Subgroups — #26034445

Order 11392.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152345	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152344	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152339	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152338	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152299	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152292	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152272	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152244	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152240	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152239	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152238	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152238	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152230	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152203	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152199	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152197	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152190	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152189	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152187	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152184	C₂	1	1	yes	maximal, characteristic, complemented
23	#19152182	C₂	1	1	yes	maximal, characteristic, complemented
24	#19152178	C₂	1	1	yes	maximal, characteristic, complemented
25	#19152160	C₂	1	1	yes	maximal, characteristic, complemented
26	#19152159	C₂	1	1	yes	maximal, characteristic, complemented
27	#19152158	C₂	1	1	yes	maximal, characteristic, complemented
28	#19152110	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#15667985	C₂	1	1	yes	maximal, characteristic, complemented
31	#551×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13083575	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
41	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
44	#15668009	C₂²	1	1	yes	characteristic, complemented
45	#15668008	C₂²	1	1	yes	characteristic, complemented
46	#15668007	C₂²	1	1	yes	characteristic, complemented
47	#15668007	C₂²	1	1	yes	characteristic, complemented
48	#15668007	C₂²	1	1	yes	characteristic, complemented
49	#15668006	C₂²	1	1	yes	characteristic, complemented
50	#15668006	C₂²	1	1	yes	characteristic, complemented
51	#15668005	C₂²	1	1	yes	characteristic, complemented
52	#15668004	C₂²	1	1	yes	characteristic, complemented
53	#15668003	C₂²	1	1	yes	characteristic, complemented
54	#15668003	C₂²	1	1	yes	characteristic, complemented
55	#15668002	C₂²	1	1	yes	characteristic, complemented
56	#15668001	C₂²	1	1	yes	characteristic, complemented
57	#15668000	C₂²	1	1	yes	characteristic, complemented
58	#15667998	C₂²	1	1	yes	characteristic, complemented
59	#15667998	C₂²	1	1	yes	characteristic, complemented
60	#15667998	C₂²	1	1	yes	characteristic, complemented
61	#15667997	C₂²	1	1	yes	characteristic, complemented
62	#15667997	C₂²	1	1	yes	characteristic, complemented
63	#15667997	C₂²	1	1	yes	characteristic, complemented
64	#15667997	C₂²	1	1	yes	characteristic, complemented
65	#15667997	C₂²	1	1	yes	characteristic, complemented
66	#15667997	C₂²	1	1	yes	characteristic, complemented
67	#15667997	C₂²	1	1	yes	characteristic, complemented
68	#15667997	C₂²	1	1	yes	characteristic, complemented
69	#15667997	C₂²	1	1	yes	characteristic, complemented
70	#15667996	C₂²	1	1	yes	characteristic, complemented
71	#15667996	C₂²	1	1	yes	characteristic, complemented
72	#15667996	C₂²	1	1	yes	characteristic, complemented
73	#15667996	C₂²	1	1	yes	characteristic, complemented
74	#15667996	C₂²	1	1	yes	characteristic, complemented
75	#15667995	C₂²	1	1	yes	characteristic, complemented
76	#15667995	C₂²	1	1	yes	characteristic, complemented
77	#15667995	C₂²	1	1	yes	characteristic, complemented
78	#15667994	C₂²	1	1	yes	characteristic, complemented
79	#15667994	C₂²	1	1	yes	characteristic, complemented
80	#15667994	C₂²	1	1	yes	characteristic, complemented
81	#15667994	C₂²	1	1	yes	characteristic, complemented
82	#15667994	C₂²	1	1	yes	characteristic, complemented
83	#15667994	C₂²	1	1	yes	characteristic, complemented
84	#15667994	C₂²	1	1	yes	characteristic, complemented
85	#15667993	C₂²	1	1	yes	characteristic, complemented
86	#15667992	C₂²	1	1	yes	characteristic, complemented
87	#15667992	C₂²	1	1	yes	characteristic, complemented
88	#15667991	C₂²	1	1	yes	characteristic, complemented
89	#15667990	C₂²	1	1	yes	characteristic, complemented
90	#15667990	C₂²	1	1	yes	characteristic, complemented
91	#15667990	C₂²	1	1	yes	characteristic, complemented
92	#15667989	C₂²	1	1	yes	characteristic, complemented
93	#15667989	C₂²	1	1	yes	characteristic, complemented
94	#15667988	C₂²	1	1	yes	characteristic, complemented
95	#15667988	C₂²	1	1	yes	characteristic, complemented
96	#15667987	C₂²	1	1	yes	characteristic, complemented
97	#15667987	C₂²	1	1	yes	characteristic, complemented
98	#15667987	C₂²	1	1	yes	characteristic, complemented
99	#15667987	C₂²	1	1	yes	characteristic, complemented
100	#15667987	C₂²	1	1	yes	characteristic, complemented
101	#15667987	C₂²	1	1	yes	characteristic, complemented
102	#15667987	C₂²	1	1	yes	characteristic, complemented
103	#15667987	C₂²	1	1	yes	characteristic, complemented
104	#15667986	C₂²	1	1	yes	characteristic
105	#15667986	C₂²	1	1	yes	characteristic, complemented
106	#15667986	C₂²	1	1	yes	characteristic, complemented
107	#15667986	C₂²	1	1	yes	characteristic, complemented
108	#15667986	C₂²	1	1	yes	characteristic, complemented
109	#15667986	C₂²	1	1	yes	characteristic, complemented
110	#15667986	C₂²	1	1	yes	characteristic, complemented
111	#15667985	C₂²	1	1	yes	characteristic
112	#15667985	C₂²	1	1	yes	characteristic, complemented
113	#15667985	C₂²	1	1	yes	characteristic, complemented
114	#15667985	C₂²	1	1	yes	characteristic, complemented
115	#15667985	C₂²	1	1	yes	characteristic, complemented
116	#15667985	C₂²	1	1	yes	characteristic, complemented
117	#15667985	C₂²	1	1	yes	characteristic, complemented
118	#15667985	C₂²	1	1	yes	characteristic, complemented
119	#15667985	C₂²	1	1	yes	characteristic, complemented
120	#15667985	C₂²	1	1	yes	characteristic, complemented
121	#15667985	C₂²	1	1	yes	characteristic, complemented
122	#15667985	C₂²	1	1	yes	characteristic, complemented
123	#15667985	C₂²	1	1	yes	characteristic, complemented
124	#15667985	C₂²	1	1	yes	characteristic, complemented
125	#15667985	C₂²	1	1	yes	characteristic, complemented
126	#15667985	C₂²	1	1	yes	characteristic, complemented
127	#15667985	C₂²	1	1	yes	characteristic, complemented
128	#15667984	C₂²	1	1	yes	characteristic
129	#15667984	C₂²	1	1	yes	characteristic, complemented
130	#15667983	C₂²	1	1	yes	characteristic, complemented
131	#15667983	C₂²	1	1	yes	characteristic, complemented
132	#15667982	C₂²	1	1	yes	characteristic
133	#15667982	C₂²	1	1	yes	characteristic, complemented
134	#15667982	C₂²	1	1	yes	characteristic, complemented
135	#15667982	C₂²	1	1	yes	characteristic, complemented
136	#15667982	C₂²	1	1	yes	characteristic, complemented
137	#15667982	C₂²	1	1	yes	characteristic, complemented
138	#15667982	C₂²	1	1	yes	characteristic, complemented
139	#15667982	C₂²	1	1	yes	characteristic, complemented
140	#15667982	C₂²	1	1	yes	characteristic, complemented
141	#15667982	C₂²	1	1	yes	characteristic, complemented
142	#15667982	C₂²	1	1	yes	characteristic, complemented
143	#15667981	C₂²	1	1	yes	characteristic, complemented
144	#15667980	C₂²	1	1	yes	characteristic, complemented
145	#15667980	C₂²	1	1	yes	characteristic, complemented
146	#15667980	C₂²	1	1	yes	characteristic, complemented
147	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
148	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
149	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
150	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
151	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
152	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
153	#15667974	C₂²	1	1	yes	characteristic, complemented
154	#15667974	C₂²	1	1	yes	characteristic, complemented
155	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
156	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
157	#15667972	C₂²	1	1	yes	characteristic, complemented
158	#15667972	C₂²	1	1	yes	characteristic, complemented
159	#15667972	C₂²	1	1	yes	characteristic, complemented
160	#15667972	C₂²	1	1	yes	characteristic, complemented
161	#15667969	C₂²	1	1	yes	characteristic, complemented
162	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
163	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
164	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
165	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
172	#126×C₈₉	C₂²	1	1	yes	characteristic, complemented
173	#126×C₈₉	C₂²	1	1	yes	characteristic, complemented
174	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
175	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
176	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
177	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	#120×C₈₉	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
183	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
184	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₈₉	C₂³	1	1	yes	characteristic
188	C₂³×D₈₉	C₂³	1	1	yes	characteristic
189	C₂³×D₈₉	C₂³	1	1	yes	characteristic
190	C₂³×D₈₉	C₂³	1	1	yes	characteristic
191	C₂³×D₈₉	C₂³	1	1	yes	characteristic
192	#13083575	—	4	2	no	—
193	#13083574	—	4	2	no	—
194	#13083574	—	4	2	no	—
195	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
196	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
197	C₂×D₃₅₆	—	4	2	no	—
198	C₂×D₃₅₆	—	4	2	no	—
199	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
200	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
201	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
202	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
203	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
204	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
205	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
206	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
207	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
208	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
209	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
210	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
211	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
212	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
213	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
214	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₈₉	—	4	2	no	—
216	C₂×C₂²⋊D₈₉	—	4	2	no	—
217	C₂×C₂²⋊D₈₉	—	4	2	no	—
218	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
236	D₄×D₈₉	—	4	2	no	—
237	D₄×D₈₉	—	4	2	no	—
238	D₄×D₈₉	—	4	2	no	—
239	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
240	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
241	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₈₉	—	4	2	no	—
243	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
258	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
259	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
260	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
261	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
262	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
263	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
264	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
265	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	#13083553	C₂³	1	1	yes	characteristic
267	#13083553	C₂³	1	1	yes	characteristic
268	#13083553	C₂³	1	1	yes	characteristic
269	#13083553	C₂³	1	1	yes	characteristic
270	#13083553	C₂³	1	1	yes	characteristic
271	#13083553	C₂³	1	1	yes	characteristic
272	#13083553	C₂³	1	1	yes	characteristic
273	#13083553	C₂³	1	1	yes	characteristic
274	#13083553	C₂³	1	1	yes	characteristic
275	#13083553	C₂³	1	1	yes	characteristic
276	#13083553	C₂³	1	1	yes	characteristic
277	#13083553	C₂³	1	1	yes	characteristic
278	#13083553	C₂³	1	1	yes	characteristic
279	#13083553	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
286	#13083551	C₂³	1	1	yes	characteristic
287	#13083551	C₂³	1	1	yes	characteristic
288	#13083551	C₂³	1	1	yes	characteristic
289	#13083551	C₂³	1	1	yes	characteristic
290	#13083551	C₂³	1	1	yes	characteristic
291	#13083551	C₂³	1	1	yes	characteristic
292	#13083551	C₂³	1	1	yes	characteristic
293	#13083551	C₂³	1	1	yes	characteristic
294	#13083551	C₂³	1	1	yes	characteristic
295	#13083551	C₂³	1	1	yes	characteristic
296	#13083551	C₂³	1	1	yes	characteristic
297	#13083551	C₂³	1	1	yes	characteristic
298	#13083551	C₂³	1	1	yes	characteristic
299	#13083551	C₂³	1	1	yes	characteristic
300	#13083551	C₂³	1	1	yes	characteristic
301	#13083551	C₂³	1	1	yes	characteristic
302	#13083551	C₂³	1	1	yes	characteristic
303	#13083551	C₂³	1	1	yes	characteristic
304	#13083551	C₂³	1	1	yes	characteristic
305	#13083551	C₂³	1	1	yes	characteristic
306	#13083551	C₂³	1	1	yes	characteristic
307	#13083551	C₂³	1	1	yes	characteristic
308	#13083551	C₂³	1	1	yes	characteristic
309	#13083551	C₂³	1	1	yes	characteristic
310	#13083551	C₂³	1	1	yes	characteristic
311	#13083551	C₂³	1	1	yes	characteristic
312	#13083551	C₂³	1	1	yes	characteristic
313	#13083551	C₂³	1	1	yes	characteristic
314	#13083551	C₂³	1	1	yes	characteristic
315	#13083551	C₂³	1	1	yes	characteristic
316	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
317	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
318	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
319	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
320	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
321	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
325	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
326	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
349	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
350	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
351	C₄²×C₈₉	C₂³	1	1	yes	characteristic
352	C₄²×C₈₉	C₂³	1	1	yes	characteristic
353	C₄²×C₈₉	C₂³	1	1	yes	characteristic
354	C₂³×C₈₉	—	2	2	no	—
355	C₂³×C₈₉	—	4	1	no	—
356	C₂³×C₈₉	—	4	1	no	—
357	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
358	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
359	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂²×D₈₉	—	2	2	no	—
362	C₂²×D₈₉	—	2	2	no	—
363	C₂²×D₈₉	—	2	2	no	—
364	C₂²×D₈₉	—	2	2	no	—
365	C₂²×D₈₉	—	4	1	no	—
366	C₂²×D₈₉	—	4	1	no	—
367	C₂²×D₈₉	—	4	1	no	—
368	C₂²×D₈₉	—	4	1	no	—
369	C₂²×D₈₉	—	4	1	no	—
370	C₂²×D₈₉	—	4	1	no	—
371	C₂²×D₈₉	—	4	1	no	—
372	C₂²×D₈₉	—	4	1	no	—
373	C₂²×D₈₉	—	4	1	no	—
374	C₂²×D₈₉	—	4	1	no	—
375	C₂²×D₈₉	—	4	1	no	—
376	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
377	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
378	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
379	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
380	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
381	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
382	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
383	Q₈×C₈₉	—	4	1	no	—
384	D₄×C₈₉	—	2	2	no	—
385	D₄×C₈₉	—	4	1	no	—
386	D₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	2	2	no	—
388	C₂×C₄×C₈₉	—	4	1	no	—
389	C₂×C₄×C₈₉	—	4	1	no	—
390	C₂×C₄×C₈₉	—	4	1	no	—
391	C₂×C₄×C₈₉	—	4	1	no	—
392	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
399	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
403	C₂²⋊D₈₉	—	2	2	no	—
404	C₂²⋊D₈₉	—	2	2	no	—
405	C₂²⋊D₈₉	—	2	2	no	—
406	C₂²⋊D₈₉	—	2	2	no	—
407	C₂²⋊D₈₉	—	2	2	no	—
408	C₂²⋊D₈₉	—	4	1	no	—
409	C₂²⋊D₈₉	—	4	1	no	—
410	C₂²⋊D₈₉	—	4	1	no	—
411	C₂²⋊D₈₉	—	4	1	no	—
412	C₂²⋊D₈₉	—	4	1	no	—
413	C₂²⋊D₈₉	—	4	1	no	—
414	C₂²⋊D₈₉	—	4	1	no	—
415	C₂²⋊D₈₉	—	4	1	no	—
416	C₂²⋊D₈₉	—	4	1	no	—
417	C₂²⋊D₈₉	—	4	1	no	—
418	C₂²⋊D₈₉	—	4	1	no	—
419	C₂²⋊D₈₉	—	4	1	no	—
420	C₂²⋊D₈₉	—	4	1	no	—
421	C₂×Dic₈₉	—	2	2	no	—
422	C₂×Dic₈₉	—	4	1	no	—
423	C₂×Dic₈₉	—	4	1	no	—
424	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
433	D₃₅₆	—	2	2	no	—
434	D₃₅₆	—	2	2	no	—
435	D₃₅₆	—	2	2	no	—
436	D₃₅₆	—	2	2	no	—
437	D₃₅₆	—	4	1	no	—
438	D₃₅₆	—	4	1	no	—
439	D₃₅₆	—	4	1	no	—
440	D₃₅₆	—	4	1	no	—
441	D₃₅₆	—	4	1	no	—
442	D₃₅₆	—	4	1	no	—
443	D₃₅₆	—	4	1	no	—
444	D₃₅₆	—	4	1	no	—
445	D₃₅₆	—	4	1	no	—
446	D₃₅₆	—	4	1	no	—
447	D₃₅₆	—	4	1	no	—
448	D₃₅₆	—	4	1	no	—
449	C₄×D₈₉	—	2	2	no	—
450	C₄×D₈₉	—	4	1	no	—
451	C₄×D₈₉	—	4	1	no	—
452	C₄×D₈₉	—	4	1	no	—
453	C₄×D₈₉	—	4	1	no	—
454	C₄×D₈₉	—	4	1	no	—
455	C₄×D₈₉	—	4	1	no	—
456	C₄×D₈₉	—	4	1	no	—
457	C₄×D₈₉	—	4	1	no	—
458	C₄×D₈₉	—	4	1	no	—
459	C₄×D₈₉	—	4	1	no	—
460	C₄×D₈₉	—	4	1	no	—
461	C₄×D₈₉	—	4	1	no	—
462	C₄×D₈₉	—	4	1	no	—
463	C₄×D₈₉	—	4	1	no	—
464	Dic₁₇₈	—	4	1	no	—
465	Dic₁₇₈	—	4	1	no	—
466	C₂²×C₈₉	—	2	1	no	—
467	C₂²×C₈₉	—	2	1	no	—
468	C₂²×C₈₉	—	2	1	no	—
469	C₂²×C₈₉	—	2	1	no	—
470	C₂²×C₈₉	—	2	1	no	—
471	C₂²×C₈₉	—	2	1	no	—
472	C₂²×C₈₉	—	2	1	no	—
473	C₂²×C₈₉	—	2	1	no	—
474	C₂²×C₈₉	—	2	1	no	—
475	C₂²×C₈₉	—	2	1	no	—
476	C₂²×C₈₉	—	2	1	no	—
477	C₂²×C₈₉	—	8	2	no	—
478	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
479	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
480	C₂×D₈₉	—	2	1	no	—
481	C₂×D₈₉	—	2	1	no	—
482	C₂×D₈₉	—	2	1	no	—
483	C₂×D₈₉	—	2	1	no	—
484	C₂×D₈₉	—	2	1	no	—
485	C₂×D₈₉	—	2	1	no	—
486	C₂×D₈₉	—	2	1	no	—
487	C₂×D₈₉	—	2	1	no	—
488	C₂×D₈₉	—	2	1	no	—
489	C₂×D₈₉	—	2	1	no	—
490	C₂×D₈₉	—	2	1	no	—
491	C₂×D₈₉	—	2	1	no	—
492	C₂×D₈₉	—	2	1	no	—
493	C₂×D₈₉	—	2	1	no	—
494	C₂×D₈₉	—	2	1	no	—
495	C₂×D₈₉	—	2	1	no	—
496	C₂×D₈₉	—	2	1	no	—
497	C₂×D₈₉	—	2	1	no	—
498	C₂×D₈₉	—	2	1	no	—
499	C₂×D₈₉	—	2	1	no	—
500	C₂×D₈₉	—	4	4	no	—
501	C₂×D₈₉	—	8	2	no	—
502	C₂×D₈₉	—	8	2	no	—
503	C₂×D₈₉	—	8	2	no	—
504	C₂×D₈₉	—	8	2	no	—
505	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
506	C₄×C₈₉	—	2	1	no	—
507	C₄×C₈₉	—	2	1	no	—
508	C₄×C₈₉	—	2	1	no	—
509	C₄×C₈₉	—	2	1	no	—
510	C₄×C₈₉	—	2	1	no	—
511	C₄×C₈₉	—	2	1	no	—
512	C₄×C₈₉	—	2	1	no	—
513	C₄×C₈₉	—	2	1	no	—
514	C₄×C₈₉	—	2	1	no	—
515	C₄×C₈₉	—	2	1	no	—
516	C₄×C₈₉	—	2	1	no	—
517	Dic₈₉	—	2	1	no	—
518	Dic₈₉	—	2	1	no	—
519	Dic₈₉	—	2	1	no	—
520	Dic₈₉	—	2	1	no	—
521	Dic₈₉	—	2	1	no	—
522	Dic₈₉	—	2	1	no	—
523	Dic₈₉	—	2	1	no	—
524	Dic₈₉	—	2	1	no	—
525	Dic₈₉	—	2	1	no	—
526	C₂×C₈₉	—	2	2	no	—
527	C₂×C₈₉	—	4	1	no	—
528	C₂×C₈₉	—	4	1	no	—
529	C₂×C₈₉	—	4	1	no	—
530	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₈₉	#585	1	1	yes	characteristic
533	D₈₉	—	2	2	no	—
534	D₈₉	—	4	1	no	—
535	D₈₉	—	4	1	no	—
536	D₈₉	—	4	1	no	—
537	D₈₉	—	4	1	no	—
538	D₈₉	—	4	1	no	—
539	D₈₉	—	4	1	no	—
540	#3534	—	89	1	no	maximal, Sylow
541	C₈₉	#3534	1	1	yes	characteristic, complemented, Sylow
542	#562	—	89	1	no	—
543	#562	—	89	1	no	—
544	#560	—	89	1	no	—
545	#560	—	89	1	no	—
546	#553	—	89	1	no	—
547	#553	—	89	1	no	—
548	#551	—	89	1	no	—
549	#551	D₈₉	1	1	yes	characteristic, complemented
550	#546	—	89	1	no	—
551	#546	—	89	1	no	—
552	#546	—	89	1	no	—
553	#546	—	89	1	no	—
554	#546	—	89	1	no	—
555	#546	—	89	1	no	—
556	D₄²	—	89	1	no	—
557	D₄²	—	89	1	no	—
558	#540	—	89	1	no	—
559	#540	—	89	1	no	—
560	#539	—	89	1	no	—
561	#539	—	89	1	no	—
562	#539	—	89	1	no	—
563	#538	—	89	1	no	—
564	#538	—	89	1	no	—
565	#538	—	89	1	no	—
566	#537	—	89	1	no	—
567	#534	—	89	1	no	—
568	#534	—	89	1	no	—
569	#534	—	89	1	no	—
570	#525	—	89	1	no	—
571	C₂×#123	—	89	1	no	—
572	C₂×#121	—	89	1	no	—
573	C₂×#41	—	89	1	no	—
574	C₂×#41	—	89	1	no	—
575	C₂×#41	—	89	1	no	—
576	C₂²×D₄	—	89	1	no	—
577	C₂²×D₄	—	89	1	no	—
578	C₂²×D₄	—	89	1	no	—
579	C₂²×D₄	—	89	1	no	—
580	C₂²×D₄	—	89	1	no	—
581	C₂²×D₄	—	89	1	no	—
582	C₂²×D₄	—	89	1	no	—
583	C₂²×D₄	—	89	1	no	—
584	C₂³×C₄	—	89	1	no	—
585	#127	—	89	1	no	—
586	#127	—	89	1	no	—
587	#126	—	89	1	no	—
588	#126	—	89	1	no	—
589	#126	—	89	1	no	—
590	#126	—	89	1	no	—
591	#126	—	89	1	no	—
592	#126	—	89	1	no	—
593	#126	C₂×D₈₉	1	1	yes	characteristic, complemented
594	#126	C₂×D₈₉	1	1	yes	characteristic, complemented
595	#125	—	89	1	no	—
596	#125	—	89	1	no	—
597	#125	—	89	1	no	—
598	#125	—	89	1	no	—
599	#124	—	89	1	no	—
600	#124	—	89	1	no	—
601	#124	—	89	1	no	—
602	#124	—	89	1	no	—
603	#124	—	89	1	no	—
604	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
605	#123	—	89	1	no	—
606	#123	—	89	1	no	—
607	#123	—	89	1	no	—
608	#123	—	89	1	no	—
609	#123	—	89	1	no	—
610	#123	—	89	1	no	—
611	#123	—	89	1	no	—
612	#123	—	89	1	no	—
613	#123	—	89	1	no	—
614	#123	—	89	1	no	—
615	#123	—	89	1	no	—
616	#123	—	89	1	no	—
617	#123	—	89	1	no	—
618	#123	—	89	1	no	—
619	#123	—	89	1	no	—
620	#123	—	89	1	no	—
621	#123	—	89	1	no	—
622	#123	—	89	1	no	—
623	#123	—	89	1	no	—
624	#123	—	89	1	no	—
625	#123	—	89	1	no	—
626	#123	—	89	1	no	—
627	#123	—	89	1	no	—
628	#123	—	89	1	no	—
629	#123	—	89	1	no	—
630	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
631	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
632	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
633	C₂²⋊Q₈	—	89	1	no	—
634	C₂²⋊Q₈	—	89	1	no	—
635	C₂²⋊Q₈	—	89	1	no	—
636	C₂²⋊Q₈	—	89	1	no	—
637	C₂²⋊Q₈	—	89	1	no	—
638	C₂²⋊Q₈	—	89	1	no	—
639	C₂²⋊Q₈	—	89	1	no	—
640	C₂²⋊Q₈	—	89	1	no	—
641	C₂²⋊Q₈	—	89	1	no	—
642	C₂²⋊Q₈	—	89	1	no	—
643	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
644	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
645	#121	—	89	1	no	—
646	#121	—	89	1	no	—
647	#121	—	89	1	no	—
648	#121	—	89	1	no	—
649	#121	—	89	1	no	—
650	#121	—	89	1	no	—
651	#121	—	89	1	no	—
652	#121	—	89	1	no	—
653	#121	—	89	1	no	—
654	#121	—	89	1	no	—
655	#121	—	89	1	no	—
656	#121	—	89	1	no	—
657	#121	—	89	1	no	—
658	#121	—	89	1	no	—
659	#121	—	89	1	no	—
660	#121	—	89	1	no	—
661	#121	—	89	1	no	—
662	#121	—	89	1	no	—
663	#121	—	89	1	no	—
664	#121	—	89	1	no	—
665	#121	—	89	1	no	—
666	#121	—	89	1	no	—
667	#121	—	89	1	no	—
668	#121	—	89	1	no	—
669	#121	—	89	1	no	—
670	#121	—	89	1	no	—
671	#121	—	89	1	no	—
672	#121	—	89	1	no	—
673	#121	—	89	1	no	—
674	#121	—	89	1	no	—
675	#121	—	89	1	no	—
676	#121	—	89	1	no	—
677	#121	—	89	1	no	—
678	#121	—	89	1	no	—
679	#121	—	89	1	no	—
680	#121	—	89	1	no	—
681	#120	—	89	1	no	—
682	#120	—	89	1	no	—
683	#120	—	89	1	no	—
684	#120	—	89	1	no	—
685	#120	—	89	1	no	—
686	#120	—	89	1	no	—
687	#120	—	89	1	no	—
688	#120	—	89	1	no	—
689	#120	—	89	1	no	—
690	#120	—	89	1	no	—
691	#120	—	89	1	no	—
692	#120	—	89	1	no	—
693	#120	—	89	1	no	—
694	#120	—	89	1	no	—
695	#120	—	89	1	no	—
696	#120	C₂×D₈₉	1	1	yes	characteristic
697	C₄×D₄	—	89	1	no	—
698	C₄×D₄	—	89	1	no	—
699	C₄×D₄	—	89	1	no	—
700	C₄×D₄	—	89	1	no	—
701	C₄×D₄	—	89	1	no	—
702	C₄×D₄	—	89	1	no	—
703	C₄×D₄	—	89	1	no	—
704	C₄×D₄	—	89	1	no	—
705	C₄×D₄	—	89	1	no	—
706	C₄×D₄	—	89	1	no	—
707	C₄×D₄	—	89	1	no	—
708	C₄×D₄	—	89	1	no	—
709	C₄×D₄	—	89	1	no	—
710	C₄×D₄	—	89	1	no	—
711	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
712	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
713	#117	—	89	1	no	—
714	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
715	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
716	C₂×C₄⋊C₄	—	89	1	no	—
717	C₂×C₄⋊C₄	—	89	1	no	—
718	C₂×C₄⋊C₄	—	89	1	no	—
719	C₂×C₂²⋊C₄	—	89	1	no	—
720	C₂×C₂²⋊C₄	—	89	1	no	—
721	C₂×C₂²⋊C₄	—	89	1	no	—
722	C₂×C₂²⋊C₄	—	89	1	no	—
723	C₂×C₂²⋊C₄	—	89	1	no	—
724	C₂×C₂²⋊C₄	—	89	1	no	—
725	C₂×C₂²⋊C₄	—	89	1	no	—
726	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
727	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
728	C₂⁴	—	89	1	no	—
729	C₂⁴	—	89	1	no	—
730	C₂⁴	—	89	1	no	—
731	C₂⁴	—	89	1	no	—
732	C₂⁴	—	89	1	no	—
733	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
734	#41	—	356	2	no	—
735	#41	—	356	2	no	—
736	#41	—	356	2	no	—
737	C₂×Q₈	—	89	1	no	—
738	C₂×Q₈	—	89	1	no	—
739	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
740	C₂×D₄	—	89	1	no	—
741	C₂×D₄	—	89	1	no	—
742	C₂×D₄	—	89	1	no	—
743	C₂×D₄	—	89	1	no	—
744	C₂×D₄	—	89	1	no	—
745	C₂×D₄	—	89	1	no	—
746	C₂×D₄	—	89	1	no	—
747	C₂×D₄	—	89	1	no	—
748	C₂×D₄	—	89	1	no	—
749	C₂×D₄	—	89	1	no	—
750	C₂×D₄	—	89	1	no	—
751	C₂×D₄	—	89	1	no	—
752	C₂×D₄	—	89	1	no	—
753	C₂×D₄	—	89	1	no	—
754	C₂×D₄	—	89	1	no	—
755	C₂×D₄	—	89	1	no	—
756	C₂×D₄	—	89	1	no	—
757	C₂×D₄	—	89	1	no	—
758	C₂×D₄	—	89	1	no	—
759	C₂×D₄	—	89	1	no	—
760	C₂×D₄	—	89	1	no	—
761	C₂×D₄	—	89	1	no	—
762	C₂×D₄	—	89	1	no	—
763	C₂×D₄	—	89	1	no	—
764	C₂×D₄	—	89	1	no	—
765	C₂×D₄	—	89	1	no	—
766	C₂×D₄	—	89	1	no	—
767	C₂×D₄	—	89	1	no	—
768	C₂×D₄	—	89	1	no	—
769	C₂×D₄	—	89	1	no	—
770	C₂×D₄	—	89	1	no	—
771	C₂×D₄	—	89	1	no	—
772	C₂×D₄	—	89	1	no	—
773	C₂×D₄	—	89	1	no	—
774	C₂×D₄	—	356	2	no	—
775	C₂×D₄	—	356	2	no	—
776	C₂×D₄	—	356	2	no	—
777	C₂×D₄	—	356	2	no	—
778	C₂×D₄	—	356	2	no	—
779	C₂×D₄	—	356	2	no	—
780	C₂×D₄	—	356	2	no	—
781	C₂×D₄	—	356	2	no	—
782	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
784	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
785	C₂²×C₄	—	89	1	no	—
786	C₂²×C₄	—	89	1	no	—
787	C₂²×C₄	—	89	1	no	—
788	C₂²×C₄	—	89	1	no	—
789	C₂²×C₄	—	89	1	no	—
790	C₂²×C₄	—	89	1	no	—
791	C₂²×C₄	—	89	1	no	—
792	C₂²×C₄	—	89	1	no	—
793	C₂²×C₄	—	89	1	no	—
794	C₂²×C₄	—	89	1	no	—
795	C₂²×C₄	—	89	1	no	—
796	C₂²×C₄	—	89	1	no	—
797	C₂²×C₄	—	89	1	no	—
798	C₂²×C₄	—	89	1	no	—
799	C₂²×C₄	—	89	1	no	—
800	C₂²×C₄	—	89	1	no	—
801	C₂²×C₄	—	89	1	no	—
802	C₂²×C₄	—	89	1	no	—
803	C₂²×C₄	—	356	2	no	—
804	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
805	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
806	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
807	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
808	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
809	C₄⋊C₄	—	89	1	no	—
810	C₄⋊C₄	—	89	1	no	—
811	C₄⋊C₄	—	89	1	no	—
812	C₄⋊C₄	—	89	1	no	—
813	C₄⋊C₄	—	89	1	no	—
814	C₄⋊C₄	—	89	1	no	—
815	C₄⋊C₄	—	89	1	no	—
816	C₄⋊C₄	—	89	1	no	—
817	C₄⋊C₄	—	89	1	no	—
818	C₄⋊C₄	—	89	1	no	—
819	C₄⋊C₄	—	89	1	no	—
820	C₄⋊C₄	—	89	1	no	—
821	C₄⋊C₄	—	89	1	no	—
822	C₄⋊C₄	—	89	1	no	—
823	C₄⋊C₄	—	89	1	no	—
824	C₄⋊C₄	—	89	1	no	—
825	C₄⋊C₄	—	89	1	no	—
826	C₄⋊C₄	—	89	1	no	—
827	C₄⋊C₄	—	89	1	no	—
828	C₄⋊C₄	—	89	1	no	—
829	C₄⋊C₄	—	89	1	no	—
830	C₄⋊C₄	—	89	1	no	—
831	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
832	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
833	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
834	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
835	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
838	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
839	C₂²⋊C₄	—	89	1	no	—
840	C₂²⋊C₄	—	89	1	no	—
841	C₂²⋊C₄	—	89	1	no	—
842	C₂²⋊C₄	—	89	1	no	—
843	C₂²⋊C₄	—	89	1	no	—
844	C₂²⋊C₄	—	89	1	no	—
845	C₂²⋊C₄	—	89	1	no	—
846	C₂²⋊C₄	—	89	1	no	—
847	C₂²⋊C₄	—	89	1	no	—
848	C₂²⋊C₄	—	89	1	no	—
849	C₂²⋊C₄	—	89	1	no	—
850	C₂²⋊C₄	—	89	1	no	—
851	C₂²⋊C₄	—	89	1	no	—
852	C₂²⋊C₄	—	89	1	no	—
853	C₂²⋊C₄	—	89	1	no	—
854	C₂²⋊C₄	—	89	1	no	—
855	C₂²⋊C₄	—	89	1	no	—
856	C₂²⋊C₄	—	89	1	no	—
857	C₂²⋊C₄	—	89	1	no	—
858	C₂²⋊C₄	—	89	1	no	—
859	C₂²⋊C₄	—	89	1	no	—
860	C₂²⋊C₄	—	89	1	no	—
861	C₂²⋊C₄	—	89	1	no	—
862	C₂²⋊C₄	—	89	1	no	—
863	C₂²⋊C₄	—	89	1	no	—
864	C₂²⋊C₄	—	89	1	no	—
865	C₂²⋊C₄	—	89	1	no	—
866	C₂²⋊C₄	—	89	1	no	—
867	C₂²⋊C₄	—	89	1	no	—
868	C₂²⋊C₄	—	89	1	no	—
869	C₂²⋊C₄	—	89	1	no	—
870	C₂²⋊C₄	—	89	1	no	—
871	C₂²⋊C₄	—	89	1	no	—
872	C₂²⋊C₄	—	89	1	no	—
873	C₂²⋊C₄	—	89	1	no	—
874	C₂²⋊C₄	—	89	1	no	—
875	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
876	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
877	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
886	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
889	C₄²	—	89	1	no	—
890	C₄²	—	89	1	no	—
891	C₄²	—	89	1	no	—
892	C₄²	C₂²×D₈₉	1	1	yes	characteristic
893	C₄²	C₂²×D₈₉	1	1	yes	characteristic
894	C₄²	C₂²×D₈₉	1	1	yes	characteristic
895	C₂³	—	2	2	no	—
896	C₂³	—	4	1	no	—
897	C₂³	—	4	1	no	—
898	C₂³	—	89	1	no	—
899	C₂³	—	89	1	no	—
900	C₂³	—	89	1	no	—
901	C₂³	—	89	1	no	—
902	C₂³	—	89	1	no	—
903	C₂³	—	89	1	no	—
904	C₂³	—	89	1	no	—
905	C₂³	—	356	1	no	—
906	C₂³	—	356	1	no	—
907	C₂³	—	356	1	no	—
908	C₂³	—	356	1	no	—
909	C₂³	—	356	1	no	—
910	C₂³	—	356	1	no	—
911	C₂³	—	356	1	no	—
912	C₂³	—	356	1	no	—
913	C₂³	—	356	1	no	—
914	C₂³	—	356	1	no	—
915	C₂³	—	356	1	no	—
916	C₂³	—	178	2	no	—
917	C₂³	—	178	2	no	—
918	C₂³	—	178	2	no	—
919	C₂³	—	178	2	no	—
920	C₂³	C₂³×D₈₉	1	1	yes	characteristic
921	C₂³	C₂³×D₈₉	1	1	yes	characteristic
922	C₂³	C₂³×D₈₉	1	1	yes	characteristic
923	C₂³	C₂³×D₈₉	1	1	yes	characteristic
924	Q₈	—	4	1	no	—
925	Q₈	—	356	1	no	—
926	Q₈	—	356	1	no	—
927	D₄	—	2	2	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	356	1	no	—
931	D₄	—	356	1	no	—
932	D₄	—	356	1	no	—
933	D₄	—	356	1	no	—
934	D₄	—	356	1	no	—
935	D₄	—	356	1	no	—
936	D₄	—	356	1	no	—
937	D₄	—	356	1	no	—
938	D₄	—	356	1	no	—
939	D₄	—	356	1	no	—
940	D₄	—	356	1	no	—
941	D₄	—	356	1	no	—
942	D₄	—	356	1	no	—
943	D₄	—	356	1	no	—
944	D₄	—	356	1	no	—
945	D₄	—	356	1	no	—
946	D₄	—	356	1	no	—
947	D₄	—	356	1	no	—
948	D₄	—	356	1	no	—
949	D₄	—	356	1	no	—
950	D₄	—	356	1	no	—
951	D₄	—	356	1	no	—
952	D₄	—	356	1	no	—
953	D₄	—	356	1	no	—
954	D₄	—	356	1	no	—
955	D₄	—	178	2	no	—
956	D₄	—	178	2	no	—
957	D₄	—	178	2	no	—
958	D₄	—	178	2	no	—
959	D₄	—	178	2	no	—
960	D₄	—	178	2	no	—
961	D₄	—	178	2	no	—
962	D₄	—	178	2	no	—
963	D₄	—	178	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	89	1	no	—
970	C₂×C₄	—	89	1	no	—
971	C₂×C₄	—	89	1	no	—
972	C₂×C₄	—	89	1	no	—
973	C₂×C₄	—	89	1	no	—
974	C₂×C₄	—	89	1	no	—
975	C₂×C₄	—	89	1	no	—
976	C₂×C₄	—	89	1	no	—
977	C₂×C₄	—	89	1	no	—
978	C₂×C₄	—	356	1	no	—
979	C₂×C₄	—	356	1	no	—
980	C₂×C₄	—	356	1	no	—
981	C₂×C₄	—	356	1	no	—
982	C₂×C₄	—	356	1	no	—
983	C₂×C₄	—	356	1	no	—
984	C₂×C₄	—	356	1	no	—
985	C₂×C₄	—	356	1	no	—
986	C₂×C₄	—	356	1	no	—
987	C₂×C₄	—	356	1	no	—
988	C₂×C₄	—	356	1	no	—
989	C₂×C₄	—	356	1	no	—
990	C₂×C₄	—	356	1	no	—
991	C₂×C₄	—	356	1	no	—
992	C₂×C₄	—	356	1	no	—
993	C₂×C₄	—	356	1	no	—
994	C₂×C₄	—	178	2	no	—
995	C₂×C₄	—	178	2	no	—
996	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
997	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1006	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	8	2	no	—
1019	C₂²	—	89	2	no	—
1020	C₂²	—	356	4	no	—
1021	C₂²	—	178	1	no	—
1022	C₂²	—	178	1	no	—
1023	C₂²	—	178	1	no	—
1024	C₂²	—	178	1	no	—
1025	C₂²	—	178	1	no	—
1026	C₂²	—	178	1	no	—
1027	C₂²	—	178	1	no	—
1028	C₂²	—	178	1	no	—
1029	C₂²	—	178	1	no	—
1030	C₂²	—	178	1	no	—
1031	C₂²	—	178	1	no	—
1032	C₂²	—	178	1	no	—
1033	C₂²	—	178	1	no	—
1034	C₂²	—	178	1	no	—
1035	C₂²	—	178	1	no	—
1036	C₂²	—	178	1	no	—
1037	C₂²	—	178	1	no	—
1038	C₂²	—	178	1	no	—
1039	C₂²	—	178	1	no	—
1040	C₂²	—	178	1	no	—
1041	C₂²	—	712	2	no	—
1042	C₂²	—	712	2	no	—
1043	C₂²	—	712	2	no	—
1044	C₂²	—	712	2	no	—
1045	C₂²	#15668058	1	2	yes	—
1046	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	178	1	no	—
1059	C₄	—	178	1	no	—
1060	C₄	—	178	1	no	—
1061	C₄	—	178	1	no	—
1062	C₄	—	178	1	no	—
1063	C₄	—	178	1	no	—
1064	C₄	—	178	1	no	—
1065	C₄	—	178	1	no	—
1066	C₄	—	178	1	no	—
1067	C₂	—	2	2	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	356	1	no	—
1072	C₂	—	356	1	no	—
1073	C₂	—	356	1	no	—
1074	C₂	—	356	1	no	—
1075	C₂	—	356	1	no	—
1076	C₂	—	356	1	no	—
1077	C₂	—	178	2	no	—
1078	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
1079	C₂	C₂×#15668058	1	1	yes	characteristic
1080	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#551×C₈₉	C₂
hypercenter	#551	D₈₉
hypocenter	C₈₉	#3534
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #19152345	C₂	semidirect
2. #19152344	C₂	semidirect
3. #19152339	C₂	semidirect
4. #19152338	C₂	semidirect
5. #19152299	C₂	semidirect
6. #19152292	C₂	semidirect
7. #19152272	C₂	semidirect
8. #19152244	C₂	semidirect
9. #19152241	C₂	semidirect
10. #19152240	C₂	semidirect
11. #19152239	C₂	semidirect
12. #19152238	C₂	semidirect
13. #19152238	C₂	semidirect
14. D₄×D₃₅₆	C₂	semidirect
15. #19152230	C₂	semidirect
16. #19152203	C₂	semidirect
17. #19152199	C₂	semidirect
18. #19152197	C₂	semidirect
19. #19152190	C₂	semidirect
20. #19152189	C₂	semidirect
21. #19152187	C₂	semidirect
22. #19152184	C₂	semidirect
23. #19152182	C₂	semidirect
24. #19152178	C₂	semidirect
25. #19152160	C₂	semidirect
26. #19152159	C₂	semidirect
27. #19152158	C₂	semidirect
28. #19152110	C₂	semidirect
29. #123×D₈₉	C₂	semidirect
30. C₂×#15667985	C₂	semidirect
31. #551×C₈₉	C₂	semidirect
32. C₂×#13083575	C₂²	semidirect
33. C₂×#13083574	C₂²	semidirect
34. C₂×#13083574	C₂²	semidirect
35. C₂²×D₃₅₆	C₂²	semidirect
36. C₂²×D₃₅₆	C₂²	semidirect
37. C₂²×C₂²⋊D₈₉	C₂²	semidirect
38. C₂²×C₂²⋊D₈₉	C₂²	semidirect
39. C₂²×C₂²⋊D₈₉	C₂²	semidirect
41. C₂×D₄×D₈₉	C₂²	semidirect
42. C₂×D₄×D₈₉	C₂²	semidirect
43. C₂²×C₄×D₈₉	C₂²	semidirect
44. #15668009	C₂²	semidirect
45. #15668008	C₂²	semidirect
46. #15668007	C₂²	semidirect
47. #15668007	C₂²	semidirect
48. #15668007	C₂²	semidirect
49. #15668006	C₂²	semidirect
50. #15668006	C₂²	semidirect
51. #15668005	C₂²	semidirect
52. #15668004	C₂²	semidirect
53. #15668003	C₂²	semidirect
54. #15668003	C₂²	semidirect
55. #15668002	C₂²	semidirect
56. #15668001	C₂²	semidirect
57. #15668000	C₂²	semidirect
58. #15667998	C₂²	semidirect
59. #15667998	C₂²	semidirect
60. #15667998	C₂²	semidirect
61. #15667997	C₂²	semidirect
62. #15667997	C₂²	semidirect
63. #15667997	C₂²	semidirect
64. #15667997	C₂²	semidirect
65. #15667997	C₂²	semidirect
66. #15667997	C₂²	semidirect
67. #15667997	C₂²	semidirect
68. #15667997	C₂²	semidirect
69. #15667997	C₂²	semidirect
70. #15667996	C₂²	semidirect
71. #15667996	C₂²	semidirect
72. #15667996	C₂²	semidirect
73. #15667996	C₂²	semidirect
74. #15667996	C₂²	semidirect
75. #15667995	C₂²	semidirect
76. #15667995	C₂²	semidirect
77. #15667995	C₂²	semidirect
78. #15667994	C₂²	semidirect
79. #15667994	C₂²	semidirect
80. #15667994	C₂²	semidirect
81. #15667994	C₂²	semidirect
82. #15667994	C₂²	semidirect
83. #15667994	C₂²	semidirect
84. #15667994	C₂²	semidirect
85. #15667993	C₂²	semidirect
86. #15667992	C₂²	semidirect
87. #15667992	C₂²	semidirect
88. #15667991	C₂²	semidirect
89. #15667990	C₂²	semidirect
90. #15667990	C₂²	semidirect
91. #15667990	C₂²	semidirect
92. #15667989	C₂²	semidirect
93. #15667989	C₂²	semidirect
94. #15667988	C₂²	semidirect
95. #15667988	C₂²	semidirect
96. #15667987	C₂²	semidirect
97. #15667987	C₂²	semidirect
98. #15667987	C₂²	semidirect
99. #15667987	C₂²	semidirect
100. #15667987	C₂²	semidirect
101. #15667987	C₂²	semidirect
102. #15667987	C₂²	semidirect
103. #15667987	C₂²	semidirect
105. #15667986	C₂²	semidirect
106. #15667986	C₂²	semidirect
107. #15667986	C₂²	semidirect
108. #15667986	C₂²	semidirect
109. #15667986	C₂²	semidirect
110. #15667986	C₂²	semidirect
112. #15667985	C₂²	semidirect
113. #15667985	C₂²	semidirect
114. #15667985	C₂²	semidirect
115. #15667985	C₂²	semidirect
116. #15667985	C₂²	semidirect
117. #15667985	C₂²	semidirect
118. #15667985	C₂²	semidirect
119. #15667985	C₂²	semidirect
120. #15667985	C₂²	semidirect
121. #15667985	C₂²	semidirect
122. #15667985	C₂²	semidirect
123. #15667985	C₂²	semidirect
124. #15667985	C₂²	semidirect
125. #15667985	C₂²	semidirect
126. #15667985	C₂²	semidirect
127. #15667985	C₂²	semidirect
129. #15667984	C₂²	semidirect
130. #15667983	C₂²	semidirect
131. #15667983	C₂²	semidirect
133. #15667982	C₂²	semidirect
134. #15667982	C₂²	semidirect
135. #15667982	C₂²	semidirect
136. #15667982	C₂²	semidirect
137. #15667982	C₂²	semidirect
138. #15667982	C₂²	semidirect
139. #15667982	C₂²	semidirect
140. #15667982	C₂²	semidirect
141. #15667982	C₂²	semidirect
142. #15667982	C₂²	semidirect
143. #15667981	C₂²	semidirect
144. #15667980	C₂²	semidirect
145. #15667980	C₂²	semidirect
146. #15667980	C₂²	semidirect
147. C₄×D₃₅₆	C₂²	semidirect
148. C₄×D₃₅₆	C₂²	semidirect
149. C₄×D₃₅₆	C₂²	semidirect
150. C₄×D₃₅₆	C₂²	semidirect
151. C₄×D₃₅₆	C₂²	semidirect
152. C₄×D₃₅₆	C₂²	semidirect
153. #15667974	C₂²	semidirect
154. #15667974	C₂²	semidirect
155. C₄×C₂²⋊D₈₉	C₂²	semidirect
156. C₄×C₂²⋊D₈₉	C₂²	semidirect
157. #15667972	C₂²	semidirect
158. #15667972	C₂²	semidirect
159. #15667972	C₂²	semidirect
160. #15667972	C₂²	semidirect
161. #15667969	C₂²	semidirect
162. C₂×#13083553	C₂²	semidirect
163. C₄⋊C₄×D₈₉	C₂²	semidirect
164. C₄⋊C₄×D₈₉	C₂²	semidirect
165. C₂×#13083551	C₂²	semidirect
166. C₂²⋊C₄×D₈₉	C₂²	semidirect
167. C₂²⋊C₄×D₈₉	C₂²	semidirect
168. C₂²⋊C₄×D₈₉	C₂²	semidirect
169. C₂²⋊C₄×D₈₉	C₂²	semidirect
170. C₂²⋊C₄×D₈₉	C₂²	semidirect
171. C₂²⋊C₄×D₈₉	C₂²	semidirect
172. #126×C₈₉	C₂²	semidirect
173. #126×C₈₉	C₂²	semidirect
174. #124×C₈₉	C₂²	semidirect
175. #123×C₈₉	C₂²	semidirect
176. #123×C₈₉	C₂²	semidirect
177. #123×C₈₉	C₂²	semidirect
178. C₂²⋊Q₈×C₈₉	C₂²	semidirect
179. C₂²⋊Q₈×C₈₉	C₂²	semidirect
181. C₄×D₄×C₈₉	C₂²	semidirect
182. C₄×D₄×C₈₉	C₂²	semidirect
183. #117×C₈₉	C₂²	semidirect
184. #117×C₈₉	C₂²	semidirect
185. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
541. C₈₉	#3534	semidirect
549. #551	D₈₉	semidirect
593. #126	C₂×D₈₉	semidirect
594. #126	C₂×D₈₉	semidirect
604. #124	C₂×D₈₉	semidirect
630. #123	C₂×D₈₉	semidirect
631. #123	C₂×D₈₉	semidirect
632. #123	C₂×D₈₉	semidirect
643. C₂²⋊Q₈	C₂×D₈₉	semidirect
644. C₂²⋊Q₈	C₂×D₈₉	semidirect
711. C₄×D₄	C₂×D₈₉	semidirect
712. C₄×D₄	C₂×D₈₉	semidirect
714. #117	C₂×D₈₉	semidirect
715. #117	C₂×D₈₉	semidirect
726. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
727. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152345	2
#19152344	2
#19152339	2
#19152338	2
#19152299	2
#19152292	2
#19152272	2
#19152244	2
#19152241	2
#19152240	2
#19152239	2
#19152238	2
D₄×D₃₅₆	2
#19152230	2
#19152203	2
#19152199	2
#19152197	2
#19152190	2
#19152189	2
#19152187	2
#19152184	2
#19152182	2
#19152178	2
#19152160	2
#19152159	2
#19152158	2
#19152110	2
#123×D₈₉	2
C₂×#15667985	2
#551×C₈₉	2
#3534	89