Subgroups — #46824568

Order 34432.

1328 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771284	C₂	1	2	yes	maximal, complemented
2	#31771282	C₂	1	2	yes	maximal, complemented
3	#31771279	C₂	1	2	yes	maximal, complemented
4	#31771278	C₂	1	2	yes	maximal, complemented
5	#31771250	C₂	1	2	yes	maximal, complemented
6	#31771247	C₂	1	2	yes	maximal, complemented
7	#31771244	C₂	1	2	yes	maximal, complemented
8	#31771243	C₂	1	2	yes	maximal, complemented
9	#31771230	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771195	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771192	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771188	C₂	1	2	yes	maximal, complemented
13	#31771163	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771116	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771111	C₂	1	2	yes	maximal, complemented
16	#120×D₂₆₉	C₂	1	2	yes	maximal, complemented
17	#31771077	C₂	1	2	yes	maximal, complemented
18	C₂²×#16864379	C₂	1	1	yes	maximal, characteristic, complemented
19	#525×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
21	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
22	C₂×#16864401	C₂²	1	2	yes	complemented
23	C₂×D₄×D₂₆₉	C₂²	1	2	yes	—
24	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
26	C₂³×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
27	#22575448	C₂²	1	2	yes	complemented
28	#22575448	C₂²	1	2	yes	complemented
29	#22575448	C₂²	1	2	yes	complemented
30	#22575447	C₂²	1	2	yes	complemented
31	#22575442	C₂²	1	2	yes	complemented
32	#22575441	C₂²	1	2	yes	complemented
33	#22575439	C₂²	1	2	yes	complemented
34	#22575439	C₂²	1	2	yes	complemented
35	#22575438	C₂²	1	2	yes	complemented
36	#22575438	C₂²	1	2	yes	complemented
37	#22575438	C₂²	1	2	yes	complemented
38	#22575437	C₂²	1	2	yes	complemented
39	#22575437	C₂²	1	2	yes	complemented
40	#22575436	C₂²	1	2	yes	complemented
41	#22575436	C₂²	1	2	yes	complemented
42	#22575435	C₂²	1	2	yes	complemented
43	#22575434	C₂²	1	2	yes	complemented
44	#22575433	C₂²	1	2	yes	complemented
45	#22575432	C₂²	1	1	yes	characteristic, complemented
46	#22575432	C₂²	1	1	yes	characteristic, complemented
47	#22575431	C₂²	1	2	yes	complemented
48	#22575431	C₂²	1	2	yes	complemented
49	#22575430	C₂²	1	2	yes	complemented
50	#22575430	C₂²	1	2	yes	complemented
51	#22575429	C₂²	1	2	yes	complemented
52	#22575428	C₂²	1	2	yes	complemented
53	#22575427	C₂²	1	1	yes	characteristic, complemented
54	#22575427	C₂²	1	1	yes	characteristic, complemented
55	#22575427	C₂²	1	2	yes	complemented
56	#22575426	C₂²	1	2	yes	complemented
57	#22575425	C₂²	1	2	yes	complemented
58	#22575425	C₂²	1	2	yes	complemented
59	#22575425	C₂²	1	2	yes	complemented
60	#22575423	C₂²	1	2	yes	—
61	#22575423	C₂²	1	2	yes	—
62	#22575423	C₂²	1	2	yes	complemented
63	#22575423	C₂²	1	2	yes	complemented
64	#22575422	C₂²	1	2	yes	complemented
65	#22575421	C₂²	1	2	yes	—
66	#22575421	C₂²	1	2	yes	—
67	#22575421	C₂²	1	2	yes	complemented
68	#22575421	C₂²	1	2	yes	complemented
69	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
70	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
71	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
72	#22575415	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
76	#22575413	C₂²	1	2	yes	complemented
77	#22575413	C₂²	1	2	yes	complemented
78	#22575413	C₂²	1	2	yes	complemented
79	#22575412	C₂²	1	1	yes	characteristic, complemented
80	#22575411	C₂²	1	2	yes	complemented
81	#22575410	C₂²	1	2	yes	complemented
82	#22575409	C₂²	1	2	yes	complemented
83	C₂×#16864379	C₂²	1	1	yes	characteristic
84	C₂×#16864379	C₂²	1	1	yes	characteristic
85	C₂×#16864379	C₂²	1	1	yes	characteristic, complemented
86	C₂×#16864379	C₂²	1	1	yes	characteristic, complemented
87	C₂×#16864379	C₂²	1	2	yes	complemented
88	C₂×#16864379	C₂²	1	2	yes	complemented
89	C₂×#16864379	C₂²	1	2	yes	complemented
90	C₂×#16864379	C₂²	1	2	yes	complemented
91	C₂×#16864379	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
93	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
96	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
98	#123×C₂₆₉	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
101	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
102	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
103	#120×C₂₆₉	C₂²	1	2	yes	complemented
104	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
105	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
106	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₆₉	—	2	4	no	—
108	C₂³×D₂₆₉	—	4	2	no	—
109	C₂³×D₂₆₉	—	4	2	no	—
110	C₂³×D₂₆₉	C₂³	1	2	yes	—
111	C₂³×D₂₆₉	C₂³	1	2	yes	—
112	C₂³×D₂₆₉	C₂³	1	2	yes	—
113	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
114	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
115	#16864402	—	4	2	no	—
116	#16864401	—	4	4	no	—
117	C₂×Dic₅₃₈	C₂³	1	2	yes	complemented
118	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic, complemented
119	C₂×D₁₀₇₆	C₂³	1	2	yes	—
120	C₂×D₁₀₇₆	C₂³	1	2	yes	—
121	C₂×D₁₀₇₆	C₂³	1	2	yes	—
122	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic, complemented
123	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
130	D₄×D₂₆₉	—	2	8	no	—
131	D₄×D₂₆₉	—	4	4	no	—
132	D₄×D₂₆₉	—	4	4	no	—
133	C₂²×Dic₂₆₉	—	4	2	no	—
134	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
135	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
137	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
138	C₂²×Dic₂₆₉	C₂³	1	2	yes	complemented
139	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
140	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
141	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
142	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
143	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
144	C₄⋊Dic₂₆₉	C₂³	1	2	yes	complemented
145	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
146	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
147	C₄⋊Dic₂₆₉	C₂³	1	2	yes	complemented
148	#16864381	C₂³	1	2	yes	complemented
149	#16864381	C₂³	1	2	yes	complemented
150	#16864381	C₂³	1	2	yes	complemented
151	#16864381	C₂³	1	2	yes	complemented
152	#16864381	C₂³	1	2	yes	complemented
153	#16864381	C₂³	1	2	yes	complemented
154	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
156	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	complemented
158	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	complemented
159	#16864379	C₂³	1	2	yes	—
160	#16864379	C₂³	1	2	yes	—
161	#16864379	C₂³	1	2	yes	—
162	#16864379	C₂³	1	2	yes	—
163	#16864379	C₂³	1	2	yes	—
164	#16864379	C₂³	1	2	yes	—
165	#16864379	C₂³	1	2	yes	—
166	#16864379	C₂³	1	2	yes	—
167	#16864379	C₂³	1	2	yes	—
168	#16864379	C₂³	1	2	yes	—
169	#16864379	C₂³	1	2	yes	—
170	#16864379	C₂³	1	2	yes	—
171	#16864379	C₂³	1	2	yes	—
172	#16864379	C₂³	1	2	yes	—
173	#16864379	C₂³	1	2	yes	complemented
174	#16864379	C₂³	1	2	yes	complemented
175	#16864379	C₂³	1	2	yes	complemented
176	#16864379	C₂³	1	2	yes	complemented
177	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
178	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
179	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
180	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
181	#41×C₂₆₉	—	4	2	no	—
182	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
183	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
184	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
185	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
186	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
187	C₂²×C₄×C₂₆₉	—	4	2	no	—
188	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	complemented
195	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
196	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
197	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
198	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
199	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
203	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
204	C₄²×C₂₆₉	C₂³	1	2	yes	complemented
205	C₂²×D₂₆₉	—	2	2	no	—
206	C₂²×D₂₆₉	—	2	4	no	—
207	C₂²×D₂₆₉	—	2	4	no	—
208	C₂²×D₂₆₉	—	2	4	no	—
209	C₂²×D₂₆₉	—	2	4	no	—
210	C₂²×D₂₆₉	—	2	4	no	—
211	C₂²×D₂₆₉	—	4	1	no	—
212	C₂²×D₂₆₉	—	4	1	no	—
213	C₂²×D₂₆₉	—	4	2	no	—
214	C₂²×D₂₆₉	—	4	2	no	—
215	C₂²×D₂₆₉	—	4	1	no	—
216	C₂²×D₂₆₉	—	4	1	no	—
217	C₂²×D₂₆₉	—	4	2	no	—
218	C₂²×D₂₆₉	—	4	2	no	—
219	C₂²×D₂₆₉	—	4	16	no	—
220	C₂²×D₂₆₉	#41	1	4	yes	complemented
221	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
222	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
223	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
224	Dic₅₃₈	—	4	2	no	—
225	Dic₅₃₈	—	4	1	no	—
226	D₁₀₇₆	—	2	4	no	—
227	D₁₀₇₆	—	4	2	no	—
228	D₁₀₇₆	—	4	2	no	—
229	D₁₀₇₆	—	4	1	no	—
230	C₂²⋊D₂₆₉	—	2	4	no	—
231	C₂²⋊D₂₆₉	—	2	4	no	—
232	C₂²⋊D₂₆₉	—	2	4	no	—
233	C₂²⋊D₂₆₉	—	2	4	no	—
234	C₂²⋊D₂₆₉	—	4	2	no	—
235	C₂²⋊D₂₆₉	—	4	2	no	—
236	C₂²⋊D₂₆₉	—	4	2	no	—
237	C₂×Dic₂₆₉	—	2	4	no	—
238	C₂×Dic₂₆₉	—	4	1	no	—
239	C₂×Dic₂₆₉	—	4	2	no	—
240	C₂×Dic₂₆₉	—	4	1	no	—
241	C₂×Dic₂₆₉	—	4	2	no	—
242	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
243	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
244	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
245	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
246	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
247	C₄×D₂₆₉	—	2	4	no	—
248	C₄×D₂₆₉	—	4	2	no	—
249	C₄×D₂₆₉	—	4	2	no	—
250	C₄×D₂₆₉	—	4	2	no	—
251	C₄×D₂₆₉	—	4	2	no	—
252	C₂³×C₂₆₉	—	2	2	no	—
253	C₂³×C₂₆₉	—	2	2	no	—
254	C₂³×C₂₆₉	—	2	2	no	—
255	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
256	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
257	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
258	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
259	Q₈×C₂₆₉	—	4	1	no	—
260	D₄×C₂₆₉	—	2	4	no	—
261	D₄×C₂₆₉	—	2	4	no	—
262	D₄×C₂₆₉	—	2	4	no	—
263	D₄×C₂₆₉	—	4	1	no	—
264	C₂×C₄×C₂₆₉	—	2	2	no	—
265	C₂×C₄×C₂₆₉	—	2	2	no	—
266	C₂×C₄×C₂₆₉	—	4	1	no	—
267	C₂×C₄×C₂₆₉	—	4	1	no	—
268	C₂×C₄×C₂₆₉	—	4	1	no	—
269	C₂×C₄×C₂₆₉	—	4	1	no	—
270	C₂×C₄×C₂₆₉	—	4	2	no	—
271	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
273	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
274	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₂₆₉	—	2	8	no	—
279	C₂²×C₂₆₉	—	2	1	no	—
280	C₂²×C₂₆₉	—	2	1	no	—
281	C₂²×C₂₆₉	—	2	1	no	—
282	C₂²×C₂₆₉	—	2	1	no	—
283	C₂²×C₂₆₉	—	2	1	no	—
284	C₂²×C₂₆₉	—	2	1	no	—
285	C₂²×C₂₆₉	—	2	2	no	—
286	C₂²×C₂₆₉	—	2	2	no	—
287	C₂²×C₂₆₉	—	2	2	no	—
288	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
289	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
290	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
291	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
292	C₂×D₂₆₉	—	2	2	no	—
293	C₂×D₂₆₉	—	2	2	no	—
294	C₂×D₂₆₉	—	2	2	no	—
295	C₂×D₂₆₉	—	2	2	no	—
296	C₂×D₂₆₉	—	2	2	no	—
297	C₂×D₂₆₉	—	2	2	no	—
298	C₂×D₂₆₉	—	2	2	no	—
299	C₂×D₂₆₉	—	2	2	no	—
300	C₂×D₂₆₉	—	4	4	no	—
301	C₂×D₂₆₉	—	4	8	no	—
302	C₂×D₂₆₉	—	4	8	no	—
303	C₂×D₂₆₉	—	4	4	no	—
304	C₂×D₂₆₉	—	8	4	no	—
305	C₂×D₂₆₉	C₂×#41	1	4	yes	—
306	C₄×C₂₆₉	—	2	2	no	—
307	C₄×C₂₆₉	—	2	1	no	—
308	C₄×C₂₆₉	—	2	1	no	—
309	C₄×C₂₆₉	—	2	1	no	—
310	C₄×C₂₆₉	—	2	1	no	—
311	C₄×C₂₆₉	—	2	2	no	—
312	C₄×C₂₆₉	—	2	2	no	—
313	Dic₂₆₉	—	2	2	no	—
314	Dic₂₆₉	—	2	2	no	—
315	Dic₂₆₉	—	2	2	no	—
316	Dic₂₆₉	—	2	2	no	—
317	Dic₂₆₉	—	2	2	no	—
318	C₂×C₂₆₉	—	2	2	no	—
319	C₂×C₂₆₉	—	2	2	no	—
320	C₂×C₂₆₉	—	2	2	no	—
321	C₂×C₂₆₉	—	4	2	no	—
322	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
323	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	D₂₆₉	—	2	4	no	—
326	D₂₆₉	—	4	2	no	—
327	D₂₆₉	—	4	2	no	—
328	C₂₆₉	#3490	1	1	yes	characteristic, complemented, Sylow
329	#3490	—	269	1	no	maximal, Sylow
330	#551	—	269	2	no	—
331	#551	—	269	2	no	—
332	#551	—	269	2	no	—
333	#551	—	269	2	no	—
334	#546	—	269	2	no	—
335	#546	—	269	2	no	—
336	#546	—	269	2	no	—
337	#546	—	269	2	no	—
338	#543	—	269	1	no	—
339	#538	—	269	1	no	—
340	#538	—	269	1	no	—
341	#538	—	269	2	no	—
342	#534	—	269	1	no	—
343	#525	—	269	1	no	—
344	#525	—	269	2	no	—
345	#525	D₂₆₉	1	1	yes	characteristic, complemented
346	C₂×#120	—	269	2	no	—
347	#518	—	269	2	no	—
348	C₂²×C₂²⋊C₄	—	269	1	no	—
349	C₂⁵	—	269	1	no	—
350	C₂×#41	—	269	2	no	—
351	C₂×#41	—	269	1	no	—
352	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic, complemented
353	C₂²×D₄	—	269	2	no	—
354	C₂²×D₄	—	269	2	no	—
355	C₂²×D₄	—	269	2	no	—
356	C₂³×C₄	—	269	1	no	—
357	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
358	#126	—	269	2	no	—
359	#126	—	269	2	no	—
360	#126	—	269	2	no	—
361	#126	—	269	2	no	—
362	#124	—	269	2	no	—
363	#124	—	269	2	no	—
364	#124	—	269	2	no	—
365	#124	—	269	2	no	—
366	#123	—	269	2	no	—
367	#123	—	269	2	no	—
368	#123	—	269	2	no	—
369	#123	—	269	2	no	—
370	#123	—	269	2	no	—
371	#123	—	269	2	no	—
372	#123	—	269	2	no	—
373	#123	—	269	2	no	—
374	#123	—	269	2	no	—
375	#123	C₂×D₂₆₉	1	2	yes	complemented
376	C₂²⋊Q₈	—	269	2	no	—
377	C₂²⋊Q₈	—	269	1	no	—
378	C₂²⋊Q₈	—	269	1	no	—
379	C₂²⋊Q₈	—	269	2	no	—
380	C₂²⋊Q₈	—	269	2	no	—
381	C₂²⋊Q₈	—	269	2	no	—
382	C₂²⋊Q₈	—	269	2	no	—
383	C₂²⋊Q₈	—	269	2	no	—
384	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
385	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
386	#121	—	269	2	no	—
387	#121	—	269	2	no	—
388	#121	—	269	2	no	—
389	#121	—	269	1	no	—
390	#121	—	269	1	no	—
391	#121	—	269	2	no	—
392	#121	—	269	2	no	—
393	#121	—	269	2	no	—
394	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
395	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
396	#120	—	269	2	no	—
397	#120	—	269	2	no	—
398	#120	—	269	2	no	—
399	#120	—	269	2	no	—
400	#120	—	269	2	no	—
401	#120	—	269	2	no	—
402	#120	—	269	2	no	—
403	#120	—	269	2	no	—
404	#120	—	269	2	no	—
405	#120	C₂×D₂₆₉	1	2	yes	complemented
406	C₄×D₄	—	269	2	no	—
407	C₄×D₄	—	269	2	no	—
408	C₄×D₄	—	269	2	no	—
409	C₄×D₄	—	269	2	no	—
410	C₄×D₄	—	269	2	no	—
411	C₄×D₄	—	269	2	no	—
412	C₄×D₄	—	269	2	no	—
413	C₄×D₄	—	269	2	no	—
414	C₄×D₄	—	269	2	no	—
415	C₄×D₄	—	269	2	no	—
416	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
417	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
418	#117	—	269	1	no	—
419	#117	—	269	2	no	—
420	#117	—	269	2	no	—
421	#117	—	269	2	no	—
422	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊C₄	—	269	1	no	—
424	C₂×C₂²⋊C₄	—	269	1	no	—
425	C₂×C₂²⋊C₄	—	269	1	no	—
426	C₂×C₂²⋊C₄	—	269	1	no	—
427	C₂×C₂²⋊C₄	—	269	2	no	—
428	C₂×C₂²⋊C₄	—	269	2	no	—
429	C₂×C₂²⋊C₄	—	269	2	no	—
430	C₂×C₂²⋊C₄	—	269	2	no	—
431	C₂×C₂²⋊C₄	—	269	2	no	—
432	C₂×C₂²⋊C₄	—	269	2	no	—
433	C₂×C₂²⋊C₄	—	269	2	no	—
434	C₂×C₂²⋊C₄	—	269	2	no	—
435	C₂×C₂²⋊C₄	—	269	2	no	—
436	C₂⁴	—	269	1	no	—
437	C₂⁴	—	269	2	no	—
438	C₂⁴	—	269	2	no	—
439	C₂⁴	—	269	1	no	—
440	C₂⁴	—	269	2	no	—
441	C₂⁴	—	538	4	no	—
442	C₂⁴	—	1076	2	no	—
443	C₂⁴	—	1076	2	no	—
444	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
445	#41	—	4	2	no	—
446	#41	—	1076	2	no	—
447	#41	—	1076	4	no	—
448	C₂×Q₈	—	269	1	no	—
449	C₂×Q₈	—	269	2	no	—
450	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
451	C₂×D₄	—	269	2	no	—
452	C₂×D₄	—	269	2	no	—
453	C₂×D₄	—	269	2	no	—
454	C₂×D₄	—	269	2	no	—
455	C₂×D₄	—	269	2	no	—
456	C₂×D₄	—	269	2	no	—
457	C₂×D₄	—	269	2	no	—
458	C₂×D₄	—	269	2	no	—
459	C₂×D₄	—	269	1	no	—
460	C₂×D₄	—	269	2	no	—
461	C₂×D₄	—	269	2	no	—
462	C₂×D₄	—	538	8	no	—
463	C₂×D₄	—	1076	4	no	—
464	C₂×D₄	—	1076	4	no	—
465	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
466	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
467	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
468	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	269	2	no	—
471	C₂²×C₄	—	269	1	no	—
472	C₂²×C₄	—	269	2	no	—
473	C₂²×C₄	—	269	1	no	—
474	C₂²×C₄	—	269	2	no	—
475	C₂²×C₄	—	269	2	no	—
476	C₂²×C₄	—	269	2	no	—
477	C₂²×C₄	—	269	2	no	—
478	C₂²×C₄	—	269	2	no	—
479	C₂²×C₄	—	269	2	no	—
480	C₂²×C₄	—	1076	2	no	—
481	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
482	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
483	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
484	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	complemented
488	C₄⋊C₄	—	269	2	no	—
489	C₄⋊C₄	—	269	2	no	—
490	C₄⋊C₄	—	269	2	no	—
491	C₄⋊C₄	—	269	2	no	—
492	C₄⋊C₄	—	269	1	no	—
493	C₄⋊C₄	—	269	2	no	—
494	C₄⋊C₄	—	269	1	no	—
495	C₄⋊C₄	—	269	2	no	—
496	C₄⋊C₄	—	269	2	no	—
497	C₄⋊C₄	—	269	2	no	—
498	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
499	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
500	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
501	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
502	C₂²⋊C₄	—	269	2	no	—
503	C₂²⋊C₄	—	269	2	no	—
504	C₂²⋊C₄	—	269	2	no	—
505	C₂²⋊C₄	—	269	2	no	—
506	C₂²⋊C₄	—	269	2	no	—
507	C₂²⋊C₄	—	269	2	no	—
508	C₂²⋊C₄	—	269	2	no	—
509	C₂²⋊C₄	—	269	2	no	—
510	C₂²⋊C₄	—	269	2	no	—
511	C₂²⋊C₄	—	269	2	no	—
512	C₂²⋊C₄	—	269	2	no	—
513	C₂²⋊C₄	—	269	2	no	—
514	C₂²⋊C₄	—	269	2	no	—
515	C₂²⋊C₄	—	269	2	no	—
516	C₂²⋊C₄	—	269	2	no	—
517	C₂²⋊C₄	—	269	2	no	—
518	C₂²⋊C₄	—	269	2	no	—
519	C₂²⋊C₄	—	269	2	no	—
520	C₂²⋊C₄	—	269	2	no	—
521	C₂²⋊C₄	—	269	2	no	—
522	C₂²⋊C₄	—	269	2	no	—
523	C₂²⋊C₄	—	269	2	no	—
524	C₂²⋊C₄	—	269	2	no	—
525	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
529	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
530	C₄²	—	269	2	no	—
531	C₄²	—	269	2	no	—
532	C₄²	—	269	2	no	—
533	C₄²	C₂²×D₂₆₉	1	2	yes	complemented
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	269	2	no	—
538	C₂³	—	269	4	no	—
539	C₂³	—	269	2	no	—
540	C₂³	—	269	2	no	—
541	C₂³	—	538	4	no	—
542	C₂³	—	538	4	no	—
543	C₂³	—	538	4	no	—
544	C₂³	—	538	2	no	—
545	C₂³	—	538	4	no	—
546	C₂³	—	538	4	no	—
547	C₂³	—	1076	1	no	—
548	C₂³	—	1076	2	no	—
549	C₂³	—	1076	1	no	—
550	C₂³	—	1076	1	no	—
551	C₂³	—	1076	2	no	—
552	C₂³	—	1076	1	no	—
553	C₂³	—	1076	2	no	—
554	C₂³	—	1076	2	no	—
555	C₂³	—	1076	16	no	—
556	C₂³	C₂³×D₂₆₉	1	2	yes	—
557	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
558	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
559	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	1076	1	no	—
562	Q₈	—	1076	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	4	no	—
566	D₄	—	4	1	no	—
567	D₄	—	538	4	no	—
568	D₄	—	538	4	no	—
569	D₄	—	538	4	no	—
570	D₄	—	538	4	no	—
571	D₄	—	538	4	no	—
572	D₄	—	1076	2	no	—
573	D₄	—	1076	2	no	—
574	D₄	—	1076	1	no	—
575	D₄	—	1076	2	no	—
576	D₄	—	1076	2	no	—
577	D₄	—	1076	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	269	2	no	—
586	C₂×C₄	—	269	2	no	—
587	C₂×C₄	—	269	2	no	—
588	C₂×C₄	—	269	2	no	—
589	C₂×C₄	—	269	2	no	—
590	C₂×C₄	—	538	4	no	—
591	C₂×C₄	—	538	4	no	—
592	C₂×C₄	—	1076	2	no	—
593	C₂×C₄	—	1076	2	no	—
594	C₂×C₄	—	1076	2	no	—
595	C₂×C₄	—	1076	2	no	—
596	C₂×C₄	—	1076	1	no	—
597	C₂×C₄	—	1076	2	no	—
598	C₂×C₄	—	1076	1	no	—
599	C₂×C₄	—	1076	2	no	—
600	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
602	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
603	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
605	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
607	C₂²	—	2	8	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	269	4	no	—
618	C₂²	—	538	2	no	—
619	C₂²	—	538	2	no	—
620	C₂²	—	538	2	no	—
621	C₂²	—	538	2	no	—
622	C₂²	—	538	2	no	—
623	C₂²	—	538	2	no	—
624	C₂²	—	538	2	no	—
625	C₂²	—	538	2	no	—
626	C₂²	—	1076	4	no	—
627	C₂²	—	1076	8	no	—
628	C₂²	—	1076	8	no	—
629	C₂²	—	1076	4	no	—
630	C₂²	—	2152	4	no	—
631	C₂²	#41×D₂₆₉	1	2	yes	—
632	C₂²	#22575498	1	2	yes	—
633	C₂²	#22575499	1	2	yes	—
634	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	2	no	—
642	C₄	—	538	2	no	—
643	C₄	—	538	2	no	—
644	C₄	—	538	2	no	—
645	C₄	—	538	2	no	—
646	C₄	—	538	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	2	2	no	—
649	C₂	—	2	2	no	—
650	C₂	—	4	2	no	—
651	C₂	—	538	4	no	—
652	C₂	—	1076	2	no	—
653	C₂	—	1076	2	no	—
654	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
655	C₂	C₂×#22575498	1	1	yes	characteristic
656	C₂	C₂×#22575499	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#525×C₂₆₉	C₂
hypercenter	#525	D₂₆₉
hypocenter	C₂₆₉	#3490
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #31771284	C₂	semidirect
2. #31771282	C₂	semidirect
3. #31771279	C₂	semidirect
4. #31771278	C₂	semidirect
5. #31771250	C₂	semidirect
6. #31771247	C₂	semidirect
7. #31771244	C₂	semidirect
8. #31771243	C₂	semidirect
9. #31771230	C₂	semidirect
10. #31771195	C₂	semidirect
11. #31771192	C₂	semidirect
12. #31771188	C₂	semidirect
13. #31771163	C₂	semidirect
14. #31771116	C₂	semidirect
15. #31771111	C₂	semidirect
16. #120×D₂₆₉	C₂	semidirect
17. #31771077	C₂	semidirect
18. C₂²×#16864379	C₂	semidirect
19. #525×C₂₆₉	C₂	semidirect
21. C₂×#16864402	C₂²	semidirect
22. C₂×#16864401	C₂²	semidirect
24. C₂×D₄×D₂₆₉	C₂²	semidirect
25. C₂×D₄×D₂₆₉	C₂²	semidirect
26. C₂³×Dic₂₆₉	C₂²	semidirect
27. #22575448	C₂²	semidirect
28. #22575448	C₂²	semidirect
29. #22575448	C₂²	semidirect
30. #22575447	C₂²	semidirect
31. #22575442	C₂²	semidirect
32. #22575441	C₂²	semidirect
33. #22575439	C₂²	semidirect
34. #22575439	C₂²	semidirect
35. #22575438	C₂²	semidirect
36. #22575438	C₂²	semidirect
37. #22575438	C₂²	semidirect
38. #22575437	C₂²	semidirect
39. #22575437	C₂²	semidirect
40. #22575436	C₂²	semidirect
41. #22575436	C₂²	semidirect
42. #22575435	C₂²	semidirect
43. #22575434	C₂²	semidirect
44. #22575433	C₂²	semidirect
45. #22575432	C₂²	semidirect
46. #22575432	C₂²	semidirect
47. #22575431	C₂²	semidirect
48. #22575431	C₂²	semidirect
49. #22575430	C₂²	semidirect
50. #22575430	C₂²	semidirect
51. #22575429	C₂²	semidirect
52. #22575428	C₂²	semidirect
53. #22575427	C₂²	semidirect
54. #22575427	C₂²	semidirect
55. #22575427	C₂²	semidirect
56. #22575426	C₂²	semidirect
57. #22575425	C₂²	semidirect
58. #22575425	C₂²	semidirect
59. #22575425	C₂²	semidirect
62. #22575423	C₂²	semidirect
63. #22575423	C₂²	semidirect
64. #22575422	C₂²	semidirect
67. #22575421	C₂²	semidirect
68. #22575421	C₂²	semidirect
69. C₄×D₁₀₇₆	C₂²	semidirect
70. D₄×Dic₂₆₉	C₂²	semidirect
71. D₄×Dic₂₆₉	C₂²	semidirect
72. #22575415	C₂²	semidirect
73. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
74. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
75. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
76. #22575413	C₂²	semidirect
77. #22575413	C₂²	semidirect
78. #22575413	C₂²	semidirect
79. #22575412	C₂²	semidirect
80. #22575411	C₂²	semidirect
81. #22575410	C₂²	semidirect
82. #22575409	C₂²	semidirect
85. C₂×#16864379	C₂²	semidirect
86. C₂×#16864379	C₂²	semidirect
87. C₂×#16864379	C₂²	semidirect
88. C₂×#16864379	C₂²	semidirect
89. C₂×#16864379	C₂²	semidirect
90. C₂×#16864379	C₂²	semidirect
91. C₂×#16864379	C₂²	semidirect
93. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
94. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
95. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
96. C₂×#41×C₂₆₉	C₂²	semidirect
97. C₂³×C₄×C₂₆₉	C₂²	semidirect
98. #123×C₂₆₉	C₂²	semidirect
99. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
100. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
101. #121×C₂₆₉	C₂²	semidirect
102. #121×C₂₆₉	C₂²	semidirect
103. #120×C₂₆₉	C₂²	semidirect
104. C₄×D₄×C₂₆₉	C₂²	semidirect
105. C₄×D₄×C₂₆₉	C₂²	semidirect
106. #117×C₂₆₉	C₂²	semidirect
117. C₂×Dic₅₃₈	C₂³	semidirect
118. C₂×Dic₅₃₈	C₂³	semidirect
122. C₂×D₁₀₇₆	C₂³	semidirect
129. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
138. C₂²×Dic₂₆₉	C₂³	semidirect
142. C₂×C₄×D₂₆₉	C₂³	semidirect
143. C₂×C₄×D₂₆₉	C₂³	semidirect
144. C₄⋊Dic₂₆₉	C₂³	semidirect
145. C₄⋊Dic₂₆₉	C₂³	semidirect
146. C₄⋊Dic₂₆₉	C₂³	semidirect
147. C₄⋊Dic₂₆₉	C₂³	semidirect
148. #16864381	C₂³	semidirect
149. #16864381	C₂³	semidirect
150. #16864381	C₂³	semidirect
151. #16864381	C₂³	semidirect
152. #16864381	C₂³	semidirect
153. #16864381	C₂³	semidirect
157. C₂²⋊Dic₂₆₉	C₂³	semidirect
158. C₂²⋊Dic₂₆₉	C₂³	semidirect
173. #16864379	C₂³	semidirect
174. #16864379	C₂³	semidirect
175. #16864379	C₂³	semidirect
176. #16864379	C₂³	semidirect
177. C₄×Dic₂₆₉	C₂³	semidirect
178. C₄×Dic₂₆₉	C₂³	semidirect
179. C₄×Dic₂₆₉	C₂³	semidirect
182. C₂×Q₈×C₂₆₉	C₂³	semidirect
186. C₂×D₄×C₂₆₉	C₂³	semidirect
194. C₂²×C₄×C₂₆₉	C₂³	semidirect
195. C₄⋊C₄×C₂₆₉	C₂³	semidirect
196. C₄⋊C₄×C₂₆₉	C₂³	semidirect
197. C₄⋊C₄×C₂₆₉	C₂³	semidirect
198. C₄⋊C₄×C₂₆₉	C₂³	semidirect
202. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
203. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
204. C₄²×C₂₆₉	C₂³	semidirect
220. C₂²×D₂₆₉	#41	semidirect
328. C₂₆₉	#3490	semidirect
345. #525	D₂₆₉	semidirect
352. C₂×#41	C₂×D₂₆₉	semidirect
357. C₂³×C₄	C₂×D₂₆₉	semidirect
375. #123	C₂×D₂₆₉	semidirect
384. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
385. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
394. #121	C₂×D₂₆₉	semidirect
395. #121	C₂×D₂₆₉	semidirect
405. #120	C₂×D₂₆₉	semidirect
416. C₄×D₄	C₂×D₂₆₉	semidirect
417. C₄×D₄	C₂×D₂₆₉	semidirect
422. #117	C₂×D₂₆₉	semidirect
450. C₂×Q₈	C₂²×D₂₆₉	semidirect
468. C₂×D₄	C₂²×D₂₆₉	semidirect
487. C₂²×C₄	C₂²×D₂₆₉	semidirect
498. C₄⋊C₄	C₂²×D₂₆₉	semidirect
499. C₄⋊C₄	C₂²×D₂₆₉	semidirect
500. C₄⋊C₄	C₂²×D₂₆₉	semidirect
501. C₄⋊C₄	C₂²×D₂₆₉	semidirect
528. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
529. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
533. C₄²	C₂²×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31771284	2
#31771282	2
#31771279	2
#31771278	2
#31771250	2
#31771247	2
#31771244	2
#31771243	2
#31771230	2
#31771195	2
#31771192	2
#31771188	2
#31771163	2
#31771116	2
#31771111	2
#120×D₂₆₉	2
#31771077	2
C₂²×#16864379	2
#525×C₂₆₉	2
#3490	269