Subgroups — #19148353

Order 5504.

1660 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063371	C₂	1	2	yes	maximal, complemented
2	#14583552	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583550	C₂	1	2	yes	maximal, complemented
4	#14583541	C₂	1	4	yes	maximal, complemented
5	#14583540	C₂	1	2	yes	maximal, complemented
6	#14583537	C₂	1	2	yes	maximal, complemented
7	D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583533	C₂	1	2	yes	maximal, complemented
10	#14583479	C₂	1	2	yes	maximal, complemented
11	#14583460	C₂	1	4	yes	maximal, complemented
12	#14583450	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13063300	C₂	1	2	yes	maximal, complemented
15	#121×D₄₃	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
18	#13063371	—	2	16	no	—
19	C₂×#10621902	C₂²	1	2	yes	complemented
20	C₂×#10621902	C₂²	1	2	yes	complemented
21	C₂×#10621898	C₂²	1	2	yes	complemented
22	C₂×#10621898	C₂²	1	4	yes	complemented
23	C₂²×D₁₇₂	C₂²	1	4	yes	complemented
24	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
25	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
26	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
28	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
29	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₄₃	C₂²	1	2	yes	complemented
32	#13063324	C₂²	1	1	yes	characteristic, complemented
33	#13063322	C₂²	1	1	yes	characteristic, complemented
34	#13063321	C₂²	1	1	yes	characteristic, complemented
35	#13063314	C₂²	1	2	yes	complemented
36	#13063311	C₂²	1	2	yes	complemented
37	#13063310	C₂²	1	4	yes	complemented
38	#13063310	C₂²	1	4	yes	complemented
39	#13063308	C₂²	1	4	yes	complemented
40	#13063303	C₂²	1	4	yes	complemented
41	#13063301	C₂²	1	2	yes	complemented
42	#13063300	C₂²	1	2	yes	complemented
43	#13063300	C₂²	1	2	yes	complemented
44	#13063300	C₂²	1	1	yes	characteristic, complemented
45	#13063300	C₂²	1	4	yes	complemented
46	#13063300	C₂²	1	2	yes	complemented
47	#13063300	C₂²	1	4	yes	complemented
48	#13063300	C₂²	1	2	yes	complemented
49	#13063300	C₂²	1	2	yes	complemented
50	#13063299	C₂²	1	2	yes	complemented
51	#13063299	C₂²	1	2	yes	complemented
52	#13063298	C₂²	1	4	yes	complemented
53	#13063298	C₂²	1	2	yes	complemented
54	#13063298	C₂²	1	4	yes	complemented
55	#13063297	C₂²	1	4	yes	complemented
56	#13063296	C₂²	1	1	yes	characteristic, complemented
57	#13063295	C₂²	1	4	yes	complemented
58	#13063295	C₂²	1	4	yes	complemented
59	#13063295	C₂²	1	4	yes	complemented
60	#13063293	C₂²	1	4	yes	complemented
61	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
62	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
63	D₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
64	#13063287	C₂²	1	1	yes	characteristic, complemented
65	#13063287	C₂²	1	2	yes	complemented
66	#13063287	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
69	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
72	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
74	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
75	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#41×C₄₃	C₂²	1	2	yes	complemented
77	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
78	#123×C₄₃	C₂²	1	4	yes	complemented
79	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
80	#121×C₄₃	C₂²	1	2	yes	complemented
81	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
84	C₂³×D₄₃	C₂³	1	4	yes	—
85	C₂³×D₄₃	C₂³	1	4	yes	—
86	C₂³×D₄₃	C₂³	1	2	yes	—
87	#41×C₄₃	—	2	8	no	—
88	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
89	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₄₃	C₂³	1	4	yes	—
91	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
94	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
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	C₂²×Dic₄₃	C₂³	1	2	yes	—
102	#10621902	—	2	8	no	—
103	#10621902	—	2	8	no	—
104	D₄×D₄₃	—	2	8	no	—
105	D₄×D₄₃	—	2	16	no	—
106	D₄×D₄₃	—	2	16	no	—
107	D₄×D₄₃	—	4	4	no	—
108	D₄×D₄₃	D₄	1	8	yes	complemented
109	#10621898	—	2	16	no	—
110	#10621898	—	2	8	no	—
111	C₂×D₁₇₂	—	2	8	no	—
112	C₂×D₁₇₂	—	2	16	no	—
113	C₂×D₁₇₂	—	4	4	no	—
114	C₂×D₁₇₂	C₂³	1	2	yes	—
115	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
116	C₂×D₁₇₂	C₂³	1	4	yes	—
117	C₂×D₁₇₂	C₂³	1	4	yes	—
118	C₂×D₁₇₂	C₂³	1	4	yes	—
119	C₂×D₁₇₂	C₂³	1	2	yes	—
120	C₂×D₁₇₂	C₂³	1	2	yes	—
121	C₂×D₁₇₂	C₂³	1	2	yes	—
122	C₂×D₁₇₂	C₂³	1	4	yes	—
123	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₄₃	—	4	4	no	—
125	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₄₃	C₂³	1	4	yes	—
127	C₂×C₄×D₄₃	C₂³	1	2	yes	—
128	C₂×C₄×D₄₃	C₂³	1	2	yes	—
129	C₂×C₄×D₄₃	C₂³	1	4	yes	—
130	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₄₃	C₂³	1	2	yes	—
132	C₂×C₄×D₄₃	C₂³	1	2	yes	—
133	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
134	C₂×Dic₈₆	C₂³	1	2	yes	—
135	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
137	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
138	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
143	C₄²×C₄₃	C₂³	1	1	yes	characteristic
144	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
145	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
146	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
147	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
148	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
149	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
151	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
152	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
153	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
154	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
155	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
157	Dic₄₃⋊C₄	C₂³	1	2	yes	—
158	Dic₄₃⋊C₄	C₂³	1	4	yes	—
159	Dic₄₃⋊C₄	C₂³	1	2	yes	—
160	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
161	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
162	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
163	C₂³×C₄₃	C₂⁴	1	2	yes	—
164	C₂³×C₄₃	C₂⁴	1	2	yes	—
165	C₂²×D₄₃	—	2	8	no	—
166	C₂²×D₄₃	—	2	8	no	—
167	C₂²×D₄₃	—	4	2	no	—
168	C₂²×D₄₃	—	4	2	no	—
169	C₂²×D₄₃	—	4	4	no	—
170	C₂²×D₄₃	—	4	4	no	—
171	C₂²×D₄₃	—	4	4	no	—
172	C₂²×D₄₃	—	4	4	no	—
173	C₂²×D₄₃	C₂×D₄	1	8	yes	complemented
174	C₂²×D₄₃	C₂⁴	1	2	yes	—
175	C₂²×D₄₃	C₂⁴	1	4	yes	—
176	C₂²×D₄₃	C₂⁴	1	2	yes	—
177	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
178	Q₈×C₄₃	—	2	4	no	—
179	D₄×C₄₃	—	2	8	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	C₂×D₄	1	4	yes	complemented
182	C₂×C₄×C₄₃	—	2	8	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
187	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
188	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
189	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
191	C₂²⋊D₄₃	—	2	8	no	—
192	C₂²⋊D₄₃	—	2	4	no	—
193	C₂²⋊D₄₃	—	2	4	no	—
194	C₂²⋊D₄₃	—	4	4	no	—
195	C₂²⋊D₄₃	—	4	2	no	—
196	C₂²⋊D₄₃	C₂×D₄	1	8	yes	complemented
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
199	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
200	C₂×Dic₄₃	C₂⁴	1	2	yes	—
201	C₂×Dic₄₃	C₂⁴	1	2	yes	—
202	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
203	D₁₇₂	—	2	8	no	—
204	D₁₇₂	—	2	4	no	—
205	D₁₇₂	—	2	8	no	—
206	D₁₇₂	—	2	8	no	—
207	D₁₇₂	—	2	4	no	—
208	D₁₇₂	—	2	2	no	—
209	D₁₇₂	—	2	4	no	—
210	D₁₇₂	—	4	4	no	—
211	D₁₇₂	—	4	2	no	—
212	D₁₇₂	C₂×D₄	1	4	yes	complemented
213	C₄×D₄₃	—	2	8	no	—
214	C₄×D₄₃	—	2	4	no	—
215	C₄×D₄₃	—	2	2	no	—
216	C₄×D₄₃	—	2	4	no	—
217	C₄×D₄₃	—	2	8	no	—
218	C₄×D₄₃	—	4	2	no	—
219	C₄×D₄₃	—	4	2	no	—
220	C₄×D₄₃	—	4	1	no	—
221	C₄×D₄₃	C₂×D₄	1	4	yes	complemented
222	Dic₈₆	—	2	4	no	—
223	C₂²×C₄₃	—	2	2	no	—
224	C₂²×C₄₃	—	2	2	no	—
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	2	no	—
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	C₂²×D₄	1	4	yes	—
229	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
230	C₂×D₄₃	—	2	2	no	—
231	C₂×D₄₃	—	2	1	no	—
232	C₂×D₄₃	—	2	2	no	—
233	C₂×D₄₃	—	2	1	no	—
234	C₂×D₄₃	—	2	2	no	—
235	C₂×D₄₃	—	2	4	no	—
236	C₂×D₄₃	—	2	2	no	—
237	C₂×D₄₃	—	2	4	no	—
238	C₂×D₄₃	—	2	4	no	—
239	C₂×D₄₃	—	2	2	no	—
240	C₂×D₄₃	—	4	8	no	—
241	C₂×D₄₃	—	8	8	no	—
242	C₂×D₄₃	—	8	8	no	—
243	C₂×D₄₃	C₂²×D₄	1	4	yes	—
244	C₂×D₄₃	C₂²×D₄	1	2	yes	—
245	C₄×C₄₃	—	2	2	no	—
246	C₄×C₄₃	—	2	4	no	—
247	C₄×C₄₃	—	2	2	no	—
248	C₄×C₄₃	—	2	1	no	—
249	C₄×C₄₃	C₂²×D₄	1	2	yes	—
250	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	complemented
251	Dic₄₃	—	2	2	no	—
252	Dic₄₃	—	2	1	no	—
253	Dic₄₃	—	2	2	no	—
254	Dic₄₃	—	2	1	no	—
255	Dic₄₃	C₂²×D₄	1	2	yes	—
256	#3496	—	43	1	no	maximal, Sylow
257	C₂×C₄₃	—	2	4	no	—
258	C₂×C₄₃	—	4	2	no	—
259	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
260	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
261	C₂×C₄₃	#585	1	1	yes	characteristic
262	D₄₃	—	2	2	no	—
263	D₄₃	—	2	4	no	—
264	D₄₃	—	4	2	no	—
265	D₄₃	—	4	4	no	—
266	C₂×H(5,𝔽₂)	—	43	2	no	—
267	#547	—	43	1	no	—
268	#547	—	43	2	no	—
269	#547	D₄₃	1	1	yes	characteristic, complemented
270	#546	—	43	2	no	—
271	#546	—	43	4	no	—
272	#546	—	43	2	no	—
273	D₄²	—	43	2	no	—
274	D₄²	—	43	1	no	—
275	D₄²	—	43	1	no	—
276	#537	—	43	2	no	—
277	#534	—	43	4	no	—
278	#532	—	43	1	no	—
279	#532	—	43	1	no	—
280	C₂×#121	—	43	2	no	—
281	C₂×#121	—	43	2	no	—
282	C₂×C₄×D₄	—	43	1	no	—
283	C₄₃	#3496	1	1	yes	characteristic, complemented, Sylow
284	H(5,𝔽₂)	—	86	16	no	—
285	C₂×#41	—	43	2	no	—
286	C₂×#41	—	43	2	no	—
287	C₂×#41	—	43	2	no	—
288	C₂×#41	—	43	4	no	—
289	C₂×#41	C₂×D₄₃	1	2	yes	complemented
290	C₂²×D₄	—	43	1	no	—
291	C₂²×D₄	—	43	4	no	—
292	C₂²×D₄	—	43	4	no	—
293	C₂²×D₄	—	43	2	no	—
294	C₂²×D₄	—	43	2	no	—
295	C₂²×D₄	—	43	4	no	—
296	C₂²×D₄	—	43	2	no	—
297	C₂²×D₄	—	43	2	no	—
298	C₂³×C₄	—	43	2	no	—
299	C₄⋊Q₈	—	43	1	no	—
300	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
301	#127	—	43	1	no	—
302	#127	—	43	1	no	—
303	#124	—	43	2	no	—
304	#124	—	43	2	no	—
305	#123	—	43	4	no	—
306	#123	—	43	4	no	—
307	#123	—	43	4	no	—
308	#123	C₂×D₄₃	1	4	yes	complemented
309	C₂²⋊Q₈	—	43	2	no	—
310	C₂²⋊Q₈	—	43	4	no	—
311	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
312	#121	—	43	1	no	—
313	#121	—	43	4	no	—
314	#121	—	43	2	no	—
315	#121	—	43	2	no	—
316	#121	—	43	2	no	—
317	#121	—	43	1	no	—
318	#121	—	43	4	no	—
319	#121	—	43	2	no	—
320	#121	—	43	2	no	—
321	#121	—	43	4	no	—
322	#121	—	43	2	no	—
323	#121	—	43	2	no	—
324	#121	—	43	4	no	—
325	#121	—	43	2	no	—
326	#121	—	43	4	no	—
327	#121	C₂×D₄₃	1	2	yes	complemented
328	#120	—	43	4	no	—
329	#120	—	43	4	no	—
330	#120	—	43	4	no	—
331	#120	—	43	4	no	—
332	C₄×D₄	—	43	1	no	—
333	C₄×D₄	—	43	2	no	—
334	C₄×D₄	—	43	2	no	—
335	C₄×D₄	—	43	1	no	—
336	C₄×D₄	—	43	2	no	—
337	C₄×D₄	—	43	2	no	—
338	C₄×D₄	—	43	2	no	—
339	C₄×D₄	—	43	1	no	—
340	C₄×D₄	—	43	1	no	—
341	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
342	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
343	C₂×C₄⋊C₄	—	43	1	no	—
344	C₂×C₄⋊C₄	—	43	2	no	—
345	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	complemented
346	C₂×C₂²⋊C₄	—	43	4	no	—
347	C₂×C₂²⋊C₄	—	43	2	no	—
348	C₂×C₂²⋊C₄	—	43	4	no	—
349	C₂×C₄²	—	43	1	no	—
350	C₂⁴	—	43	2	no	—
351	C₂⁴	—	43	4	no	—
352	C₂⁴	—	43	4	no	—
353	#41	—	2	8	no	—
354	#41	—	86	8	no	—
355	#41	—	86	16	no	—
356	#41	—	86	8	no	—
357	#41	—	86	8	no	—
358	C₂×Q₈	—	43	2	no	—
359	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
360	C₂×D₄	—	43	2	no	—
361	C₂×D₄	—	43	8	no	—
362	C₂×D₄	—	43	4	no	—
363	C₂×D₄	—	43	2	no	—
364	C₂×D₄	—	43	2	no	—
365	C₂×D₄	—	43	2	no	—
366	C₂×D₄	—	43	4	no	—
367	C₂×D₄	—	43	1	no	—
368	C₂×D₄	—	43	2	no	—
369	C₂×D₄	—	43	1	no	—
370	C₂×D₄	—	43	4	no	—
371	C₂×D₄	—	43	4	no	—
372	C₂×D₄	—	43	4	no	—
373	C₂×D₄	—	43	2	no	—
374	C₂×D₄	—	43	2	no	—
375	C₂×D₄	—	43	2	no	—
376	C₂×D₄	—	43	4	no	—
377	C₂×D₄	—	86	8	no	—
378	C₂×D₄	—	86	16	no	—
379	C₂×D₄	—	86	16	no	—
380	C₂×D₄	—	86	16	no	—
381	C₂×D₄	—	86	8	no	—
382	C₂×D₄	—	172	4	no	—
383	C₂×D₄	—	172	4	no	—
384	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
385	C₂×D₄	C₂²×D₄₃	1	4	yes	—
386	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
387	C₂²×C₄	—	43	1	no	—
388	C₂²×C₄	—	43	2	no	—
389	C₂²×C₄	—	43	1	no	—
390	C₂²×C₄	—	43	4	no	—
391	C₂²×C₄	—	43	2	no	—
392	C₂²×C₄	—	43	4	no	—
393	C₂²×C₄	—	43	2	no	—
394	C₂²×C₄	—	43	1	no	—
395	C₂²×C₄	—	43	2	no	—
396	C₂²×C₄	—	43	2	no	—
397	C₂²×C₄	—	172	4	no	—
398	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
399	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
400	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
401	C₄⋊C₄	—	43	1	no	—
402	C₄⋊C₄	—	43	2	no	—
403	C₄⋊C₄	—	43	1	no	—
404	C₄⋊C₄	—	43	4	no	—
405	C₄⋊C₄	—	43	2	no	—
406	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
407	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
410	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
411	C₂²⋊C₄	—	43	2	no	—
412	C₂²⋊C₄	—	43	2	no	—
413	C₂²⋊C₄	—	43	4	no	—
414	C₂²⋊C₄	—	43	2	no	—
415	C₂²⋊C₄	—	43	2	no	—
416	C₂²⋊C₄	—	43	2	no	—
417	C₂²⋊C₄	—	43	4	no	—
418	C₂²⋊C₄	—	43	4	no	—
419	C₂²⋊C₄	—	43	4	no	—
420	C₂²⋊C₄	—	43	4	no	—
421	C₂²⋊C₄	—	43	2	no	—
422	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
423	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
424	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
425	C₄²	—	43	1	no	—
426	C₄²	—	43	1	no	—
427	C₄²	—	43	1	no	—
428	C₄²	C₂²×D₄₃	1	1	yes	characteristic
429	C₂³	—	43	2	no	—
430	C₂³	—	43	1	no	—
431	C₂³	—	43	8	no	—
432	C₂³	—	43	4	no	—
433	C₂³	—	43	2	no	—
434	C₂³	—	86	8	no	—
435	C₂³	—	86	8	no	—
436	C₂³	—	172	4	no	—
437	C₂³	—	172	4	no	—
438	C₂³	—	172	4	no	—
439	C₂³	—	172	4	no	—
440	C₂³	—	172	2	no	—
441	C₂³	—	172	2	no	—
442	C₂³	C₂³×D₄₃	1	2	yes	—
443	C₂³	C₂³×D₄₃	1	2	yes	—
444	Q₈	—	2	4	no	—
445	Q₈	—	86	4	no	—
446	D₄	—	2	8	no	—
447	D₄	—	2	2	no	—
448	D₄	—	43	8	no	—
449	D₄	—	43	4	no	—
450	D₄	—	86	4	no	—
451	D₄	—	86	8	no	—
452	D₄	—	86	8	no	—
453	D₄	—	86	8	no	—
454	D₄	—	86	4	no	—
455	D₄	—	86	4	no	—
456	D₄	—	86	8	no	—
457	D₄	—	86	4	no	—
458	D₄	—	86	2	no	—
459	D₄	—	86	4	no	—
460	D₄	—	172	4	no	—
461	D₄	—	172	2	no	—
462	D₄	—	172	4	no	—
463	D₄	—	172	2	no	—
464	D₄	D₄×D₄₃	1	4	yes	complemented
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	43	1	no	—
469	C₂×C₄	—	43	4	no	—
470	C₂×C₄	—	43	1	no	—
471	C₂×C₄	—	43	1	no	—
472	C₂×C₄	—	43	2	no	—
473	C₂×C₄	—	43	2	no	—
474	C₂×C₄	—	86	8	no	—
475	C₂×C₄	—	86	8	no	—
476	C₂×C₄	—	86	4	no	—
477	C₂×C₄	—	86	2	no	—
478	C₂×C₄	—	86	4	no	—
479	C₂×C₄	—	172	2	no	—
480	C₂×C₄	—	172	2	no	—
481	C₂×C₄	—	172	1	no	—
482	C₂×C₄	—	172	2	no	—
483	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₄₃	1	2	yes	—
485	C₂×C₄	C₂³×D₄₃	1	4	yes	—
486	C₂×C₄	C₂³×D₄₃	1	2	yes	—
487	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	43	2	no	—
495	C₂²	—	43	4	no	—
496	C₂²	—	86	1	no	—
497	C₂²	—	86	2	no	—
498	C₂²	—	86	1	no	—
499	C₂²	—	86	2	no	—
500	C₂²	—	86	4	no	—
501	C₂²	—	86	2	no	—
502	C₂²	—	86	2	no	—
503	C₂²	—	86	4	no	—
504	C₂²	—	86	4	no	—
505	C₂²	—	86	2	no	—
506	C₂²	—	344	8	no	—
507	C₂²	—	344	8	no	—
508	C₂²	—	172	8	no	—
509	C₂²	C₂×D₄×D₄₃	1	4	yes	—
510	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	4	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	1	no	—
515	C₄	—	43	2	no	—
516	C₄	—	86	2	no	—
517	C₄	—	86	1	no	—
518	C₄	—	86	2	no	—
519	C₄	—	86	1	no	—
520	C₄	C₂×D₄×D₄₃	1	2	yes	—
521	C₄	#13063371	1	2	yes	complemented
522	C₂	—	2	4	no	—
523	C₂	—	4	2	no	—
524	C₂	—	86	4	no	—
525	C₂	—	86	2	no	—
526	C₂	—	172	2	no	—
527	C₂	—	172	4	no	—
528	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic
529	C₂	C₂×#13063371	1	1	yes	characteristic
530	C₂	#14583736	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#547	C₂
hypercenter	#547	D₄₃
hypocenter	C₄₃	#3496
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#13063371	C₂	semidirect
2. #14583552	C₂	semidirect
3. #14583550	C₂	semidirect
4. #14583541	C₂	semidirect
5. #14583540	C₂	semidirect
6. #14583537	C₂	semidirect
7. D₄×D₁₇₂	C₂	semidirect
8. D₄×D₁₇₂	C₂	semidirect
9. #14583533	C₂	semidirect
10. #14583479	C₂	semidirect
11. #14583460	C₂	semidirect
12. #14583450	C₂	semidirect
13. #14583446	C₂	semidirect
14. C₂×#13063300	C₂	semidirect
15. #121×D₄₃	C₂	semidirect
16. C₄×D₄×D₄₃	C₂	semidirect
17. C₄₃×#547	C₂	semidirect
19. C₂×#10621902	C₂²	semidirect
20. C₂×#10621902	C₂²	semidirect
21. C₂×#10621898	C₂²	semidirect
22. C₂×#10621898	C₂²	semidirect
23. C₂²×D₁₇₂	C₂²	semidirect
24. C₂²×D₁₇₂	C₂²	semidirect
25. C₂²×D₁₇₂	C₂²	semidirect
27. C₂×D₄×D₄₃	C₂²	semidirect
28. C₂×D₄×D₄₃	C₂²	semidirect
29. C₂×D₄×D₄₃	C₂²	semidirect
30. C₂×D₄×D₄₃	C₂²	semidirect
31. C₂²×C₄×D₄₃	C₂²	semidirect
32. #13063324	C₂²	semidirect
33. #13063322	C₂²	semidirect
34. #13063321	C₂²	semidirect
35. #13063314	C₂²	semidirect
36. #13063311	C₂²	semidirect
37. #13063310	C₂²	semidirect
38. #13063310	C₂²	semidirect
39. #13063308	C₂²	semidirect
40. #13063303	C₂²	semidirect
41. #13063301	C₂²	semidirect
42. #13063300	C₂²	semidirect
43. #13063300	C₂²	semidirect
44. #13063300	C₂²	semidirect
45. #13063300	C₂²	semidirect
46. #13063300	C₂²	semidirect
47. #13063300	C₂²	semidirect
48. #13063300	C₂²	semidirect
49. #13063300	C₂²	semidirect
50. #13063299	C₂²	semidirect
51. #13063299	C₂²	semidirect
52. #13063298	C₂²	semidirect
53. #13063298	C₂²	semidirect
54. #13063298	C₂²	semidirect
55. #13063297	C₂²	semidirect
56. #13063296	C₂²	semidirect
57. #13063295	C₂²	semidirect
58. #13063295	C₂²	semidirect
59. #13063295	C₂²	semidirect
60. #13063293	C₂²	semidirect
61. C₄×D₁₇₂	C₂²	semidirect
62. C₄×D₁₇₂	C₂²	semidirect
63. D₄×Dic₄₃	C₂²	semidirect
64. #13063287	C₂²	semidirect
65. #13063287	C₂²	semidirect
66. #13063287	C₂²	semidirect
67. C₄×C₂²⋊D₄₃	C₂²	semidirect
68. C₄×C₂²⋊D₄₃	C₂²	semidirect
69. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
70. C₄⋊C₄×D₄₃	C₂²	semidirect
71. C₄⋊C₄×D₄₃	C₂²	semidirect
72. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
73. C₂²⋊C₄×D₄₃	C₂²	semidirect
74. C₂²⋊C₄×D₄₃	C₂²	semidirect
75. C₄²×D₄₃	C₂²	semidirect
76. C₂×#41×C₄₃	C₂²	semidirect
77. C₄⋊Q₈×C₄₃	C₂²	semidirect
78. #123×C₄₃	C₂²	semidirect
79. C₂²⋊Q₈×C₄₃	C₂²	semidirect
80. #121×C₄₃	C₂²	semidirect
81. C₄×D₄×C₄₃	C₂²	semidirect
82. C₄×D₄×C₄₃	C₂²	semidirect
83. C₂×C₄⋊C₄×C₄₃	C₂²	semidirect
108. D₄×D₄₃	D₄	semidirect
173. C₂²×D₄₃	C₂×D₄	semidirect
181. D₄×C₄₃	C₂×D₄	semidirect
196. C₂²⋊D₄₃	C₂×D₄	semidirect
212. D₁₇₂	C₂×D₄	semidirect
221. C₄×D₄₃	C₂×D₄	semidirect
250. C₄×C₄₃	H(5,𝔽₂)	semidirect
269. #547	D₄₃	semidirect
283. C₄₃	#3496	semidirect
289. C₂×#41	C₂×D₄₃	semidirect
300. C₄⋊Q₈	C₂×D₄₃	semidirect
308. #123	C₂×D₄₃	semidirect
311. C₂²⋊Q₈	C₂×D₄₃	semidirect
327. #121	C₂×D₄₃	semidirect
341. C₄×D₄	C₂×D₄₃	semidirect
342. C₄×D₄	C₂×D₄₃	semidirect
345. C₂×C₄⋊C₄	C₂×D₄₃	semidirect
464. D₄	D₄×D₄₃	semidirect
521. C₄	#13063371	semidirect