Subgroups — #36461709

Order 22784.

836 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151646	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19151580	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151580	C₂	1	1	yes	maximal, characteristic
4	#26028696	C₂	1	1	yes	maximal, characteristic
5	#26019978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151356	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1738	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083574	C₂²	1	1	yes	characteristic
9	C₂²×#13083558	C₂²	1	1	yes	characteristic
10	C₂²×#13083558	C₂²	1	1	yes	characteristic
11	C₂²×#13083558	C₂²	1	1	yes	characteristic
12	#19151646	—	2	2	no	—
13	#19151646	—	2	2	no	—
14	C₂×#15667947	—	2	2	no	—
15	#19151580	—	2	2	no	—
16	#19151580	—	2	2	no	—
17	#19151580	—	2	2	no	—
18	#19151580	—	2	2	no	—
19	C₂×#15667930	—	2	1	no	—
20	C₂×#15667930	—	2	1	no	—
21	C₂×#15667928	—	2	1	no	—
22	C₂×#15667928	—	2	1	no	—
23	#19151566	—	2	2	no	—
24	#19151564	—	2	2	no	—
25	#19151561	C₄	1	4	yes	—
26	#19151362	—	2	2	no	—
27	#19151356	—	2	2	no	—
28	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
31	#341×C₈₉	—	2	2	no	—
32	C₂×#13083574	—	2	1	no	—
33	C₂×#13083574	—	2	1	no	—
34	C₂×#13083574	—	2	1	no	—
35	C₂×#13083574	—	2	1	no	—
36	C₂×#13083574	—	2	1	no	—
37	C₂×#13083574	—	2	1	no	—
38	C₂×#13083574	—	2	1	no	—
39	C₂×#13083574	—	2	1	no	—
40	C₂×#13083574	—	2	1	no	—
41	C₂×#13083574	—	2	1	no	—
42	C₂×#13083574	—	2	1	no	—
43	C₂×#13083574	—	2	1	no	—
44	C₂²×Dic₁₇₈	D₄	1	1	yes	characteristic
45	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
46	C₂²×C₂²⋊D₈₉	Q₈	1	2	yes	—
47	C₂²×C₄×D₈₉	C₂×C₄	1	2	yes	—
48	C₂×#13083558	—	2	1	no	—
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083558	—	2	1	no	—
53	C₂×#13083558	—	2	1	no	—
54	C₂×#13083558	—	2	1	no	—
55	C₂×#13083558	—	2	1	no	—
56	C₂×#13083558	—	2	1	no	—
57	C₂×#13083558	—	2	1	no	—
58	C₂×#13083558	—	2	1	no	—
59	C₂×#13083558	—	2	1	no	—
60	C₂×#13083558	—	2	1	no	—
61	C₂×#13083558	—	2	1	no	—
62	C₂×#13083558	C₂×C₄	1	2	yes	—
63	C₂×#13083558	D₄	1	2	yes	—
64	C₂×#13083558	D₄	1	2	yes	—
65	C₂×#13083558	D₄	1	2	yes	—
66	C₂²×#10623494	—	2	1	no	—
67	C₂²×#10623494	—	2	1	no	—
68	C₂²×#10623494	D₄	1	2	yes	—
69	#15667947	—	2	8	no	—
70	#15667930	—	2	4	no	—
71	#15667930	—	2	4	no	—
72	#15667928	—	2	4	no	—
73	#15667928	—	2	4	no	—
74	#15667924	—	2	8	no	—
75	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₈₉	—	2	1	no	—
77	C₂×M₁₆×C₈₉	—	2	1	no	—
78	C₂×M₁₆×C₈₉	—	2	1	no	—
79	C₂×M₁₆×C₈₉	—	2	1	no	—
80	C₂×M₁₆×C₈₉	—	2	1	no	—
81	C₂×M₁₆×C₈₉	—	2	1	no	—
82	C₂×M₁₆×C₈₉	—	2	1	no	—
83	C₂×M₁₆×C₈₉	—	2	1	no	—
84	C₂×M₁₆×C₈₉	—	2	1	no	—
85	C₂×M₁₆×C₈₉	—	2	1	no	—
86	C₂×M₁₆×C₈₉	—	2	1	no	—
87	C₂×M₁₆×C₈₉	—	2	1	no	—
88	C₂×M₁₆×C₈₉	—	2	1	no	—
89	C₂×M₁₆×C₈₉	—	2	1	no	—
90	C₂×M₁₆×C₈₉	—	2	1	no	—
91	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
92	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
93	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
94	C₂²×C₈×C₈₉	—	2	1	no	—
95	C₂²×C₈×C₈₉	—	2	1	no	—
96	C₂²×C₈×C₈₉	—	2	1	no	—
97	C₂³×D₈₉	C₄⋊C₄	1	2	yes	—
98	#13083574	—	4	1	no	—
99	#13083574	—	4	1	no	—
100	#13083574	—	4	1	no	—
101	#13083574	—	4	1	no	—
102	#13083574	—	4	1	no	—
103	#13083574	—	4	1	no	—
104	#13083574	—	4	1	no	—
105	#13083574	—	4	1	no	—
106	#13083574	—	4	1	no	—
107	#13083574	—	4	1	no	—
108	#13083574	—	4	1	no	—
109	#13083574	—	4	1	no	—
110	#13083574	—	4	1	no	—
111	#13083574	—	4	1	no	—
112	#13083574	—	4	1	no	—
113	#13083574	—	4	1	no	—
114	C₂×Dic₁₇₈	—	2	1	no	—
115	C₂×Dic₁₇₈	—	2	1	no	—
116	C₂×Dic₁₇₈	—	2	1	no	—
117	C₂×Dic₁₇₈	—	2	1	no	—
118	C₂×Dic₁₇₈	—	2	1	no	—
119	C₂×Dic₁₇₈	—	2	1	no	—
120	C₂×D₃₅₆	—	2	1	no	—
121	C₂×D₃₅₆	—	2	1	no	—
122	C₂×D₃₅₆	—	2	1	no	—
123	C₂×D₃₅₆	—	2	1	no	—
124	C₂×D₃₅₆	—	2	1	no	—
125	C₂×D₃₅₆	—	2	1	no	—
126	C₂×C₂²⋊D₈₉	—	2	2	no	—
127	C₂×C₂²⋊D₈₉	—	2	2	no	—
128	C₂×C₂²⋊D₈₉	—	2	2	no	—
129	C₂×C₂²⋊D₈₉	—	2	2	no	—
130	C₂×C₂²⋊D₈₉	—	2	2	no	—
131	C₂×C₂²⋊D₈₉	—	2	2	no	—
132	C₂²×Dic₈₉	C₄⋊C₄	1	2	yes	—
133	C₂×C₄×D₈₉	—	2	2	no	—
134	C₂×C₄×D₈₉	—	2	2	no	—
135	C₂×C₄×D₈₉	—	2	2	no	—
136	C₂×C₄×D₈₉	—	2	2	no	—
137	C₂×C₄×D₈₉	—	2	2	no	—
138	C₂×C₄×D₈₉	—	2	2	no	—
139	#13083558	—	2	2	no	—
140	#13083558	—	2	2	no	—
141	#13083558	—	2	2	no	—
142	#13083558	—	2	2	no	—
143	#13083558	—	2	2	no	—
144	#13083558	—	2	2	no	—
145	#13083558	—	2	2	no	—
146	#13083558	—	2	2	no	—
147	#13083558	—	4	1	no	—
148	#13083558	—	4	1	no	—
149	#13083558	—	4	1	no	—
150	#13083558	—	4	1	no	—
151	C₂×#10623494	—	2	2	no	—
152	C₂×#10623494	—	2	2	no	—
153	C₂×#10623494	—	2	2	no	—
154	C₂×#10623494	—	2	2	no	—
155	C₂×#10623494	—	4	1	no	—
156	C₂×#10623494	—	4	1	no	—
157	C₂×#10623494	—	4	1	no	—
158	C₂×#10623494	—	4	1	no	—
159	C₂×#10623494	C₂²⋊C₄	1	4	yes	—
160	C₂⁴×C₈₉	C₂×Q₈	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
175	M₁₆×C₈₉	—	2	2	no	—
176	M₁₆×C₈₉	—	2	2	no	—
177	M₁₆×C₈₉	—	2	2	no	—
178	M₁₆×C₈₉	—	2	2	no	—
179	M₁₆×C₈₉	—	2	2	no	—
180	M₁₆×C₈₉	—	2	2	no	—
181	M₁₆×C₈₉	—	4	1	no	—
182	M₁₆×C₈₉	—	4	1	no	—
183	M₁₆×C₈₉	—	4	1	no	—
184	M₁₆×C₈₉	—	4	1	no	—
185	M₁₆×C₈₉	—	4	1	no	—
186	M₁₆×C₈₉	—	4	1	no	—
187	C₂×C₈×C₈₉	—	2	2	no	—
188	C₂×C₈×C₈₉	—	2	2	no	—
189	C₂×C₈×C₈₉	—	2	2	no	—
190	C₂×C₈×C₈₉	—	4	1	no	—
191	C₂×C₈×C₈₉	—	4	1	no	—
192	C₂×C₈×C₈₉	—	4	1	no	—
193	C₂×C₈×C₈₉	—	4	1	no	—
194	C₂×C₈×C₈₉	—	4	1	no	—
195	C₂×C₈×C₈₉	—	4	1	no	—
196	C₂³×C₈₉	—	8	1	no	—
197	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂³×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂²×D₈₉	—	2	2	no	—
205	C₂²×D₈₉	—	2	2	no	—
206	C₂²×D₈₉	—	2	2	no	—
207	C₂²×D₈₉	—	8	2	no	—
208	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
215	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
216	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
217	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
218	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
221	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
222	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
223	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
224	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
225	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
226	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
227	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
228	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
229	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
230	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
231	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
232	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
233	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
234	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
235	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
236	C₂²⋊D₈₉	—	4	2	no	—
237	C₂²⋊D₈₉	—	4	2	no	—
238	C₂²⋊D₈₉	—	4	2	no	—
239	C₂²⋊D₈₉	—	4	2	no	—
240	C₂×Dic₈₉	—	2	2	no	—
241	C₂×Dic₈₉	—	2	2	no	—
242	C₂×Dic₈₉	—	2	2	no	—
243	D₃₅₆	—	4	1	no	—
244	D₃₅₆	—	4	1	no	—
245	D₃₅₆	—	4	1	no	—
246	D₃₅₆	—	4	1	no	—
247	C₄×D₈₉	—	4	2	no	—
248	C₄×D₈₉	—	4	2	no	—
249	C₄×D₈₉	—	4	2	no	—
250	C₄×D₈₉	—	4	2	no	—
251	Dic₁₇₈	—	4	1	no	—
252	Dic₁₇₈	—	4	1	no	—
253	Dic₁₇₈	—	4	1	no	—
254	Dic₁₇₈	—	4	1	no	—
255	C₈×C₈₉	—	4	2	no	—
256	C₈×C₈₉	—	4	2	no	—
257	C₈×C₈₉	—	4	2	no	—
258	#10623494	—	2	4	no	—
259	#10623494	—	4	2	no	—
260	#10623494	—	4	2	no	—
261	C₂²×C₈₉	—	4	1	no	—
262	C₂²×C₈₉	—	4	1	no	—
263	C₂²×C₈₉	—	4	1	no	—
264	C₂²×C₈₉	—	4	1	no	—
265	C₂²×C₈₉	—	4	1	no	—
266	C₂²×C₈₉	—	4	1	no	—
267	C₂²×C₈₉	—	4	1	no	—
268	C₂²×C₈₉	#380	1	1	yes	characteristic
269	C₂²×C₈₉	#385	1	1	yes	characteristic
270	C₂²×C₈₉	#385	1	1	yes	characteristic
271	C₂²×C₈₉	#393	1	1	yes	characteristic
272	C₂²×C₈₉	#396	1	1	yes	characteristic
273	C₂²×C₈₉	#396	1	1	yes	characteristic
274	C₂²×C₈₉	#399	1	1	yes	characteristic
275	C₂×D₈₉	—	4	4	no	—
276	C₂×D₈₉	—	4	2	no	—
277	C₂×D₈₉	—	8	2	no	—
278	C₂×D₈₉	—	8	2	no	—
279	C₄×C₈₉	#386	1	1	yes	characteristic
280	C₄×C₈₉	#388	1	1	yes	characteristic
281	C₄×C₈₉	#388	1	1	yes	characteristic
282	C₄×C₈₉	#390	1	1	yes	characteristic
283	C₄×C₈₉	#392	1	1	yes	characteristic
284	C₄×C₈₉	#394	1	1	yes	characteristic
285	C₄×C₈₉	#394	1	1	yes	characteristic
286	C₄×C₈₉	#397	1	1	yes	characteristic
287	Dic₈₉	—	4	2	no	—
288	#11103	—	89	1	no	maximal, Sylow
289	C₂×C₈₉	—	2	1	no	—
290	C₂×C₈₉	—	2	1	no	—
291	C₂×C₈₉	—	2	1	no	—
292	C₂×C₈₉	—	2	1	no	—
293	C₂×C₈₉	—	2	1	no	—
294	C₂×C₈₉	—	2	1	no	—
295	C₂×C₈₉	—	2	1	no	—
296	C₂×C₈₉	#1439	1	1	yes	characteristic
297	D₈₉	—	8	2	no	—
298	C₂×#430	—	89	1	no	—
299	C₂×#413	—	89	1	no	—
300	C₂×#413	—	89	1	no	—
301	#2879	—	89	1	no	—
302	#1738	—	89	1	no	—
303	#1738	D₈₉	1	1	yes	characteristic, complemented
304	C₂×#338	—	89	1	no	—
305	C₈₉	#11103	1	1	yes	characteristic, complemented, Sylow
306	C₂²×#41	—	89	1	no	—
307	C₂²×M₁₆	—	89	1	no	—
308	C₂²×M₁₆	—	89	1	no	—
309	C₂²×M₁₆	—	89	1	no	—
310	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
311	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
312	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
313	#430	—	178	2	no	—
314	#430	—	178	2	no	—
315	C₂×#108	—	178	2	no	—
316	#413	—	178	2	no	—
317	#413	—	178	2	no	—
318	#413	—	178	2	no	—
319	#413	—	178	2	no	—
320	C₂×#101	—	178	1	no	—
321	C₂×#101	—	178	1	no	—
322	C₂×#100	—	178	1	no	—
323	C₂×#100	—	178	1	no	—
324	#408	—	178	2	no	—
325	#408	—	178	2	no	—
326	#407	—	89	4	no	—
327	#341	—	2	2	no	—
328	#341	—	178	2	no	—
329	#338	—	178	2	no	—
330	C₂×#41	—	178	1	no	—
331	C₂×#41	—	178	1	no	—
332	C₂×#41	—	178	1	no	—
333	C₂×#41	—	178	1	no	—
334	C₂×#41	—	178	1	no	—
335	C₂×#41	—	178	1	no	—
336	C₂×#41	—	178	1	no	—
337	C₂×#41	—	178	1	no	—
338	C₂×#41	—	178	1	no	—
339	C₂×#41	—	178	1	no	—
340	C₂×#41	—	178	1	no	—
341	C₂×#41	—	178	1	no	—
342	C₂²×Q₈	—	89	1	no	—
343	C₂²×D₄	—	89	2	no	—
344	C₂²×D₄	—	89	1	no	—
345	C₂³×C₄	—	89	2	no	—
346	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	89	2	no	—
363	C₂×M₁₆	—	89	2	no	—
364	C₂×M₁₆	—	89	2	no	—
365	C₂×M₁₆	—	89	2	no	—
366	C₂×M₁₆	—	178	1	no	—
367	C₂×M₁₆	—	178	1	no	—
368	C₂×M₁₆	—	178	1	no	—
369	C₂×M₁₆	—	178	1	no	—
370	C₂×M₁₆	—	178	1	no	—
371	C₂×M₁₆	—	178	1	no	—
372	C₂×M₁₆	—	178	1	no	—
373	C₂×M₁₆	—	178	1	no	—
374	C₂×M₁₆	—	178	1	no	—
375	C₂×M₁₆	—	178	1	no	—
376	C₂×M₁₆	—	178	1	no	—
377	C₂×M₁₆	—	178	1	no	—
378	C₂×M₁₆	—	178	1	no	—
379	C₂×M₁₆	—	178	1	no	—
380	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
381	C₂×M₁₆	D₃₅₆	1	2	yes	—
382	C₂×M₁₆	C₂²⋊D₈₉	1	2	yes	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	89	2	no	—
387	C₂²×C₈	—	178	1	no	—
388	C₂²×C₈	—	178	1	no	—
389	#108	—	178	8	no	—
390	#101	—	178	4	no	—
391	#101	—	178	4	no	—
392	#100	—	178	4	no	—
393	#100	—	178	4	no	—
394	C₂²⋊C₈	—	178	8	no	—
395	C₂⁴	—	89	2	no	—
396	C₂⁴	Q₈×D₈₉	1	1	yes	characteristic
397	#41	—	356	1	no	—
398	#41	—	356	1	no	—
399	#41	—	356	1	no	—
400	#41	—	356	1	no	—
401	#41	—	356	1	no	—
402	#41	—	356	1	no	—
403	#41	—	356	1	no	—
404	#41	—	356	1	no	—
405	#41	—	356	1	no	—
406	#41	—	356	1	no	—
407	#41	—	356	1	no	—
408	#41	—	356	1	no	—
409	#41	—	356	1	no	—
410	#41	—	356	1	no	—
411	#41	—	356	1	no	—
412	#41	—	356	1	no	—
413	C₂×Q₈	—	178	1	no	—
414	C₂×Q₈	—	178	1	no	—
415	C₂×Q₈	—	178	1	no	—
416	C₂×Q₈	—	178	1	no	—
417	C₂×Q₈	—	178	1	no	—
418	C₂×Q₈	—	178	1	no	—
419	C₂×D₄	—	178	2	no	—
420	C₂×D₄	—	178	2	no	—
421	C₂×D₄	—	178	2	no	—
422	C₂×D₄	—	178	2	no	—
423	C₂×D₄	—	178	2	no	—
424	C₂×D₄	—	178	2	no	—
425	C₂×D₄	—	178	1	no	—
426	C₂×D₄	—	178	1	no	—
427	C₂×D₄	—	178	1	no	—
428	C₂×D₄	—	178	1	no	—
429	C₂×D₄	—	178	1	no	—
430	C₂×D₄	—	178	1	no	—
431	C₂²×C₄	—	89	2	no	—
432	C₂²×C₄	—	178	2	no	—
433	C₂²×C₄	—	178	2	no	—
434	C₂²×C₄	—	178	2	no	—
435	C₂²×C₄	—	178	2	no	—
436	C₂²×C₄	—	178	2	no	—
437	C₂²×C₄	—	178	2	no	—
438	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
439	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
441	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
442	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
443	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
446	C₂²×C₄	#13083573	1	1	yes	characteristic
447	C₂²×C₄	#13083574	1	1	yes	characteristic
448	C₂²×C₄	#13083574	1	1	yes	characteristic
449	C₂²×C₄	#13083574	1	1	yes	characteristic
450	C₂²×C₄	#13083574	1	1	yes	characteristic
451	C₂²×C₄	#13083575	1	1	yes	characteristic
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	4	1	no	—
459	M₁₆	—	4	1	no	—
460	M₁₆	—	4	1	no	—
461	M₁₆	—	4	1	no	—
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	M₁₆	—	356	1	no	—
465	M₁₆	—	356	1	no	—
466	M₁₆	—	356	1	no	—
467	M₁₆	—	356	1	no	—
468	M₁₆	—	178	2	no	—
469	M₁₆	—	178	2	no	—
470	M₁₆	—	178	2	no	—
471	M₁₆	—	178	2	no	—
472	M₁₆	—	178	2	no	—
473	M₁₆	—	178	2	no	—
474	M₁₆	—	178	2	no	—
475	M₁₆	—	178	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	89	4	no	—
486	C₂×C₈	—	356	1	no	—
487	C₂×C₈	—	356	1	no	—
488	C₂×C₈	—	356	1	no	—
489	C₂×C₈	—	356	1	no	—
490	C₂×C₈	—	178	2	no	—
491	C₂×C₈	—	178	2	no	—
492	C₂×C₈	—	178	2	no	—
493	C₂×C₈	—	178	2	no	—
494	C₂³	—	8	1	no	—
495	C₂³	—	178	2	no	—
496	C₂³	—	178	2	no	—
497	C₂³	—	178	2	no	—
498	C₂³	—	712	2	no	—
499	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
500	C₂³	#15667988	1	1	yes	characteristic
501	C₂³	#15667990	1	1	yes	characteristic
502	C₂³	#15667990	1	1	yes	characteristic
503	C₂³	#15667990	1	1	yes	characteristic
504	C₂³	#15667990	1	1	yes	characteristic
505	C₂³	#15667992	1	1	yes	characteristic
506	Q₈	—	356	1	no	—
507	Q₈	—	356	1	no	—
508	Q₈	—	356	1	no	—
509	Q₈	—	356	1	no	—
510	D₄	—	356	2	no	—
511	D₄	—	356	2	no	—
512	D₄	—	356	2	no	—
513	D₄	—	356	2	no	—
514	D₄	—	356	1	no	—
515	D₄	—	356	1	no	—
516	D₄	—	356	1	no	—
517	D₄	—	356	1	no	—
518	C₂×C₄	—	356	2	no	—
519	C₂×C₄	—	356	2	no	—
520	C₂×C₄	—	356	2	no	—
521	C₂×C₄	—	356	2	no	—
522	C₂×C₄	—	178	2	no	—
523	C₂×C₄	—	178	2	no	—
524	C₂×C₄	—	178	2	no	—
525	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
526	C₂×C₄	#15667969	1	1	yes	characteristic
527	C₂×C₄	#15667972	1	1	yes	characteristic
528	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
529	C₂×C₄	#15667974	1	1	yes	characteristic
530	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
531	C₂×C₄	#15667980	1	1	yes	characteristic
532	C₂×C₄	#15667982	1	1	yes	characteristic
533	C₂×C₄	#15667982	1	1	yes	characteristic
534	C₂×C₄	#15667984	1	1	yes	characteristic
535	C₂×C₄	#15667985	1	1	yes	characteristic
536	C₂×C₄	#15667985	1	1	yes	characteristic
537	C₂×C₄	#15667985	1	1	yes	characteristic
538	C₂×C₄	#15667985	1	1	yes	characteristic
539	C₂×C₄	#15667985	1	1	yes	characteristic
540	C₂×C₄	#15667986	1	1	yes	characteristic
541	C₂×C₄	#15667987	1	1	yes	characteristic
542	C₂×C₄	#15667994	1	1	yes	characteristic
543	C₂×C₄	#15667995	1	1	yes	characteristic
544	C₂×C₄	#15667997	1	1	yes	characteristic
545	C₂×C₄	#15667997	1	1	yes	characteristic
546	C₂×C₄	#15667997	1	1	yes	characteristic
547	C₂×C₄	#15667998	1	1	yes	characteristic
548	C₂×C₄	#15667998	1	1	yes	characteristic
549	C₂×C₄	#15668000	1	1	yes	characteristic
550	C₂×C₄	#15668006	1	1	yes	characteristic
551	C₂×C₄	#15668007	1	1	yes	characteristic
552	C₂×C₄	#15668008	1	1	yes	characteristic
553	C₈	—	4	2	no	—
554	C₈	—	4	2	no	—
555	C₈	—	4	2	no	—
556	C₈	—	356	2	no	—
557	C₈	—	356	2	no	—
558	C₈	—	178	4	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	356	4	no	—
567	C₂²	—	356	2	no	—
568	C₂²	—	712	2	no	—
569	C₂²	—	712	2	no	—
570	C₂²	#19151457	1	1	yes	characteristic
571	C₂²	#19151469	1	1	yes	characteristic
572	C₂²	#19151472	1	1	yes	characteristic
573	C₂²	#19151511	1	1	yes	characteristic
574	C₂²	#19151520	1	1	yes	characteristic
575	C₂²	#19151522	1	1	yes	characteristic
576	C₂²	#19151533	1	1	yes	characteristic
577	C₄	—	356	2	no	—
578	C₄	#19151476	1	1	yes	characteristic
579	C₄	#19151487	1	1	yes	characteristic
580	C₄	#19151489	1	1	yes	characteristic
581	C₄	#19151498	1	1	yes	characteristic
582	C₄	#19151507	1	1	yes	characteristic
583	C₄	#19151513	1	1	yes	characteristic
584	C₄	#19151516	1	1	yes	characteristic
585	C₄	#19151527	1	1	yes	characteristic
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	712	2	no	—
594	C₂	#26018496	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19151498
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₈₉×#1738	C₂
socle	C₂×C₈₉	#1439
prime radical	C₂²×#13083574	C₂²
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	#1738	D₈₉
hypocenter	C₈₉	#11103
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1738

Complements

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

N	H ≅ G/N	type
1. C₂×#19151646	C₂	semidirect
5. #26019978	C₂	semidirect
6. C₂×#19151356	C₂	semidirect
7. C₈₉×#1738	C₂	semidirect
303. #1738	D₈₉	semidirect
305. C₈₉	#11103	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151646	2
C₂×#19151580	2
#26028696	2
#26019978	2
C₂×#19151356	2
C₈₉×#1738	2
#11103	89