Subgroups — #26034820

Order 11392.

1032 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152352	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152346	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152342	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152315	C₂	1	2	yes	maximal, complemented
5	#19152275	C₂	1	2	yes	maximal, complemented
6	#19152273	C₂	1	2	yes	maximal, complemented
7	#19152263	C₂	1	2	yes	maximal, complemented
8	#19152258	C₂	1	2	yes	maximal, complemented
9	#19152240	C₂	1	2	yes	maximal, complemented
10	#19152223	C₂	1	2	yes	maximal, complemented
11	#19152222	C₂	1	2	yes	maximal, complemented
12	#19152216	C₂	1	2	yes	maximal, complemented
13	#19152214	C₂	1	2	yes	maximal, complemented
14	#19152187	C₂	1	2	yes	maximal, complemented
15	#19152171	C₂	1	2	yes	maximal, complemented
16	#19152154	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152133	C₂	1	1	yes	maximal, characteristic, complemented
18	#124×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#563×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13083574	C₂²	1	2	yes	—
21	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
22	C₂×Q₈×D₈₉	C₂²	1	2	yes	complemented
23	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
24	#15668011	C₂²	1	1	yes	characteristic, complemented
25	#15668011	C₂²	1	1	yes	characteristic, complemented
26	#15668011	C₂²	1	2	yes	complemented
27	#15668011	C₂²	1	2	yes	complemented
28	#15668007	C₂²	1	2	yes	complemented
29	#15668007	C₂²	1	2	yes	complemented
30	#15668007	C₂²	1	2	yes	complemented
31	#15668007	C₂²	1	2	yes	complemented
32	#15668005	C₂²	1	2	yes	complemented
33	#15668004	C₂²	1	1	yes	characteristic, complemented
34	#15668001	C₂²	1	1	yes	characteristic
35	#15668001	C₂²	1	2	yes	complemented
36	#15668000	C₂²	1	1	yes	characteristic
37	#15668000	C₂²	1	1	yes	characteristic, complemented
38	#15668000	C₂²	1	2	yes	complemented
39	#15667999	C₂²	1	1	yes	characteristic
40	#15667998	C₂²	1	2	yes	—
41	#15667998	C₂²	1	2	yes	—
42	#15667998	C₂²	1	2	yes	—
43	#15667998	C₂²	1	2	yes	complemented
44	#15667998	C₂²	1	2	yes	complemented
45	#15667997	C₂²	1	2	yes	—
46	#15667997	C₂²	1	2	yes	—
47	#15667997	C₂²	1	2	yes	complemented
48	#15667997	C₂²	1	2	yes	complemented
49	#15667997	C₂²	1	2	yes	complemented
50	#15667996	C₂²	1	2	yes	complemented
51	#15667994	C₂²	1	2	yes	complemented
52	#15667994	C₂²	1	2	yes	complemented
53	#15667992	C₂²	1	1	yes	characteristic
54	#15667992	C₂²	1	2	yes	complemented
55	#15667992	C₂²	1	2	yes	complemented
56	#15667991	C₂²	1	2	yes	complemented
57	#15667990	C₂²	1	2	yes	—
58	#15667990	C₂²	1	2	yes	—
59	#15667990	C₂²	1	2	yes	—
60	#15667990	C₂²	1	2	yes	complemented
61	#15667990	C₂²	1	2	yes	complemented
62	#15667990	C₂²	1	2	yes	complemented
63	#15667990	C₂²	1	2	yes	complemented
64	#15667989	C₂²	1	2	yes	complemented
65	#15667989	C₂²	1	2	yes	complemented
66	#15667988	C₂²	1	2	yes	—
67	#15667988	C₂²	1	2	yes	complemented
68	#15667988	C₂²	1	2	yes	complemented
69	#15667987	C₂²	1	1	yes	characteristic
70	#15667987	C₂²	1	2	yes	—
71	#15667987	C₂²	1	2	yes	complemented
72	#15667985	C₂²	1	2	yes	—
73	#15667985	C₂²	1	2	yes	complemented
74	#15667984	C₂²	1	2	yes	—
75	#15667982	C₂²	1	2	yes	—
76	#15667982	C₂²	1	2	yes	—
77	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
78	#15667977	C₂²	1	1	yes	characteristic, complemented
79	#15667977	C₂²	1	2	yes	complemented
80	#15667977	C₂²	1	2	yes	complemented
81	C₄×D₃₅₆	C₂²	1	2	yes	—
82	#15667974	C₂²	1	2	yes	—
83	#15667974	C₂²	1	2	yes	—
84	#15667974	C₂²	1	1	yes	characteristic, complemented
85	#15667974	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
87	#15667972	C₂²	1	2	yes	—
88	#15667970	C₂²	1	1	yes	characteristic
89	#15667970	C₂²	1	1	yes	characteristic
90	#15667970	C₂²	1	2	yes	complemented
91	#15667969	C₂²	1	2	yes	complemented
92	#15667968	C₂²	1	2	yes	complemented
93	C₂×#13083551	C₂²	1	2	yes	—
94	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
97	C₄²×D₈₉	C₂²	1	1	yes	characteristic
98	C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
99	#126×C₈₉	C₂²	1	2	yes	complemented
100	#126×C₈₉	C₂²	1	2	yes	complemented
101	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
103	#124×C₈₉	C₂²	1	1	yes	characteristic
104	#123×C₈₉	C₂²	1	2	yes	—
105	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
106	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
107	C₂³×D₈₉	C₂³	1	2	yes	—
108	#13083574	—	4	4	no	—
109	C₂×Dic₁₇₈	C₂³	1	2	yes	—
110	C₂×Dic₁₇₈	C₂³	1	2	yes	—
111	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₇₈	C₂³	1	2	yes	—
113	C₂×Dic₁₇₈	C₂³	1	2	yes	—
114	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
115	Q₈×D₈₉	—	4	2	no	—
116	Q₈×D₈₉	—	4	4	no	—
117	C₂×D₃₅₆	C₂³	1	2	yes	—
118	C₂×D₃₅₆	C₂³	1	2	yes	—
119	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
120	C₂×D₃₅₆	C₂³	1	2	yes	—
121	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
125	D₄×D₈₉	—	4	2	no	—
126	C₂²×Dic₈₉	C₂³	1	2	yes	—
127	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄×D₈₉	C₂³	1	2	yes	—
129	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄×D₈₉	C₂³	1	2	yes	—
131	C₂×C₄×D₈₉	C₂³	1	2	yes	—
132	C₂×C₄×D₈₉	C₂³	1	2	yes	—
133	C₂×C₄×D₈₉	C₂³	1	2	yes	—
134	C₂×C₄×D₈₉	C₂³	1	2	yes	—
135	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₈₉	C₂³	1	2	yes	—
139	C₄⋊Dic₈₉	C₂³	1	2	yes	—
140	C₄⋊Dic₈₉	C₂³	1	2	yes	—
141	#13083553	C₂³	1	2	yes	—
142	#13083553	C₂³	1	2	yes	—
143	#13083553	C₂³	1	2	yes	—
144	#13083553	C₂³	1	2	yes	—
145	#13083553	C₂³	1	2	yes	—
146	#13083553	C₂³	1	2	yes	—
147	#13083553	C₂³	1	2	yes	—
148	#13083553	C₂³	1	2	yes	—
149	#13083553	C₂³	1	2	yes	—
150	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
151	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
152	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
153	#13083551	C₂³	1	2	yes	—
154	#13083551	C₂³	1	2	yes	—
155	#13083551	C₂³	1	2	yes	—
156	#13083551	C₂³	1	2	yes	—
157	#13083551	C₂³	1	2	yes	—
158	#13083551	C₂³	1	2	yes	—
159	#13083551	C₂³	1	2	yes	—
160	#13083551	C₂³	1	2	yes	—
161	#13083551	C₂³	1	2	yes	—
162	#13083551	C₂³	1	2	yes	—
163	#13083551	C₂³	1	2	yes	—
164	#13083551	C₂³	1	2	yes	—
165	#13083551	C₂³	1	2	yes	—
166	#13083551	C₂³	1	2	yes	—
167	#13083551	C₂³	1	2	yes	—
168	#13083551	C₂³	1	2	yes	—
169	#13083551	C₂³	1	2	yes	—
170	C₄×Dic₈₉	C₂³	1	2	yes	—
171	C₄×Dic₈₉	C₂³	1	2	yes	—
172	C₄×Dic₈₉	C₂³	1	2	yes	—
173	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
174	C₄×Dic₈₉	C₂³	1	2	yes	—
175	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
176	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
178	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
181	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₄²×C₈₉	C₂³	1	2	yes	—
197	C₄²×C₈₉	C₂³	1	1	yes	characteristic
198	C₂³×C₈₉	C₂⁴	1	2	yes	—
199	C₂²×D₈₉	—	2	4	no	—
200	C₂²×D₈₉	—	4	2	no	—
201	C₂²×D₈₉	—	4	2	no	—
202	C₂²×D₈₉	C₂⁴	1	2	yes	—
203	C₂²×D₈₉	C₂⁴	1	2	yes	—
204	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
205	Q₈×C₈₉	—	4	1	no	—
206	Q₈×C₈₉	—	4	2	no	—
207	D₄×C₈₉	—	4	1	no	—
208	C₂×C₄×C₈₉	—	4	2	no	—
209	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
210	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²⋊D₈₉	—	2	4	no	—
218	C₂²⋊D₈₉	—	4	2	no	—
219	C₂²⋊D₈₉	—	4	2	no	—
220	C₂×Dic₈₉	—	4	2	no	—
221	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
222	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₈₉	C₂⁴	1	2	yes	—
224	C₂×Dic₈₉	C₂⁴	1	2	yes	—
225	C₂×Dic₈₉	C₂⁴	1	2	yes	—
226	C₂×Dic₈₉	C₂⁴	1	2	yes	—
227	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
228	D₃₅₆	—	2	4	no	—
229	D₃₅₆	—	4	1	no	—
230	D₃₅₆	—	4	2	no	—
231	D₃₅₆	—	4	1	no	—
232	D₃₅₆	—	4	2	no	—
233	C₄×D₈₉	—	2	2	no	—
234	C₄×D₈₉	—	2	2	no	—
235	C₄×D₈₉	—	2	4	no	—
236	C₄×D₈₉	—	4	1	no	—
237	C₄×D₈₉	—	4	2	no	—
238	C₄×D₈₉	—	4	2	no	—
239	C₄×D₈₉	—	4	2	no	—
240	C₄×D₈₉	—	4	2	no	—
241	C₄×D₈₉	—	4	2	no	—
242	Dic₁₇₈	—	2	4	no	—
243	Dic₁₇₈	—	2	4	no	—
244	Dic₁₇₈	—	4	1	no	—
245	Dic₁₇₈	—	4	2	no	—
246	Dic₁₇₈	—	4	2	no	—
247	Dic₁₇₈	—	4	1	no	—
248	C₂²×C₈₉	—	2	2	no	—
249	C₂²×C₈₉	—	2	2	no	—
250	C₂²×C₈₉	—	2	2	no	—
251	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
252	C₂×D₈₉	—	2	1	no	—
253	C₂×D₈₉	—	2	1	no	—
254	C₂×D₈₉	—	2	2	no	—
255	C₂×D₈₉	—	2	2	no	—
256	C₂×D₈₉	—	2	2	no	—
257	C₂×D₈₉	—	2	2	no	—
258	C₂×D₈₉	—	2	2	no	—
259	C₂×D₈₉	—	2	2	no	—
260	C₂×D₈₉	—	8	4	no	—
261	C₂×D₈₉	2₋¹⁺⁴	1	2	yes	—
262	C₄×C₈₉	—	2	2	no	—
263	C₄×C₈₉	—	2	2	no	—
264	C₄×C₈₉	—	2	2	no	—
265	C₄×C₈₉	—	2	1	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	2	2	no	—
268	C₄×C₈₉	—	2	2	no	—
269	C₄×C₈₉	—	2	1	no	—
270	Dic₈₉	—	2	2	no	—
271	Dic₈₉	—	2	2	no	—
272	Dic₈₉	—	2	1	no	—
273	Dic₈₉	—	2	1	no	—
274	Dic₈₉	—	2	2	no	—
275	Dic₈₉	—	2	2	no	—
276	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₈₉	—	4	2	no	—
278	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
280	C₂×C₈₉	#585	1	1	yes	characteristic
281	D₈₉	—	2	2	no	—
282	D₈₉	—	4	2	no	—
283	D₈₉	—	4	2	no	—
284	#3561	—	89	1	no	maximal, Sylow
285	C₈₉	#3561	1	1	yes	characteristic, complemented, Sylow
286	#563	—	89	1	no	—
287	#563	D₈₉	1	1	yes	characteristic, complemented
288	#562	—	89	1	no	—
289	#562	—	89	1	no	—
290	#556	—	89	2	no	—
291	#551	—	89	2	no	—
292	#551	—	89	2	no	—
293	D₄×Q₈	—	89	2	no	—
294	#548	—	89	2	no	—
295	#546	—	89	2	no	—
296	#543	—	89	2	no	—
297	#542	—	89	2	no	—
298	#542	—	89	2	no	—
299	#542	—	89	2	no	—
300	#538	—	89	2	no	—
301	#536	—	89	2	no	—
302	#533	—	89	1	no	—
303	#529	—	89	1	no	—
304	C₂×#124	—	89	1	no	—
305	C₂×#41	—	89	2	no	—
306	C₂²×Q₈	—	89	1	no	—
307	C₂²×Q₈	—	89	2	no	—
308	C₂²×D₄	—	89	1	no	—
309	C₄⋊Q₈	—	89	1	no	—
310	C₄⋊Q₈	—	89	1	no	—
311	C₄⋊Q₈	—	89	2	no	—
312	C₄⋊Q₈	—	89	2	no	—
313	C₄⋊Q₈	C₂×D₈₉	1	2	yes	complemented
314	#126	—	89	2	no	—
315	#126	—	89	2	no	—
316	#126	—	89	2	no	—
317	#126	—	89	2	no	—
318	#126	—	89	2	no	—
319	#126	C₂×D₈₉	1	2	yes	complemented
320	#126	C₂×D₈₉	1	2	yes	complemented
321	#125	—	89	1	no	—
322	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
323	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
324	#124	—	89	1	no	—
325	#124	—	89	2	no	—
326	#124	—	89	1	no	—
327	#124	—	89	2	no	—
328	#124	—	89	2	no	—
329	#124	—	89	2	no	—
330	#124	—	89	2	no	—
331	#124	—	89	2	no	—
332	#124	—	89	1	no	—
333	#124	—	89	1	no	—
334	#124	—	89	2	no	—
335	#124	C₂×D₈₉	1	1	yes	characteristic
336	#123	—	89	2	no	—
337	#123	—	89	2	no	—
338	#123	—	89	2	no	—
339	#123	—	89	2	no	—
340	#123	—	89	2	no	—
341	#123	—	89	2	no	—
342	#123	—	89	2	no	—
343	#123	—	89	2	no	—
344	#123	C₂×D₈₉	1	2	yes	—
345	C₂²⋊Q₈	—	89	2	no	—
346	C₂²⋊Q₈	—	89	2	no	—
347	C₂²⋊Q₈	—	89	2	no	—
348	C₂²⋊Q₈	—	89	2	no	—
349	C₂²⋊Q₈	—	89	1	no	—
350	C₂²⋊Q₈	—	89	2	no	—
351	C₂²⋊Q₈	—	89	2	no	—
352	C₂²⋊Q₈	—	89	2	no	—
353	C₂²⋊Q₈	—	89	2	no	—
354	C₂²⋊Q₈	—	89	2	no	—
355	C₂²⋊Q₈	—	89	2	no	—
356	C₂²⋊Q₈	—	89	2	no	—
357	C₂²⋊Q₈	—	89	2	no	—
358	C₂²⋊Q₈	—	89	2	no	—
359	C₂²⋊Q₈	—	89	2	no	—
360	C₂²⋊Q₈	—	89	2	no	—
361	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
362	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
363	#121	—	89	2	no	—
364	#121	—	89	1	no	—
365	#121	—	89	2	no	—
366	#121	—	89	2	no	—
367	#121	—	89	2	no	—
368	#121	—	89	2	no	—
369	#120	—	89	2	no	—
370	#120	—	89	2	no	—
371	C₄×Q₈	—	89	1	no	—
372	C₄×Q₈	—	89	2	no	—
373	C₄×Q₈	—	89	2	no	—
374	C₄×Q₈	—	89	2	no	—
375	C₄×D₄	—	89	2	no	—
376	C₄×D₄	—	89	2	no	—
377	C₄×D₄	—	89	2	no	—
378	C₄×D₄	—	89	1	no	—
379	C₄×D₄	—	89	2	no	—
380	C₄×D₄	—	89	2	no	—
381	C₄×D₄	—	89	2	no	—
382	#117	—	89	1	no	—
383	#117	—	89	1	no	—
384	#117	—	89	2	no	—
385	#117	—	89	2	no	—
386	#117	—	89	2	no	—
387	C₂×C₂²⋊C₄	—	89	2	no	—
388	C₂×C₂²⋊C₄	—	89	2	no	—
389	C₂×C₂²⋊C₄	—	89	2	no	—
390	C₂×C₂²⋊C₄	—	89	2	no	—
391	C₂×C₄²	—	89	1	no	—
392	C₂⁴	—	89	2	no	—
393	#41	—	356	4	no	—
394	C₂×Q₈	—	89	1	no	—
395	C₂×Q₈	—	89	2	no	—
396	C₂×Q₈	—	89	2	no	—
397	C₂×Q₈	—	89	1	no	—
398	C₂×Q₈	—	89	2	no	—
399	C₂×Q₈	—	89	2	no	—
400	C₂×Q₈	—	356	2	no	—
401	C₂×Q₈	—	356	4	no	—
402	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
403	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
404	C₂×D₄	—	89	2	no	—
405	C₂×D₄	—	89	2	no	—
406	C₂×D₄	—	89	2	no	—
407	C₂×D₄	—	89	2	no	—
408	C₂×D₄	—	89	1	no	—
409	C₂×D₄	—	89	2	no	—
410	C₂×D₄	—	89	1	no	—
411	C₂×D₄	—	89	2	no	—
412	C₂×D₄	—	356	2	no	—
413	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
414	C₂²×C₄	—	89	2	no	—
415	C₂²×C₄	—	89	1	no	—
416	C₂²×C₄	—	89	2	no	—
417	C₂²×C₄	—	89	2	no	—
418	C₂²×C₄	—	89	2	no	—
419	C₂²×C₄	—	89	2	no	—
420	C₂²×C₄	—	89	2	no	—
421	C₂²×C₄	—	89	1	no	—
422	C₂²×C₄	—	89	1	no	—
423	C₂²×C₄	—	89	2	no	—
424	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
425	C₄⋊C₄	—	89	2	no	—
426	C₄⋊C₄	—	89	2	no	—
427	C₄⋊C₄	—	89	2	no	—
428	C₄⋊C₄	—	89	2	no	—
429	C₄⋊C₄	—	89	1	no	—
430	C₄⋊C₄	—	89	1	no	—
431	C₄⋊C₄	—	89	2	no	—
432	C₄⋊C₄	—	89	2	no	—
433	C₄⋊C₄	—	89	2	no	—
434	C₄⋊C₄	—	89	2	no	—
435	C₄⋊C₄	—	89	2	no	—
436	C₄⋊C₄	—	89	2	no	—
437	C₄⋊C₄	—	89	2	no	—
438	C₄⋊C₄	—	89	2	no	—
439	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
440	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
442	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
443	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
444	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
445	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
446	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
447	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
448	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
449	C₂²⋊C₄	—	89	2	no	—
450	C₂²⋊C₄	—	89	2	no	—
451	C₂²⋊C₄	—	89	2	no	—
452	C₂²⋊C₄	—	89	2	no	—
453	C₂²⋊C₄	—	89	2	no	—
454	C₂²⋊C₄	—	89	2	no	—
455	C₂²⋊C₄	—	89	2	no	—
456	C₂²⋊C₄	—	89	2	no	—
457	C₂²⋊C₄	—	89	2	no	—
458	C₂²⋊C₄	—	89	2	no	—
459	C₂²⋊C₄	—	89	2	no	—
460	C₂²⋊C₄	—	89	2	no	—
461	C₂²⋊C₄	—	89	2	no	—
462	C₂²⋊C₄	—	89	2	no	—
463	C₂²⋊C₄	—	89	2	no	—
464	C₂²⋊C₄	—	89	2	no	—
465	C₂²⋊C₄	—	89	2	no	—
466	C₂²⋊C₄	—	89	2	no	—
467	C₂²⋊C₄	—	89	2	no	—
468	C₂²⋊C₄	—	89	2	no	—
469	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
470	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
471	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
472	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
473	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
474	C₄²	—	89	1	no	—
475	C₄²	—	89	1	no	—
476	C₄²	—	89	1	no	—
477	C₄²	—	89	2	no	—
478	C₄²	—	89	2	no	—
479	C₄²	—	89	2	no	—
480	C₄²	—	89	2	no	—
481	C₄²	C₂²×D₈₉	1	1	yes	characteristic
482	C₄²	C₂²×D₈₉	1	2	yes	—
483	C₂³	—	89	1	no	—
484	C₂³	—	89	2	no	—
485	C₂³	—	89	2	no	—
486	C₂³	—	356	2	no	—
487	C₂³	—	356	2	no	—
488	C₂³	—	178	4	no	—
489	C₂³	C₂³×D₈₉	1	2	yes	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	356	1	no	—
493	Q₈	—	356	2	no	—
494	Q₈	—	356	2	no	—
495	Q₈	—	356	1	no	—
496	Q₈	—	178	4	no	—
497	Q₈	—	178	4	no	—
498	D₄	—	4	1	no	—
499	D₄	—	356	2	no	—
500	D₄	—	356	1	no	—
501	D₄	—	356	1	no	—
502	D₄	—	356	2	no	—
503	D₄	—	356	2	no	—
504	D₄	—	356	2	no	—
505	D₄	—	178	4	no	—
506	D₄	—	178	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	89	1	no	—
509	C₂×C₄	—	89	1	no	—
510	C₂×C₄	—	89	1	no	—
511	C₂×C₄	—	89	2	no	—
512	C₂×C₄	—	89	2	no	—
513	C₂×C₄	—	89	2	no	—
514	C₂×C₄	—	89	2	no	—
515	C₂×C₄	—	356	2	no	—
516	C₂×C₄	—	356	1	no	—
517	C₂×C₄	—	356	2	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	4	no	—
524	C₂×C₄	—	178	2	no	—
525	C₂×C₄	C₂³×D₈₉	1	2	yes	—
526	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
527	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₈₉	1	2	yes	—
529	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
530	C₂×C₄	C₂³×D₈₉	1	2	yes	—
531	C₂×C₄	C₂³×D₈₉	1	2	yes	—
532	C₂×C₄	C₂³×D₈₉	1	2	yes	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	89	2	no	—
537	C₂²	—	178	2	no	—
538	C₂²	—	178	2	no	—
539	C₂²	—	178	2	no	—
540	C₂²	—	178	2	no	—
541	C₂²	—	178	2	no	—
542	C₂²	—	178	2	no	—
543	C₂²	—	178	1	no	—
544	C₂²	—	178	1	no	—
545	C₂²	—	712	4	no	—
546	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	89	2	no	—
556	C₄	—	178	2	no	—
557	C₄	—	178	2	no	—
558	C₄	—	178	1	no	—
559	C₄	—	178	2	no	—
560	C₄	—	178	2	no	—
561	C₄	—	178	1	no	—
562	C₂	—	4	2	no	—
563	C₂	—	356	2	no	—
564	C₂	—	356	2	no	—
565	C₂	—	178	2	no	—
566	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
567	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
568	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#563×C₈₉	C₂
hypercenter	#563	D₈₉
hypocenter	C₈₉	#3561
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #19152352	C₂	semidirect
2. #19152346	C₂	semidirect
3. #19152342	C₂	semidirect
4. #19152315	C₂	semidirect
5. #19152275	C₂	semidirect
6. #19152273	C₂	semidirect
7. #19152263	C₂	semidirect
8. #19152258	C₂	semidirect
9. #19152240	C₂	semidirect
10. #19152223	C₂	semidirect
11. #19152222	C₂	semidirect
12. #19152216	C₂	semidirect
13. #19152214	C₂	semidirect
14. #19152187	C₂	semidirect
15. #19152171	C₂	semidirect
16. #19152154	C₂	semidirect
17. #19152133	C₂	semidirect
18. #124×D₈₉	C₂	semidirect
19. #563×C₈₉	C₂	semidirect
22. C₂×Q₈×D₈₉	C₂²	semidirect
24. #15668011	C₂²	semidirect
25. #15668011	C₂²	semidirect
26. #15668011	C₂²	semidirect
27. #15668011	C₂²	semidirect
28. #15668007	C₂²	semidirect
29. #15668007	C₂²	semidirect
30. #15668007	C₂²	semidirect
31. #15668007	C₂²	semidirect
32. #15668005	C₂²	semidirect
33. #15668004	C₂²	semidirect
35. #15668001	C₂²	semidirect
37. #15668000	C₂²	semidirect
38. #15668000	C₂²	semidirect
43. #15667998	C₂²	semidirect
44. #15667998	C₂²	semidirect
47. #15667997	C₂²	semidirect
48. #15667997	C₂²	semidirect
49. #15667997	C₂²	semidirect
50. #15667996	C₂²	semidirect
51. #15667994	C₂²	semidirect
52. #15667994	C₂²	semidirect
54. #15667992	C₂²	semidirect
55. #15667992	C₂²	semidirect
56. #15667991	C₂²	semidirect
60. #15667990	C₂²	semidirect
61. #15667990	C₂²	semidirect
62. #15667990	C₂²	semidirect
63. #15667990	C₂²	semidirect
64. #15667989	C₂²	semidirect
65. #15667989	C₂²	semidirect
67. #15667988	C₂²	semidirect
68. #15667988	C₂²	semidirect
71. #15667987	C₂²	semidirect
73. #15667985	C₂²	semidirect
77. C₄×Dic₁₇₈	C₂²	semidirect
78. #15667977	C₂²	semidirect
79. #15667977	C₂²	semidirect
80. #15667977	C₂²	semidirect
84. #15667974	C₂²	semidirect
85. #15667974	C₂²	semidirect
86. C₄×C₂²⋊D₈₉	C₂²	semidirect
90. #15667970	C₂²	semidirect
91. #15667969	C₂²	semidirect
92. #15667968	C₂²	semidirect
98. C₄⋊Q₈×C₈₉	C₂²	semidirect
99. #126×C₈₉	C₂²	semidirect
100. #126×C₈₉	C₂²	semidirect
101. #125×C₈₉	C₂²	semidirect
102. #125×C₈₉	C₂²	semidirect
105. C₂²⋊Q₈×C₈₉	C₂²	semidirect
106. C₂²⋊Q₈×C₈₉	C₂²	semidirect
285. C₈₉	#3561	semidirect
287. #563	D₈₉	semidirect
313. C₄⋊Q₈	C₂×D₈₉	semidirect
319. #126	C₂×D₈₉	semidirect
320. #126	C₂×D₈₉	semidirect
322. #125	C₂×D₈₉	semidirect
323. #125	C₂×D₈₉	semidirect
361. C₂²⋊Q₈	C₂×D₈₉	semidirect
362. C₂²⋊Q₈	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152352	2
#19152346	2
#19152342	2
#19152315	2
#19152275	2
#19152273	2
#19152263	2
#19152258	2
#19152240	2
#19152223	2
#19152222	2
#19152216	2
#19152214	2
#19152187	2
#19152171	2
#19152154	2
#19152133	2
#124×D₈₉	2
#563×C₈₉	2
#3561	89