Subgroups — #26034754

Order 11392.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152350	C₂	1	2	yes	maximal, complemented
2	#19152350	C₂	1	2	yes	maximal, complemented
3	#19152331	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152330	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152325	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152324	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152320	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152317	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152304	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152287	C₂	1	2	yes	maximal, complemented
12	#19152281	C₂	1	2	yes	maximal, complemented
13	#19152221	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152216	C₂	1	2	yes	maximal, complemented
15	#19152215	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152213	C₂	1	2	yes	maximal, complemented
17	#19152208	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152201	C₂	1	1	yes	maximal, characteristic
19	#19152191	C₂	1	2	yes	maximal, complemented
20	#19152190	C₂	1	2	yes	maximal, complemented
21	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152132	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#15668012	C₂²	1	1	yes	characteristic
25	#15668012	C₂²	1	1	yes	characteristic
26	#15668011	C₂²	1	2	yes	—
27	#15668011	C₂²	1	1	yes	characteristic
28	#15668011	C₂²	1	2	yes	—
29	#15668011	C₂²	1	1	yes	characteristic
30	#15668010	C₂²	1	1	yes	characteristic
31	#15668008	C₂²	1	1	yes	characteristic
32	#15668007	C₂²	1	2	yes	—
33	#15668007	C₂²	1	2	yes	—
34	#15668006	C₂²	1	2	yes	—
35	#15668006	C₂²	1	2	yes	—
36	#15668005	C₂²	1	2	yes	—
37	#15668005	C₂²	1	2	yes	—
38	#15668005	C₂²	1	2	yes	—
39	#15668005	C₂²	1	2	yes	—
40	#15668005	C₂²	1	2	yes	—
41	#15668004	C₂²	1	1	yes	characteristic
42	#15668004	C₂²	1	1	yes	characteristic
43	#15668004	C₂²	1	1	yes	characteristic
44	#15668004	C₂²	1	2	yes	—
45	#15668003	C₂²	1	2	yes	—
46	#15668003	C₂²	1	1	yes	characteristic
47	#15668003	C₂²	1	2	yes	—
48	#15668003	C₂²	1	1	yes	characteristic
49	#15668002	C₂²	1	2	yes	—
50	#15668002	C₂²	1	2	yes	—
51	#15668002	C₂²	1	2	yes	—
52	#15668001	C₂²	1	1	yes	characteristic
53	#15668000	C₂²	1	1	yes	characteristic
54	#15667999	C₂²	1	2	yes	—
55	#15667999	C₂²	1	1	yes	characteristic
56	#15667998	C₂²	1	2	yes	—
57	#15667998	C₂²	1	2	yes	—
58	#15667998	C₂²	1	2	yes	—
59	#15667996	C₂²	1	2	yes	—
60	#15667996	C₂²	1	2	yes	—
61	#15667995	C₂²	1	2	yes	—
62	#15667995	C₂²	1	2	yes	—
63	#15667994	C₂²	1	2	yes	—
64	#15667994	C₂²	1	2	yes	—
65	#15667994	C₂²	1	2	yes	—
66	#15667994	C₂²	1	2	yes	—
67	#15667993	C₂²	1	2	yes	—
68	#15667992	C₂²	1	2	yes	—
69	#15667992	C₂²	1	2	yes	—
70	#15667991	C₂²	1	1	yes	characteristic
71	#15667991	C₂²	1	1	yes	characteristic
72	#15667991	C₂²	1	1	yes	characteristic
73	#15667991	C₂²	1	1	yes	characteristic
74	#15667991	C₂²	1	1	yes	characteristic
75	#15667991	C₂²	1	2	yes	—
76	#15667990	C₂²	1	2	yes	—
77	#15667990	C₂²	1	2	yes	—
78	#15667990	C₂²	1	2	yes	—
79	#15667989	C₂²	1	2	yes	—
80	#15667989	C₂²	1	2	yes	—
81	#15667989	C₂²	1	2	yes	—
82	#15667989	C₂²	1	2	yes	—
83	#15667986	C₂²	1	1	yes	characteristic
84	#15667984	C₂²	1	2	yes	—
85	#15667983	C₂²	1	2	yes	—
86	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
87	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
90	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
91	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
93	C₄×Dic₁₇₈	C₂²	1	2	yes	—
94	#15667977	C₂²	1	1	yes	characteristic
95	#15667977	C₂²	1	1	yes	characteristic
96	#15667977	C₂²	1	2	yes	—
97	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
98	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
99	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
100	#15667974	C₂²	1	1	yes	characteristic
101	#15667974	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
104	#15667972	C₂²	1	2	yes	—
105	#15667971	C₂²	1	1	yes	characteristic
106	#15667971	C₂²	1	1	yes	characteristic
107	#15667969	C₂²	1	2	yes	—
108	#15667969	C₂²	1	2	yes	—
109	#15667968	C₂²	1	2	yes	—
110	C₂×#13083553	C₂²	1	2	yes	—
111	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
112	#126×C₈₉	C₂²	1	2	yes	—
113	#125×C₈₉	C₂²	1	1	yes	characteristic
114	#124×C₈₉	C₂²	1	1	yes	characteristic
115	#123×C₈₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
117	#121×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₈₉	C₂²	1	2	yes	—
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	#117×C₈₉	C₂²	1	2	yes	—
122	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
123	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
124	C₂×Dic₁₇₈	C₂³	1	2	yes	—
125	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
130	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
134	C₂²×Dic₈₉	C₂³	1	2	yes	—
135	C₂²×Dic₈₉	C₂³	1	2	yes	—
136	C₂×C₄×D₈₉	C₂³	1	2	yes	—
137	C₂×C₄×D₈₉	C₂³	1	2	yes	—
138	C₂×C₄×D₈₉	C₂³	1	2	yes	—
139	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₈₉	C₂³	1	2	yes	—
146	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₈₉	C₂³	1	2	yes	—
151	C₄⋊Dic₈₉	C₂³	1	2	yes	—
152	C₄⋊Dic₈₉	C₂³	1	2	yes	—
153	#13083553	C₂³	1	1	yes	characteristic
154	#13083553	C₂³	1	2	yes	—
155	#13083553	C₂³	1	1	yes	characteristic
156	#13083553	C₂³	1	2	yes	—
157	#13083553	C₂³	1	2	yes	—
158	#13083553	C₂³	1	2	yes	—
159	#13083553	C₂³	1	1	yes	characteristic
160	#13083553	C₂³	1	1	yes	characteristic
161	#13083553	C₂³	1	2	yes	—
162	#13083553	C₂³	1	1	yes	characteristic
163	#13083553	C₂³	1	2	yes	—
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	1	yes	characteristic
167	#13083553	C₂³	1	2	yes	—
168	#13083553	C₂³	1	1	yes	characteristic
169	#13083553	C₂³	1	1	yes	characteristic
170	#13083553	C₂³	1	2	yes	—
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	2	yes	—
173	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
182	#13083551	C₂³	1	2	yes	—
183	#13083551	C₂³	1	2	yes	—
184	#13083551	C₂³	1	2	yes	—
185	#13083551	C₂³	1	2	yes	—
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	2	yes	—
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	2	yes	—
190	C₄×Dic₈₉	C₂³	1	2	yes	—
191	C₄×Dic₈₉	C₂³	1	2	yes	—
192	C₄×Dic₈₉	C₂³	1	2	yes	—
193	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
201	C₂×D₄×C₈₉	C₂³	1	2	yes	—
202	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
205	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
217	C₄²×C₈₉	C₂³	1	1	yes	characteristic
218	C₄²×C₈₉	C₂³	1	2	yes	—
219	C₄²×C₈₉	C₂³	1	1	yes	characteristic
220	C₄²×C₈₉	C₂³	1	1	yes	characteristic
221	C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₂³×C₈₉	C₂⁴	1	2	yes	—
223	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
224	C₂²×D₈₉	C₂⁴	1	2	yes	—
225	Q₈×C₈₉	—	2	2	no	—
226	D₄×C₈₉	—	2	2	no	—
227	D₄×C₈₉	—	4	2	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	4	2	no	—
232	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²⋊D₈₉	—	4	2	no	—
242	C₂²⋊D₈₉	—	4	2	no	—
243	C₂²⋊D₈₉	—	4	2	no	—
244	C₂×Dic₈₉	—	4	2	no	—
245	C₂×Dic₈₉	—	4	2	no	—
246	C₂×Dic₈₉	C₂⁴	1	2	yes	—
247	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₈₉	C₂⁴	1	2	yes	—
252	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₉	C₂⁴	1	2	yes	—
255	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
257	D₃₅₆	—	2	2	no	—
258	C₄×D₈₉	—	4	2	no	—
259	C₄×D₈₉	—	4	2	no	—
260	C₄×D₈₉	—	4	2	no	—
261	Dic₁₇₈	—	2	2	no	—
262	Dic₁₇₈	—	4	2	no	—
263	Dic₁₇₈	—	4	2	no	—
264	Dic₁₇₈	—	4	1	no	—
265	Dic₁₇₈	—	4	1	no	—
266	Dic₁₇₈	—	4	1	no	—
267	Dic₁₇₈	—	4	1	no	—
268	C₂²×C₈₉	—	2	1	no	—
269	C₂²×C₈₉	—	2	2	no	—
270	C₂²×C₈₉	—	2	2	no	—
271	C₂²×C₈₉	—	2	2	no	—
272	C₂²×C₈₉	—	2	1	no	—
273	C₂²×C₈₉	—	2	1	no	—
274	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
275	C₂×D₈₉	—	2	2	no	—
276	C₂×D₈₉	—	2	2	no	—
277	C₂×D₈₉	—	2	2	no	—
278	C₄×C₈₉	—	2	1	no	—
279	C₄×C₈₉	—	2	2	no	—
280	C₄×C₈₉	—	2	1	no	—
281	C₄×C₈₉	—	2	1	no	—
282	C₄×C₈₉	—	2	2	no	—
283	C₄×C₈₉	—	2	2	no	—
284	C₄×C₈₉	—	2	1	no	—
285	C₄×C₈₉	—	2	1	no	—
286	C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
287	Dic₈₉	—	2	2	no	—
288	Dic₈₉	—	2	1	no	—
289	Dic₈₉	—	2	1	no	—
290	Dic₈₉	—	2	1	no	—
291	Dic₈₉	—	2	1	no	—
292	Dic₈₉	—	2	2	no	—
293	Dic₈₉	—	2	1	no	—
294	Dic₈₉	—	2	1	no	—
295	Dic₈₉	—	2	2	no	—
296	Dic₈₉	—	2	1	no	—
297	Dic₈₉	—	2	1	no	—
298	C₂×C₈₉	—	4	1	no	—
299	C₂×C₈₉	—	4	2	no	—
300	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
301	C₂×C₈₉	#585	1	1	yes	characteristic
302	C₂×C₈₉	#585	1	1	yes	characteristic
303	D₈₉	—	4	2	no	—
304	#3557	—	89	1	no	maximal, Sylow
305	C₈₉	#3557	1	1	yes	characteristic, complemented, Sylow
306	#563	—	89	2	no	—
307	#563	—	89	2	no	—
308	#559	—	89	1	no	—
309	#559	—	89	1	no	—
310	#557	—	89	1	no	—
311	#557	—	89	1	no	—
312	#556	—	89	1	no	—
313	#556	—	89	1	no	—
314	#554	—	89	1	no	—
315	#554	—	89	1	no	—
316	#552	—	89	2	no	—
317	#552	—	89	2	no	—
318	#542	—	89	2	no	—
319	#542	—	89	1	no	—
320	#542	—	89	1	no	—
321	#542	—	89	2	no	—
322	#541	—	89	1	no	—
323	#540	—	89	1	no	—
324	#539	—	89	2	no	—
325	#539	—	89	2	no	—
326	#533	—	89	1	no	—
327	#529	—	89	1	no	—
328	#529	D₈₉	1	1	yes	characteristic, complemented
329	C₄⋊Q₈	—	89	1	no	—
330	C₄⋊Q₈	—	89	1	no	—
331	C₄⋊Q₈	—	89	1	no	—
332	C₄⋊Q₈	—	89	2	no	—
333	C₄⋊Q₈	—	89	2	no	—
334	C₄⋊Q₈	—	89	1	no	—
335	C₄⋊Q₈	—	89	1	no	—
336	#127	—	89	1	no	—
337	#126	—	89	2	no	—
338	#126	—	89	2	no	—
339	#126	—	89	2	no	—
340	#126	—	89	2	no	—
341	#126	—	89	2	no	—
342	#126	—	89	2	no	—
343	#126	—	89	2	no	—
344	#126	—	89	2	no	—
345	#126	—	89	2	no	—
346	#126	C₂×D₈₉	1	2	yes	—
347	#125	—	89	2	no	—
348	#125	—	89	2	no	—
349	#125	—	89	2	no	—
350	#125	—	89	1	no	—
351	#125	—	89	2	no	—
352	#125	—	89	2	no	—
353	#125	—	89	1	no	—
354	#125	—	89	1	no	—
355	#125	—	89	1	no	—
356	#125	—	89	1	no	—
357	#125	—	89	2	no	—
358	#125	C₂×D₈₉	1	1	yes	characteristic
359	#124	—	89	1	no	—
360	#124	—	89	2	no	—
361	#124	—	89	1	no	—
362	#124	—	89	2	no	—
363	#124	—	89	2	no	—
364	#124	—	89	2	no	—
365	#124	—	89	1	no	—
366	#124	C₂×D₈₉	1	1	yes	characteristic
367	#123	—	89	2	no	—
368	#123	—	89	2	no	—
369	#123	—	89	2	no	—
370	#123	—	89	2	no	—
371	#123	—	89	2	no	—
372	#123	—	89	2	no	—
373	#123	—	89	2	no	—
374	#123	—	89	2	no	—
375	#123	—	89	2	no	—
376	#123	C₂×D₈₉	1	2	yes	—
377	C₂²⋊Q₈	—	89	1	no	—
378	C₂²⋊Q₈	—	89	1	no	—
379	C₂²⋊Q₈	—	89	1	no	—
380	C₂²⋊Q₈	—	89	1	no	—
381	C₂²⋊Q₈	—	89	1	no	—
382	C₂²⋊Q₈	—	89	2	no	—
383	C₂²⋊Q₈	—	89	2	no	—
384	C₂²⋊Q₈	—	89	2	no	—
385	C₂²⋊Q₈	—	89	2	no	—
386	C₂²⋊Q₈	—	89	2	no	—
387	C₂²⋊Q₈	—	89	2	no	—
388	C₂²⋊Q₈	—	89	2	no	—
389	C₂²⋊Q₈	—	89	2	no	—
390	C₂²⋊Q₈	—	89	2	no	—
391	C₂²⋊Q₈	—	89	2	no	—
392	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
393	#121	—	89	2	no	—
394	#121	—	89	2	no	—
395	#121	—	89	1	no	—
396	#121	C₂×D₈₉	1	1	yes	characteristic
397	C₄×Q₈	—	89	1	no	—
398	C₄×Q₈	—	89	1	no	—
399	C₄×Q₈	—	89	1	no	—
400	C₄×Q₈	—	89	2	no	—
401	C₄×Q₈	—	89	1	no	—
402	C₄×Q₈	—	89	1	no	—
403	C₄×Q₈	—	89	1	no	—
404	C₄×Q₈	—	89	1	no	—
405	C₄×Q₈	—	89	1	no	—
406	C₄×Q₈	—	89	1	no	—
407	C₄×Q₈	—	89	2	no	—
408	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	89	1	no	—
411	C₄×D₄	—	89	2	no	—
412	C₄×D₄	—	89	2	no	—
413	C₄×D₄	—	89	1	no	—
414	C₄×D₄	—	89	1	no	—
415	C₄×D₄	—	89	2	no	—
416	C₄×D₄	—	89	1	no	—
417	C₄×D₄	C₂×D₈₉	1	2	yes	—
418	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
419	#117	—	89	1	no	—
420	#117	—	89	1	no	—
421	#117	—	89	2	no	—
422	#117	—	89	2	no	—
423	#117	—	89	2	no	—
424	#117	C₂×D₈₉	1	2	yes	—
425	C₂×C₄⋊C₄	—	89	2	no	—
426	C₂×C₄⋊C₄	—	89	2	no	—
427	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
428	C₂×Q₈	—	89	1	no	—
429	C₂×Q₈	—	89	1	no	—
430	C₂×Q₈	—	89	2	no	—
431	C₂×Q₈	—	89	2	no	—
432	C₂×Q₈	—	89	1	no	—
433	C₂×Q₈	—	89	1	no	—
434	C₂×Q₈	—	89	1	no	—
435	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
436	C₂×D₄	—	89	2	no	—
437	C₂×D₄	—	89	2	no	—
438	C₂×D₄	—	89	2	no	—
439	C₂×D₄	—	89	1	no	—
440	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
441	C₂×D₄	C₂²×D₈₉	1	2	yes	—
442	C₂²×C₄	—	89	2	no	—
443	C₂²×C₄	—	89	2	no	—
444	C₂²×C₄	—	89	2	no	—
445	C₂²×C₄	—	89	2	no	—
446	C₂²×C₄	—	89	2	no	—
447	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
450	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
451	C₄⋊C₄	—	89	1	no	—
452	C₄⋊C₄	—	89	1	no	—
453	C₄⋊C₄	—	89	2	no	—
454	C₄⋊C₄	—	89	2	no	—
455	C₄⋊C₄	—	89	2	no	—
456	C₄⋊C₄	—	89	2	no	—
457	C₄⋊C₄	—	89	2	no	—
458	C₄⋊C₄	—	89	1	no	—
459	C₄⋊C₄	—	89	1	no	—
460	C₄⋊C₄	—	89	2	no	—
461	C₄⋊C₄	—	89	1	no	—
462	C₄⋊C₄	—	89	1	no	—
463	C₄⋊C₄	—	89	2	no	—
464	C₄⋊C₄	—	89	2	no	—
465	C₄⋊C₄	—	89	1	no	—
466	C₄⋊C₄	—	89	1	no	—
467	C₄⋊C₄	—	89	1	no	—
468	C₄⋊C₄	—	89	1	no	—
469	C₄⋊C₄	—	89	1	no	—
470	C₄⋊C₄	—	89	1	no	—
471	C₄⋊C₄	—	89	2	no	—
472	C₄⋊C₄	—	89	1	no	—
473	C₄⋊C₄	—	89	1	no	—
474	C₄⋊C₄	—	89	2	no	—
475	C₄⋊C₄	—	89	2	no	—
476	C₄⋊C₄	—	89	1	no	—
477	C₄⋊C₄	—	89	1	no	—
478	C₄⋊C₄	—	89	2	no	—
479	C₄⋊C₄	—	89	2	no	—
480	C₄⋊C₄	—	89	1	no	—
481	C₄⋊C₄	—	89	1	no	—
482	C₄⋊C₄	—	89	2	no	—
483	C₄⋊C₄	—	89	2	no	—
484	C₄⋊C₄	—	89	2	no	—
485	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
486	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
487	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
490	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
491	C₂²⋊C₄	—	89	1	no	—
492	C₂²⋊C₄	—	89	1	no	—
493	C₂²⋊C₄	—	89	1	no	—
494	C₂²⋊C₄	—	89	1	no	—
495	C₂²⋊C₄	—	89	2	no	—
496	C₂²⋊C₄	—	89	2	no	—
497	C₂²⋊C₄	—	89	2	no	—
498	C₂²⋊C₄	—	89	2	no	—
499	C₂²⋊C₄	—	89	2	no	—
500	C₂²⋊C₄	—	89	2	no	—
501	C₂²⋊C₄	—	89	2	no	—
502	C₂²⋊C₄	—	89	2	no	—
503	C₂²⋊C₄	—	89	2	no	—
504	C₂²⋊C₄	—	89	2	no	—
505	C₂²⋊C₄	—	89	2	no	—
506	C₂²⋊C₄	—	89	2	no	—
507	C₂²⋊C₄	—	89	2	no	—
508	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
510	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
511	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
512	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
513	C₄²	—	89	2	no	—
514	C₄²	—	89	1	no	—
515	C₄²	—	89	1	no	—
516	C₄²	—	89	1	no	—
517	C₄²	—	89	1	no	—
518	C₄²	—	89	2	no	—
519	C₄²	—	89	2	no	—
520	C₄²	—	89	2	no	—
521	C₄²	—	89	2	no	—
522	C₄²	C₂²×D₈₉	1	1	yes	characteristic
523	C₄²	C₂²×D₈₉	1	1	yes	characteristic
524	C₄²	C₂²×D₈₉	1	1	yes	characteristic
525	C₄²	C₂²×D₈₉	1	1	yes	characteristic
526	C₄²	C₂²×D₈₉	1	2	yes	—
527	C₂³	—	89	2	no	—
528	C₂³	C₂³×D₈₉	1	1	yes	characteristic
529	C₂³	C₂³×D₈₉	1	2	yes	—
530	Q₈	—	2	2	no	—
531	Q₈	—	356	2	no	—
532	Q₈	—	356	1	no	—
533	Q₈	—	356	1	no	—
534	Q₈	—	356	1	no	—
535	Q₈	—	356	1	no	—
536	Q₈	—	356	2	no	—
537	Q₈	—	178	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	356	2	no	—
541	D₄	—	356	2	no	—
542	D₄	—	356	2	no	—
543	D₄	—	178	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	89	2	no	—
549	C₂×C₄	—	89	1	no	—
550	C₂×C₄	—	89	1	no	—
551	C₂×C₄	—	89	1	no	—
552	C₂×C₄	—	89	1	no	—
553	C₂×C₄	—	89	2	no	—
554	C₂×C₄	—	89	1	no	—
555	C₂×C₄	—	89	1	no	—
556	C₂×C₄	—	89	2	no	—
557	C₂×C₄	—	89	1	no	—
558	C₂×C₄	—	89	1	no	—
559	C₂×C₄	—	356	2	no	—
560	C₂×C₄	—	356	2	no	—
561	C₂×C₄	—	356	2	no	—
562	C₂×C₄	—	356	2	no	—
563	C₂×C₄	—	356	2	no	—
564	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₈₉	1	2	yes	—
566	C₂×C₄	C₂³×D₈₉	1	2	yes	—
567	C₂×C₄	C₂³×D₈₉	1	2	yes	—
568	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	178	2	no	—
580	C₂²	—	178	2	no	—
581	C₂²	—	178	2	no	—
582	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	178	2	no	—
592	C₄	—	178	1	no	—
593	C₄	—	178	1	no	—
594	C₄	—	178	2	no	—
595	C₄	—	178	1	no	—
596	C₄	—	178	1	no	—
597	C₄	—	178	2	no	—
598	C₄	—	178	1	no	—
599	C₄	—	178	1	no	—
600	C₄	—	178	1	no	—
601	C₄	—	178	1	no	—
602	C₄	#15668059	1	2	yes	—
603	C₂	—	4	1	no	—
604	C₂	—	4	2	no	—
605	C₂	—	356	2	no	—
606	C₂	C₂×#15668059	1	1	yes	characteristic
607	C₂	#19152434	1	1	yes	characteristic
608	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#529×C₈₉	C₂
prime radical	#19152201	C₂
hypercenter	#529	D₈₉
hypocenter	C₈₉	#3557
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19152350	C₂	semidirect
2. #19152350	C₂	semidirect
3. #19152331	C₂	semidirect
4. #19152330	C₂	semidirect
5. #19152325	C₂	semidirect
6. #19152324	C₂	semidirect
7. #19152320	C₂	semidirect
8. #19152317	C₂	semidirect
9. #19152307	C₂	semidirect
10. #19152304	C₂	semidirect
11. #19152287	C₂	semidirect
12. #19152281	C₂	semidirect
13. #19152221	C₂	semidirect
14. #19152216	C₂	semidirect
15. #19152215	C₂	semidirect
16. #19152213	C₂	semidirect
17. #19152208	C₂	semidirect
19. #19152191	C₂	semidirect
20. #19152190	C₂	semidirect
21. #19152155	C₂	semidirect
22. #19152132	C₂	semidirect
23. #529×C₈₉	C₂	semidirect
305. C₈₉	#3557	semidirect
328. #529	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152350	2
#19152331	2
#19152330	2
#19152325	2
#19152324	2
#19152320	2
#19152317	2
#19152307	2
#19152304	2
#19152287	2
#19152281	2
#19152221	2
#19152216	2
#19152215	2
#19152213	2
#19152208	2
#19152201	2
#19152191	2
#19152190	2
#19152155	2
#19152132	2
#529×C₈₉	2
#3557	89