Subgroups — #26034122

Order 11392.

1232 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152334	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152333	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152331	C₂	1	2	yes	maximal, complemented
4	#19152269	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152268	C₂	1	2	yes	maximal, complemented
6	#19152245	C₂	1	2	yes	maximal, complemented
7	#19152237	C₂	1	4	yes	maximal, complemented
8	#19152236	C₂	1	2	yes	maximal, complemented
9	#19152198	C₂	1	4	yes	maximal, complemented
10	#19152161	C₂	1	2	yes	maximal, complemented
11	#19152152	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152144	C₂	1	2	yes	maximal, complemented
13	#19152143	C₂	1	2	yes	maximal, complemented
14	#127×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152070	C₂	1	2	yes	maximal, complemented
16	C₄×#13083573	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13083574	C₂²	1	2	yes	complemented
19	C₂×#13083573	C₂²	1	1	yes	characteristic
20	C₂×#13083573	C₂²	1	4	yes	complemented
21	C₂×D₄×D₈₉	C₂²	1	2	yes	—
22	C₂×D₄×D₈₉	C₂²	1	2	yes	—
23	C₂×D₄×D₈₉	C₂²	1	2	yes	—
24	#15668011	C₂²	1	1	yes	characteristic, complemented
25	#15668010	C₂²	1	1	yes	characteristic, complemented
26	#15668009	C₂²	1	1	yes	characteristic
27	#15668008	C₂²	1	2	yes	—
28	#15668008	C₂²	1	2	yes	—
29	#15668008	C₂²	1	2	yes	—
30	#15668008	C₂²	1	2	yes	complemented
31	#15668002	C₂²	1	2	yes	complemented
32	#15668001	C₂²	1	2	yes	complemented
33	#15668000	C₂²	1	2	yes	complemented
34	#15667999	C₂²	1	2	yes	complemented
35	#15667999	C₂²	1	2	yes	complemented
36	#15667998	C₂²	1	4	yes	complemented
37	#15667997	C₂²	1	4	yes	complemented
38	#15667995	C₂²	1	4	yes	complemented
39	#15667994	C₂²	1	4	yes	complemented
40	#15667993	C₂²	1	4	yes	complemented
41	#15667992	C₂²	1	1	yes	characteristic
42	#15667990	C₂²	1	2	yes	—
43	#15667988	C₂²	1	1	yes	characteristic
44	#15667986	C₂²	1	2	yes	complemented
45	#15667985	C₂²	1	4	yes	complemented
46	#15667984	C₂²	1	4	yes	complemented
47	#15667984	C₂²	1	4	yes	complemented
48	#15667984	C₂²	1	4	yes	complemented
49	#15667984	C₂²	1	4	yes	complemented
50	#15667983	C₂²	1	4	yes	complemented
51	#15667980	C₂²	1	4	yes	—
52	#15667980	C₂²	1	4	yes	—
53	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
54	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
56	#15667977	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₃₅₆	C₂²	1	2	yes	complemented
58	D₄×Dic₈₉	C₂²	1	2	yes	complemented
59	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
60	D₄×Dic₈₉	C₂²	1	2	yes	complemented
61	#15667974	C₂²	1	2	yes	complemented
62	#15667974	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	complemented
65	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	complemented
66	#15667972	C₂²	1	2	yes	—
67	#15667972	C₂²	1	4	yes	complemented
68	#15667970	C₂²	1	1	yes	characteristic
69	#15667969	C₂²	1	2	yes	—
70	#15667968	C₂²	1	2	yes	complemented
71	C₂×#13083551	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	—
73	C₂×C₄×Dic₈₉	C₂²	1	2	yes	complemented
74	C₄²×D₈₉	C₂²	1	1	yes	characteristic
75	C₂×#41×C₈₉	C₂²	1	2	yes	complemented
76	#127×C₈₉	C₂²	1	1	yes	characteristic
77	#127×C₈₉	C₂²	1	2	yes	complemented
78	#121×C₈₉	C₂²	1	2	yes	complemented
79	#121×C₈₉	C₂²	1	4	yes	complemented
80	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
83	C₂³×D₈₉	C₂³	1	4	yes	—
84	#13083574	—	4	4	no	—
85	#13083573	—	2	4	no	—
86	#13083573	—	4	8	no	—
87	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
88	C₂×Dic₁₇₈	C₂³	1	2	yes	—
89	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
90	C₂×D₃₅₆	C₂³	1	2	yes	—
91	C₂×D₃₅₆	C₂³	1	2	yes	—
92	C₂×D₃₅₆	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
99	D₄×D₈₉	—	2	8	no	—
100	D₄×D₈₉	—	4	4	no	—
101	D₄×D₈₉	—	4	4	no	—
102	C₂²×Dic₈₉	C₂³	1	2	yes	—
103	C₂²×Dic₈₉	C₂³	1	2	yes	—
104	C₂²×Dic₈₉	C₂³	1	4	yes	—
105	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₂³	1	4	yes	—
108	C₂×C₄×D₈₉	C₂³	1	4	yes	—
109	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₈₉	C₂³	1	2	yes	—
113	#13083553	C₂³	1	2	yes	—
114	#13083553	C₂³	1	2	yes	—
115	#13083553	C₂³	1	2	yes	—
116	#13083553	C₂³	1	2	yes	—
117	#13083553	C₂³	1	2	yes	—
118	#13083553	C₂³	1	2	yes	—
119	#13083553	C₂³	1	2	yes	—
120	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
121	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
123	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
124	#13083551	C₂³	1	2	yes	—
125	#13083551	C₂³	1	2	yes	—
126	#13083551	C₂³	1	2	yes	—
127	#13083551	C₂³	1	4	yes	—
128	#13083551	C₂³	1	4	yes	—
129	#13083551	C₂³	1	4	yes	—
130	#13083551	C₂³	1	4	yes	—
131	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
132	C₄×Dic₈₉	C₂³	1	2	yes	—
133	C₄×Dic₈₉	C₂³	1	2	yes	—
134	C₄×Dic₈₉	C₂³	1	2	yes	—
135	C₄×Dic₈₉	C₂³	1	2	yes	—
136	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
138	#41×C₈₉	—	4	4	no	—
139	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₈₉	C₂³	1	2	yes	—
141	C₂×D₄×C₈₉	C₂³	1	2	yes	—
142	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₈₉	C₂³	1	4	yes	—
144	C₂×D₄×C₈₉	C₂³	1	4	yes	—
145	C₂×D₄×C₈₉	C₂³	1	2	yes	—
146	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
147	C₂²×C₄×C₈₉	C₂³	1	4	yes	—
148	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
153	C₄²×C₈₉	C₂³	1	2	yes	—
154	C₄²×C₈₉	C₂³	1	1	yes	characteristic
155	C₂³×C₈₉	C₂⁴	1	4	yes	—
156	C₂³×C₈₉	C₂⁴	1	2	yes	—
157	C₂²×D₈₉	—	2	8	no	—
158	C₂²×D₈₉	—	4	4	no	—
159	C₂²×D₈₉	—	4	4	no	—
160	C₂²×D₈₉	C₂⁴	1	4	yes	—
161	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
162	Q₈×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	2	4	no	—
164	D₄×C₈₉	—	2	2	no	—
165	D₄×C₈₉	—	2	4	no	—
166	D₄×C₈₉	—	4	4	no	—
167	D₄×C₈₉	—	4	2	no	—
168	D₄×C₈₉	—	4	4	no	—
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	4	4	no	—
171	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
173	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
174	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
175	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂²⋊D₈₉	—	2	4	no	—
178	C₂²⋊D₈₉	—	2	8	no	—
179	C₂²⋊D₈₉	—	2	8	no	—
180	C₂²⋊D₈₉	—	4	4	no	—
181	C₂²⋊D₈₉	—	4	4	no	—
182	C₂²⋊D₈₉	—	4	4	no	—
183	C₂×Dic₈₉	—	2	4	no	—
184	C₂×Dic₈₉	—	2	4	no	—
185	C₂×Dic₈₉	—	4	4	no	—
186	C₂×Dic₈₉	C₂⁴	1	2	yes	—
187	C₂×Dic₈₉	C₂⁴	1	2	yes	—
188	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₈₉	C₂⁴	1	2	yes	—
190	C₂×Dic₈₉	C₂⁴	1	2	yes	—
191	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
193	D₃₅₆	—	2	4	no	—
194	D₃₅₆	—	2	4	no	—
195	D₃₅₆	—	4	2	no	—
196	C₄×D₈₉	—	2	2	no	—
197	C₄×D₈₉	—	2	2	no	—
198	C₄×D₈₉	—	4	4	no	—
199	C₄×D₈₉	—	4	4	no	—
200	C₄×D₈₉	#41	1	4	yes	complemented
201	Dic₁₇₈	—	2	2	no	—
202	Dic₁₇₈	—	2	2	no	—
203	Dic₁₇₈	—	2	4	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	2	4	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	2	4	no	—
208	C₂²×C₈₉	—	2	2	no	—
209	C₂²×C₈₉	—	2	4	no	—
210	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
211	C₂×D₈₉	—	2	1	no	—
212	C₂×D₈₉	—	2	1	no	—
213	C₂×D₈₉	—	2	4	no	—
214	C₂×D₈₉	—	2	4	no	—
215	C₂×D₈₉	—	2	4	no	—
216	C₂×D₈₉	—	8	8	no	—
217	C₂×D₈₉	C₂×#41	1	2	yes	—
218	C₄×C₈₉	—	2	2	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	2	2	no	—
221	C₄×C₈₉	—	2	2	no	—
222	C₄×C₈₉	C₂×#41	1	2	yes	—
223	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
224	Dic₈₉	—	2	2	no	—
225	Dic₈₉	—	2	2	no	—
226	Dic₈₉	—	2	2	no	—
227	Dic₈₉	—	2	1	no	—
228	Dic₈₉	—	2	2	no	—
229	Dic₈₉	C₂×#41	1	2	yes	—
230	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
231	C₂×C₈₉	—	4	4	no	—
232	C₂×C₈₉	—	4	2	no	—
233	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
234	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	D₈₉	—	2	2	no	—
237	D₈₉	—	4	4	no	—
238	#3508	—	89	1	no	maximal, Sylow
239	C₈₉	#3508	1	1	yes	characteristic, complemented, Sylow
240	#559	—	89	1	no	—
241	#559	—	89	1	no	—
242	#559	—	89	2	no	—
243	#550	—	89	2	no	—
244	#550	—	89	1	no	—
245	#550	D₈₉	1	1	yes	characteristic, complemented
246	#546	—	89	2	no	—
247	#546	—	89	4	no	—
248	#546	—	89	2	no	—
249	#540	—	89	4	no	—
250	#535	—	89	2	no	—
251	#533	—	89	1	no	—
252	#532	—	89	2	no	—
253	#532	—	89	2	no	—
254	C₂×#127	—	89	1	no	—
255	#518	—	89	2	no	—
256	C₄×#41	—	89	1	no	—
257	C₂×#41	—	89	4	no	—
258	C₂×#41	—	89	1	no	—
259	C₂×#41	—	89	2	no	—
260	C₂×#41	C₂×D₈₉	1	2	yes	complemented
261	C₂²×D₄	—	89	2	no	—
262	C₂²×D₄	—	89	2	no	—
263	C₂²×D₄	—	89	2	no	—
264	C₄⋊Q₈	—	89	1	no	—
265	C₄⋊Q₈	—	89	1	no	—
266	#127	—	89	2	no	—
267	#127	—	89	2	no	—
268	#127	—	89	2	no	—
269	#127	—	89	2	no	—
270	#127	—	89	1	no	—
271	#127	C₂×D₈₉	1	1	yes	characteristic
272	#127	C₂×D₈₉	1	2	yes	complemented
273	#125	—	89	2	no	—
274	#124	—	89	2	no	—
275	#124	—	89	2	no	—
276	#124	—	89	2	no	—
277	#124	—	89	4	no	—
278	#124	—	89	2	no	—
279	#123	—	89	4	no	—
280	#123	—	89	4	no	—
281	#123	—	89	4	no	—
282	#123	—	89	4	no	—
283	C₂²⋊Q₈	—	89	1	no	—
284	C₂²⋊Q₈	—	89	2	no	—
285	C₂²⋊Q₈	—	89	1	no	—
286	#121	—	89	4	no	—
287	#121	—	89	4	no	—
288	#121	—	89	4	no	—
289	#121	—	89	4	no	—
290	#121	—	89	4	no	—
291	#121	—	89	2	no	—
292	#121	—	89	4	no	—
293	#121	C₂×D₈₉	1	2	yes	complemented
294	#121	C₂×D₈₉	1	4	yes	complemented
295	#120	—	89	4	no	—
296	#120	—	89	4	no	—
297	C₄×Q₈	—	89	1	no	—
298	C₄×Q₈	—	89	1	no	—
299	C₄×Q₈	—	89	2	no	—
300	C₄×Q₈	—	89	1	no	—
301	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
302	C₄×D₄	—	89	1	no	—
303	C₄×D₄	—	89	2	no	—
304	C₄×D₄	—	89	2	no	—
305	C₄×D₄	—	89	2	no	—
306	C₄×D₄	—	89	4	no	—
307	C₄×D₄	—	89	4	no	—
308	C₄×D₄	—	89	2	no	—
309	C₄×D₄	—	89	2	no	—
310	C₄×D₄	—	89	2	no	—
311	C₄×D₄	—	89	4	no	—
312	C₄×D₄	—	89	2	no	—
313	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
314	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
315	#117	—	89	1	no	—
316	#117	—	89	2	no	—
317	#117	—	89	2	no	—
318	C₂×C₂²⋊C₄	—	89	4	no	—
319	C₂×C₂²⋊C₄	—	89	4	no	—
320	C₂×C₄²	—	89	2	no	—
321	C₂×C₄²	—	89	1	no	—
322	C₂⁴	—	89	4	no	—
323	#41	—	4	4	no	—
324	#41	—	356	4	no	—
325	#41	—	356	8	no	—
326	#41	—	178	4	no	—
327	C₂×Q₈	—	89	1	no	—
328	C₂×Q₈	—	89	2	no	—
329	C₂×Q₈	—	89	1	no	—
330	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
331	C₂×D₄	—	89	4	no	—
332	C₂×D₄	—	89	4	no	—
333	C₂×D₄	—	89	4	no	—
334	C₂×D₄	—	89	2	no	—
335	C₂×D₄	—	89	4	no	—
336	C₂×D₄	—	89	4	no	—
337	C₂×D₄	—	89	2	no	—
338	C₂×D₄	—	89	2	no	—
339	C₂×D₄	—	89	2	no	—
340	C₂×D₄	—	356	4	no	—
341	C₂×D₄	—	356	4	no	—
342	C₂×D₄	—	178	8	no	—
343	C₂×D₄	C₂²×D₈₉	1	2	yes	—
344	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
345	C₂×D₄	C₂²×D₈₉	1	2	yes	—
346	C₂×D₄	C₂²×D₈₉	1	4	yes	—
347	C₂×D₄	C₂²×D₈₉	1	4	yes	—
348	C₂×D₄	C₂²×D₈₉	1	2	yes	—
349	C₂²×C₄	—	89	1	no	—
350	C₂²×C₄	—	89	4	no	—
351	C₂²×C₄	—	89	2	no	—
352	C₂²×C₄	—	89	2	no	—
353	C₂²×C₄	—	89	4	no	—
354	C₂²×C₄	—	89	4	no	—
355	C₂²×C₄	—	89	1	no	—
356	C₂²×C₄	—	89	1	no	—
357	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
358	C₂²×C₄	C₂²×D₈₉	1	4	yes	—
359	C₄⋊C₄	—	89	1	no	—
360	C₄⋊C₄	—	89	2	no	—
361	C₄⋊C₄	—	89	2	no	—
362	C₄⋊C₄	—	89	2	no	—
363	C₄⋊C₄	—	89	2	no	—
364	C₄⋊C₄	—	89	2	no	—
365	C₄⋊C₄	—	89	1	no	—
366	C₄⋊C₄	—	89	2	no	—
367	C₄⋊C₄	—	89	2	no	—
368	C₄⋊C₄	—	89	2	no	—
369	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
372	C₂²⋊C₄	—	89	4	no	—
373	C₂²⋊C₄	—	89	2	no	—
374	C₂²⋊C₄	—	89	4	no	—
375	C₂²⋊C₄	—	89	4	no	—
376	C₂²⋊C₄	—	89	2	no	—
377	C₂²⋊C₄	—	89	2	no	—
378	C₂²⋊C₄	—	89	2	no	—
379	C₂²⋊C₄	—	89	4	no	—
380	C₂²⋊C₄	—	89	4	no	—
381	C₂²⋊C₄	—	89	4	no	—
382	C₂²⋊C₄	—	89	4	no	—
383	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
384	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
385	C₄²	—	89	1	no	—
386	C₄²	—	89	2	no	—
387	C₄²	—	89	1	no	—
388	C₄²	—	89	2	no	—
389	C₄²	—	89	2	no	—
390	C₄²	—	89	1	no	—
391	C₄²	—	89	2	no	—
392	C₄²	C₂²×D₈₉	1	1	yes	characteristic
393	C₄²	C₂²×D₈₉	1	2	yes	—
394	C₂³	—	89	1	no	—
395	C₂³	—	89	4	no	—
396	C₂³	—	356	4	no	—
397	C₂³	—	356	4	no	—
398	C₂³	—	178	8	no	—
399	C₂³	C₂³×D₈₉	1	4	yes	—
400	C₂³	C₂³×D₈₉	1	2	yes	—
401	Q₈	—	2	2	no	—
402	Q₈	—	178	4	no	—
403	Q₈	—	178	2	no	—
404	Q₈	—	178	2	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	356	2	no	—
412	D₄	—	356	4	no	—
413	D₄	—	356	4	no	—
414	D₄	—	356	4	no	—
415	D₄	—	178	8	no	—
416	D₄	—	178	8	no	—
417	D₄	—	178	4	no	—
418	D₄	—	178	4	no	—
419	D₄	—	178	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	89	1	no	—
423	C₂×C₄	—	89	1	no	—
424	C₂×C₄	—	89	4	no	—
425	C₂×C₄	—	89	2	no	—
426	C₂×C₄	—	89	2	no	—
427	C₂×C₄	—	89	1	no	—
428	C₂×C₄	—	89	2	no	—
429	C₂×C₄	—	89	2	no	—
430	C₂×C₄	—	356	4	no	—
431	C₂×C₄	—	356	4	no	—
432	C₂×C₄	—	356	4	no	—
433	C₂×C₄	—	178	2	no	—
434	C₂×C₄	—	178	4	no	—
435	C₂×C₄	—	178	4	no	—
436	C₂×C₄	—	178	2	no	—
437	C₂×C₄	C₂³×D₈₉	1	2	yes	—
438	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₈₉	1	2	yes	—
440	C₂×C₄	C₂³×D₈₉	1	2	yes	—
441	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
442	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	89	2	no	—
450	C₂²	—	178	4	no	—
451	C₂²	—	178	4	no	—
452	C₂²	—	178	4	no	—
453	C₂²	—	178	1	no	—
454	C₂²	—	178	1	no	—
455	C₂²	—	712	8	no	—
456	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	89	2	no	—
462	C₄	—	89	2	no	—
463	C₄	—	178	2	no	—
464	C₄	—	178	2	no	—
465	C₄	—	178	2	no	—
466	C₄	—	178	2	no	—
467	C₄	—	178	1	no	—
468	C₄	#41×D₈₉	1	2	yes	—
469	C₄	#15668057	1	2	yes	—
470	C₂	—	4	2	no	—
471	C₂	—	4	4	no	—
472	C₂	—	356	4	no	—
473	C₂	—	178	2	no	—
474	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
475	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
476	C₂	C₂×#15668057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#550×C₈₉	C₂
hypercenter	#550	D₈₉
hypocenter	C₈₉	#3508
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #19152334	C₂	semidirect
2. #19152333	C₂	semidirect
3. #19152331	C₂	semidirect
4. #19152269	C₂	semidirect
5. #19152268	C₂	semidirect
6. #19152245	C₂	semidirect
7. #19152237	C₂	semidirect
8. #19152236	C₂	semidirect
9. #19152198	C₂	semidirect
10. #19152161	C₂	semidirect
11. #19152152	C₂	semidirect
12. #19152144	C₂	semidirect
13. #19152143	C₂	semidirect
14. #127×D₈₉	C₂	semidirect
15. #19152070	C₂	semidirect
16. C₄×#13083573	C₂	semidirect
17. #550×C₈₉	C₂	semidirect
18. C₂×#13083574	C₂²	semidirect
20. C₂×#13083573	C₂²	semidirect
24. #15668011	C₂²	semidirect
25. #15668010	C₂²	semidirect
30. #15668008	C₂²	semidirect
31. #15668002	C₂²	semidirect
32. #15668001	C₂²	semidirect
33. #15668000	C₂²	semidirect
34. #15667999	C₂²	semidirect
35. #15667999	C₂²	semidirect
36. #15667998	C₂²	semidirect
37. #15667997	C₂²	semidirect
38. #15667995	C₂²	semidirect
39. #15667994	C₂²	semidirect
40. #15667993	C₂²	semidirect
44. #15667986	C₂²	semidirect
45. #15667985	C₂²	semidirect
46. #15667984	C₂²	semidirect
47. #15667984	C₂²	semidirect
48. #15667984	C₂²	semidirect
49. #15667984	C₂²	semidirect
50. #15667983	C₂²	semidirect
53. C₄×Dic₁₇₈	C₂²	semidirect
54. C₄×Dic₁₇₈	C₂²	semidirect
55. C₄×Dic₁₇₈	C₂²	semidirect
56. #15667977	C₂²	semidirect
57. C₄×D₃₅₆	C₂²	semidirect
58. D₄×Dic₈₉	C₂²	semidirect
59. D₄×Dic₈₉	C₂²	semidirect
60. D₄×Dic₈₉	C₂²	semidirect
61. #15667974	C₂²	semidirect
62. #15667974	C₂²	semidirect
64. C₄×C₂²⋊D₈₉	C₂²	semidirect
65. C₄×C₂²⋊D₈₉	C₂²	semidirect
67. #15667972	C₂²	semidirect
70. #15667968	C₂²	semidirect
73. C₂×C₄×Dic₈₉	C₂²	semidirect
75. C₂×#41×C₈₉	C₂²	semidirect
77. #127×C₈₉	C₂²	semidirect
78. #121×C₈₉	C₂²	semidirect
79. #121×C₈₉	C₂²	semidirect
80. C₄×Q₈×C₈₉	C₂²	semidirect
81. C₄×D₄×C₈₉	C₂²	semidirect
82. C₄×D₄×C₈₉	C₂²	semidirect
200. C₄×D₈₉	#41	semidirect
239. C₈₉	#3508	semidirect
245. #550	D₈₉	semidirect
260. C₂×#41	C₂×D₈₉	semidirect
272. #127	C₂×D₈₉	semidirect
293. #121	C₂×D₈₉	semidirect
294. #121	C₂×D₈₉	semidirect
301. C₄×Q₈	C₂×D₈₉	semidirect
313. C₄×D₄	C₂×D₈₉	semidirect
314. C₄×D₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152334	2
#19152333	2
#19152331	2
#19152269	2
#19152268	2
#19152245	2
#19152237	2
#19152236	2
#19152198	2
#19152161	2
#19152152	2
#19152144	2
#19152143	2
#127×D₈₉	2
#19152070	2
C₄×#13083573	2
#550×C₈₉	2
#3508	89