Subgroups — #36564793

Order 22784.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151660	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151658	C₂	1	1	yes	maximal, characteristic
3	#26022732	C₂	1	1	yes	maximal, characteristic
4	#26020975	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020974	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020972	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020971	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020969	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020968	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020967	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020235	C₂	1	1	yes	maximal, characteristic
12	#26020233	C₂	1	1	yes	maximal, characteristic
13	#26020231	C₂	1	1	yes	maximal, characteristic
14	#26020229	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15667969	C₂²	1	1	yes	characteristic
17	C₂×#15667969	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
19	#19151660	—	2	4	no	—
20	#19151658	—	2	4	no	—
21	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
24	C₂×#15667941	C₂²	1	1	yes	characteristic
25	C₂×#15667941	C₂²	1	1	yes	characteristic
26	C₂×#15667941	C₂²	1	1	yes	characteristic
27	C₂×#15667941	C₂²	1	1	yes	characteristic
28	C₂×#15667941	C₂²	1	1	yes	characteristic
29	C₂×#15667941	C₂²	1	1	yes	characteristic
30	C₂×#15667924	C₂²	1	1	yes	characteristic
31	C₂×#15667924	C₂²	1	1	yes	characteristic
32	C₂×#15667924	C₂²	1	1	yes	characteristic
33	C₂×#15667924	C₂²	1	1	yes	characteristic
34	C₂×#15667922	C₂²	1	1	yes	characteristic
35	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
37	#19151495	C₄	1	1	yes	characteristic
38	#19151495	C₄	1	1	yes	characteristic
39	#19151493	C₄	1	1	yes	characteristic
40	#19151493	C₄	1	1	yes	characteristic
41	#19151472	C₄	1	1	yes	characteristic
42	#19151472	C₄	1	1	yes	characteristic
43	#19151469	C₄	1	1	yes	characteristic
44	#19151469	C₄	1	1	yes	characteristic
45	C₄×#13083553	C₂²	1	1	yes	characteristic
46	C₄×#13083553	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
48	#19151353	C₂²	1	1	yes	characteristic
49	#19151353	C₂²	1	1	yes	characteristic
50	#19151352	C₂²	1	1	yes	characteristic
51	#19151352	C₂²	1	1	yes	characteristic
52	#19151352	C₂²	1	1	yes	characteristic
53	#19151352	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
59	#336×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₈₉	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	C₂²×#10623494	C₂³	1	1	yes	characteristic
68	#15667969	—	4	1	no	—
69	#15667969	—	4	1	no	—
70	#15667969	D₄	1	4	yes	—
71	#15667969	Q₈	1	4	yes	—
72	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
75	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
76	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
77	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
78	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
79	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
80	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
81	C₂×#13083553	C₂×C₄	1	1	yes	characteristic
82	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
83	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
84	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
85	C₂×#13083551	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	C₄²×D₈₉	—	4	1	no	—
92	C₄²×D₈₉	—	4	1	no	—
93	C₄⋊#10623494	—	2	2	no	—
94	C₄⋊#10623494	—	4	1	no	—
95	C₄⋊#10623494	—	4	1	no	—
96	#15667941	—	2	2	no	—
97	#15667941	—	2	2	no	—
98	#15667941	—	4	1	no	—
99	#15667941	—	4	1	no	—
100	#15667941	—	4	1	no	—
101	#15667941	—	4	1	no	—
102	#15667924	—	2	2	no	—
103	#15667924	—	2	2	no	—
104	#15667924	—	2	2	no	—
105	#15667924	—	2	2	no	—
106	#15667922	—	2	2	no	—
107	C₄×#10623494	—	2	2	no	—
108	C₈×Dic₈₉	—	2	2	no	—
109	#15667919	C₂×C₄	1	1	yes	characteristic
110	#15667919	C₂×C₄	1	1	yes	characteristic
111	#15667919	C₂×C₄	1	1	yes	characteristic
112	#15667919	C₂×C₄	1	1	yes	characteristic
113	#15667919	C₂×C₄	1	1	yes	characteristic
114	#15667919	C₂×C₄	1	1	yes	characteristic
115	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₈₉	—	2	2	no	—
125	C₄⋊C₈×C₈₉	—	4	1	no	—
126	C₄⋊C₈×C₈₉	—	4	1	no	—
127	#97×C₈₉	—	2	2	no	—
128	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
129	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₂³×D₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₈₉	—	2	1	no	—
139	C₂×C₄×D₈₉	—	2	1	no	—
140	C₂×C₄×D₈₉	—	2	1	no	—
141	C₂×C₄×D₈₉	—	2	1	no	—
142	C₂×C₄×D₈₉	—	2	2	no	—
143	C₂×C₄×D₈₉	—	2	2	no	—
144	C₂×C₄×D₈₉	—	4	1	no	—
145	C₂×C₄×D₈₉	—	4	1	no	—
146	C₂×C₄×D₈₉	—	4	1	no	—
147	C₂×C₄×D₈₉	—	4	1	no	—
148	C₂×C₄×D₈₉	C₂×D₄	1	2	yes	—
149	C₂×C₄×D₈₉	C₂×Q₈	1	2	yes	—
150	C₂×#10623494	—	2	1	no	—
151	C₂×#10623494	—	2	1	no	—
152	C₂×#10623494	—	2	1	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	—	2	1	no	—
155	C₂×#10623494	—	2	1	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₄⋊Dic₈₉	—	2	2	no	—
163	C₄⋊Dic₈₉	—	4	1	no	—
164	#13083553	—	2	2	no	—
165	#13083553	—	2	2	no	—
166	#13083553	—	4	1	no	—
167	#13083553	—	4	1	no	—
168	#13083553	—	4	1	no	—
169	#13083553	—	4	1	no	—
170	#13083553	C₄⋊C₄	1	4	yes	—
171	#13083553	C₄⋊C₄	1	4	yes	—
172	#13083551	—	4	1	no	—
173	#13083551	—	4	1	no	—
174	#13083551	C₄⋊C₄	1	4	yes	—
175	#13083551	C₄⋊C₄	1	4	yes	—
176	C₄×Dic₈₉	—	2	1	no	—
177	C₄×Dic₈₉	—	2	1	no	—
178	C₄×Dic₈₉	—	2	1	no	—
179	C₄×Dic₈₉	—	2	1	no	—
180	C₄×Dic₈₉	—	4	1	no	—
181	C₄×Dic₈₉	—	4	1	no	—
182	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
183	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
184	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₈×C₈₉	—	2	1	no	—
192	C₂×C₈×C₈₉	—	2	1	no	—
193	C₂×C₈×C₈₉	—	2	1	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	—	2	1	no	—
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	—	2	1	no	—
203	C₄⋊C₄×C₈₉	—	2	2	no	—
204	C₄⋊C₄×C₈₉	—	4	1	no	—
205	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	—	2	1	no	—
207	C₄²×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	—	2	1	no	—
209	C₄²×C₈₉	C₂×D₄	1	2	yes	—
210	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
211	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
212	C₂²×D₈₉	—	2	1	no	—
213	C₂²×D₈₉	—	2	1	no	—
214	C₂²×D₈₉	—	2	1	no	—
215	C₂²×D₈₉	—	2	1	no	—
216	C₂²×D₈₉	—	2	1	no	—
217	C₂²×D₈₉	—	2	1	no	—
218	C₂²×D₈₉	C₂×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	2	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	2	1	no	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	2	1	no	—
234	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
235	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
236	C₂×C₄×C₈₉	#131	1	2	yes	—
237	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
239	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
242	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
243	C₂×Dic₈₉	—	2	1	no	—
244	C₂×Dic₈₉	—	2	1	no	—
245	C₂×Dic₈₉	—	2	1	no	—
246	C₂×Dic₈₉	—	2	1	no	—
247	C₂×Dic₈₉	—	2	1	no	—
248	C₂×Dic₈₉	—	2	1	no	—
249	C₂×Dic₈₉	—	2	1	no	—
250	C₂×Dic₈₉	—	2	1	no	—
251	C₂×Dic₈₉	—	2	1	no	—
252	C₂×Dic₈₉	—	2	1	no	—
253	C₂×Dic₈₉	—	2	1	no	—
254	C₂×Dic₈₉	—	2	1	no	—
255	C₂×Dic₈₉	—	2	1	no	—
256	C₂×Dic₈₉	—	2	1	no	—
257	C₂×Dic₈₉	—	2	1	no	—
258	C₂×Dic₈₉	—	2	1	no	—
259	C₂×Dic₈₉	—	2	1	no	—
260	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
261	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
262	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
263	C₂×Dic₈₉	#131	1	2	yes	—
264	C₄×D₈₉	—	2	2	no	—
265	C₄×D₈₉	—	2	2	no	—
266	C₄×D₈₉	—	2	2	no	—
267	C₄×D₈₉	—	2	2	no	—
268	C₄×D₈₉	—	4	4	no	—
269	C₄×D₈₉	—	4	4	no	—
270	C₈×C₈₉	—	4	1	no	—
271	C₈×C₈₉	—	4	1	no	—
272	C₈×C₈₉	—	4	1	no	—
273	C₈×C₈₉	—	4	1	no	—
274	#10623494	—	4	1	no	—
275	#10623494	—	4	1	no	—
276	#10623494	—	4	1	no	—
277	#10623494	—	4	1	no	—
278	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
279	C₂²×C₈₉	#518	1	1	yes	characteristic
280	C₂²×C₈₉	#519	1	1	yes	characteristic
281	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
282	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
283	C₂²×C₈₉	#568	1	1	yes	characteristic
284	C₂²×C₈₉	#568	1	1	yes	characteristic
285	C₂×D₈₉	—	2	2	no	—
286	C₂×D₈₉	—	2	2	no	—
287	C₂×D₈₉	—	2	2	no	—
288	C₂×D₈₉	—	4	1	no	—
289	C₂×D₈₉	—	4	1	no	—
290	C₂×D₈₉	—	4	1	no	—
291	C₂×D₈₉	—	4	1	no	—
292	C₄×C₈₉	—	2	2	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	2	2	no	—
295	C₄×C₈₉	—	4	1	no	—
296	C₄×C₈₉	—	4	1	no	—
297	C₄×C₈₉	—	4	1	no	—
298	C₄×C₈₉	#537	1	1	yes	characteristic
299	C₄×C₈₉	#537	1	1	yes	characteristic
300	C₄×C₈₉	#544	1	1	yes	characteristic
301	C₄×C₈₉	#544	1	1	yes	characteristic
302	Dic₈₉	—	2	2	no	—
303	Dic₈₉	—	2	2	no	—
304	Dic₈₉	—	2	2	no	—
305	Dic₈₉	—	2	2	no	—
306	Dic₈₉	—	4	1	no	—
307	Dic₈₉	—	4	1	no	—
308	Dic₈₉	—	4	1	no	—
309	#21958	—	89	1	no	maximal, Sylow
310	C₂×C₈₉	#2316	1	1	yes	characteristic
311	C₂×C₈₉	#2906	1	1	yes	characteristic
312	C₂×C₈₉	#2906	1	1	yes	characteristic
313	C₂×C₈₉	#2977	1	1	yes	characteristic
314	C₂×C₈₉	#2978	1	1	yes	characteristic
315	C₂×C₈₉	#2985	1	1	yes	characteristic
316	C₂×C₈₉	#2985	1	1	yes	characteristic
317	D₈₉	—	4	2	no	—
318	C₂×#433	—	89	1	no	—
319	C₂×#433	—	89	1	no	—
320	#2296	—	89	1	no	—
321	#1940	—	89	1	no	—
322	#1940	—	89	1	no	—
323	#1940	—	89	1	no	—
324	#1940	D₈₉	1	1	yes	characteristic, complemented
325	#1939	—	89	1	no	—
326	#1939	—	89	1	no	—
327	#1939	—	89	1	no	—
328	#1939	—	89	1	no	—
329	#1798	—	89	1	no	—
330	#1798	—	89	1	no	—
331	#1797	—	89	1	no	—
332	#1797	—	89	1	no	—
333	C₈₉	#21958	1	1	yes	characteristic, complemented, Sylow
334	C₂×#117	—	89	1	no	—
335	C₂×#117	—	89	1	no	—
336	C₂²×C₄²	—	89	1	no	—
337	#433	—	178	4	no	—
338	#433	—	178	4	no	—
339	C₂×C₄⋊C₈	—	89	1	no	—
340	C₂×C₄⋊C₈	—	89	1	no	—
341	C₂×C₄⋊C₈	—	89	1	no	—
342	C₂×C₄⋊C₈	—	89	1	no	—
343	C₂×C₄⋊C₈	—	89	1	no	—
344	C₂×C₄⋊C₈	—	89	1	no	—
345	C₂×C₄⋊C₈	—	89	1	no	—
346	C₂×C₄⋊C₈	—	89	1	no	—
347	C₂×C₄⋊C₈	—	89	1	no	—
348	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
350	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	—	89	1	no	—
352	C₂×C₂²⋊C₈	—	89	1	no	—
353	C₂×C₂²⋊C₈	—	89	1	no	—
354	C₂×C₂²⋊C₈	—	89	1	no	—
355	C₂×#97	—	89	1	no	—
356	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
357	C₂×C₄×C₈	—	89	1	no	—
358	C₂×C₄×C₈	—	89	1	no	—
359	#389	—	89	1	no	—
360	#389	—	89	1	no	—
361	#389	—	89	1	no	—
362	#389	—	89	1	no	—
363	#385	—	89	1	no	—
364	#385	—	89	1	no	—
365	#385	—	89	1	no	—
366	#385	—	89	1	no	—
367	C₄×C₄⋊C₄	—	89	1	no	—
368	C₄×C₄⋊C₄	—	89	1	no	—
369	C₄×C₄⋊C₄	—	89	1	no	—
370	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
371	#336	—	89	1	no	—
372	#336	—	89	1	no	—
373	#336	—	89	1	no	—
374	#336	—	89	1	no	—
375	#336	—	89	1	no	—
376	#336	—	89	1	no	—
377	#336	C₂×D₈₉	1	1	yes	characteristic
378	#336	C₂×D₈₉	1	1	yes	characteristic
379	C₂³×C₄	—	89	1	no	—
380	C₂³×C₄	—	89	1	no	—
381	C₂³×C₄	—	89	1	no	—
382	C₂²×C₈	—	89	1	no	—
383	C₂²×C₈	—	89	1	no	—
384	C₂²×C₈	—	89	1	no	—
385	C₂²×C₈	—	89	1	no	—
386	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
387	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
388	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
389	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
390	#117	—	89	4	no	—
391	#117	—	89	4	no	—
392	#117	—	356	1	no	—
393	#117	—	356	1	no	—
394	C₂×C₄⋊C₄	—	89	1	no	—
395	C₂×C₄⋊C₄	—	89	1	no	—
396	C₂×C₄⋊C₄	—	89	1	no	—
397	C₂×C₄⋊C₄	—	89	1	no	—
398	C₂×C₄⋊C₄	—	89	1	no	—
399	C₂×C₄⋊C₄	—	89	1	no	—
400	C₂×C₄⋊C₄	—	89	1	no	—
401	C₂×C₄⋊C₄	—	89	1	no	—
402	C₂×C₄⋊C₄	—	89	1	no	—
403	C₂×C₄⋊C₄	—	89	1	no	—
404	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	—	89	1	no	—
407	C₂×C₂²⋊C₄	—	89	1	no	—
408	C₂×C₂²⋊C₄	—	89	1	no	—
409	C₂×C₂²⋊C₄	—	89	1	no	—
410	C₂×C₄²	—	89	1	no	—
411	C₂×C₄²	—	89	1	no	—
412	C₂×C₄²	—	89	1	no	—
413	C₂×C₄²	—	89	1	no	—
414	C₂×C₄²	—	89	1	no	—
415	C₂×C₄²	—	356	1	no	—
416	C₂×C₄²	—	356	1	no	—
417	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
418	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
419	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	4	1	no	—
422	C₄⋊C₈	—	4	1	no	—
423	C₄⋊C₈	—	356	1	no	—
424	C₄⋊C₈	—	356	1	no	—
425	C₄⋊C₈	—	356	1	no	—
426	C₄⋊C₈	—	356	1	no	—
427	C₄⋊C₈	—	356	1	no	—
428	C₄⋊C₈	—	356	1	no	—
429	C₄⋊C₈	—	178	2	no	—
430	C₄⋊C₈	—	178	2	no	—
431	C₄⋊C₈	—	178	2	no	—
432	C₂²⋊C₈	—	178	2	no	—
433	C₂²⋊C₈	—	178	2	no	—
434	C₂²⋊C₈	—	178	2	no	—
435	C₂²⋊C₈	—	178	2	no	—
436	#97	—	2	2	no	—
437	#97	—	178	2	no	—
438	C₄×C₈	—	178	2	no	—
439	C₄×C₈	—	178	2	no	—
440	#95	—	89	1	no	—
441	#95	—	89	1	no	—
442	#95	—	89	1	no	—
443	#95	—	89	1	no	—
444	#95	—	89	1	no	—
445	#95	—	89	1	no	—
446	#95	C₄×D₈₉	1	1	yes	characteristic
447	#95	C₄×D₈₉	1	1	yes	characteristic
448	C₂⁴	—	89	1	no	—
449	C₂²×C₄	—	89	1	no	—
450	C₂²×C₄	—	89	1	no	—
451	C₂²×C₄	—	89	1	no	—
452	C₂²×C₄	—	89	1	no	—
453	C₂²×C₄	—	89	2	no	—
454	C₂²×C₄	—	89	2	no	—
455	C₂²×C₄	—	89	1	no	—
456	C₂²×C₄	—	89	1	no	—
457	C₂²×C₄	—	89	1	no	—
458	C₂²×C₄	—	356	1	no	—
459	C₂²×C₄	—	356	1	no	—
460	C₂²×C₄	—	356	1	no	—
461	C₂²×C₄	—	356	1	no	—
462	C₂²×C₄	—	178	2	no	—
463	C₂²×C₄	—	178	2	no	—
464	C₂²×C₄	—	178	1	no	—
465	C₂²×C₄	—	178	1	no	—
466	C₂²×C₄	—	178	1	no	—
467	C₂²×C₄	—	178	1	no	—
468	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	178	1	no	—
488	C₂×C₈	—	178	1	no	—
489	C₂×C₈	—	178	1	no	—
490	C₂×C₈	—	178	1	no	—
491	C₂×C₈	—	178	1	no	—
492	C₂×C₈	—	178	1	no	—
493	C₂×C₈	—	178	1	no	—
494	C₂×C₈	—	178	1	no	—
495	C₂×C₈	—	178	1	no	—
496	C₂×C₈	—	178	1	no	—
497	C₂×C₈	—	178	1	no	—
498	C₂×C₈	—	178	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	89	4	no	—
502	C₄⋊C₄	—	89	4	no	—
503	C₄⋊C₄	—	356	1	no	—
504	C₄⋊C₄	—	356	1	no	—
505	C₄⋊C₄	—	356	1	no	—
506	C₄⋊C₄	—	356	1	no	—
507	C₄⋊C₄	—	356	1	no	—
508	C₄⋊C₄	—	178	2	no	—
509	C₄⋊C₄	—	178	2	no	—
510	C₄⋊C₄	—	178	2	no	—
511	C₂²⋊C₄	—	89	4	no	—
512	C₂²⋊C₄	—	89	4	no	—
513	C₂²⋊C₄	—	356	1	no	—
514	C₂²⋊C₄	—	356	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	89	2	no	—
520	C₄²	—	89	2	no	—
521	C₄²	—	356	1	no	—
522	C₄²	—	356	1	no	—
523	C₄²	—	178	1	no	—
524	C₄²	—	178	1	no	—
525	C₄²	—	178	1	no	—
526	C₄²	—	178	1	no	—
527	C₄²	D₄×D₈₉	1	2	yes	—
528	C₄²	Q₈×D₈₉	1	2	yes	—
529	C₂³	—	89	2	no	—
530	C₂³	—	178	1	no	—
531	C₂³	—	178	1	no	—
532	C₂³	—	178	1	no	—
533	C₂³	—	178	1	no	—
534	C₂³	—	178	1	no	—
535	C₂³	—	178	1	no	—
536	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	89	2	no	—
553	C₂×C₄	—	89	2	no	—
554	C₂×C₄	—	89	2	no	—
555	C₂×C₄	—	89	2	no	—
556	C₂×C₄	—	356	4	no	—
557	C₂×C₄	—	356	4	no	—
558	C₂×C₄	—	178	1	no	—
559	C₂×C₄	—	178	1	no	—
560	C₂×C₄	—	178	1	no	—
561	C₂×C₄	—	178	1	no	—
562	C₂×C₄	—	178	1	no	—
563	C₂×C₄	—	178	1	no	—
564	C₂×C₄	—	178	1	no	—
565	C₂×C₄	—	178	1	no	—
566	C₂×C₄	—	178	1	no	—
567	C₂×C₄	—	178	1	no	—
568	C₂×C₄	—	178	1	no	—
569	C₂×C₄	—	178	1	no	—
570	C₂×C₄	—	178	1	no	—
571	C₂×C₄	—	178	1	no	—
572	C₂×C₄	—	178	1	no	—
573	C₂×C₄	—	178	1	no	—
574	C₂×C₄	—	178	1	no	—
575	C₂×C₄	—	178	2	no	—
576	C₂×C₄	—	178	2	no	—
577	C₂×C₄	—	178	2	no	—
578	C₂×C₄	—	178	2	no	—
579	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
580	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
581	C₂×C₄	#15668020	1	2	yes	—
582	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
583	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
584	C₂×C₄	#15668057	1	1	yes	characteristic
585	C₂×C₄	#15668058	1	1	yes	characteristic
586	C₂×C₄	#15668059	1	1	yes	characteristic
587	C₂×C₄	#15668060	1	1	yes	characteristic
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	356	1	no	—
593	C₈	—	356	1	no	—
594	C₈	—	356	1	no	—
595	C₈	—	356	1	no	—
596	C₂²	—	356	1	no	—
597	C₂²	—	356	1	no	—
598	C₂²	—	356	1	no	—
599	C₂²	—	356	1	no	—
600	C₂²	—	178	2	no	—
601	C₂²	—	178	2	no	—
602	C₂²	—	178	2	no	—
603	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
604	C₂²	#19152070	1	1	yes	characteristic
605	C₂²	#19152074	1	1	yes	characteristic
606	C₂²	#131×D₈₉	1	1	yes	characteristic
607	C₂²	C₂×#15668020	1	1	yes	characteristic
608	C₂²	#19152363	1	1	yes	characteristic
609	C₂²	#19152364	1	1	yes	characteristic
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	356	1	no	—
617	C₄	—	356	1	no	—
618	C₄	—	356	1	no	—
619	C₄	—	178	2	no	—
620	C₄	—	178	2	no	—
621	C₄	—	178	2	no	—
622	C₄	—	178	2	no	—
623	C₄	#19152177	1	1	yes	characteristic
624	C₄	#19152178	1	1	yes	characteristic
625	C₄	#19152225	1	1	yes	characteristic
626	C₄	#19152228	1	1	yes	characteristic
627	C₂	—	356	2	no	—
628	C₂	#26022867	1	1	yes	characteristic
629	C₂	#26028819	1	1	yes	characteristic
630	C₂	#26028821	1	1	yes	characteristic
631	C₂	#26029303	1	1	yes	characteristic
632	C₂	#26029311	1	1	yes	characteristic
633	C₂	#26029345	1	1	yes	characteristic
634	C₂	#26029348	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1940	C₂
prime radical	C₂³×D₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1940	D₈₉
hypocenter	C₈₉	#21958
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1940

Complements

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

N	H ≅ G/N	type
4. #26020975	C₂	semidirect
5. #26020974	C₂	semidirect
6. #26020972	C₂	semidirect
7. #26020971	C₂	semidirect
8. #26020969	C₂	semidirect
9. #26020968	C₂	semidirect
10. #26020967	C₂	semidirect
15. C₈₉×#1940	C₂	semidirect
324. #1940	D₈₉	semidirect
333. C₈₉	#21958	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151660	2
C₂×#19151658	2
#26022732	2
#26020975	2
#26020974	2
#26020972	2
#26020971	2
#26020969	2
#26020968	2
#26020967	2
#26020235	2
#26020233	2
#26020231	2
#26020229	2
C₈₉×#1940	2
#21958	89