Subgroups — #36560873

Order 22784.

922 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151715	C₂	1	2	yes	maximal, complemented
2	#26028964	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#15668019	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021172	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020902	C₂	1	2	yes	maximal, complemented
7	#26020581	C₂	1	2	yes	maximal, complemented
8	#26020272	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020117	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020092	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3035	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	C₂×#15668019	C₂²	1	1	yes	characteristic
14	C₂×#15668019	C₂²	1	1	yes	characteristic
15	#19151715	—	2	8	no	—
16	#19151676	—	2	1	no	—
17	#19151676	—	2	1	no	—
18	D₄×#10623494	—	2	1	no	—
19	D₄×#10623494	—	2	1	no	—
20	C₂×#15667948	C₂²	1	2	yes	—
21	#19151622	C₂²	1	1	yes	characteristic
22	C₂×#15667939	C₂²	1	2	yes	—
23	C₂×#15667939	C₂²	1	2	yes	—
24	C₂×#15667939	C₂²	1	2	yes	—
25	#19151565	C₂²	1	2	yes	—
26	#19151554	—	2	1	no	—
27	#19151554	—	2	1	no	—
28	#19151554	C₂²	1	1	yes	characteristic
29	#19151554	C₂²	1	1	yes	characteristic
30	C₄×#13083558	—	2	1	no	—
31	C₄×#13083558	C₂²	1	1	yes	characteristic
32	C₂×C₄×#10623494	—	2	1	no	—
33	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
36	#19151363	C₂²	1	2	yes	—
37	#19151357	C₂²	1	2	yes	—
38	#19151352	C₂²	1	2	yes	—
39	C₂×#135×C₈₉	C₂²	1	2	yes	—
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
42	#464×C₈₉	C₄	1	2	yes	complemented
43	#463×C₈₉	C₄	1	2	yes	complemented
44	#462×C₈₉	C₄	1	1	yes	characteristic, complemented
45	#461×C₈₉	C₄	1	1	yes	characteristic, complemented
46	#460×C₈₉	C₄	1	1	yes	characteristic, complemented
47	#459×C₈₉	C₄	1	1	yes	characteristic, complemented
48	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	#416×C₈₉	C₂²	1	2	yes	—
50	#15668019	—	2	2	no	—
51	#15668019	—	2	2	no	—
52	#15668019	—	2	4	no	—
53	#15668019	—	2	4	no	—
54	#15668019	—	2	2	no	—
55	#15668019	D₄	1	4	yes	complemented
56	C₂×#13083558	—	2	1	no	—
57	C₂×#13083558	—	2	1	no	—
58	C₂×#13083558	—	2	2	no	—
59	C₂×#13083558	C₂³	1	2	yes	—
60	C₂×#13083558	C₂³	1	1	yes	characteristic
61	C₂×#13083558	C₂³	1	1	yes	characteristic
62	C₂²×#10623494	—	2	1	no	—
63	C₂²×#10623494	—	2	1	no	—
64	C₂²×#10623494	—	2	2	no	—
65	C₂²×#10623494	C₂³	1	1	yes	characteristic
66	C₂²×#10623494	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
69	#15667948	—	2	4	no	—
70	C₄⋊#10623494	—	2	1	no	—
71	C₄⋊#10623494	—	2	1	no	—
72	#15667939	—	2	4	no	—
73	#15667939	—	2	4	no	—
74	#15667939	—	2	4	no	—
75	C₂²⋊#10623494	—	2	2	no	—
76	C₂²⋊#10623494	—	2	2	no	—
77	#15667923	—	2	1	no	—
78	#15667923	—	2	1	no	—
79	#15667923	—	2	1	no	—
80	C₄×#10623494	—	2	1	no	—
81	C₄×#10623494	—	2	1	no	—
82	C₄×#10623494	—	2	1	no	—
83	C₄×#10623494	D₄	1	1	yes	characteristic
84	C₄×#10623494	D₄	1	1	yes	characteristic
85	C₄×#10623494	D₄	1	1	yes	characteristic
86	C₄×#10623494	D₄	1	1	yes	characteristic
87	C₈×Dic₈₉	—	2	4	no	—
88	#15667919	—	2	1	no	—
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
91	#135×C₈₉	—	2	4	no	—
92	#135×C₈₉	—	2	4	no	—
93	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
94	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
95	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
96	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
97	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
99	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
100	#124×C₈₉	C₂×C₄	1	2	yes	—
101	#121×C₈₉	—	2	1	no	—
102	#121×C₈₉	—	2	1	no	—
103	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₈₉	—	2	1	no	—
106	C₄×D₄×C₈₉	—	2	1	no	—
107	C₄×D₄×C₈₉	—	2	1	no	—
108	C₄×D₄×C₈₉	—	2	1	no	—
109	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
110	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
111	#117×C₈₉	—	2	1	no	—
112	#117×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₈₉	—	2	1	no	—
114	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
116	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
117	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
118	#103×C₈₉	C₂×C₄	1	2	yes	—
119	#103×C₈₉	C₂×C₄	1	2	yes	—
120	#102×C₈₉	C₂×C₄	1	2	yes	—
121	#102×C₈₉	C₂×C₄	1	2	yes	—
122	C₂²×Dic₈₉	—	2	2	no	—
123	#13083558	—	2	4	no	—
124	#13083558	—	2	1	no	—
125	#13083558	—	2	1	no	—
126	#13083558	—	2	4	no	—
127	#13083558	—	2	2	no	—
128	#13083558	—	2	2	no	—
129	#13083558	—	4	4	no	—
130	#13083558	C₂×D₄	1	2	yes	—
131	#13083558	#41	1	2	yes	—
132	C₂×#10623494	—	2	4	no	—
133	C₂×#10623494	—	2	1	no	—
134	C₂×#10623494	—	2	1	no	—
135	C₂×#10623494	—	2	1	no	—
136	C₂×#10623494	—	2	1	no	—
137	C₂×#10623494	—	2	4	no	—
138	C₂×#10623494	—	2	2	no	—
139	C₂×#10623494	—	4	4	no	—
140	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
141	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
142	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
143	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
144	C₂×#10623494	C₂×D₄	1	2	yes	—
145	C₂×#10623494	#41	1	2	yes	—
146	C₄⋊Dic₈₉	—	2	4	no	—
147	C₄×Dic₈₉	—	2	2	no	—
148	C₄×Dic₈₉	—	2	2	no	—
149	#41×C₈₉	—	2	1	no	—
150	#41×C₈₉	—	2	1	no	—
151	#41×C₈₉	—	2	2	no	—
152	#41×C₈₉	—	2	2	no	—
153	#41×C₈₉	—	2	2	no	—
154	#41×C₈₉	—	2	2	no	—
155	#41×C₈₉	C₂×D₄	1	2	yes	—
156	#41×C₈₉	#41	1	2	yes	—
157	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
158	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₈₉	—	2	1	no	—
160	C₂×D₄×C₈₉	—	2	2	no	—
161	C₂×D₄×C₈₉	—	2	1	no	—
162	C₂×D₄×C₈₉	—	2	1	no	—
163	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	—	2	1	no	—
167	C₂²×C₄×C₈₉	—	2	1	no	—
168	C₂²×C₄×C₈₉	—	2	2	no	—
169	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	Q₁₆×C₈₉	—	2	4	no	—
173	SD₁₆×C₈₉	—	2	4	no	—
174	SD₁₆×C₈₉	—	2	4	no	—
175	D₈×C₈₉	—	2	4	no	—
176	C₂×C₈×C₈₉	—	2	2	no	—
177	C₂×C₈×C₈₉	—	2	2	no	—
178	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
179	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
180	C₄⋊C₄×C₈₉	—	2	1	no	—
181	C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	—	2	1	no	—
184	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
186	C₂²⋊C₄×C₈₉	—	2	1	no	—
187	C₂²⋊C₄×C₈₉	—	2	1	no	—
188	C₂²⋊C₄×C₈₉	—	2	1	no	—
189	C₂²⋊C₄×C₈₉	—	2	2	no	—
190	C₂²⋊C₄×C₈₉	—	2	2	no	—
191	C₄²×C₈₉	—	2	1	no	—
192	C₄²×C₈₉	—	2	1	no	—
193	C₄²×C₈₉	—	2	1	no	—
194	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
195	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
196	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₈₉	—	2	1	no	—
199	C₂³×C₈₉	—	2	2	no	—
200	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
201	Q₈×C₈₉	—	2	1	no	—
202	Q₈×C₈₉	—	2	2	no	—
203	Q₈×C₈₉	—	2	2	no	—
204	Q₈×C₈₉	C₄×D₄	1	2	yes	—
205	D₄×C₈₉	—	2	2	no	—
206	D₄×C₈₉	—	2	2	no	—
207	D₄×C₈₉	—	2	2	no	—
208	D₄×C₈₉	—	2	1	no	—
209	D₄×C₈₉	—	2	2	no	—
210	D₄×C₈₉	—	4	2	no	—
211	D₄×C₈₉	—	4	2	no	—
212	D₄×C₈₉	—	4	2	no	—
213	D₄×C₈₉	—	4	2	no	—
214	D₄×C₈₉	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	2	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	2	no	—
224	C₂×C₄×C₈₉	—	4	2	no	—
225	C₂×C₄×C₈₉	—	4	2	no	—
226	C₂×C₄×C₈₉	—	4	2	no	—
227	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
237	C₂×Dic₈₉	—	2	4	no	—
238	C₂×Dic₈₉	—	4	2	no	—
239	C₂×Dic₈₉	—	4	2	no	—
240	C₈×C₈₉	—	2	2	no	—
241	C₈×C₈₉	—	2	2	no	—
242	#10623494	—	2	2	no	—
243	#10623494	—	2	1	no	—
244	#10623494	—	2	2	no	—
245	#10623494	—	2	1	no	—
246	#10623494	—	4	2	no	—
247	#10623494	#121	1	2	yes	—
248	#10623494	#121	1	2	yes	—
249	C₂²×C₈₉	—	2	1	no	—
250	C₂²×C₈₉	—	2	1	no	—
251	C₂²×C₈₉	—	2	2	no	—
252	C₂²×C₈₉	—	4	1	no	—
253	C₂²×C₈₉	—	4	1	no	—
254	C₂²×C₈₉	—	4	2	no	—
255	C₂²×C₈₉	—	4	2	no	—
256	C₂²×C₈₉	—	4	2	no	—
257	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₈₉	#529	1	1	yes	characteristic
259	C₂²×C₈₉	#532	1	1	yes	characteristic
260	C₄×C₈₉	—	2	1	no	—
261	C₄×C₈₉	—	2	1	no	—
262	C₄×C₈₉	—	2	1	no	—
263	C₄×C₈₉	—	2	2	no	—
264	C₄×C₈₉	—	4	1	no	—
265	C₄×C₈₉	—	4	1	no	—
266	C₄×C₈₉	—	4	2	no	—
267	C₄×C₈₉	#443	1	2	yes	complemented
268	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
270	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
271	C₄×C₈₉	#525	1	1	yes	characteristic
272	Dic₈₉	—	4	4	no	—
273	#21517	—	89	1	no	maximal, Sylow
274	C₂×C₈₉	—	2	1	no	—
275	C₂×C₈₉	—	2	1	no	—
276	C₂×C₈₉	—	4	2	no	—
277	C₂×C₈₉	—	8	2	no	—
278	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
279	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
280	C₂×C₈₉	#2955	1	1	yes	characteristic
281	#3035	D₈₉	1	1	yes	characteristic
282	C₂×#443	—	89	2	no	—
283	#2931	—	89	1	no	—
284	C₄×#131	—	89	1	no	—
285	#1980	—	89	1	no	—
286	#1950	—	89	1	no	—
287	#1929	—	89	2	no	—
288	#1876	—	89	2	no	—
289	#1806	—	89	1	no	—
290	C₈×C₄⋊C₄	—	89	1	no	—
291	#1764	—	89	2	no	—
292	C₈₉	#21517	1	1	yes	characteristic, complemented, Sylow
293	C₂×#135	C₂×D₈₉	1	2	yes	—
294	C₂×#131	—	89	1	no	—
295	C₂×#131	—	89	1	no	—
296	C₂×#131	—	89	2	no	—
297	#532	C₂×D₈₉	1	1	yes	characteristic
298	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
299	#464	Dic₈₉	1	2	yes	complemented
300	#463	Dic₈₉	1	2	yes	complemented
301	#462	Dic₈₉	1	1	yes	characteristic, complemented
302	#461	Dic₈₉	1	1	yes	characteristic, complemented
303	#460	Dic₈₉	1	1	yes	characteristic, complemented
304	#459	Dic₈₉	1	1	yes	characteristic, complemented
305	#443	—	178	8	no	—
306	#436	—	178	1	no	—
307	#436	—	178	1	no	—
308	C₈×D₄	—	178	1	no	—
309	C₈×D₄	—	178	1	no	—
310	C₂×#108	—	89	2	no	—
311	#423	—	89	1	no	—
312	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
313	C₂×#104	—	89	2	no	—
314	C₂×#104	—	89	2	no	—
315	C₂×#104	—	89	2	no	—
316	#416	C₂×D₈₉	1	2	yes	—
317	#408	—	89	2	no	—
318	#405	—	89	1	no	—
319	#405	—	89	1	no	—
320	#405	—	178	1	no	—
321	#405	—	178	1	no	—
322	C₄×M₁₆	—	89	1	no	—
323	C₄×M₁₆	—	178	1	no	—
324	C₂×C₄×C₈	—	89	1	no	—
325	C₂×C₄×C₈	—	89	2	no	—
326	C₂×C₄×C₈	—	178	1	no	—
327	C₄×C₄⋊C₄	—	89	1	no	—
328	#341	—	89	2	no	—
329	#339	—	89	2	no	—
330	#336	—	89	2	no	—
331	C₂×#41	C₂²×D₈₉	1	2	yes	—
332	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
333	#135	—	2	4	no	—
334	#135	—	2	4	no	—
335	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
336	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
337	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
338	C₂×D₈	C₂×Dic₈₉	1	2	yes	—
339	#131	—	89	4	no	—
340	#131	—	178	4	no	—
341	#131	—	178	4	no	—
342	#131	—	178	2	no	—
343	#131	—	178	2	no	—
344	#131	—	178	2	no	—
345	C₂×M₁₆	—	89	1	no	—
346	C₂×M₁₆	—	89	1	no	—
347	C₂×M₁₆	—	89	2	no	—
348	C₂×M₁₆	—	178	2	no	—
349	C₂×M₁₆	—	178	1	no	—
350	C₂×M₁₆	—	178	1	no	—
351	C₂²×C₈	—	89	1	no	—
352	C₂²×C₈	—	89	1	no	—
353	C₂²×C₈	—	178	2	no	—
354	C₂²×C₈	—	178	1	no	—
355	C₂²×C₈	—	178	1	no	—
356	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
357	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic
358	#127	C₂×Dic₈₉	1	1	yes	characteristic
359	#124	C₂×Dic₈₉	1	2	yes	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
363	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
369	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	C₂²×D₈₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	—	178	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	89	2	no	—
375	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
376	#108	—	178	4	no	—
377	C₄⋊C₈	—	178	1	no	—
378	C₄⋊C₈	—	178	1	no	—
379	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂×Dic₈₉	1	1	yes	characteristic
381	C₄⋊C₈	C₂×Dic₈₉	1	2	yes	—
382	#104	—	178	4	no	—
383	#104	—	178	4	no	—
384	#104	—	178	4	no	—
385	#103	C₂×Dic₈₉	1	2	yes	—
386	#103	C₂×Dic₈₉	1	2	yes	—
387	#102	C₂×Dic₈₉	1	2	yes	—
388	#102	C₂×Dic₈₉	1	2	yes	—
389	C₂²⋊C₈	—	178	2	no	—
390	C₂²⋊C₈	—	178	2	no	—
391	#97	—	178	1	no	—
392	#97	—	178	1	no	—
393	#97	—	178	1	no	—
394	C₄×C₈	—	89	1	no	—
395	C₄×C₈	—	89	1	no	—
396	C₄×C₈	—	89	1	no	—
397	C₄×C₈	—	89	1	no	—
398	C₄×C₈	—	178	1	no	—
399	C₄×C₈	—	178	1	no	—
400	C₄×C₈	—	178	4	no	—
401	C₄×C₈	—	178	1	no	—
402	#95	—	178	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	D₄×D₈₉	1	2	yes	—
410	#41	#13083573	1	2	yes	—
411	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
412	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
418	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	178	2	no	—
424	C₂²×C₄	#13083573	1	1	yes	characteristic
425	C₂²×C₄	#13083573	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
427	Q₁₆	—	2	4	no	—
428	SD₁₆	—	2	4	no	—
429	SD₁₆	—	2	4	no	—
430	D₈	—	2	4	no	—
431	M₁₆	—	89	2	no	—
432	M₁₆	—	89	2	no	—
433	M₁₆	—	356	4	no	—
434	M₁₆	—	178	4	no	—
435	M₁₆	—	178	2	no	—
436	M₁₆	—	178	2	no	—
437	M₁₆	—	178	4	no	—
438	M₁₆	—	178	1	no	—
439	M₁₆	—	178	1	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	89	2	no	—
443	C₂×C₈	—	89	1	no	—
444	C₂×C₈	—	89	1	no	—
445	C₂×C₈	—	89	2	no	—
446	C₂×C₈	—	89	1	no	—
447	C₂×C₈	—	89	1	no	—
448	C₂×C₈	—	356	4	no	—
449	C₂×C₈	—	178	4	no	—
450	C₂×C₈	—	178	2	no	—
451	C₂×C₈	—	178	4	no	—
452	C₂×C₈	—	178	1	no	—
453	C₂×C₈	—	178	1	no	—
454	C₂×C₈	—	178	1	no	—
455	C₂×C₈	—	178	1	no	—
456	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
457	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	178	4	no	—
463	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	178	2	no	—
474	C₄²	—	178	2	no	—
475	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
476	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
477	C₄²	D₄×D₈₉	1	1	yes	characteristic
478	C₄²	D₄×D₈₉	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂×#13083573	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	D₄×Dic₈₉	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	D₄×Dic₈₉	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	356	2	no	—
509	C₂×C₄	—	356	2	no	—
510	C₂×C₄	—	178	4	no	—
511	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
512	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
513	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
514	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
515	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
518	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
519	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
520	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	89	2	no	—
524	C₈	—	89	2	no	—
525	C₈	—	356	2	no	—
526	C₈	—	178	2	no	—
527	C₈	—	178	1	no	—
528	C₈	—	178	1	no	—
529	C₈	—	178	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
539	C₂²	#19152129	1	1	yes	characteristic
540	C₂²	#19152143	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	356	4	no	—
549	C₄	#19151715	1	2	yes	complemented
550	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
551	C₄	#41×Dic₈₉	1	1	yes	characteristic
552	C₄	#121×D₈₉	1	1	yes	characteristic
553	C₄	#19152108	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	#121×Dic₈₉	1	1	yes	characteristic
559	C₂	C₂×#19151715	1	1	yes	characteristic
560	C₂	#26029155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3035	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3035	D₈₉
hypocenter	C₈₉	#21517
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. C₂×#19151715	C₂	semidirect
2. #26028964	C₂	semidirect
3. C₄×#15668019	C₂	semidirect
4. #26021172	C₂	semidirect
5. #26021028	C₂	semidirect
6. #26020902	C₂	semidirect
7. #26020581	C₂	semidirect
8. #26020272	C₂	semidirect
9. #26020117	C₂	semidirect
10. #26020092	C₂	semidirect
42. #464×C₈₉	C₄	semidirect
43. #463×C₈₉	C₄	semidirect
44. #462×C₈₉	C₄	semidirect
45. #461×C₈₉	C₄	semidirect
46. #460×C₈₉	C₄	semidirect
47. #459×C₈₉	C₄	semidirect
55. #15668019	D₄	semidirect
267. C₄×C₈₉	#443	semidirect
292. C₈₉	#21517	semidirect
299. #464	Dic₈₉	semidirect
300. #463	Dic₈₉	semidirect
301. #462	Dic₈₉	semidirect
302. #461	Dic₈₉	semidirect
303. #460	Dic₈₉	semidirect
304. #459	Dic₈₉	semidirect
549. C₄	#19151715	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151715	2
#26028964	2
C₄×#15668019	2
#26021172	2
#26021028	2
#26020902	2
#26020581	2
#26020272	2
#26020117	2
#26020092	2
C₈₉×#3035	2
#21517	89