Subgroups — #36552702

Order 22784.

926 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151554	C₂	1	1	yes	maximal, characteristic
2	#26022750	C₂	1	1	yes	maximal, characteristic
3	#26020129	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020129	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020122	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020117	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020038	C₂	1	1	yes	maximal, characteristic
8	#26020038	C₂	1	1	yes	maximal, characteristic
9	#26020031	C₂	1	1	yes	maximal, characteristic
10	#26020026	C₂	1	1	yes	maximal, characteristic
11	#26020005	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019997	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019938	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#433×C₈₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#13083558	C₂²	1	1	yes	characteristic
17	C₂³×#10623494	C₂²	1	1	yes	characteristic
18	#19151554	C₄	1	8	yes	complemented
19	C₂×#15667923	C₂²	1	1	yes	characteristic
20	C₂×#15667923	C₂²	1	1	yes	characteristic
21	C₂×#15667922	C₂²	1	1	yes	characteristic
22	C₂×#15667922	C₂²	1	1	yes	characteristic
23	C₂×#15667922	C₂²	1	1	yes	characteristic
24	C₂×#15667922	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151491	C₄	1	2	yes	—
32	#19151491	C₄	1	2	yes	—
33	#19151484	C₄	1	2	yes	—
34	#19151484	C₄	1	2	yes	—
35	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
39	#19151444	C₂²	1	1	yes	characteristic
40	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
41	#19151352	C₂²	1	1	yes	characteristic
42	#19151352	C₂²	1	1	yes	characteristic
43	#19151352	C₂²	1	1	yes	characteristic
44	#19151352	C₂²	1	1	yes	characteristic
45	#19151352	C₂²	1	1	yes	characteristic
46	#19151352	C₂²	1	1	yes	characteristic
47	#19151352	C₂²	1	1	yes	characteristic
48	#19151352	C₂²	1	1	yes	characteristic
49	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
50	#433×C₈₉	C₄	1	8	yes	complemented
51	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#13083558	—	2	2	no	—
58	C₂×#13083558	—	2	2	no	—
59	C₂×#13083558	C₂×C₄	1	4	yes	—
60	C₂²×#10623494	—	2	2	no	—
61	C₂²×#10623494	—	2	2	no	—
62	C₂²×#10623494	C₂×C₄	1	4	yes	—
63	C₂²×#10623494	C₂³	1	1	yes	characteristic
64	C₂²×#10623494	C₂³	1	1	yes	characteristic
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂²×#10623494	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
77	#15667923	C₂×C₄	1	4	yes	—
78	#15667923	C₂×C₄	1	4	yes	—
79	#15667922	—	2	2	no	—
80	#15667922	—	2	2	no	—
81	#15667922	—	2	2	no	—
82	#15667922	—	2	2	no	—
83	C₄×#10623494	C₂×C₄	1	4	yes	—
84	C₄×#10623494	C₂×C₄	1	4	yes	—
85	C₈×Dic₈₉	—	2	2	no	—
86	C₈×Dic₈₉	—	2	2	no	—
87	C₈×Dic₈₉	—	2	2	no	—
88	C₈×Dic₈₉	—	2	2	no	—
89	#15667919	C₂×C₄	1	2	yes	—
90	#15667919	C₂×C₄	1	2	yes	—
91	#15667919	C₂×C₄	1	2	yes	—
92	#15667919	C₂×C₄	1	2	yes	—
93	#15667919	C₂×C₄	1	2	yes	—
94	#15667919	C₂×C₄	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	#117×C₈₉	C₂×C₄	1	4	yes	—
101	#117×C₈₉	C₂×C₄	1	4	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
109	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
110	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
111	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
112	#97×C₈₉	C₂×C₄	1	4	yes	—
113	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
114	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
117	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
118	#13083558	—	2	8	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	8	no	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₂×#10623494	C₂²×C₄	1	2	yes	—
126	C₂×#10623494	C₂²×C₄	1	2	yes	—
127	C₂×#10623494	C₂²×C₄	1	2	yes	—
128	C₂×#10623494	#41	1	2	yes	—
129	C₂×#10623494	#41	1	2	yes	—
130	C₂×#10623494	#41	1	2	yes	—
131	C₂×#10623494	#41	1	2	yes	—
132	C₄⋊Dic₈₉	—	2	4	no	—
133	C₄⋊Dic₈₉	—	4	2	no	—
134	C₂²⋊Dic₈₉	—	2	4	no	—
135	C₂²⋊Dic₈₉	—	4	2	no	—
136	C₄×Dic₈₉	—	2	1	no	—
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	—	2	1	no	—
143	C₄×Dic₈₉	—	2	1	no	—
144	C₄×Dic₈₉	—	2	4	no	—
145	C₄×Dic₈₉	—	4	2	no	—
146	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₈₉	—	2	1	no	—
160	C₂×C₈×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₂×C₈×C₈₉	—	2	1	no	—
167	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₈₉	C₄²	1	4	yes	—
172	C₄⋊C₄×C₈₉	C₄²	1	4	yes	—
173	C₂²⋊C₄×C₈₉	C₄²	1	4	yes	—
174	C₂²⋊C₄×C₈₉	C₄²	1	4	yes	—
175	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
176	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
177	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
178	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
179	C₂³×C₈₉	—	2	1	no	—
180	C₂³×C₈₉	—	2	1	no	—
181	C₂³×C₈₉	—	2	2	no	—
182	C₂³×C₈₉	—	2	2	no	—
183	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
184	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
196	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
197	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
198	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
199	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
200	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
206	C₂×Dic₈₉	—	2	2	no	—
207	C₂×Dic₈₉	—	2	2	no	—
208	C₂×Dic₈₉	—	2	2	no	—
209	C₂×Dic₈₉	—	2	2	no	—
210	C₂×Dic₈₉	—	2	2	no	—
211	C₂×Dic₈₉	—	2	2	no	—
212	C₂×Dic₈₉	—	2	2	no	—
213	C₂×Dic₈₉	—	2	2	no	—
214	C₂×Dic₈₉	—	2	2	no	—
215	C₂×Dic₈₉	—	2	2	no	—
216	C₂×Dic₈₉	—	2	2	no	—
217	C₂×Dic₈₉	#131	1	4	yes	—
218	C₈×C₈₉	—	2	2	no	—
219	C₈×C₈₉	—	2	2	no	—
220	C₈×C₈₉	—	2	2	no	—
221	C₈×C₈₉	—	2	2	no	—
222	#10623494	—	2	2	no	—
223	#10623494	—	2	2	no	—
224	#10623494	#117	1	4	yes	—
225	#10623494	#117	1	4	yes	—
226	C₂²×C₈₉	—	2	2	no	—
227	C₂²×C₈₉	—	2	2	no	—
228	C₂²×C₈₉	—	2	2	no	—
229	C₂²×C₈₉	—	4	2	no	—
230	C₂²×C₈₉	—	4	2	no	—
231	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
232	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
233	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
234	C₂²×C₈₉	C₂×#131	1	2	yes	—
235	C₂²×C₈₉	#568	1	2	yes	—
236	C₄×C₈₉	—	2	2	no	—
237	C₄×C₈₉	—	2	2	no	—
238	C₄×C₈₉	—	2	2	no	—
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	2	2	no	—
241	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
242	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
243	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
244	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
245	Dic₈₉	—	2	4	no	—
246	Dic₈₉	—	4	2	no	—
247	Dic₈₉	—	4	2	no	—
248	Dic₈₉	—	4	2	no	—
249	#20478	—	89	1	no	maximal, Sylow
250	C₂×C₈₉	—	4	2	no	—
251	C₂×C₈₉	C₄×#117	1	1	yes	characteristic
252	C₂×C₈₉	C₄×#131	1	1	yes	characteristic
253	C₂×C₈₉	#2875	1	1	yes	characteristic
254	C₂×C₈₉	#2968	1	2	yes	—
255	C₂×C₈₉	#2969	1	2	yes	—
256	C₂×#433	D₈₉	1	1	yes	characteristic
257	C₂×#405	—	89	1	no	—
258	#2298	—	89	1	no	—
259	#1771	—	89	1	no	—
260	#1771	—	89	1	no	—
261	#1770	—	89	1	no	—
262	C₈×C₄⋊C₄	—	89	1	no	—
263	#1753	—	89	1	no	—
264	#1753	—	89	1	no	—
265	#1752	—	89	1	no	—
266	C₈×C₂²⋊C₄	—	89	1	no	—
267	#1746	—	89	1	no	—
268	#1744	—	89	1	no	—
269	#1726	—	89	1	no	—
270	C₄×#97	—	89	1	no	—
271	C₈₉	#20478	1	1	yes	characteristic, complemented, Sylow
272	C₂²×M₁₆	—	89	1	no	—
273	C₂³×C₈	—	89	1	no	—
274	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
275	#433	Dic₈₉	1	8	yes	complemented
276	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic
280	#405	—	89	8	no	—
281	C₂×#97	—	89	1	no	—
282	C₂×#97	—	89	1	no	—
283	C₂×#97	—	89	1	no	—
284	C₂×#97	—	89	1	no	—
285	C₂×#97	—	89	1	no	—
286	C₂×#97	—	89	1	no	—
287	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
288	C₂×C₄×C₈	—	89	1	no	—
289	C₂×C₄×C₈	—	89	1	no	—
290	C₂×C₄×C₈	—	89	1	no	—
291	C₂×C₄×C₈	—	89	1	no	—
292	C₂×C₄×C₈	—	89	1	no	—
293	C₂×C₄×C₈	—	89	1	no	—
294	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
295	#388	—	89	2	no	—
296	#388	—	89	2	no	—
297	#387	—	89	2	no	—
298	#387	—	89	2	no	—
299	C₄×C₄⋊C₄	—	89	1	no	—
300	C₄×C₄⋊C₄	—	89	1	no	—
301	C₄×C₂²⋊C₄	—	89	1	no	—
302	C₄×C₂²⋊C₄	—	89	1	no	—
303	#376	—	89	1	no	—
304	C₄³	—	89	1	no	—
305	#336	—	89	1	no	—
306	#336	—	89	1	no	—
307	#336	—	89	1	no	—
308	#336	—	89	1	no	—
309	#336	—	89	1	no	—
310	#336	—	89	1	no	—
311	#336	—	89	1	no	—
312	#336	—	89	1	no	—
313	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
314	C₂×M₁₆	—	89	4	no	—
315	C₂×M₁₆	—	178	2	no	—
316	C₂×M₁₆	—	178	2	no	—
317	C₂²×C₈	—	89	1	no	—
318	C₂²×C₈	—	89	1	no	—
319	C₂²×C₈	—	89	4	no	—
320	C₂²×C₈	—	89	1	no	—
321	C₂²×C₈	—	89	1	no	—
322	C₂²×C₈	—	178	2	no	—
323	C₂²×C₈	—	178	2	no	—
324	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
328	#117	C₄×D₈₉	1	4	yes	—
329	#117	C₂×Dic₈₉	1	4	yes	—
330	C₂×C₄⋊C₄	—	89	2	no	—
331	C₂×C₄⋊C₄	—	89	2	no	—
332	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	89	2	no	—
335	C₂×C₂²⋊C₄	—	89	2	no	—
336	C₂×C₂²⋊C₄	C₄×D₈₉	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₄×D₈₉	1	1	yes	characteristic
338	C₂×C₄²	—	89	2	no	—
339	C₂×C₄²	—	89	2	no	—
340	C₂×C₄²	—	89	1	no	—
341	C₂×C₄²	—	89	1	no	—
342	C₂×C₄²	—	89	1	no	—
343	C₂×C₄²	—	89	1	no	—
344	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
345	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
346	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
347	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
348	C₂²⋊C₈	C₂×Dic₈₉	1	4	yes	—
349	C₂²⋊C₈	C₂×Dic₈₉	1	4	yes	—
350	#97	—	89	4	no	—
351	#97	—	89	4	no	—
352	#97	—	178	2	no	—
353	#97	—	178	2	no	—
354	#97	—	178	2	no	—
355	#97	—	178	2	no	—
356	#97	C₂×Dic₈₉	1	4	yes	—
357	C₄×C₈	—	89	4	no	—
358	C₄×C₈	—	89	4	no	—
359	C₄×C₈	—	178	2	no	—
360	C₄×C₈	—	178	2	no	—
361	C₄×C₈	—	178	2	no	—
362	C₄×C₈	—	178	2	no	—
363	C₄×C₈	C₂×Dic₈₉	1	4	yes	—
364	#95	—	89	2	no	—
365	#95	—	89	2	no	—
366	#95	—	89	2	no	—
367	#95	—	89	2	no	—
368	#95	—	89	2	no	—
369	#95	—	89	2	no	—
370	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	89	2	no	—
376	C₂²×C₄	—	89	2	no	—
377	C₂²×C₄	—	89	2	no	—
378	C₂²×C₄	—	89	2	no	—
379	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
380	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
386	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
387	M₁₆	—	178	8	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	89	2	no	—
397	C₂×C₈	—	89	2	no	—
398	C₂×C₈	—	89	2	no	—
399	C₂×C₈	—	89	2	no	—
400	C₂×C₈	—	89	2	no	—
401	C₂×C₈	—	89	2	no	—
402	C₂×C₈	—	89	2	no	—
403	C₂×C₈	—	89	2	no	—
404	C₂×C₈	—	178	8	no	—
405	C₂×C₈	—	178	1	no	—
406	C₂×C₈	—	178	1	no	—
407	C₂×C₈	—	178	1	no	—
408	C₂×C₈	—	178	1	no	—
409	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
410	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
411	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
412	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
413	C₄⋊C₄	—	356	2	no	—
414	C₄⋊C₄	—	178	4	no	—
415	C₄⋊C₄	C₄×Dic₈₉	1	4	yes	—
416	C₄⋊C₄	C₄×Dic₈₉	1	4	yes	—
417	C₂²⋊C₄	—	356	2	no	—
418	C₂²⋊C₄	—	178	4	no	—
419	C₂²⋊C₄	C₄×Dic₈₉	1	4	yes	—
420	C₂²⋊C₄	C₄×Dic₈₉	1	4	yes	—
421	C₄²	—	356	2	no	—
422	C₄²	—	178	4	no	—
423	C₄²	—	178	1	no	—
424	C₄²	—	178	1	no	—
425	C₄²	—	178	1	no	—
426	C₄²	—	178	1	no	—
427	C₄²	—	178	1	no	—
428	C₄²	—	178	1	no	—
429	C₄²	—	178	1	no	—
430	C₄²	—	178	1	no	—
431	C₄²	C₂×C₄×D₈₉	1	2	yes	—
432	C₄²	C₂×C₄×D₈₉	1	2	yes	—
433	C₄²	C₂²×Dic₈₉	1	2	yes	—
434	C₄²	C₂²×Dic₈₉	1	2	yes	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₂×C₄×Dic₈₉	1	2	yes	—
440	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	89	4	no	—
452	C₂×C₄	—	178	2	no	—
453	C₂×C₄	—	178	2	no	—
454	C₂×C₄	—	178	2	no	—
455	C₂×C₄	—	178	2	no	—
456	C₂×C₄	—	178	2	no	—
457	C₂×C₄	—	178	2	no	—
458	C₂×C₄	—	178	2	no	—
459	C₂×C₄	—	178	2	no	—
460	C₂×C₄	—	178	2	no	—
461	C₂×C₄	—	178	2	no	—
462	C₂×C₄	—	178	2	no	—
463	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
464	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
465	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
466	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
467	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
468	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
469	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
470	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
471	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
472	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
473	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	89	4	no	—
479	C₈	—	89	4	no	—
480	C₈	—	178	2	no	—
481	C₈	—	178	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
488	C₂²	#19152066	1	1	yes	characteristic
489	C₂²	#19152066	1	1	yes	characteristic
490	C₂²	#131×D₈₉	1	2	yes	—
491	C₂²	#19152363	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	356	2	no	—
498	C₄	—	356	2	no	—
499	C₄	—	356	2	no	—
500	C₄	—	178	4	no	—
501	C₄	#117×D₈₉	1	1	yes	characteristic
502	C₄	#117×D₈₉	1	1	yes	characteristic
503	C₄	#41×Dic₈₉	1	1	yes	characteristic
504	C₄	#41×Dic₈₉	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	#117×Dic₈₉	1	1	yes	characteristic
507	C₂	#131×Dic₈₉	1	1	yes	characteristic
508	C₂	#26028678	1	1	yes	characteristic
509	C₂	#26029244	1	2	yes	—
510	C₂	#26029254	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₂×#433×C₈₉	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×#433	D₈₉
hypocenter	C₈₉	#20478
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#433

Complements

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

N	H ≅ G/N	type
3. #26020129	C₂	semidirect
4. #26020129	C₂	semidirect
5. #26020122	C₂	semidirect
6. #26020117	C₂	semidirect
11. #26020005	C₂	semidirect
12. #26019997	C₂	semidirect
13. #26019938	C₂	semidirect
14. #97×Dic₈₉	C₂	semidirect
18. #19151554	C₄	semidirect
50. #433×C₈₉	C₄	semidirect
271. C₈₉	#20478	semidirect
275. #433	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151554	2
#26022750	2
#26020129	2
#26020122	2
#26020117	2
#26020038	2
#26020031	2
#26020026	2
#26020005	2
#26019997	2
#26019938	2
#97×Dic₈₉	2
C₂×#433×C₈₉	2
#20478	89