Subgroups — #26034774

Order 11392.

1160 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152346	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152340	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152340	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152332	C₂	1	2	yes	maximal, complemented
5	#19152258	C₂	1	2	yes	maximal, complemented
6	#19152240	C₂	1	2	yes	maximal, complemented
7	#19152239	C₂	1	2	yes	maximal, complemented
8	#19152237	C₂	1	2	yes	maximal, complemented
9	#19152232	C₂	1	2	yes	maximal, complemented
10	#19152218	C₂	1	2	yes	maximal, complemented
11	#19152188	C₂	1	2	yes	maximal, complemented
12	#19152184	C₂	1	2	yes	maximal, complemented
13	#19152180	C₂	1	2	yes	maximal, complemented
14	#19152164	C₂	1	2	yes	maximal, complemented
15	#19152159	C₂	1	2	yes	maximal, complemented
16	#19152147	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	#562×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13083575	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083574	C₂²	1	2	yes	complemented
22	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
23	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₃₅₆	C₂²	1	2	yes	complemented
25	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
27	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
28	#15668010	C₂²	1	1	yes	characteristic, complemented
29	#15668008	C₂²	1	2	yes	—
30	#15668008	C₂²	1	1	yes	characteristic, complemented
31	#15668007	C₂²	1	2	yes	complemented
32	#15668007	C₂²	1	2	yes	complemented
33	#15668005	C₂²	1	2	yes	complemented
34	#15668001	C₂²	1	1	yes	characteristic, complemented
35	#15668001	C₂²	1	2	yes	complemented
36	#15668001	C₂²	1	2	yes	complemented
37	#15668000	C₂²	1	1	yes	characteristic, complemented
38	#15668000	C₂²	1	1	yes	characteristic, complemented
39	#15668000	C₂²	1	1	yes	characteristic, complemented
40	#15667999	C₂²	1	1	yes	characteristic, complemented
41	#15667998	C₂²	1	2	yes	complemented
42	#15667998	C₂²	1	2	yes	complemented
43	#15667998	C₂²	1	2	yes	complemented
44	#15667998	C₂²	1	2	yes	complemented
45	#15667998	C₂²	1	2	yes	complemented
46	#15667998	C₂²	1	2	yes	complemented
47	#15667998	C₂²	1	2	yes	complemented
48	#15667997	C₂²	1	2	yes	complemented
49	#15667997	C₂²	1	2	yes	complemented
50	#15667997	C₂²	1	2	yes	complemented
51	#15667997	C₂²	1	2	yes	complemented
52	#15667997	C₂²	1	2	yes	complemented
53	#15667995	C₂²	1	2	yes	complemented
54	#15667993	C₂²	1	2	yes	complemented
55	#15667992	C₂²	1	1	yes	characteristic, complemented
56	#15667990	C₂²	1	2	yes	complemented
57	#15667990	C₂²	1	2	yes	complemented
58	#15667990	C₂²	1	2	yes	complemented
59	#15667987	C₂²	1	1	yes	characteristic
60	#15667987	C₂²	1	2	yes	complemented
61	#15667987	C₂²	1	2	yes	complemented
62	#15667987	C₂²	1	2	yes	complemented
63	#15667987	C₂²	1	2	yes	complemented
64	#15667986	C₂²	1	2	yes	complemented
65	#15667985	C₂²	1	2	yes	—
66	#15667985	C₂²	1	2	yes	complemented
67	#15667985	C₂²	1	2	yes	complemented
68	#15667985	C₂²	1	2	yes	complemented
69	#15667984	C₂²	1	2	yes	complemented
70	#15667983	C₂²	1	2	yes	complemented
71	#15667982	C₂²	1	2	yes	complemented
72	#15667982	C₂²	1	2	yes	complemented
73	#15667982	C₂²	1	2	yes	complemented
74	#15667982	C₂²	1	2	yes	complemented
75	#15667982	C₂²	1	2	yes	complemented
76	#15667982	C₂²	1	2	yes	complemented
77	#15667980	C₂²	1	2	yes	complemented
78	#15667980	C₂²	1	2	yes	complemented
79	#15667980	C₂²	1	2	yes	complemented
80	#15667980	C₂²	1	2	yes	complemented
81	#15667977	C₂²	1	1	yes	characteristic, complemented
82	#15667977	C₂²	1	2	yes	complemented
83	#15667974	C₂²	1	2	yes	complemented
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	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
89	#15667972	C₂²	1	2	yes	complemented
90	#15667972	C₂²	1	2	yes	complemented
91	#15667972	C₂²	1	2	yes	complemented
92	#15667970	C₂²	1	2	yes	complemented
93	C₂×#13083551	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
97	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
98	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#123×C₈₉	C₂²	1	2	yes	complemented
102	#123×C₈₉	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
105	#121×C₈₉	C₂²	1	2	yes	complemented
106	#121×C₈₉	C₂²	1	2	yes	complemented
107	C₂³×D₈₉	C₂³	1	2	yes	—
108	C₂³×D₈₉	C₂³	1	2	yes	—
109	C₂³×D₈₉	C₂³	1	2	yes	—
110	#13083575	—	4	2	no	—
111	#13083574	—	4	4	no	—
112	#13083573	—	4	2	no	—
113	C₂×Dic₁₇₈	C₂³	1	2	yes	—
114	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
115	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
116	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
117	Q₈×D₈₉	—	4	2	no	—
118	C₂×D₃₅₆	—	4	4	no	—
119	C₂×D₃₅₆	C₂³	1	2	yes	—
120	C₂×D₃₅₆	C₂³	1	2	yes	—
121	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
122	C₂×D₃₅₆	C₂³	1	2	yes	—
123	C₂×D₃₅₆	C₂³	1	2	yes	—
124	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
125	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
126	C₂×D₃₅₆	C₂³	1	2	yes	—
127	C₂×D₃₅₆	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	D₄×D₈₉	—	4	2	no	—
137	D₄×D₈₉	—	4	4	no	—
138	D₄×D₈₉	—	4	4	no	—
139	C₂²×Dic₈₉	C₂³	1	2	yes	—
140	C₂×C₄×D₈₉	C₂³	1	2	yes	—
141	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₉	C₂³	1	2	yes	—
144	C₂×C₄×D₈₉	C₂³	1	2	yes	—
145	C₂×C₄×D₈₉	C₂³	1	2	yes	—
146	C₂×C₄×D₈₉	C₂³	1	2	yes	—
147	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₈₉	C₂³	1	2	yes	—
149	#13083553	C₂³	1	2	yes	—
150	#13083553	C₂³	1	2	yes	—
151	#13083553	C₂³	1	2	yes	—
152	#13083553	C₂³	1	2	yes	—
153	#13083553	C₂³	1	2	yes	—
154	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
156	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₈₉	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	#13083551	C₂³	1	2	yes	—
171	#13083551	C₂³	1	2	yes	—
172	#13083551	C₂³	1	2	yes	—
173	#13083551	C₂³	1	2	yes	—
174	#13083551	C₂³	1	2	yes	—
175	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
176	C₄×Dic₈₉	C₂³	1	2	yes	—
177	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
178	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
179	C₄×Dic₈₉	C₂³	1	2	yes	—
180	C₄×Dic₈₉	C₂³	1	2	yes	—
181	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×D₄×C₈₉	C₂³	1	2	yes	—
186	C₂×D₄×C₈₉	C₂³	1	2	yes	—
187	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
188	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₄²×C₈₉	C₂³	1	1	yes	characteristic
202	C₂³×C₈₉	C₂⁴	1	2	yes	—
203	C₂³×C₈₉	C₂⁴	1	2	yes	—
204	C₂²×D₈₉	—	2	4	no	—
205	C₂²×D₈₉	—	4	2	no	—
206	C₂²×D₈₉	—	4	2	no	—
207	C₂²×D₈₉	—	4	2	no	—
208	C₂²×D₈₉	—	4	2	no	—
209	C₂²×D₈₉	—	4	2	no	—
210	C₂²×D₈₉	—	4	2	no	—
211	C₂²×D₈₉	—	4	2	no	—
212	C₂²×D₈₉	—	4	2	no	—
213	C₂²×D₈₉	C₂⁴	1	2	yes	—
214	C₂²×D₈₉	C₂⁴	1	2	yes	—
215	C₂²×D₈₉	C₂⁴	1	2	yes	—
216	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
217	Q₈×C₈₉	—	4	1	no	—
218	Q₈×C₈₉	—	4	1	no	—
219	D₄×C₈₉	—	4	1	no	—
220	D₄×C₈₉	—	4	2	no	—
221	D₄×C₈₉	—	4	2	no	—
222	D₄×C₈₉	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	2	no	—
224	C₂×C₄×C₈₉	—	4	2	no	—
225	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
232	C₂²⋊D₈₉	—	2	4	no	—
233	C₂²⋊D₈₉	—	2	4	no	—
234	C₂²⋊D₈₉	—	2	4	no	—
235	C₂²⋊D₈₉	—	4	2	no	—
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	—	4	2	no	—
241	C₂×Dic₈₉	C₂⁴	1	2	yes	—
242	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₈₉	C₂⁴	1	2	yes	—
245	C₂×Dic₈₉	C₂⁴	1	2	yes	—
246	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
247	D₃₅₆	—	2	4	no	—
248	D₃₅₆	—	2	4	no	—
249	D₃₅₆	—	4	1	no	—
250	D₃₅₆	—	4	2	no	—
251	D₃₅₆	—	4	2	no	—
252	D₃₅₆	—	4	2	no	—
253	D₃₅₆	—	4	1	no	—
254	D₃₅₆	—	4	2	no	—
255	D₃₅₆	—	4	1	no	—
256	C₄×D₈₉	—	2	2	no	—
257	C₄×D₈₉	—	2	2	no	—
258	C₄×D₈₉	—	2	4	no	—
259	C₄×D₈₉	—	4	1	no	—
260	C₄×D₈₉	—	4	2	no	—
261	C₄×D₈₉	—	4	2	no	—
262	C₄×D₈₉	—	4	2	no	—
263	C₄×D₈₉	—	4	2	no	—
264	Dic₁₇₈	—	2	4	no	—
265	Dic₁₇₈	—	4	1	no	—
266	Dic₁₇₈	—	4	1	no	—
267	Dic₁₇₈	—	4	1	no	—
268	C₂²×C₈₉	—	2	2	no	—
269	C₂²×C₈₉	—	2	2	no	—
270	C₂²×C₈₉	—	2	2	no	—
271	C₂²×C₈₉	—	2	2	no	—
272	C₂²×C₈₉	—	2	2	no	—
273	C₂²×C₈₉	—	2	2	no	—
274	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
275	C₂×D₈₉	—	2	1	no	—
276	C₂×D₈₉	—	2	1	no	—
277	C₂×D₈₉	—	2	2	no	—
278	C₂×D₈₉	—	2	2	no	—
279	C₂×D₈₉	—	2	2	no	—
280	C₂×D₈₉	—	2	2	no	—
281	C₂×D₈₉	—	2	2	no	—
282	C₂×D₈₉	—	2	2	no	—
283	C₂×D₈₉	—	2	2	no	—
284	C₂×D₈₉	—	2	2	no	—
285	C₂×D₈₉	—	2	2	no	—
286	C₂×D₈₉	—	8	4	no	—
287	C₂×D₈₉	—	8	4	no	—
288	C₂×D₈₉	—	8	4	no	—
289	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
290	C₄×C₈₉	—	2	2	no	—
291	C₄×C₈₉	—	2	1	no	—
292	C₄×C₈₉	—	2	1	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	2	2	no	—
295	C₄×C₈₉	—	2	2	no	—
296	C₄×C₈₉	—	2	1	no	—
297	Dic₈₉	—	2	2	no	—
298	Dic₈₉	—	2	2	no	—
299	Dic₈₉	—	2	1	no	—
300	Dic₈₉	—	2	2	no	—
301	Dic₈₉	—	2	1	no	—
302	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
303	C₂×C₈₉	—	4	2	no	—
304	C₂×C₈₉	—	4	2	no	—
305	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×C₈₉	#585	1	1	yes	characteristic
308	D₈₉	—	2	2	no	—
309	D₈₉	—	4	2	no	—
310	D₈₉	—	4	2	no	—
311	D₈₉	—	4	2	no	—
312	#3558	—	89	1	no	maximal, Sylow
313	C₈₉	#3558	1	1	yes	characteristic, complemented, Sylow
314	#562	—	89	1	no	—
315	#562	D₈₉	1	1	yes	characteristic, complemented
316	H(3,𝔽₄)	—	89	1	no	—
317	H(3,𝔽₄)	—	89	1	no	—
318	#559	—	89	2	no	—
319	#548	—	89	2	no	—
320	#546	—	89	2	no	—
321	#546	—	89	2	no	—
322	#546	—	89	2	no	—
323	D₄²	—	89	2	no	—
324	#542	—	89	2	no	—
325	#538	—	89	2	no	—
326	#538	—	89	2	no	—
327	#538	—	89	2	no	—
328	#535	—	89	2	no	—
329	#534	—	89	2	no	—
330	#532	—	89	1	no	—
331	#529	—	89	1	no	—
332	C₂×#124	—	89	1	no	—
333	C₂×#41	—	89	1	no	—
334	C₂×#41	—	89	1	no	—
335	C₂×#41	—	89	2	no	—
336	C₂²×Q₈	—	89	1	no	—
337	C₂²×D₄	—	89	1	no	—
338	C₂²×D₄	—	89	2	no	—
339	C₂²×D₄	—	89	2	no	—
340	C₂²×D₄	—	89	2	no	—
341	C₄⋊Q₈	—	89	1	no	—
342	#127	—	89	1	no	—
343	#127	—	89	2	no	—
344	#126	—	89	2	no	—
345	#126	—	89	2	no	—
346	#126	—	89	2	no	—
347	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
348	#124	—	89	1	no	—
349	#124	—	89	2	no	—
350	#124	—	89	2	no	—
351	#124	—	89	1	no	—
352	#124	—	89	2	no	—
353	#124	—	89	2	no	—
354	#124	—	89	2	no	—
355	#124	—	89	2	no	—
356	#124	—	89	2	no	—
357	#124	—	89	2	no	—
358	#124	—	89	2	no	—
359	#124	—	89	1	no	—
360	#124	—	89	1	no	—
361	#124	—	89	1	no	—
362	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
363	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
364	#123	—	89	2	no	—
365	#123	—	89	2	no	—
366	#123	—	89	2	no	—
367	#123	—	89	2	no	—
368	#123	—	89	2	no	—
369	#123	—	89	2	no	—
370	#123	—	89	2	no	—
371	#123	C₂×D₈₉	1	2	yes	complemented
372	#123	C₂×D₈₉	1	2	yes	complemented
373	C₂²⋊Q₈	—	89	1	no	—
374	C₂²⋊Q₈	—	89	2	no	—
375	C₂²⋊Q₈	—	89	2	no	—
376	C₂²⋊Q₈	—	89	2	no	—
377	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
378	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
379	#121	—	89	2	no	—
380	#121	—	89	2	no	—
381	#121	—	89	2	no	—
382	#121	—	89	1	no	—
383	#121	—	89	2	no	—
384	#121	—	89	2	no	—
385	#121	—	89	2	no	—
386	#121	—	89	2	no	—
387	#121	—	89	2	no	—
388	#121	—	89	2	no	—
389	#121	—	89	2	no	—
390	#121	—	89	2	no	—
391	#121	C₂×D₈₉	1	2	yes	complemented
392	#121	C₂×D₈₉	1	2	yes	complemented
393	#120	—	89	2	no	—
394	#120	—	89	2	no	—
395	#120	—	89	2	no	—
396	#120	—	89	2	no	—
397	#120	—	89	2	no	—
398	#120	—	89	2	no	—
399	#120	—	89	2	no	—
400	#120	—	89	2	no	—
401	#120	—	89	2	no	—
402	#120	—	89	2	no	—
403	C₄×Q₈	—	89	1	no	—
404	C₄×Q₈	—	89	2	no	—
405	C₄×D₄	—	89	2	no	—
406	C₄×D₄	—	89	2	no	—
407	C₄×D₄	—	89	2	no	—
408	C₄×D₄	—	89	2	no	—
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	89	2	no	—
411	C₄×D₄	—	89	2	no	—
412	C₄×D₄	—	89	2	no	—
413	C₄×D₄	—	89	2	no	—
414	#117	—	89	2	no	—
415	C₂×C₂²⋊C₄	—	89	2	no	—
416	C₂×C₂²⋊C₄	—	89	2	no	—
417	C₂×C₂²⋊C₄	—	89	2	no	—
418	C₂×C₂²⋊C₄	—	89	2	no	—
419	C₂×C₄²	—	89	1	no	—
420	C₂⁴	—	89	2	no	—
421	C₂⁴	—	89	2	no	—
422	C₂⁴	—	89	2	no	—
423	#41	—	356	4	no	—
424	#41	—	356	2	no	—
425	#41	—	356	2	no	—
426	C₂×Q₈	—	89	1	no	—
427	C₂×Q₈	—	89	1	no	—
428	C₂×Q₈	—	89	1	no	—
429	C₂×Q₈	—	89	2	no	—
430	C₂×Q₈	—	356	2	no	—
431	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
432	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₂×D₄	—	89	2	no	—
434	C₂×D₄	—	89	2	no	—
435	C₂×D₄	—	89	2	no	—
436	C₂×D₄	—	89	2	no	—
437	C₂×D₄	—	89	2	no	—
438	C₂×D₄	—	89	2	no	—
439	C₂×D₄	—	89	2	no	—
440	C₂×D₄	—	89	2	no	—
441	C₂×D₄	—	89	1	no	—
442	C₂×D₄	—	89	2	no	—
443	C₂×D₄	—	89	2	no	—
444	C₂×D₄	—	89	1	no	—
445	C₂×D₄	—	89	1	no	—
446	C₂×D₄	—	89	2	no	—
447	C₂×D₄	—	89	2	no	—
448	C₂×D₄	—	89	2	no	—
449	C₂×D₄	—	89	2	no	—
450	C₂×D₄	—	356	4	no	—
451	C₂×D₄	—	356	4	no	—
452	C₂×D₄	—	356	2	no	—
453	C₂×D₄	—	356	4	no	—
454	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
456	C₂×D₄	C₂²×D₈₉	1	2	yes	—
457	C₂×D₄	C₂²×D₈₉	1	2	yes	—
458	C₂²×C₄	—	89	2	no	—
459	C₂²×C₄	—	89	1	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	1	no	—
465	C₂²×C₄	—	89	1	no	—
466	C₂²×C₄	—	89	2	no	—
467	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
468	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
469	C₄⋊C₄	—	89	2	no	—
470	C₄⋊C₄	—	89	2	no	—
471	C₄⋊C₄	—	89	2	no	—
472	C₄⋊C₄	—	89	2	no	—
473	C₄⋊C₄	—	89	2	no	—
474	C₄⋊C₄	—	89	2	no	—
475	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
476	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
477	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
478	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
480	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
481	C₂²⋊C₄	—	89	2	no	—
482	C₂²⋊C₄	—	89	2	no	—
483	C₂²⋊C₄	—	89	2	no	—
484	C₂²⋊C₄	—	89	2	no	—
485	C₂²⋊C₄	—	89	2	no	—
486	C₂²⋊C₄	—	89	2	no	—
487	C₂²⋊C₄	—	89	2	no	—
488	C₂²⋊C₄	—	89	2	no	—
489	C₂²⋊C₄	—	89	2	no	—
490	C₂²⋊C₄	—	89	2	no	—
491	C₂²⋊C₄	—	89	2	no	—
492	C₂²⋊C₄	—	89	2	no	—
493	C₂²⋊C₄	—	89	2	no	—
494	C₂²⋊C₄	—	89	2	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	C₂²×D₈₉	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
506	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
508	C₄²	—	89	1	no	—
509	C₄²	—	89	1	no	—
510	C₄²	—	89	1	no	—
511	C₄²	—	89	2	no	—
512	C₄²	—	89	2	no	—
513	C₄²	—	89	2	no	—
514	C₄²	C₂²×D₈₉	1	1	yes	characteristic
515	C₂³	—	89	1	no	—
516	C₂³	—	89	2	no	—
517	C₂³	—	89	2	no	—
518	C₂³	—	89	2	no	—
519	C₂³	—	356	2	no	—
520	C₂³	—	356	2	no	—
521	C₂³	—	356	2	no	—
522	C₂³	—	356	2	no	—
523	C₂³	—	356	2	no	—
524	C₂³	—	356	2	no	—
525	C₂³	—	356	2	no	—
526	C₂³	—	356	2	no	—
527	C₂³	—	178	4	no	—
528	C₂³	C₂³×D₈₉	1	2	yes	—
529	C₂³	C₂³×D₈₉	1	2	yes	—
530	Q₈	—	4	1	no	—
531	Q₈	—	4	1	no	—
532	Q₈	—	356	1	no	—
533	Q₈	—	356	1	no	—
534	Q₈	—	356	1	no	—
535	Q₈	—	178	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	356	1	no	—
541	D₄	—	356	2	no	—
542	D₄	—	356	2	no	—
543	D₄	—	356	2	no	—
544	D₄	—	356	1	no	—
545	D₄	—	356	2	no	—
546	D₄	—	356	1	no	—
547	D₄	—	356	2	no	—
548	D₄	—	356	2	no	—
549	D₄	—	356	2	no	—
550	D₄	—	356	2	no	—
551	D₄	—	356	2	no	—
552	D₄	—	178	4	no	—
553	D₄	—	178	4	no	—
554	D₄	—	178	4	no	—
555	D₄	—	178	4	no	—
556	D₄	—	178	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	89	1	no	—
560	C₂×C₄	—	89	2	no	—
561	C₂×C₄	—	89	1	no	—
562	C₂×C₄	—	89	1	no	—
563	C₂×C₄	—	89	2	no	—
564	C₂×C₄	—	89	2	no	—
565	C₂×C₄	—	356	1	no	—
566	C₂×C₄	—	356	2	no	—
567	C₂×C₄	—	356	2	no	—
568	C₂×C₄	—	356	2	no	—
569	C₂×C₄	—	356	2	no	—
570	C₂×C₄	—	356	2	no	—
571	C₂×C₄	—	178	2	no	—
572	C₂×C₄	—	178	4	no	—
573	C₂×C₄	—	178	2	no	—
574	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
575	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
576	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
577	C₂×C₄	C₂³×D₈₉	1	2	yes	—
578	C₂×C₄	C₂³×D₈₉	1	2	yes	—
579	C₂×C₄	C₂³×D₈₉	1	2	yes	—
580	C₂×C₄	C₂³×D₈₉	1	2	yes	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	89	2	no	—
588	C₂²	—	178	2	no	—
589	C₂²	—	178	2	no	—
590	C₂²	—	178	2	no	—
591	C₂²	—	178	2	no	—
592	C₂²	—	178	2	no	—
593	C₂²	—	178	2	no	—
594	C₂²	—	178	2	no	—
595	C₂²	—	178	2	no	—
596	C₂²	—	178	2	no	—
597	C₂²	—	178	1	no	—
598	C₂²	—	178	1	no	—
599	C₂²	—	712	4	no	—
600	C₂²	—	712	4	no	—
601	C₂²	—	712	4	no	—
602	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	89	2	no	—
611	C₄	—	178	1	no	—
612	C₄	—	178	2	no	—
613	C₄	—	178	2	no	—
614	C₄	—	178	1	no	—
615	C₄	—	178	2	no	—
616	C₂	—	4	2	no	—
617	C₂	—	4	2	no	—
618	C₂	—	356	2	no	—
619	C₂	—	356	2	no	—
620	C₂	—	356	2	no	—
621	C₂	—	178	2	no	—
622	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
623	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
624	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#562×C₈₉	C₂
hypercenter	#562	D₈₉
hypocenter	C₈₉	#3558
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #19152346	C₂	semidirect
2. #19152340	C₂	semidirect
3. #19152340	C₂	semidirect
4. #19152332	C₂	semidirect
5. #19152258	C₂	semidirect
6. #19152240	C₂	semidirect
7. #19152239	C₂	semidirect
8. #19152237	C₂	semidirect
9. #19152232	C₂	semidirect
10. #19152218	C₂	semidirect
11. #19152188	C₂	semidirect
12. #19152184	C₂	semidirect
13. #19152180	C₂	semidirect
14. #19152164	C₂	semidirect
15. #19152159	C₂	semidirect
16. #19152147	C₂	semidirect
17. #19152133	C₂	semidirect
18. #124×D₈₉	C₂	semidirect
19. #562×C₈₉	C₂	semidirect
20. C₂×#13083575	C₂²	semidirect
21. C₂×#13083574	C₂²	semidirect
22. C₂×#13083573	C₂²	semidirect
23. C₂×Q₈×D₈₉	C₂²	semidirect
24. C₂²×D₃₅₆	C₂²	semidirect
26. C₂×D₄×D₈₉	C₂²	semidirect
27. C₂×D₄×D₈₉	C₂²	semidirect
28. #15668010	C₂²	semidirect
30. #15668008	C₂²	semidirect
31. #15668007	C₂²	semidirect
32. #15668007	C₂²	semidirect
33. #15668005	C₂²	semidirect
34. #15668001	C₂²	semidirect
35. #15668001	C₂²	semidirect
36. #15668001	C₂²	semidirect
37. #15668000	C₂²	semidirect
38. #15668000	C₂²	semidirect
39. #15668000	C₂²	semidirect
40. #15667999	C₂²	semidirect
41. #15667998	C₂²	semidirect
42. #15667998	C₂²	semidirect
43. #15667998	C₂²	semidirect
44. #15667998	C₂²	semidirect
45. #15667998	C₂²	semidirect
46. #15667998	C₂²	semidirect
47. #15667998	C₂²	semidirect
48. #15667997	C₂²	semidirect
49. #15667997	C₂²	semidirect
50. #15667997	C₂²	semidirect
51. #15667997	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667995	C₂²	semidirect
54. #15667993	C₂²	semidirect
55. #15667992	C₂²	semidirect
56. #15667990	C₂²	semidirect
57. #15667990	C₂²	semidirect
58. #15667990	C₂²	semidirect
60. #15667987	C₂²	semidirect
61. #15667987	C₂²	semidirect
62. #15667987	C₂²	semidirect
63. #15667987	C₂²	semidirect
64. #15667986	C₂²	semidirect
66. #15667985	C₂²	semidirect
67. #15667985	C₂²	semidirect
68. #15667985	C₂²	semidirect
69. #15667984	C₂²	semidirect
70. #15667983	C₂²	semidirect
71. #15667982	C₂²	semidirect
72. #15667982	C₂²	semidirect
73. #15667982	C₂²	semidirect
74. #15667982	C₂²	semidirect
75. #15667982	C₂²	semidirect
76. #15667982	C₂²	semidirect
77. #15667980	C₂²	semidirect
78. #15667980	C₂²	semidirect
79. #15667980	C₂²	semidirect
80. #15667980	C₂²	semidirect
81. #15667977	C₂²	semidirect
82. #15667977	C₂²	semidirect
83. #15667974	C₂²	semidirect
84. #15667974	C₂²	semidirect
85. #15667974	C₂²	semidirect
86. C₄×C₂²⋊D₈₉	C₂²	semidirect
87. C₄×C₂²⋊D₈₉	C₂²	semidirect
88. C₄×C₂²⋊D₈₉	C₂²	semidirect
89. #15667972	C₂²	semidirect
90. #15667972	C₂²	semidirect
91. #15667972	C₂²	semidirect
92. #15667970	C₂²	semidirect
93. C₂×#13083551	C₂²	semidirect
94. C₂²⋊C₄×D₈₉	C₂²	semidirect
95. C₂²⋊C₄×D₈₉	C₂²	semidirect
96. C₂²⋊C₄×D₈₉	C₂²	semidirect
97. C₄²×D₈₉	C₂²	semidirect
98. #125×C₈₉	C₂²	semidirect
99. #124×C₈₉	C₂²	semidirect
100. #124×C₈₉	C₂²	semidirect
101. #123×C₈₉	C₂²	semidirect
102. #123×C₈₉	C₂²	semidirect
103. C₂²⋊Q₈×C₈₉	C₂²	semidirect
104. C₂²⋊Q₈×C₈₉	C₂²	semidirect
105. #121×C₈₉	C₂²	semidirect
106. #121×C₈₉	C₂²	semidirect
313. C₈₉	#3558	semidirect
315. #562	D₈₉	semidirect
347. #125	C₂×D₈₉	semidirect
362. #124	C₂×D₈₉	semidirect
363. #124	C₂×D₈₉	semidirect
371. #123	C₂×D₈₉	semidirect
372. #123	C₂×D₈₉	semidirect
377. C₂²⋊Q₈	C₂×D₈₉	semidirect
378. C₂²⋊Q₈	C₂×D₈₉	semidirect
391. #121	C₂×D₈₉	semidirect
392. #121	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152346	2
#19152340	2
#19152332	2
#19152258	2
#19152240	2
#19152239	2
#19152237	2
#19152232	2
#19152218	2
#19152188	2
#19152184	2
#19152180	2
#19152164	2
#19152159	2
#19152147	2
#19152133	2
#124×D₈₉	2
#562×C₈₉	2
#3558	89