Subgroups — #36557646

Order 22784.

800 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	C₄×#15668032	C₂	1	1	yes	maximal, characteristic
2	C₄×#15668018	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020897	C₂	1	2	yes	maximal, complemented
4	#26020848	C₂	1	2	yes	maximal, complemented
5	#26020582	C₂	1	2	yes	maximal
6	#26020526	C₂	1	2	yes	maximal, complemented
7	C₄×#15667947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#15667938	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#15667939	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019997	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	C₂²	1	1	yes	characteristic
13	C₂×#15668018	C₂²	1	2	yes	—
14	C₄×#13083574	C₂²	1	1	yes	characteristic
15	C₄×#13083564	C₄	1	1	yes	characteristic, complemented
16	C₄×#13083564	C₄	1	1	yes	characteristic, complemented
17	C₄×#13083561	C₄	1	1	yes	characteristic, complemented
18	C₄×#13083561	C₄	1	1	yes	characteristic, complemented
19	C₄×#13083562	C₄	1	1	yes	characteristic, complemented
20	C₄×#13083562	C₄	1	1	yes	characteristic, complemented
21	C₄×#13083559	C₄	1	1	yes	characteristic, complemented
22	C₄×#13083559	C₄	1	1	yes	characteristic, complemented
23	C₂×#15667947	C₂²	1	2	yes	—
24	#19151634	C₂²	1	1	yes	characteristic
25	C₂×#15667939	C₂²	1	2	yes	—
26	C₂×#15667938	C₂²	1	2	yes	—
27	#19151594	C₂²	1	1	yes	characteristic
28	#19151592	C₂²	1	1	yes	characteristic
29	#19151553	C₂²	1	2	yes	—
30	#19151552	—	2	2	no	—
31	C₄×#13083558	C₂²	1	1	yes	characteristic
32	C₄×#13083557	—	2	1	no	—
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₈₉	—	2	1	no	—
35	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
36	#19151362	C₂²	1	2	yes	—
37	#19151359	C₂²	1	2	yes	—
38	#19151357	C₂²	1	2	yes	—
39	#19151352	C₂²	1	2	yes	—
40	#19151352	C₂²	1	2	yes	—
41	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
42	#433×C₈₉	—	2	2	no	—
43	#431×C₈₉	—	2	1	no	—
44	#431×C₈₉	—	2	1	no	—
45	#424×C₈₉	C₂²	1	2	yes	—
46	#408×C₈₉	C₂²	1	2	yes	—
47	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	C₂³	1	1	yes	characteristic
50	#15668032	—	2	4	no	—
51	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
55	#15668018	—	2	4	no	—
56	#15668018	—	2	4	no	—
57	C₂×#13083558	C₂³	1	2	yes	—
58	C₂×#13083557	—	2	2	no	—
59	C₂²×#10623494	C₂³	1	1	yes	characteristic
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₈₉	—	2	2	no	—
62	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₈₉	—	2	1	no	—
67	C₄×C₂²⋊D₈₉	—	2	1	no	—
68	#15667971	C₂³	1	1	yes	characteristic
69	#15667969	—	2	1	no	—
70	C₂×C₄×Dic₈₉	—	2	1	no	—
71	C₂×C₄×Dic₈₉	—	2	1	no	—
72	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
73	C₄²×D₈₉	—	2	1	no	—
74	#15667947	—	2	4	no	—
75	#15667945	C₂×C₄	1	1	yes	characteristic
76	#15667945	C₂×C₄	1	1	yes	characteristic
77	#15667943	C₂×C₄	1	1	yes	characteristic
78	#15667943	C₂×C₄	1	1	yes	characteristic
79	#15667939	—	2	4	no	—
80	#15667938	—	2	4	no	—
81	#15667936	C₂×C₄	1	1	yes	characteristic
82	#15667936	C₂×C₄	1	1	yes	characteristic
83	#15667935	C₂×C₄	1	1	yes	characteristic
84	#15667935	C₂×C₄	1	1	yes	characteristic
85	#15667933	C₂×C₄	1	1	yes	characteristic
86	#15667933	C₂×C₄	1	1	yes	characteristic
87	#15667932	C₂×C₄	1	1	yes	characteristic
88	#15667932	C₂×C₄	1	1	yes	characteristic
89	#15667923	—	2	1	no	—
90	#15667922	—	2	2	no	—
91	C₄×#10623494	—	2	1	no	—
92	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
93	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
94	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
95	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
99	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
100	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
102	C₄×D₄×C₈₉	—	2	1	no	—
103	C₄×D₄×C₈₉	—	2	1	no	—
104	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#117×C₈₉	—	2	1	no	—
107	#117×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	—	2	1	no	—
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₈₉	—	2	2	no	—
111	C₄⋊C₈×C₈₉	—	2	2	no	—
112	C₂²⋊C₈×C₈₉	—	2	2	no	—
113	C₂²⋊C₈×C₈₉	—	2	2	no	—
114	#97×C₈₉	—	2	1	no	—
115	C₄×C₈×C₈₉	—	2	1	no	—
116	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
117	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
118	C₄×C₈×C₈₉	D₄	1	2	yes	—
119	#13083574	—	2	2	no	—
120	#13083574	#41	1	4	yes	—
121	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊D₈₉	—	2	1	no	—
124	C₂²×Dic₈₉	—	2	2	no	—
125	C₂×C₄×D₈₉	—	2	1	no	—
126	C₂×C₄×D₈₉	—	2	1	no	—
127	C₂×C₄×D₈₉	—	2	1	no	—
128	#13083564	—	2	2	no	—
129	#13083562	—	2	2	no	—
130	#13083561	—	2	2	no	—
131	#13083559	—	2	2	no	—
132	#13083558	—	2	2	no	—
133	#13083558	#41	1	4	yes	—
134	#13083557	—	2	8	no	—
135	C₂×#10623494	—	2	2	no	—
136	C₂×#10623494	—	2	2	no	—
137	C₂×#10623494	—	2	2	no	—
138	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
139	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
140	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
141	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
142	C₈×D₈₉	—	2	8	no	—
143	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
145	#13083553	—	2	1	no	—
146	#13083553	—	2	1	no	—
147	C₂²⋊Dic₈₉	—	2	1	no	—
148	#13083551	—	2	1	no	—
149	#13083551	—	2	1	no	—
150	C₄×Dic₈₉	—	2	4	no	—
151	C₄×Dic₈₉	—	2	1	no	—
152	C₄×Dic₈₉	—	2	1	no	—
153	C₄×Dic₈₉	—	2	1	no	—
154	C₄×Dic₈₉	—	2	2	no	—
155	C₄×Dic₈₉	—	2	2	no	—
156	C₄×Dic₈₉	—	4	2	no	—
157	#41×C₈₉	—	2	2	no	—
158	#41×C₈₉	—	2	2	no	—
159	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₈₉	—	2	1	no	—
161	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	—	2	1	no	—
164	C₂²×C₄×C₈₉	—	2	1	no	—
165	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
168	M₁₆×C₈₉	—	2	2	no	—
169	M₁₆×C₈₉	—	2	2	no	—
170	C₂×C₈×C₈₉	—	2	2	no	—
171	C₂×C₈×C₈₉	—	2	2	no	—
172	C₂×C₈×C₈₉	—	2	2	no	—
173	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²⋊C₄×C₈₉	—	2	1	no	—
180	C₂²⋊C₄×C₈₉	—	2	1	no	—
181	C₂²⋊C₄×C₈₉	—	2	1	no	—
182	C₄²×C₈₉	—	2	1	no	—
183	C₄²×C₈₉	—	2	1	no	—
184	C₄²×C₈₉	—	2	1	no	—
185	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₈₉	—	2	1	no	—
190	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
191	C₂²×D₈₉	—	2	1	no	—
192	Q₈×C₈₉	—	2	1	no	—
193	Q₈×C₈₉	—	2	1	no	—
194	D₄×C₈₉	—	2	1	no	—
195	D₄×C₈₉	—	2	1	no	—
196	D₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	—	2	2	no	—
198	C₂×C₄×C₈₉	—	2	2	no	—
199	C₂×C₄×C₈₉	—	2	1	no	—
200	C₂×C₄×C₈₉	—	2	1	no	—
201	C₂×C₄×C₈₉	—	2	1	no	—
202	C₂×C₄×C₈₉	—	4	2	no	—
203	C₂×C₄×C₈₉	—	4	2	no	—
204	C₂×C₄×C₈₉	—	4	2	no	—
205	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
213	C₂²⋊D₈₉	—	2	4	no	—
214	C₂×Dic₈₉	—	2	1	no	—
215	C₂×Dic₈₉	—	2	4	no	—
216	C₂×Dic₈₉	—	2	1	no	—
217	C₂×Dic₈₉	—	2	1	no	—
218	C₂×Dic₈₉	—	4	2	no	—
219	C₂×Dic₈₉	—	4	2	no	—
220	D₃₅₆	—	2	1	no	—
221	D₃₅₆	#117	1	2	yes	—
222	C₄×D₈₉	—	2	4	no	—
223	C₄×D₈₉	—	4	2	no	—
224	C₄×D₈₉	—	4	2	no	—
225	Dic₁₇₈	—	2	1	no	—
226	Dic₁₇₈	#117	1	2	yes	—
227	C₈×C₈₉	—	2	2	no	—
228	C₈×C₈₉	—	2	2	no	—
229	C₈×C₈₉	—	4	2	no	—
230	#10623494	—	2	1	no	—
231	#10623494	—	2	1	no	—
232	#10623494	—	2	1	no	—
233	#10623494	—	2	1	no	—
234	#10623494	—	2	4	no	—
235	C₂²×C₈₉	—	2	1	no	—
236	C₂²×C₈₉	—	2	1	no	—
237	C₂²×C₈₉	—	4	1	no	—
238	C₂²×C₈₉	—	4	1	no	—
239	C₂²×C₈₉	—	4	1	no	—
240	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂²×C₈₉	#529	1	2	yes	—
242	C₂×D₈₉	—	2	2	no	—
243	C₂×D₈₉	—	4	1	no	—
244	C₂×D₈₉	—	4	1	no	—
245	C₄×C₈₉	—	2	1	no	—
246	C₄×C₈₉	—	2	1	no	—
247	C₄×C₈₉	—	4	1	no	—
248	C₄×C₈₉	—	4	1	no	—
249	C₄×C₈₉	—	4	1	no	—
250	C₄×C₈₉	#443	1	2	yes	—
251	C₄×C₈₉	#444	1	2	yes	—
252	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
253	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
254	C₄×C₈₉	#525	1	2	yes	—
255	Dic₈₉	—	2	2	no	—
256	Dic₈₉	—	4	4	no	—
257	Dic₈₉	—	4	1	no	—
258	Dic₈₉	—	4	1	no	—
259	#21137	—	89	1	no	maximal, Sylow
260	C₂×C₈₉	—	2	2	no	—
261	C₂×C₈₉	—	8	1	no	—
262	C₂×C₈₉	#2290	1	1	yes	characteristic
263	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
264	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
265	D₈₉	—	4	2	no	—
266	C₄×#135	—	89	1	no	—
267	#2922	D₈₉	1	1	yes	characteristic, complemented
268	C₄×#131	—	89	1	no	—
269	#1929	—	89	2	no	—
270	#1922	—	89	2	no	—
271	#1876	—	89	2	no	—
272	#1866	—	89	2	no	—
273	C₄×#108	—	89	1	no	—
274	C₄×#104	—	89	1	no	—
275	C₄×#104	—	89	1	no	—
276	#1744	—	89	1	no	—
277	C₈₉	#21137	1	1	yes	characteristic, complemented, Sylow
278	C₂×#135	—	89	1	no	—
279	C₂×#131	—	89	2	no	—
280	C₄×#41	—	89	1	no	—
281	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
282	C₄×Q₁₆	—	89	1	no	—
283	C₄×Q₁₆	—	89	1	no	—
284	C₄×SD₁₆	—	89	1	no	—
285	C₄×SD₁₆	—	89	1	no	—
286	C₄×SD₁₆	—	89	1	no	—
287	C₄×SD₁₆	—	89	1	no	—
288	C₄×D₈	—	89	1	no	—
289	C₄×D₈	—	89	1	no	—
290	#433	—	2	2	no	—
291	#431	—	2	1	no	—
292	#431	—	2	1	no	—
293	C₂×#108	—	89	2	no	—
294	#427	—	89	1	no	—
295	#424	C₂×D₈₉	1	2	yes	—
296	C₂×#104	—	89	2	no	—
297	C₂×#104	—	89	2	no	—
298	#416	—	89	1	no	—
299	#416	—	89	1	no	—
300	#408	C₂×D₈₉	1	2	yes	—
301	#405	—	89	2	no	—
302	#405	—	178	2	no	—
303	C₄×M₁₆	—	89	1	no	—
304	C₄×M₁₆	—	178	1	no	—
305	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
306	C₂×C₄×C₈	—	89	1	no	—
307	C₂×C₄×C₈	—	178	1	no	—
308	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
309	C₄³	—	89	1	no	—
310	#341	—	89	2	no	—
311	#339	—	89	2	no	—
312	#339	—	89	2	no	—
313	#336	—	89	2	no	—
314	#336	—	89	2	no	—
315	C₂×#41	—	89	1	no	—
316	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
317	#135	—	178	4	no	—
318	C₂×Q₁₆	—	89	1	no	—
319	C₂×SD₁₆	—	89	1	no	—
320	C₂×SD₁₆	—	89	1	no	—
321	C₂×D₈	—	89	1	no	—
322	#131	—	178	4	no	—
323	#131	—	178	4	no	—
324	C₂×M₁₆	—	89	2	no	—
325	C₂×M₁₆	—	178	2	no	—
326	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
327	C₂²×C₈	—	89	1	no	—
328	C₂²×C₈	—	89	1	no	—
329	C₂²×C₈	—	178	2	no	—
330	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
331	C₄×Q₈	—	89	1	no	—
332	C₄×Q₈	—	89	1	no	—
333	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
334	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	89	1	no	—
338	C₄×D₄	—	89	1	no	—
339	C₄×D₄	—	178	1	no	—
340	C₄×D₄	—	178	1	no	—
341	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
342	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
343	#117	—	2	1	no	—
344	#117	—	89	1	no	—
345	#117	—	178	1	no	—
346	#117	C₂²×D₈₉	1	1	yes	characteristic
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	89	2	no	—
349	C₂×C₄²	—	178	1	no	—
350	C₂×C₄²	—	178	1	no	—
351	C₂×C₄²	—	178	1	no	—
352	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
353	#108	—	178	4	no	—
354	#107	—	89	1	no	—
355	#107	—	89	1	no	—
356	#106	—	89	1	no	—
357	#106	—	89	1	no	—
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	2	2	no	—
360	#104	—	178	4	no	—
361	#104	—	178	4	no	—
362	#103	—	89	1	no	—
363	#103	—	89	1	no	—
364	#103	—	89	1	no	—
365	#103	—	89	1	no	—
366	#102	—	89	1	no	—
367	#102	—	89	1	no	—
368	#102	—	89	1	no	—
369	#102	—	89	1	no	—
370	C₂²⋊C₈	—	2	2	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	#97	—	2	1	no	—
373	#97	—	178	2	no	—
374	#97	—	178	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	—	89	1	no	—
377	C₄×C₈	—	89	1	no	—
378	C₄×C₈	—	89	1	no	—
379	C₄×C₈	—	89	1	no	—
380	C₄×C₈	—	178	2	no	—
381	C₄×C₈	—	178	1	no	—
382	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
383	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
384	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	89	4	no	—
388	#41	—	178	2	no	—
389	C₂×Q₈	—	89	1	no	—
390	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	89	1	no	—
393	C₂×D₄	—	178	1	no	—
394	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	178	2	no	—
399	C₂²×C₄	—	178	1	no	—
400	C₂²×C₄	—	178	1	no	—
401	C₂²×C₄	—	178	1	no	—
402	C₂²×C₄	#13083574	1	1	yes	characteristic
403	C₂²×C₄	#13083574	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
405	Q₁₆	—	178	2	no	—
406	SD₁₆	—	178	2	no	—
407	SD₁₆	—	178	2	no	—
408	D₈	—	178	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	89	4	no	—
412	M₁₆	—	178	8	no	—
413	M₁₆	—	178	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	89	1	no	—
418	C₂×C₈	—	89	1	no	—
419	C₂×C₈	—	89	1	no	—
420	C₂×C₈	—	89	1	no	—
421	C₂×C₈	—	178	8	no	—
422	C₂×C₈	—	178	2	no	—
423	C₂×C₈	—	178	2	no	—
424	C₂×C₈	—	178	2	no	—
425	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
426	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	89	1	no	—
430	C₄⋊C₄	—	89	1	no	—
431	C₄⋊C₄	—	178	1	no	—
432	C₄⋊C₄	—	178	1	no	—
433	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
434	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	178	1	no	—
439	C₂²⋊C₄	—	178	1	no	—
440	C₂²⋊C₄	—	178	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	356	2	no	—
445	C₄²	—	178	4	no	—
446	C₄²	—	178	2	no	—
447	C₄²	—	178	2	no	—
448	C₄²	—	178	1	no	—
449	C₄²	—	178	1	no	—
450	C₄²	—	178	1	no	—
451	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
452	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
453	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
454	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
455	C₂³	—	2	1	no	—
456	C₂³	—	178	1	no	—
457	C₂³	C₂×#13083574	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	89	2	no	—
461	Q₈	—	178	1	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	89	2	no	—
466	D₄	—	178	4	no	—
467	D₄	—	178	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	356	2	no	—
477	C₂×C₄	—	356	2	no	—
478	C₂×C₄	—	356	2	no	—
479	C₂×C₄	—	356	2	no	—
480	C₂×C₄	—	178	4	no	—
481	C₂×C₄	—	178	1	no	—
482	C₂×C₄	—	178	1	no	—
483	C₂×C₄	—	178	1	no	—
484	C₂×C₄	—	178	4	no	—
485	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
486	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
487	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
488	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
489	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
490	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
491	C₂×C₄	#41×D₈₉	1	2	yes	—
492	C₂×C₄	#41×D₈₉	1	2	yes	—
493	C₈	—	2	2	no	—
494	C₈	—	2	2	no	—
495	C₈	—	4	2	no	—
496	C₈	—	178	1	no	—
497	C₈	—	178	1	no	—
498	C₈	—	178	1	no	—
499	C₈	—	178	1	no	—
500	C₈	—	178	4	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	356	1	no	—
507	C₂²	—	356	1	no	—
508	C₂²	—	178	2	no	—
509	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
510	C₂²	#19152126	1	2	yes	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	356	4	no	—
517	C₄	—	356	1	no	—
518	C₄	—	356	1	no	—
519	C₄	—	178	2	no	—
520	C₄	#19151713	1	2	yes	—
521	C₄	#19151718	1	2	yes	—
522	C₄	#117×D₈₉	1	1	yes	characteristic
523	C₄	#19152066	1	1	yes	characteristic
524	C₄	#19152105	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	8	1	no	—
527	C₂	—	356	2	no	—
528	C₂	#26022689	1	1	yes	characteristic
529	C₂	C₂×#19151713	1	1	yes	characteristic
530	C₂	C₂×#19151718	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2922	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2922	D₈₉
hypocenter	C₈₉	#21137
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #2922

Complements

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

N	H ≅ G/N	type
2. C₄×#15668018	C₂	semidirect
3. #26020897	C₂	semidirect
4. #26020848	C₂	semidirect
6. #26020526	C₂	semidirect
7. C₄×#15667947	C₂	semidirect
8. C₄×#15667938	C₂	semidirect
9. C₄×#15667939	C₂	semidirect
10. #26019997	C₂	semidirect
11. C₈₉×#2922	C₂	semidirect
15. C₄×#13083564	C₄	semidirect
16. C₄×#13083564	C₄	semidirect
17. C₄×#13083561	C₄	semidirect
18. C₄×#13083561	C₄	semidirect
19. C₄×#13083562	C₄	semidirect
20. C₄×#13083562	C₄	semidirect
21. C₄×#13083559	C₄	semidirect
22. C₄×#13083559	C₄	semidirect
267. #2922	D₈₉	semidirect
277. C₈₉	#21137	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15668032	2
C₄×#15668018	2
#26020897	2
#26020848	2
#26020582	2
#26020526	2
C₄×#15667947	2
C₄×#15667938	2
C₄×#15667939	2
#26019997	2
C₈₉×#2922	2
#21137	89