂²	semidirect
42. #13063299	C₂²	semidirect
43. #13063298	C₂²	semidirect
44. #13063297	C₂²	semidirect
45. #13063297	C₂²	semidirect
46. #13063297	C₂²	semidirect
47. #13063296	C₂²	semidirect
48. #13063296	C₂²	semidirect
49. #13063295	C₂²	semidirect
50. #13063295	C₂²	semidirect
51. #13063294	C₂²	semidirect
52. #13063294	C₂²	semidirect
53. #13063293	C₂²	semidirect
54. #13063293	C₂²	semidirect
55. #13063293	C₂²	semidirect
56. D₄×Dic₄₃	C₂²	semidirect
57. D₄×Dic₄₃	C₂²	semidirect
58. #13063287	C₂²	semidirect
59. C₄×C₂²⋊D₄₃	C₂²	semidirect
60. C₄×C₂²⋊D₄₃	C₂²	semidirect
61. C₄×C₂²⋊D₄₃	C₂²	semidirect
62. #13063284	C₂²	semidirect
63. #13063283	C₂²	semidirect
64. C₂×C₄⋊Dic₄₃	C₂²	semidirect
65. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
66. C₂²×D₄×C₄₃	C₂²	semidirect
67. C₂²×D₄×C₄₃	C₂²	semidirect
68. C₂³×C₄×C₄₃	C₂²	semidirect
69. #121×C₄₃	C₂²	semidirect
70. #121×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
255. C₂×#121	D₄₃	semidirect
256. C₄₃	#3537	semidirect
263. C₂²×D₄	C₂×D₄₃	semidirect
264. C₂²×D₄	C₂×D₄₃	semidirect
265. C₂³×C₄	C₂×D₄₃	semidirect
293. #121	C₂×D₄₃	semidirect
294. #121	C₂×D₄₃	semidirect
295. #121	C₂×D₄₃	semidirect
296. #121	C₂×D₄₃	semidirect
313. C₂×C₄⋊C₄	C₂×D₄₃	semidirect
315. C₂×C₂²⋊C₄	C₂×D₄₃	semidirect