Subgroups — #36565064

Order 22784.

658 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028888	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151658	C₂	1	1	yes	maximal, characteristic
3	#26028814	C₂	1	1	yes	maximal, characteristic
4	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021027	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021025	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020458	C₂	1	1	yes	maximal, characteristic
8	#26020458	C₂	1	1	yes	maximal, characteristic
9	#26020455	C₂	1	1	yes	maximal, characteristic
10	#26020455	C₂	1	1	yes	maximal, characteristic
11	#26020425	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020422	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020391	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020388	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×M₁₆×D₈₉	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×#15667969	C₂²	1	1	yes	characteristic
19	#19151660	—	2	1	no	—
20	#19151660	—	2	1	no	—
21	#19151658	C₄	1	2	yes	—
22	#19151658	C₄	1	2	yes	—
23	#19151658	C₄	1	2	yes	—
24	#19151658	C₄	1	2	yes	—
25	#19151657	—	2	1	no	—
26	#19151657	—	2	1	no	—
27	C₂×#15667948	C₂²	1	1	yes	characteristic
28	C₂×#15667948	C₂²	1	1	yes	characteristic
29	C₂×#15667947	C₂²	1	1	yes	characteristic
30	C₂×#15667947	C₂²	1	1	yes	characteristic
31	C₂×#15667947	C₂²	1	1	yes	characteristic
32	C₂×#15667947	C₂²	1	1	yes	characteristic
33	#19151623	—	2	1	no	—
34	#19151623	—	2	1	no	—
35	#19151623	—	2	1	no	—
36	#19151623	—	2	1	no	—
37	#19151622	C₂²	1	1	yes	characteristic
38	#19151621	C₂²	1	1	yes	characteristic
39	#19151621	C₂²	1	1	yes	characteristic
40	#19151621	C₂²	1	1	yes	characteristic
41	#19151621	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
43	#19151561	C₂²	1	1	yes	characteristic
44	#19151561	C₂²	1	1	yes	characteristic
45	C₂×#15667924	C₂²	1	1	yes	characteristic
46	C₂×#15667924	C₂²	1	1	yes	characteristic
47	C₄×#13083558	C₂²	1	1	yes	characteristic
48	C₂×#15667922	C₂²	1	1	yes	characteristic
49	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
50	#19151363	C₂²	1	1	yes	characteristic
51	#19151363	C₂²	1	1	yes	characteristic
52	#19151362	C₂²	1	1	yes	characteristic
53	#19151362	C₂²	1	1	yes	characteristic
54	#19151362	C₂²	1	1	yes	characteristic
55	#19151362	C₂²	1	1	yes	characteristic
56	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
58	#423×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
60	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
61	#341×C₈₉	C₂²	1	1	yes	characteristic
62	#341×C₈₉	C₂²	1	1	yes	characteristic
63	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
64	C₂×#13083558	C₂³	1	1	yes	characteristic
65	C₂×#13083558	C₂³	1	1	yes	characteristic
66	C₂×#13083558	C₂³	1	1	yes	characteristic
67	C₂×#13083558	C₂³	1	1	yes	characteristic
68	C₂×#13083557	—	2	1	no	—
69	C₂×#13083557	—	2	1	no	—
70	M₁₆×D₈₉	—	4	1	no	—
71	M₁₆×D₈₉	—	4	1	no	—
72	M₁₆×D₈₉	—	4	1	no	—
73	M₁₆×D₈₉	—	4	1	no	—
74	C₂²×#10623494	C₂³	1	1	yes	characteristic
75	C₂²×#10623494	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₂×C₈×D₈₉	—	2	1	no	—
78	#15667969	C₂×C₄	1	1	yes	characteristic
79	#15667969	C₂×C₄	1	1	yes	characteristic
80	#15667969	C₂×C₄	1	1	yes	characteristic
81	#15667969	C₂×C₄	1	1	yes	characteristic
82	#15667969	D₄	1	1	yes	characteristic
83	#15667969	D₄	1	1	yes	characteristic
84	#15667969	D₄	1	1	yes	characteristic
85	#15667969	D₄	1	1	yes	characteristic
86	C₂×#13083553	Q₈	1	1	yes	characteristic
87	C₂×#13083553	Q₈	1	1	yes	characteristic
88	C₂×#13083551	Q₈	1	1	yes	characteristic
89	C₂×#13083551	Q₈	1	1	yes	characteristic
90	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
91	#15667948	—	4	1	no	—
92	#15667948	—	4	1	no	—
93	#15667947	—	4	1	no	—
94	#15667947	—	4	1	no	—
95	#15667947	—	4	1	no	—
96	#15667947	—	4	1	no	—
97	C₄⋊#10623494	—	2	1	no	—
98	C₄⋊#10623494	—	2	1	no	—
99	C₄⋊#10623494	C₂×C₄	1	2	yes	—
100	C₄⋊#10623494	C₂×C₄	1	2	yes	—
101	#15667941	—	2	1	no	—
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667924	—	2	1	no	—
110	#15667924	—	2	1	no	—
111	#15667924	—	2	1	no	—
112	#15667924	—	2	1	no	—
113	#15667924	C₂×C₄	1	2	yes	—
114	#15667924	C₂×C₄	1	2	yes	—
115	#15667924	C₂×C₄	1	2	yes	—
116	#15667924	C₂×C₄	1	2	yes	—
117	#15667923	—	2	1	no	—
118	#15667922	C₂×C₄	1	2	yes	—
119	#15667922	C₂×C₄	1	2	yes	—
120	C₄×#10623494	—	2	1	no	—
121	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
122	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
123	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	#108×C₈₉	—	4	1	no	—
131	#108×C₈₉	—	4	1	no	—
132	C₄⋊C₈×C₈₉	—	2	1	no	—
133	C₄⋊C₈×C₈₉	—	2	1	no	—
134	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
135	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
136	#97×C₈₉	—	2	1	no	—
137	C₄×C₈×C₈₉	—	2	1	no	—
138	C₂³×D₈₉	C₂×Q₈	1	1	yes	characteristic
139	C₂²×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
140	C₂²×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
141	C₂²×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
142	C₂×C₄×D₈₉	—	2	1	no	—
143	C₂×C₄×D₈₉	—	2	1	no	—
144	C₂×C₄×D₈₉	—	2	1	no	—
145	C₂×C₄×D₈₉	—	2	1	no	—
146	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
150	#13083558	—	2	1	no	—
151	#13083558	—	2	1	no	—
152	#13083558	—	2	1	no	—
153	#13083558	—	2	1	no	—
154	#13083558	—	2	1	no	—
155	#13083558	—	2	1	no	—
156	#13083558	—	2	1	no	—
157	#13083558	—	2	1	no	—
158	#13083557	—	4	2	no	—
159	#13083557	—	4	2	no	—
160	C₂×#10623494	—	2	1	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	—	2	1	no	—
163	C₂×#10623494	—	2	1	no	—
164	C₂×#10623494	—	2	1	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	2	1	no	—
168	C₂×#10623494	C₂²×C₄	1	2	yes	—
169	C₂×#10623494	C₂²×C₄	1	2	yes	—
170	C₈×D₈₉	—	4	2	no	—
171	C₈×D₈₉	—	4	2	no	—
172	#13083553	C₄⋊C₄	1	1	yes	characteristic
173	#13083553	C₄⋊C₄	1	1	yes	characteristic
174	#13083553	C₄⋊C₄	1	1	yes	characteristic
175	#13083553	C₄⋊C₄	1	1	yes	characteristic
176	#13083553	C₄⋊C₄	1	1	yes	characteristic
177	#13083553	C₄⋊C₄	1	1	yes	characteristic
178	#13083553	C₄⋊C₄	1	1	yes	characteristic
179	#13083553	C₄⋊C₄	1	1	yes	characteristic
180	#13083551	C₄⋊C₄	1	1	yes	characteristic
181	#13083551	C₄⋊C₄	1	1	yes	characteristic
182	#13083551	C₄⋊C₄	1	1	yes	characteristic
183	#13083551	C₄⋊C₄	1	1	yes	characteristic
184	#13083551	C₄⋊C₄	1	1	yes	characteristic
185	#13083551	C₄⋊C₄	1	1	yes	characteristic
186	#13083551	C₄⋊C₄	1	1	yes	characteristic
187	#13083551	C₄⋊C₄	1	1	yes	characteristic
188	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
193	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
195	M₁₆×C₈₉	—	2	1	no	—
196	M₁₆×C₈₉	—	2	1	no	—
197	M₁₆×C₈₉	—	2	1	no	—
198	M₁₆×C₈₉	—	2	1	no	—
199	M₁₆×C₈₉	—	2	1	no	—
200	M₁₆×C₈₉	—	2	1	no	—
201	M₁₆×C₈₉	—	2	1	no	—
202	M₁₆×C₈₉	—	2	1	no	—
203	C₂×C₈×C₈₉	—	2	1	no	—
204	C₂×C₈×C₈₉	—	2	1	no	—
205	C₂×C₈×C₈₉	—	2	1	no	—
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	1	no	—
209	C₂×C₈×C₈₉	—	2	1	no	—
210	C₂×C₈×C₈₉	—	2	1	no	—
211	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
213	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₈₉	C₂²×Q₈	1	1	yes	characteristic
218	C₂²×D₈₉	—	2	1	no	—
219	C₂²×D₈₉	—	2	1	no	—
220	C₂²×D₈₉	—	4	1	no	—
221	C₂²×D₈₉	—	4	1	no	—
222	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	2	1	no	—
238	C₂×Dic₈₉	—	4	1	no	—
239	C₂×Dic₈₉	—	4	1	no	—
240	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₄×D₈₉	—	2	1	no	—
247	C₄×D₈₉	—	2	1	no	—
248	C₄×D₈₉	—	2	1	no	—
249	C₄×D₈₉	—	2	1	no	—
250	C₄×D₈₉	—	2	1	no	—
251	C₄×D₈₉	—	2	1	no	—
252	C₄×D₈₉	—	2	1	no	—
253	C₄×D₈₉	—	2	1	no	—
254	C₈×C₈₉	—	2	2	no	—
255	C₈×C₈₉	—	2	2	no	—
256	C₈×C₈₉	—	4	1	no	—
257	C₈×C₈₉	—	4	1	no	—
258	C₈×C₈₉	—	4	1	no	—
259	C₈×C₈₉	—	4	1	no	—
260	#10623494	—	2	2	no	—
261	#10623494	—	2	2	no	—
262	#10623494	—	4	1	no	—
263	#10623494	—	4	1	no	—
264	#10623494	—	4	1	no	—
265	#10623494	—	4	1	no	—
266	C₂²×C₈₉	—	2	1	no	—
267	C₂²×C₈₉	—	2	1	no	—
268	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₈₉	#544	1	1	yes	characteristic
270	C₂²×C₈₉	#544	1	1	yes	characteristic
271	C₂×D₈₉	—	2	1	no	—
272	C₂×D₈₉	—	2	1	no	—
273	C₂×D₈₉	—	2	1	no	—
274	C₂×D₈₉	—	2	1	no	—
275	C₂×D₈₉	—	2	1	no	—
276	C₂×D₈₉	—	2	1	no	—
277	C₂×D₈₉	—	8	1	no	—
278	C₂×D₈₉	—	8	1	no	—
279	C₄×C₈₉	—	2	1	no	—
280	C₄×C₈₉	—	2	1	no	—
281	C₄×C₈₉	—	2	1	no	—
282	C₄×C₈₉	—	2	1	no	—
283	C₄×C₈₉	#520	1	1	yes	characteristic
284	C₄×C₈₉	#520	1	1	yes	characteristic
285	C₄×C₈₉	#535	1	1	yes	characteristic
286	C₄×C₈₉	#536	1	1	yes	characteristic
287	Dic₈₉	—	2	1	no	—
288	Dic₈₉	—	2	1	no	—
289	Dic₈₉	—	2	1	no	—
290	Dic₈₉	—	2	1	no	—
291	Dic₈₉	—	2	1	no	—
292	Dic₈₉	—	2	1	no	—
293	#21995	—	89	1	no	maximal, Sylow
294	C₂×C₈₉	—	2	1	no	—
295	C₂×C₈₉	—	2	1	no	—
296	C₂×C₈₉	#2317	1	1	yes	characteristic
297	C₂×C₈₉	#2916	1	1	yes	characteristic
298	C₂×C₈₉	#2916	1	1	yes	characteristic
299	D₈₉	—	4	1	no	—
300	D₈₉	—	4	1	no	—
301	#2921	—	89	1	no	—
302	C₂×#433	—	89	1	no	—
303	#2905	—	89	1	no	—
304	#1950	—	89	1	no	—
305	#1950	—	89	1	no	—
306	#1950	—	89	1	no	—
307	#1950	D₈₉	1	1	yes	characteristic, complemented
308	#1855	—	89	1	no	—
309	#1855	—	89	1	no	—
310	#1855	—	89	1	no	—
311	#1855	—	89	1	no	—
312	#1849	—	89	1	no	—
313	#1848	—	89	1	no	—
314	#1838	—	89	1	no	—
315	#1837	—	89	1	no	—
316	C₈₉	#21995	1	1	yes	characteristic, complemented, Sylow
317	C₂²×M₁₆	—	89	1	no	—
318	C₂²×M₁₆	—	89	1	no	—
319	C₂×#117	—	89	1	no	—
320	#433	—	89	2	no	—
321	#433	—	89	2	no	—
322	#433	—	89	2	no	—
323	#433	—	89	2	no	—
324	#433	—	178	1	no	—
325	#433	—	178	1	no	—
326	#433	—	178	1	no	—
327	#433	—	178	1	no	—
328	C₂×#108	—	89	1	no	—
329	C₂×#108	—	89	1	no	—
330	C₂×#108	—	89	1	no	—
331	C₂×#108	—	89	1	no	—
332	C₂×#108	—	89	1	no	—
333	C₂×#108	—	89	1	no	—
334	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
335	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
336	#424	—	178	1	no	—
337	#424	—	178	1	no	—
338	#424	—	178	1	no	—
339	#424	—	178	1	no	—
340	#423	—	89	1	no	—
341	#423	—	89	1	no	—
342	#423	—	89	1	no	—
343	#423	—	89	1	no	—
344	#423	—	89	1	no	—
345	#423	C₂×D₈₉	1	1	yes	characteristic
346	C₂×C₄⋊C₈	—	89	1	no	—
347	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
348	#407	—	89	1	no	—
349	#407	—	89	1	no	—
350	C₂×C₂²⋊C₈	—	89	1	no	—
351	C₂×C₂²⋊C₈	—	89	1	no	—
352	C₄×M₁₆	—	89	1	no	—
353	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
354	C₂×#97	—	89	1	no	—
355	C₂×C₄×C₈	—	89	1	no	—
356	#341	—	89	1	no	—
357	#341	—	89	1	no	—
358	#341	—	89	1	no	—
359	#341	—	89	1	no	—
360	#341	—	89	1	no	—
361	#341	—	89	1	no	—
362	#341	C₂×D₈₉	1	1	yes	characteristic
363	#341	C₂×D₈₉	1	1	yes	characteristic
364	C₂³×C₄	—	89	1	no	—
365	C₂×M₁₆	—	89	1	no	—
366	C₂×M₁₆	—	89	1	no	—
367	C₂×M₁₆	—	89	1	no	—
368	C₂×M₁₆	—	89	1	no	—
369	C₂×M₁₆	—	356	1	no	—
370	C₂×M₁₆	—	356	1	no	—
371	C₂×M₁₆	—	356	1	no	—
372	C₂×M₁₆	—	356	1	no	—
373	C₂×M₁₆	—	178	1	no	—
374	C₂×M₁₆	—	178	1	no	—
375	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
376	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
377	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
378	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
379	C₂²×C₈	—	89	1	no	—
380	C₂²×C₈	—	89	1	no	—
381	C₂²×C₈	—	178	1	no	—
382	C₂²×C₈	—	178	1	no	—
383	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
384	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
385	#117	—	89	1	no	—
386	#117	—	89	1	no	—
387	#117	—	89	1	no	—
388	#117	—	89	1	no	—
389	#117	—	89	1	no	—
390	#117	—	89	1	no	—
391	#117	—	89	1	no	—
392	#117	—	89	1	no	—
393	C₂×C₄⋊C₄	—	89	1	no	—
394	C₂×C₄⋊C₄	—	89	1	no	—
395	C₂×C₂²⋊C₄	—	89	1	no	—
396	C₂×C₂²⋊C₄	—	89	1	no	—
397	C₂×C₄²	—	89	1	no	—
398	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
399	#108	—	4	1	no	—
400	#108	—	4	1	no	—
401	#108	—	356	1	no	—
402	#108	—	356	1	no	—
403	#108	—	356	1	no	—
404	#108	—	356	1	no	—
405	#108	—	356	1	no	—
406	#108	—	356	1	no	—
407	C₄⋊C₈	—	2	1	no	—
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	89	2	no	—
410	C₄⋊C₈	—	89	2	no	—
411	C₄⋊C₈	—	178	1	no	—
412	C₄⋊C₈	—	178	1	no	—
413	C₄⋊C₈	—	178	1	no	—
414	C₄⋊C₈	—	178	1	no	—
415	C₄⋊C₈	—	178	1	no	—
416	C₄⋊C₈	—	178	1	no	—
417	C₄⋊C₈	—	178	1	no	—
418	C₄⋊C₈	—	178	1	no	—
419	C₄⋊C₈	—	178	1	no	—
420	C₄⋊C₈	—	178	1	no	—
421	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
422	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
423	C₂²⋊C₈	—	89	2	no	—
424	C₂²⋊C₈	—	89	2	no	—
425	C₂²⋊C₈	—	89	2	no	—
426	C₂²⋊C₈	—	89	2	no	—
427	C₂²⋊C₈	—	178	1	no	—
428	C₂²⋊C₈	—	178	1	no	—
429	C₂²⋊C₈	—	178	1	no	—
430	C₂²⋊C₈	—	178	1	no	—
431	#97	—	2	1	no	—
432	#97	—	89	2	no	—
433	#97	—	89	2	no	—
434	#97	—	178	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	89	2	no	—
437	C₄×C₈	—	89	2	no	—
438	C₄×C₈	—	178	1	no	—
439	C₂⁴	—	89	1	no	—
440	C₂²×C₄	—	89	1	no	—
441	C₂²×C₄	—	89	1	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	89	1	no	—
444	C₂²×C₄	—	89	1	no	—
445	C₂²×C₄	—	89	1	no	—
446	C₂²×C₄	—	89	1	no	—
447	C₂²×C₄	—	178	1	no	—
448	C₂²×C₄	—	178	1	no	—
449	C₂²×C₄	—	178	1	no	—
450	C₂²×C₄	—	178	1	no	—
451	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
452	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
453	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
454	M₁₆	—	2	1	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	1	no	—
458	M₁₆	—	2	1	no	—
459	M₁₆	—	2	1	no	—
460	M₁₆	—	2	1	no	—
461	M₁₆	—	2	1	no	—
462	M₁₆	—	356	2	no	—
463	M₁₆	—	356	2	no	—
464	M₁₆	—	178	1	no	—
465	M₁₆	—	178	1	no	—
466	M₁₆	—	178	1	no	—
467	M₁₆	—	178	1	no	—
468	M₁₆	—	178	1	no	—
469	M₁₆	—	178	1	no	—
470	M₁₆	—	178	1	no	—
471	M₁₆	—	178	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
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	—	89	2	no	—
481	C₂×C₈	—	89	2	no	—
482	C₂×C₈	—	356	2	no	—
483	C₂×C₈	—	356	2	no	—
484	C₂×C₈	—	178	1	no	—
485	C₂×C₈	—	178	1	no	—
486	C₂×C₈	—	178	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	C₂×C₄×D₈₉	1	2	yes	—
493	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
494	C₄⋊C₄	—	89	1	no	—
495	C₄⋊C₄	—	89	1	no	—
496	C₄⋊C₄	—	89	1	no	—
497	C₄⋊C₄	—	89	1	no	—
498	C₄⋊C₄	—	89	1	no	—
499	C₄⋊C₄	—	89	1	no	—
500	C₄⋊C₄	—	89	1	no	—
501	C₄⋊C₄	—	89	1	no	—
502	C₂²⋊C₄	—	89	1	no	—
503	C₂²⋊C₄	—	89	1	no	—
504	C₂²⋊C₄	—	89	1	no	—
505	C₂²⋊C₄	—	89	1	no	—
506	C₂²⋊C₄	—	89	1	no	—
507	C₂²⋊C₄	—	89	1	no	—
508	C₂²⋊C₄	—	89	1	no	—
509	C₂²⋊C₄	—	89	1	no	—
510	C₄²	—	89	1	no	—
511	C₄²	—	89	1	no	—
512	C₄²	—	89	1	no	—
513	C₄²	—	89	1	no	—
514	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
515	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
516	C₄²	D₄×D₈₉	1	1	yes	characteristic
517	C₄²	D₄×D₈₉	1	1	yes	characteristic
518	C₂³	—	89	1	no	—
519	C₂³	—	89	1	no	—
520	C₂³	—	356	1	no	—
521	C₂³	—	356	1	no	—
522	C₂³	—	178	1	no	—
523	C₂³	—	178	1	no	—
524	C₂³	C₂×Q₈×D₈₉	1	1	yes	characteristic
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	89	1	no	—
528	C₂×C₄	—	89	1	no	—
529	C₂×C₄	—	89	1	no	—
530	C₂×C₄	—	89	1	no	—
531	C₂×C₄	—	89	1	no	—
532	C₂×C₄	—	89	1	no	—
533	C₂×C₄	—	356	1	no	—
534	C₂×C₄	—	356	1	no	—
535	C₂×C₄	—	178	1	no	—
536	C₂×C₄	—	178	1	no	—
537	C₂×C₄	—	178	1	no	—
538	C₂×C₄	—	178	1	no	—
539	C₂×C₄	—	178	1	no	—
540	C₂×C₄	—	178	1	no	—
541	C₂×C₄	—	178	1	no	—
542	C₂×C₄	—	178	1	no	—
543	C₂×C₄	—	178	1	no	—
544	C₂×C₄	—	178	1	no	—
545	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
546	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
547	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
548	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
551	C₂×C₄	#15668057	1	1	yes	characteristic
552	C₂×C₄	#15668058	1	1	yes	characteristic
553	C₂×C₄	#15668059	1	1	yes	characteristic
554	C₂×C₄	#15668060	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	356	1	no	—
562	C₈	—	356	1	no	—
563	C₈	—	356	1	no	—
564	C₈	—	356	1	no	—
565	C₈	—	178	2	no	—
566	C₈	—	178	2	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	178	1	no	—
570	C₂²	—	178	1	no	—
571	C₂²	—	178	1	no	—
572	C₂²	—	178	1	no	—
573	C₂²	—	178	1	no	—
574	C₂²	—	178	1	no	—
575	C₂²	—	712	1	no	—
576	C₂²	—	712	1	no	—
577	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
578	C₂²	#19152225	1	1	yes	characteristic
579	C₂²	#19152228	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	178	1	no	—
585	C₄	—	178	1	no	—
586	C₄	—	178	1	no	—
587	C₄	—	178	1	no	—
588	C₄	—	178	1	no	—
589	C₄	—	178	1	no	—
590	C₄	#19152077	1	1	yes	characteristic
591	C₄	#19152080	1	1	yes	characteristic
592	C₄	#19152164	1	1	yes	characteristic
593	C₄	#19152171	1	1	yes	characteristic
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	356	1	no	—
597	C₂	—	356	1	no	—
598	C₂	#26022874	1	1	yes	characteristic
599	C₂	#26028860	1	1	yes	characteristic
600	C₂	#26028862	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	C₈₉×#1950	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₂×Q₈
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1950	D₈₉
hypocenter	C₈₉	#21995
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #26021028	C₂	semidirect
5. #26021027	C₂	semidirect
6. #26021025	C₂	semidirect
11. #26020425	C₂	semidirect
12. #26020422	C₂	semidirect
13. #26020391	C₂	semidirect
14. #26020388	C₂	semidirect
15. C₈₉×#1950	C₂	semidirect
307. #1950	D₈₉	semidirect
316. C₈₉	#21995	semidirect

Maximal subgroups

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

subgroup	index
#26028888	2
C₂×#19151658	2
#26028814	2
#26021028	2
#26021027	2
#26021025	2
#26020458	2
#26020455	2
#26020425	2
#26020422	2
#26020391	2
#26020388	2
C₈₉×#1950	2
#21995	89