Subgroups — #36558849

Order 22784.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029050	C₂	1	1	yes	maximal, characteristic
2	#26028897	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028896	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021142	C₂	1	1	yes	maximal, characteristic
5	#26021137	C₂	1	1	yes	maximal, characteristic
6	#26021004	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020999	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020964	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020960	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020957	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020953	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020159	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020063	C₂	1	1	yes	maximal, characteristic, complemented
14	#26019939	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1759	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668032	C₂²	1	1	yes	characteristic
17	C₄×#13083574	C₂²	1	1	yes	characteristic
18	#19151708	C₄	1	2	yes	complemented
19	#19151703	C₄	1	2	yes	complemented
20	#19151698	C₄	1	2	yes	complemented
21	#19151696	C₄	1	2	yes	complemented
22	#19151660	—	2	2	no	—
23	#19151659	—	2	2	no	—
24	#19151651	—	2	2	no	—
25	#19151649	—	2	2	no	—
26	C₂×#15667947	C₂²	1	1	yes	characteristic
27	C₂×#15667947	C₂²	1	1	yes	characteristic
28	#19151634	C₂²	1	1	yes	characteristic
29	#19151626	C₂²	1	1	yes	characteristic
30	#19151626	C₂²	1	1	yes	characteristic
31	#19151625	C₂²	1	1	yes	characteristic
32	#19151625	C₂²	1	1	yes	characteristic
33	C₂×#15667940	C₂²	1	1	yes	characteristic
34	C₂×#15667940	C₂²	1	1	yes	characteristic
35	#19151594	C₂²	1	1	yes	characteristic
36	#19151592	C₂²	1	1	yes	characteristic
37	#19151566	C₂²	1	1	yes	characteristic
38	#19151566	C₂²	1	1	yes	characteristic
39	#19151565	C₂²	1	1	yes	characteristic
40	#19151565	C₂²	1	1	yes	characteristic
41	C₄×#13083558	C₂²	1	1	yes	characteristic
42	C₂×#15667923	C₂²	1	1	yes	characteristic
43	C₂×#15667923	C₂²	1	1	yes	characteristic
44	C₂×#15667923	C₂²	1	1	yes	characteristic
45	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
46	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
47	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
48	#19151362	C₂²	1	1	yes	characteristic
49	#19151362	C₂²	1	1	yes	characteristic
50	#19151358	C₂²	1	1	yes	characteristic
51	#19151358	C₂²	1	1	yes	characteristic
52	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
55	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	#376×C₈₉	C₂²	1	1	yes	characteristic
57	#339×C₈₉	C₂²	1	1	yes	characteristic
58	#339×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083574	C₂³	1	1	yes	characteristic
60	#15668032	—	2	2	no	—
61	#15668032	—	2	2	no	—
62	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
63	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
64	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
65	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
66	C₂×#13083558	C₂³	1	1	yes	characteristic
67	C₂×#13083558	C₂³	1	1	yes	characteristic
68	C₂²×#10623494	C₂³	1	1	yes	characteristic
69	C₂²×#10623494	C₂³	1	1	yes	characteristic
70	C₂²×#10623494	C₂³	1	1	yes	characteristic
71	C₂²×#10623494	C₂³	1	1	yes	characteristic
72	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
73	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
74	C₄×C₂²⋊D₈₉	—	2	2	no	—
75	#15667971	C₂³	1	1	yes	characteristic
76	#15667969	—	2	1	no	—
77	C₄²×D₈₉	—	2	1	no	—
78	#15667947	—	2	2	no	—
79	#15667947	—	2	2	no	—
80	#15667945	C₂×C₄	1	2	yes	—
81	#15667943	C₂×C₄	1	2	yes	—
82	C₄⋊#10623494	—	2	2	no	—
83	C₄⋊#10623494	—	2	2	no	—
84	#15667941	—	2	2	no	—
85	#15667941	—	2	2	no	—
86	#15667940	—	2	2	no	—
87	#15667940	—	2	2	no	—
88	#15667936	C₂×C₄	1	2	yes	—
89	#15667935	C₂×C₄	1	2	yes	—
90	#15667933	C₂×C₄	1	2	yes	—
91	#15667932	C₂×C₄	1	2	yes	—
92	C₂²⋊#10623494	—	2	2	no	—
93	C₂²⋊#10623494	—	2	2	no	—
94	#15667924	—	2	2	no	—
95	#15667924	—	2	2	no	—
96	#15667923	—	2	2	no	—
97	#15667923	—	2	1	no	—
98	#15667923	—	2	2	no	—
99	#15667923	C₂×C₄	1	2	yes	—
100	#15667923	C₂×C₄	1	2	yes	—
101	C₄×#10623494	—	2	2	no	—
102	C₄×#10623494	—	2	1	no	—
103	C₄×#10623494	—	2	2	no	—
104	C₄×#10623494	D₄	1	2	yes	—
105	C₄×#10623494	D₄	1	2	yes	—
106	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₈₉	—	2	2	no	—
111	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
112	#117×C₈₉	—	2	1	no	—
113	#117×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₈₉	—	2	1	no	—
115	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	#104×C₈₉	—	2	2	no	—
119	#104×C₈₉	—	2	2	no	—
120	#97×C₈₉	—	2	1	no	—
121	C₄×C₈×C₈₉	—	2	1	no	—
122	#95×C₈₉	—	2	2	no	—
123	#13083574	—	2	1	no	—
124	#13083574	—	2	1	no	—
125	#13083574	—	2	1	no	—
126	#13083574	—	2	1	no	—
127	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₈₉	—	2	1	no	—
130	C₂×C₄×D₈₉	—	2	2	no	—
131	C₂×C₄×D₈₉	—	2	1	no	—
132	#13083564	—	2	2	no	—
133	#13083562	—	2	2	no	—
134	#13083561	—	2	2	no	—
135	#13083559	—	2	2	no	—
136	#13083558	—	2	1	no	—
137	#13083558	—	2	1	no	—
138	#13083558	—	2	1	no	—
139	#13083558	—	2	1	no	—
140	C₂×#10623494	—	2	1	no	—
141	C₂×#10623494	—	2	1	no	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₂×#10623494	—	2	1	no	—
145	C₂×#10623494	—	2	1	no	—
146	C₂×#10623494	—	2	1	no	—
147	C₂×#10623494	—	2	1	no	—
148	C₂×#10623494	C₂²×C₄	1	2	yes	—
149	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
150	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
151	C₂×#10623494	C₂×D₄	1	2	yes	—
152	C₂×#10623494	C₂×D₄	1	2	yes	—
153	C₂×#10623494	#41	1	2	yes	—
154	C₂×#10623494	#41	1	2	yes	—
155	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
156	#13083553	—	2	2	no	—
157	C₂²⋊Dic₈₉	—	2	1	no	—
158	#13083551	—	2	2	no	—
159	C₄×Dic₈₉	—	2	2	no	—
160	C₄×Dic₈₉	—	2	1	no	—
161	#41×C₈₉	—	2	1	no	—
162	#41×C₈₉	—	2	1	no	—
163	#41×C₈₉	—	2	1	no	—
164	#41×C₈₉	—	2	1	no	—
165	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	—	2	1	no	—
169	C₂²×C₄×C₈₉	—	2	1	no	—
170	C₂²×C₄×C₈₉	—	2	2	no	—
171	C₂²×C₄×C₈₉	—	2	1	no	—
172	C₂²×C₄×C₈₉	#41	1	2	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₈₉	—	2	1	no	—
175	M₁₆×C₈₉	—	2	1	no	—
176	M₁₆×C₈₉	—	2	1	no	—
177	M₁₆×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	2	1	no	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	2	2	no	—
181	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
182	C₂²⋊C₄×C₈₉	—	2	1	no	—
183	C₂²⋊C₄×C₈₉	—	2	2	no	—
184	C₄²×C₈₉	—	2	2	no	—
185	C₄²×C₈₉	—	2	1	no	—
186	C₄²×C₈₉	—	2	1	no	—
187	C₄²×C₈₉	—	2	1	no	—
188	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
189	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₈₉	#41	1	2	yes	—
192	C₄²×C₈₉	#41	1	2	yes	—
193	C₂³×C₈₉	—	2	1	no	—
194	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
195	C₂²×D₈₉	—	2	1	no	—
196	Q₈×C₈₉	—	2	1	no	—
197	Q₈×C₈₉	—	2	1	no	—
198	D₄×C₈₉	—	2	1	no	—
199	D₄×C₈₉	—	2	1	no	—
200	D₄×C₈₉	—	4	1	no	—
201	D₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	—	2	2	no	—
203	C₂×C₄×C₈₉	—	2	1	no	—
204	C₂×C₄×C₈₉	—	2	2	no	—
205	C₂×C₄×C₈₉	—	2	2	no	—
206	C₂×C₄×C₈₉	—	4	2	no	—
207	C₂×C₄×C₈₉	—	4	4	no	—
208	C₂×C₄×C₈₉	—	4	2	no	—
209	C₂×C₄×C₈₉	—	4	2	no	—
210	C₂×C₄×C₈₉	—	4	1	no	—
211	C₂×C₄×C₈₉	—	4	1	no	—
212	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
220	C₂²⋊D₈₉	—	4	1	no	—
221	C₂²⋊D₈₉	—	4	1	no	—
222	C₂×Dic₈₉	—	2	2	no	—
223	C₂×Dic₈₉	—	2	1	no	—
224	D₃₅₆	—	2	1	no	—
225	D₃₅₆	—	2	1	no	—
226	C₄×D₈₉	—	4	4	no	—
227	C₄×D₈₉	—	4	1	no	—
228	C₄×D₈₉	—	4	1	no	—
229	Dic₁₇₈	—	2	1	no	—
230	Dic₁₇₈	—	2	1	no	—
231	C₈×C₈₉	—	4	1	no	—
232	C₈×C₈₉	—	4	1	no	—
233	#10623494	—	2	2	no	—
234	#10623494	—	2	2	no	—
235	#10623494	—	2	2	no	—
236	#10623494	—	4	1	no	—
237	#10623494	—	4	1	no	—
238	#10623494	#117	1	2	yes	—
239	#10623494	#117	1	2	yes	—
240	C₂²×C₈₉	—	2	2	no	—
241	C₂²×C₈₉	—	4	2	no	—
242	C₂²×C₈₉	—	4	1	no	—
243	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×C₈₉	#529	1	1	yes	characteristic
245	C₂²×C₈₉	#529	1	1	yes	characteristic
246	C₂×D₈₉	—	4	2	no	—
247	C₂×D₈₉	—	4	1	no	—
248	C₄×C₈₉	—	2	2	no	—
249	C₄×C₈₉	—	2	2	no	—
250	C₄×C₈₉	—	4	2	no	—
251	C₄×C₈₉	—	4	2	no	—
252	C₄×C₈₉	—	4	2	no	—
253	C₄×C₈₉	—	4	1	no	—
254	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
255	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
256	C₄×C₈₉	#532	1	1	yes	characteristic
257	C₄×C₈₉	#532	1	1	yes	characteristic
258	Dic₈₉	—	4	2	no	—
259	Dic₈₉	—	4	1	no	—
260	#21296	—	89	1	no	maximal, Sylow
261	C₂×C₈₉	—	2	1	no	—
262	C₂×C₈₉	—	2	1	no	—
263	C₂×C₈₉	—	8	1	no	—
264	C₂×C₈₉	#2293	1	1	yes	characteristic
265	C₂×C₈₉	#2955	1	2	yes	—
266	D₈₉	—	8	1	no	—
267	#2943	—	89	1	no	—
268	#2922	—	89	1	no	—
269	#2922	—	89	1	no	—
270	#1975	—	89	1	no	—
271	#1974	—	89	1	no	—
272	#1946	—	89	1	no	—
273	#1945	—	89	1	no	—
274	#1938	—	89	1	no	—
275	#1938	—	89	1	no	—
276	#1937	—	89	1	no	—
277	#1937	—	89	1	no	—
278	#1778	—	89	1	no	—
279	#1759	—	89	1	no	—
280	#1759	D₈₉	1	1	yes	characteristic, complemented
281	#1726	—	89	1	no	—
282	C₈₉	#21296	1	1	yes	characteristic, complemented, Sylow
283	C₂×#135	—	89	1	no	—
284	C₄×#41	—	89	1	no	—
285	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
286	#442	—	89	2	no	—
287	#441	—	89	2	no	—
288	#440	—	89	2	no	—
289	#440	—	89	2	no	—
290	#433	—	178	2	no	—
291	#433	—	178	2	no	—
292	#431	—	178	2	no	—
293	#431	—	178	2	no	—
294	C₂×#108	—	89	1	no	—
295	C₂×#108	—	89	1	no	—
296	#427	—	89	1	no	—
297	#424	—	89	1	no	—
298	#424	—	89	1	no	—
299	#424	—	89	1	no	—
300	#424	—	89	1	no	—
301	C₂×#104	—	89	1	no	—
302	C₂×#104	—	89	1	no	—
303	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
304	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
305	#416	—	89	1	no	—
306	#416	—	89	1	no	—
307	#408	—	89	1	no	—
308	#408	—	89	1	no	—
309	#408	—	89	1	no	—
310	#408	—	89	1	no	—
311	C₄×M₁₆	—	89	1	no	—
312	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
313	C₂×#97	—	89	1	no	—
314	C₂×#97	—	89	1	no	—
315	C₂×#97	—	89	1	no	—
316	C₂×C₄×C₈	—	89	1	no	—
317	C₂×C₄×C₈	—	89	1	no	—
318	C₂×C₄×C₈	—	89	1	no	—
319	#376	C₂×D₈₉	1	1	yes	characteristic
320	#341	—	89	1	no	—
321	#341	—	89	1	no	—
322	#339	—	89	1	no	—
323	#339	—	89	1	no	—
324	#339	C₂×D₈₉	1	1	yes	characteristic
325	#339	C₂×D₈₉	1	1	yes	characteristic
326	C₂×#41	—	89	1	no	—
327	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
328	#135	—	178	2	no	—
329	#135	—	178	2	no	—
330	C₂×Q₁₆	—	89	1	no	—
331	C₂×SD₁₆	—	89	1	no	—
332	C₂×SD₁₆	—	89	1	no	—
333	C₂×D₈	—	89	1	no	—
334	C₂×M₁₆	—	89	1	no	—
335	C₂×M₁₆	—	89	1	no	—
336	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
337	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
338	C₂²×C₈	—	89	1	no	—
339	C₂²×C₈	—	89	1	no	—
340	C₂²×C₈	—	89	1	no	—
341	C₂²×C₈	—	89	1	no	—
342	C₄×Q₈	—	89	2	no	—
343	C₄×Q₈	C₄×D₈₉	1	2	yes	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	89	2	no	—
346	C₄×D₄	—	178	2	no	—
347	C₄×D₄	C₄×D₈₉	1	2	yes	—
348	#117	—	2	1	no	—
349	#117	—	89	1	no	—
350	#117	—	178	1	no	—
351	#117	C₂²×D₈₉	1	1	yes	characteristic
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	178	1	no	—
354	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
357	#108	—	178	2	no	—
358	#108	—	178	2	no	—
359	#107	—	89	2	no	—
360	#106	—	89	2	no	—
361	C₄⋊C₈	—	178	2	no	—
362	C₄⋊C₈	—	178	2	no	—
363	C₄⋊C₈	—	178	2	no	—
364	C₄⋊C₈	—	178	2	no	—
365	#104	—	2	2	no	—
366	#104	—	2	2	no	—
367	#104	—	178	2	no	—
368	#104	—	178	2	no	—
369	#103	—	89	2	no	—
370	#103	—	89	2	no	—
371	#102	—	89	2	no	—
372	#102	—	89	2	no	—
373	C₂²⋊C₈	—	178	2	no	—
374	C₂²⋊C₈	—	178	2	no	—
375	C₂²⋊C₈	—	178	2	no	—
376	C₂²⋊C₈	—	178	2	no	—
377	#97	—	2	1	no	—
378	#97	—	89	2	no	—
379	#97	—	89	2	no	—
380	#97	—	178	2	no	—
381	#97	—	178	1	no	—
382	#97	—	178	2	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	89	2	no	—
385	C₄×C₈	—	89	2	no	—
386	C₄×C₈	—	178	2	no	—
387	C₄×C₈	—	178	1	no	—
388	C₄×C₈	—	178	2	no	—
389	#95	—	2	2	no	—
390	#41	—	2	1	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	178	1	no	—
395	#41	—	178	1	no	—
396	#41	—	178	1	no	—
397	#41	—	178	1	no	—
398	C₂×Q₈	—	89	1	no	—
399	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	89	1	no	—
402	C₂×D₄	—	178	1	no	—
403	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	178	2	no	—
409	C₂²×C₄	—	178	1	no	—
410	C₂²×C₄	#13083573	1	2	yes	—
411	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
412	Q₁₆	—	178	2	no	—
413	SD₁₆	—	178	2	no	—
414	SD₁₆	—	178	2	no	—
415	D₈	—	178	2	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	178	1	no	—
421	M₁₆	—	178	1	no	—
422	M₁₆	—	178	1	no	—
423	M₁₆	—	178	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	89	1	no	—
427	C₂×C₈	—	89	1	no	—
428	C₂×C₈	—	89	2	no	—
429	C₂×C₈	—	89	2	no	—
430	C₂×C₈	—	89	2	no	—
431	C₂×C₈	—	89	2	no	—
432	C₂×C₈	—	89	2	no	—
433	C₂×C₈	—	178	1	no	—
434	C₂×C₈	—	178	1	no	—
435	C₂×C₈	—	178	1	no	—
436	C₂×C₈	—	178	1	no	—
437	C₂×C₈	—	178	1	no	—
438	C₂×C₈	—	178	1	no	—
439	C₂×C₈	—	178	1	no	—
440	C₂×C₈	—	178	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	89	2	no	—
443	C₄⋊C₄	—	178	2	no	—
444	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	178	1	no	—
448	C₂²⋊C₄	—	178	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	178	2	no	—
454	C₄²	—	178	1	no	—
455	C₄²	C₂×C₄×D₈₉	1	2	yes	—
456	C₄²	D₄×D₈₉	1	1	yes	characteristic
457	C₄²	D₄×D₈₉	1	1	yes	characteristic
458	C₄²	#13083574	1	2	yes	—
459	C₄²	#13083574	1	2	yes	—
460	C₂³	—	2	1	no	—
461	C₂³	—	178	1	no	—
462	C₂³	C₂×#13083573	1	1	yes	characteristic
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	178	1	no	—
466	Q₈	—	178	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	1	no	—
471	D₄	—	356	1	no	—
472	D₄	—	356	1	no	—
473	D₄	—	178	1	no	—
474	D₄	—	178	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	356	4	no	—
486	C₂×C₄	—	356	1	no	—
487	C₂×C₄	—	356	1	no	—
488	C₂×C₄	—	178	2	no	—
489	C₂×C₄	—	178	1	no	—
490	C₂×C₄	#15667972	1	2	yes	—
491	C₂×C₄	#15667972	1	2	yes	—
492	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
494	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
495	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
496	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
497	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
498	C₈	—	4	1	no	—
499	C₈	—	4	1	no	—
500	C₈	—	89	2	no	—
501	C₈	—	89	2	no	—
502	C₈	—	356	1	no	—
503	C₈	—	356	1	no	—
504	C₈	—	178	2	no	—
505	C₈	—	178	2	no	—
506	C₈	—	178	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	356	1	no	—
511	C₂²	—	356	2	no	—
512	C₂²	C₂×#15667972	1	1	yes	characteristic
513	C₂²	#19152128	1	1	yes	characteristic
514	C₂²	#19152128	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	356	1	no	—
522	C₄	—	356	2	no	—
523	C₄	#117×D₈₉	1	1	yes	characteristic
524	C₄	C₄×#13083574	1	1	yes	characteristic
525	C₄	#19152145	1	1	yes	characteristic
526	C₄	#19152145	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	1	no	—
530	C₂	—	712	1	no	—
531	C₂	#26022715	1	1	yes	characteristic
532	C₂	#26029151	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1759	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1759	D₈₉
hypocenter	C₈₉	#21296
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1759

Complements

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

N	H ≅ G/N	type
2. #26028897	C₂	semidirect
3. #26028896	C₂	semidirect
6. #26021004	C₂	semidirect
7. #26020999	C₂	semidirect
8. #26020964	C₂	semidirect
9. #26020960	C₂	semidirect
10. #26020957	C₂	semidirect
11. #26020953	C₂	semidirect
12. #26020159	C₂	semidirect
13. #26020063	C₂	semidirect
14. #26019939	C₂	semidirect
15. C₈₉×#1759	C₂	semidirect
18. #19151708	C₄	semidirect
19. #19151703	C₄	semidirect
20. #19151698	C₄	semidirect
21. #19151696	C₄	semidirect
280. #1759	D₈₉	semidirect
282. C₈₉	#21296	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#26029050	2
#26028897	2
#26028896	2
#26021142	2
#26021137	2
#26021004	2
#26020999	2
#26020964	2
#26020960	2
#26020957	2
#26020953	2
#26020159	2
#26020063	2
#26019939	2
C₈₉×#1759	2
#21296	89