Subgroups — #46824571

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	#31771285	C₂	1	2	yes	maximal, complemented
2	#31771283	C₂	1	2	yes	maximal, complemented
3	#31771280	C₂	1	2	yes	maximal, complemented
4	#31771280	C₂	1	2	yes	maximal, complemented
5	#31771252	C₂	1	2	yes	maximal, complemented
6	#31771248	C₂	1	2	yes	maximal, complemented
7	#31771247	C₂	1	2	yes	maximal, complemented
8	#31771244	C₂	1	2	yes	maximal, complemented
9	#31771230	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771193	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771190	C₂	1	2	yes	maximal, complemented
12	#31771163	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771118	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771115	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771114	C₂	1	2	yes	maximal, complemented
16	#120×D₂₆₉	C₂	1	2	yes	maximal, complemented
17	#31771077	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#538×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic
21	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
22	C₂×#16864402	C₂²	1	2	yes	complemented
23	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₄×D₂₆₉	C₂²	1	2	yes	—
25	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
29	#22575446	C₂²	1	2	yes	complemented
30	#22575446	C₂²	1	2	yes	complemented
31	#22575446	C₂²	1	2	yes	complemented
32	#22575440	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	#22575435	C₂²	1	2	yes	complemented
39	#22575435	C₂²	1	2	yes	complemented
40	#22575435	C₂²	1	2	yes	complemented
41	#22575435	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	#22575433	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	#22575431	C₂²	1	2	yes	complemented
50	#22575430	C₂²	1	2	yes	complemented
51	#22575429	C₂²	1	2	yes	complemented
52	#22575429	C₂²	1	1	yes	characteristic, complemented
53	#22575428	C₂²	1	1	yes	characteristic, complemented
54	#22575427	C₂²	1	1	yes	characteristic, complemented
55	#22575426	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	#22575424	C₂²	1	2	yes	complemented
60	#22575424	C₂²	1	1	yes	characteristic, complemented
61	#22575423	C₂²	1	2	yes	—
62	#22575423	C₂²	1	2	yes	—
63	#22575423	C₂²	1	2	yes	complemented
64	#22575423	C₂²	1	2	yes	complemented
65	#22575422	C₂²	1	2	yes	complemented
66	#22575421	C₂²	1	2	yes	—
67	#22575421	C₂²	1	2	yes	—
68	#22575421	C₂²	1	2	yes	complemented
69	#22575421	C₂²	1	2	yes	complemented
70	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
71	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
72	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
73	#22575415	C₂²	1	2	yes	complemented
74	#22575415	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
78	#22575413	C₂²	1	2	yes	complemented
79	#22575413	C₂²	1	2	yes	complemented
80	#22575413	C₂²	1	2	yes	complemented
81	#22575411	C₂²	1	1	yes	characteristic, complemented
82	#22575411	C₂²	1	2	yes	complemented
83	#22575411	C₂²	1	1	yes	characteristic, complemented
84	#22575410	C₂²	1	2	yes	complemented
85	#22575410	C₂²	1	2	yes	complemented
86	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
87	C₂×#16864379	C₂²	1	1	yes	characteristic
88	C₂×#16864379	C₂²	1	1	yes	characteristic
89	C₂×#16864379	C₂²	1	2	yes	complemented
90	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
91	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
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	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
98	#126×C₂₆₉	C₂²	1	2	yes	complemented
99	#124×C₂₆₉	C₂²	1	2	yes	complemented
100	#123×C₂₆₉	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
102	#121×C₂₆₉	C₂²	1	2	yes	complemented
103	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
104	#120×C₂₆₉	C₂²	1	2	yes	complemented
105	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×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	1	yes	characteristic
111	C₂³×D₂₆₉	C₂³	1	2	yes	—
112	C₂³×D₂₆₉	C₂³	1	2	yes	—
113	C₂³×D₂₆₉	C₂³	1	2	yes	—
114	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
115	#16864403	—	4	2	no	—
116	#16864402	—	4	4	no	—
117	#16864401	—	4	2	no	—
118	C₂×Dic₅₃₈	C₂³	1	2	yes	complemented
119	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic, complemented
120	C₂×D₁₀₇₆	C₂³	1	2	yes	—
121	C₂×D₁₀₇₆	C₂³	1	2	yes	—
122	C₂×D₁₀₇₆	C₂³	1	2	yes	—
123	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic, complemented
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	—
130	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
131	D₄×D₂₆₉	—	2	8	no	—
132	D₄×D₂₆₉	—	4	4	no	—
133	D₄×D₂₆₉	—	4	4	no	—
134	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₂₆₉	C₂³	1	2	yes	complemented
137	C₂×C₄×D₂₆₉	—	4	2	no	—
138	C₂×C₄×D₂₆₉	—	4	2	no	—
139	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
140	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
141	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
144	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
145	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
147	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
149	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
150	C₄⋊Dic₂₆₉	C₂³	1	2	yes	complemented
151	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
152	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
153	C₄⋊Dic₂₆₉	C₂³	1	2	yes	complemented
154	#16864381	C₂³	1	2	yes	complemented
155	#16864381	C₂³	1	2	yes	complemented
156	#16864381	C₂³	1	2	yes	complemented
157	#16864381	C₂³	1	2	yes	complemented
158	#16864381	C₂³	1	2	yes	complemented
159	#16864381	C₂³	1	2	yes	complemented
160	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
161	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
162	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
163	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
164	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
165	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	complemented
166	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	complemented
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	—
174	#16864379	C₂³	1	2	yes	—
175	#16864379	C₂³	1	2	yes	—
176	#16864379	C₂³	1	2	yes	—
177	#16864379	C₂³	1	2	yes	complemented
178	#16864379	C₂³	1	2	yes	complemented
179	#16864379	C₂³	1	2	yes	complemented
180	#16864379	C₂³	1	2	yes	complemented
181	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
182	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
183	C₄×Dic₂₆₉	C₂³	1	2	yes	complemented
184	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
185	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
186	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
187	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
188	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
189	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
190	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	complemented
193	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
194	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
195	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
196	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
197	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
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	2	no	—
207	C₂²×D₂₆₉	—	2	2	no	—
208	C₂²×D₂₆₉	—	2	4	no	—
209	C₂²×D₂₆₉	—	2	4	no	—
210	C₂²×D₂₆₉	—	2	4	no	—
211	C₂²×D₂₆₉	—	2	4	no	—
212	C₂²×D₂₆₉	—	2	4	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	1	yes	characteristic
224	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
225	Dic₅₃₈	—	4	1	no	—
226	Dic₅₃₈	—	4	2	no	—
227	D₁₀₇₆	—	2	4	no	—
228	D₁₀₇₆	—	2	4	no	—
229	D₁₀₇₆	—	2	4	no	—
230	D₁₀₇₆	—	4	1	no	—
231	C₂²⋊D₂₆₉	—	2	4	no	—
232	C₂²⋊D₂₆₉	—	2	4	no	—
233	C₂²⋊D₂₆₉	—	2	4	no	—
234	C₂²⋊D₂₆₉	—	2	4	no	—
235	C₂²⋊D₂₆₉	—	4	2	no	—
236	C₂²⋊D₂₆₉	—	4	2	no	—
237	C₂²⋊D₂₆₉	—	4	2	no	—
238	C₂×Dic₂₆₉	—	4	1	no	—
239	C₂×Dic₂₆₉	—	4	1	no	—
240	C₂×Dic₂₆₉	—	4	2	no	—
241	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
243	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
249	C₄×D₂₆₉	—	2	4	no	—
250	C₄×D₂₆₉	—	2	2	no	—
251	C₄×D₂₆₉	—	4	1	no	—
252	C₄×D₂₆₉	—	4	1	no	—
253	C₄×D₂₆₉	—	4	2	no	—
254	C₄×D₂₆₉	—	4	2	no	—
255	C₄×D₂₆₉	—	4	2	no	—
256	C₄×D₂₆₉	—	4	2	no	—
257	C₄×D₂₆₉	—	4	2	no	—
258	C₂³×C₂₆₉	—	2	2	no	—
259	C₂³×C₂₆₉	—	4	1	no	—
260	C₂³×C₂₆₉	—	4	1	no	—
261	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
262	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
263	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
264	Q₈×C₂₆₉	—	4	1	no	—
265	D₄×C₂₆₉	—	2	4	no	—
266	D₄×C₂₆₉	—	4	2	no	—
267	D₄×C₂₆₉	—	4	2	no	—
268	D₄×C₂₆₉	—	4	1	no	—
269	C₂×C₄×C₂₆₉	—	4	1	no	—
270	C₂×C₄×C₂₆₉	—	4	1	no	—
271	C₂×C₄×C₂₆₉	—	4	2	no	—
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	2	yes	—
278	C₂²×C₂₆₉	—	2	1	no	—
279	C₂²×C₂₆₉	—	2	1	no	—
280	C₂²×C₂₆₉	—	2	2	no	—
281	C₂²×C₂₆₉	—	2	2	no	—
282	C₂²×C₂₆₉	—	2	2	no	—
283	C₂²×C₂₆₉	—	2	2	no	—
284	C₂²×C₂₆₉	—	2	2	no	—
285	C₂²×C₂₆₉	—	2	2	no	—
286	C₂²×C₂₆₉	—	4	4	no	—
287	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
288	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
289	C₂×D₂₆₉	—	2	8	no	—
290	C₂×D₂₆₉	—	2	1	no	—
291	C₂×D₂₆₉	—	2	1	no	—
292	C₂×D₂₆₉	—	2	1	no	—
293	C₂×D₂₆₉	—	2	1	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	—	4	4	no	—
300	C₂×D₂₆₉	—	4	8	no	—
301	C₂×D₂₆₉	—	4	8	no	—
302	C₂×D₂₆₉	—	8	4	no	—
303	C₂×D₂₆₉	C₂×#41	1	4	yes	—
304	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	—
305	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	—
306	C₄×C₂₆₉	—	2	2	no	—
307	C₄×C₂₆₉	—	2	2	no	—
308	C₄×C₂₆₉	—	2	1	no	—
309	C₄×C₂₆₉	—	2	2	no	—
310	C₄×C₂₆₉	—	2	1	no	—
311	C₄×C₂₆₉	—	2	2	no	—
312	Dic₂₆₉	—	2	2	no	—
313	Dic₂₆₉	—	2	1	no	—
314	Dic₂₆₉	—	2	1	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	—	4	2	no	—
320	C₂×C₂₆₉	—	4	2	no	—
321	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
322	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	D₂₆₉	—	2	2	no	—
325	D₂₆₉	—	2	2	no	—
326	D₂₆₉	—	2	4	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	2	no	—
340	#538	—	269	1	no	—
341	#538	D₂₆₉	1	1	yes	characteristic, complemented
342	#534	—	269	1	no	—
343	#525	—	269	1	no	—
344	#525	—	269	1	no	—
345	#525	—	269	2	no	—
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	1	no	—
351	C₂×#41	—	269	1	no	—
352	C₂×#41	—	269	2	no	—
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	—	269	1	no	—
358	#126	—	269	2	no	—
359	#126	—	269	2	no	—
360	#126	—	269	2	no	—
361	#126	C₂×D₂₆₉	1	2	yes	complemented
362	#124	—	269	2	no	—
363	#124	—	269	2	no	—
364	#124	—	269	2	no	—
365	#124	C₂×D₂₆₉	1	2	yes	complemented
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	1	no	—
377	C₂²⋊Q₈	—	269	2	no	—
378	C₂²⋊Q₈	—	269	1	no	—
379	C₂²⋊Q₈	—	269	2	no	—
380	C₂²⋊Q₈	—	269	1	no	—
381	C₂²⋊Q₈	—	269	2	no	—
382	C₂²⋊Q₈	—	269	2	no	—
383	C₂²⋊Q₈	—	269	2	no	—
384	C₂²⋊Q₈	—	269	2	no	—
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	1	no	—
392	#121	—	269	2	no	—
393	#121	—	269	2	no	—
394	#121	C₂×D₂₆₉	1	2	yes	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	—	269	2	no	—
417	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
418	#117	—	269	2	no	—
419	#117	—	269	1	no	—
420	#117	—	269	1	no	—
421	#117	—	269	2	no	—
422	#117	—	269	2	no	—
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	2	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	C₂×D₂₆₉	1	1	yes	characteristic, complemented
436	C₂⁴	—	269	1	no	—
437	C₂⁴	—	269	1	no	—
438	C₂⁴	—	269	2	no	—
439	C₂⁴	—	269	2	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	—	1076	4	no	—
446	#41	—	1076	2	no	—
447	#41	—	1076	2	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	2	no	—
460	C₂×D₄	—	269	2	no	—
461	C₂×D₄	—	269	1	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	—	269	1	no	—
470	C₂²×C₄	—	269	1	no	—
471	C₂²×C₄	—	269	2	no	—
472	C₂²×C₄	—	269	2	no	—
473	C₂²×C₄	—	269	1	no	—
474	C₂²×C₄	—	269	1	no	—
475	C₂²×C₄	—	269	2	no	—
476	C₂²×C₄	—	269	1	no	—
477	C₂²×C₄	—	269	1	no	—
478	C₂²×C₄	—	269	2	no	—
479	C₂²×C₄	—	269	2	no	—
480	C₂²×C₄	—	269	2	no	—
481	C₂²×C₄	—	269	2	no	—
482	C₂²×C₄	—	269	2	no	—
483	C₂²×C₄	—	1076	2	no	—
484	C₂²×C₄	—	1076	2	no	—
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	C₂²×D₂₆₉	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
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	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	269	2	no	—
538	C₂³	—	269	1	no	—
539	C₂³	—	269	1	no	—
540	C₂³	—	269	4	no	—
541	C₂³	—	269	2	no	—
542	C₂³	—	538	2	no	—
543	C₂³	—	538	2	no	—
544	C₂³	—	538	4	no	—
545	C₂³	—	538	4	no	—
546	C₂³	—	538	4	no	—
547	C₂³	—	538	4	no	—
548	C₂³	—	538	4	no	—
549	C₂³	—	538	2	no	—
550	C₂³	—	1076	1	no	—
551	C₂³	—	1076	1	no	—
552	C₂³	—	1076	2	no	—
553	C₂³	—	1076	2	no	—
554	C₂³	—	1076	2	no	—
555	C₂³	—	1076	2	no	—
556	C₂³	—	1076	16	no	—
557	C₂³	C₂³×D₂₆₉	1	2	yes	—
558	C₂³	C₂³×D₂₆₉	1	2	yes	—
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	—	4	2	no	—
565	D₄	—	4	2	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	—	538	4	no	—
573	D₄	—	538	4	no	—
574	D₄	—	1076	1	no	—
575	D₄	—	1076	2	no	—
576	D₄	—	1076	2	no	—
577	D₄	—	1076	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	269	2	no	—
582	C₂×C₄	—	269	1	no	—
583	C₂×C₄	—	269	1	no	—
584	C₂×C₄	—	269	2	no	—
585	C₂×C₄	—	269	2	no	—
586	C₂×C₄	—	269	2	no	—
587	C₂×C₄	—	538	4	no	—
588	C₂×C₄	—	538	2	no	—
589	C₂×C₄	—	538	2	no	—
590	C₂×C₄	—	538	4	no	—
591	C₂×C₄	—	1076	2	no	—
592	C₂×C₄	—	1076	1	no	—
593	C₂×C₄	—	1076	1	no	—
594	C₂×C₄	—	1076	2	no	—
595	C₂×C₄	—	1076	2	no	—
596	C₂×C₄	—	1076	2	no	—
597	C₂×C₄	—	1076	2	no	—
598	C₂×C₄	—	1076	1	no	—
599	C₂×C₄	—	1076	1	no	—
600	C₂×C₄	—	1076	2	no	—
601	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
602	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
603	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
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	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	269	4	no	—
617	C₂²	—	269	2	no	—
618	C₂²	—	269	2	no	—
619	C₂²	—	538	8	no	—
620	C₂²	—	538	1	no	—
621	C₂²	—	538	1	no	—
622	C₂²	—	538	1	no	—
623	C₂²	—	538	1	no	—
624	C₂²	—	538	2	no	—
625	C₂²	—	538	2	no	—
626	C₂²	—	538	2	no	—
627	C₂²	—	538	2	no	—
628	C₂²	—	538	2	no	—
629	C₂²	—	1076	4	no	—
630	C₂²	—	1076	8	no	—
631	C₂²	—	1076	8	no	—
632	C₂²	—	2152	4	no	—
633	C₂²	#41×D₂₆₉	1	2	yes	—
634	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	538	2	no	—
642	C₄	—	538	1	no	—
643	C₄	—	538	1	no	—
644	C₄	—	538	2	no	—
645	C₄	—	538	2	no	—
646	C₄	—	538	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	538	2	no	—
651	C₂	—	538	2	no	—
652	C₂	—	538	4	no	—
653	C₂	—	1076	2	no	—
654	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
655	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
656	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#538×C₂₆₉	C₂
hypercenter	#538	D₂₆₉
hypocenter	C₂₆₉	#3490
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #31771285	C₂	semidirect
2. #31771283	C₂	semidirect
3. #31771280	C₂	semidirect
4. #31771280	C₂	semidirect
5. #31771252	C₂	semidirect
6. #31771248	C₂	semidirect
7. #31771247	C₂	semidirect
8. #31771244	C₂	semidirect
9. #31771230	C₂	semidirect
10. #31771193	C₂	semidirect
11. #31771190	C₂	semidirect
12. #31771163	C₂	semidirect
13. #31771118	C₂	semidirect
14. #31771115	C₂	semidirect
15. #31771114	C₂	semidirect
16. #120×D₂₆₉	C₂	semidirect
17. #31771077	C₂	semidirect
18. C₂×C₂²⋊C₄×D₂₆₉	C₂	semidirect
19. #538×C₂₆₉	C₂	semidirect
21. C₂×#16864403	C₂²	semidirect
22. C₂×#16864402	C₂²	semidirect
23. C₂×#16864401	C₂²	semidirect
25. C₂×D₄×D₂₆₉	C₂²	semidirect
26. C₂×D₄×D₂₆₉	C₂²	semidirect
27. C₂²×C₄×D₂₆₉	C₂²	semidirect
28. C₂²×C₄×D₂₆₉	C₂²	semidirect
29. #22575446	C₂²	semidirect
30. #22575446	C₂²	semidirect
31. #22575446	C₂²	semidirect
32. #22575440	C₂²	semidirect
33. #22575439	C₂²	semidirect
34. #22575439	C₂²	semidirect
35. #22575438	C₂²	semidirect
36. #22575438	C₂²	semidirect
37. #22575438	C₂²	semidirect
38. #22575435	C₂²	semidirect
39. #22575435	C₂²	semidirect
40. #22575435	C₂²	semidirect
41. #22575435	C₂²	semidirect
42. #22575435	C₂²	semidirect
43. #22575434	C₂²	semidirect
44. #22575433	C₂²	semidirect
45. #22575433	C₂²	semidirect
46. #22575432	C₂²	semidirect
47. #22575431	C₂²	semidirect
48. #22575431	C₂²	semidirect
49. #22575431	C₂²	semidirect
50. #22575430	C₂²	semidirect
51. #22575429	C₂²	semidirect
52. #22575429	C₂²	semidirect
53. #22575428	C₂²	semidirect
54. #22575427	C₂²	semidirect
55. #22575426	C₂²	semidirect
56. #22575426	C₂²	semidirect
57. #22575425	C₂²	semidirect
58. #22575425	C₂²	semidirect
59. #22575424	C₂²	semidirect
60. #22575424	C₂²	semidirect
63. #22575423	C₂²	semidirect
64. #22575423	C₂²	semidirect
65. #22575422	C₂²	semidirect
68. #22575421	C₂²	semidirect
69. #22575421	C₂²	semidirect
70. C₄×D₁₀₇₆	C₂²	semidirect
71. C₄×D₁₀₇₆	C₂²	semidirect
72. D₄×Dic₂₆₉	C₂²	semidirect
73. #22575415	C₂²	semidirect
74. #22575415	C₂²	semidirect
75. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
76. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
77. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
78. #22575413	C₂²	semidirect
79. #22575413	C₂²	semidirect
80. #22575413	C₂²	semidirect
81. #22575411	C₂²	semidirect
82. #22575411	C₂²	semidirect
83. #22575411	C₂²	semidirect
84. #22575410	C₂²	semidirect
85. #22575410	C₂²	semidirect
86. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
89. C₂×#16864379	C₂²	semidirect
91. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
92. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
93. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
94. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
95. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
96. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
97. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
98. #126×C₂₆₉	C₂²	semidirect
99. #124×C₂₆₉	C₂²	semidirect
100. #123×C₂₆₉	C₂²	semidirect
101. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
102. #121×C₂₆₉	C₂²	semidirect
103. #121×C₂₆₉	C₂²	semidirect
104. #120×C₂₆₉	C₂²	semidirect
105. C₄×D₄×C₂₆₉	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
118. C₂×Dic₅₃₈	C₂³	semidirect
119. C₂×Dic₅₃₈	C₂³	semidirect
123. C₂×D₁₀₇₆	C₂³	semidirect
130. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
136. C₂²×Dic₂₆₉	C₂³	semidirect
148. C₂×C₄×D₂₆₉	C₂³	semidirect
149. C₂×C₄×D₂₆₉	C₂³	semidirect
150. C₄⋊Dic₂₆₉	C₂³	semidirect
151. C₄⋊Dic₂₆₉	C₂³	semidirect
152. C₄⋊Dic₂₆₉	C₂³	semidirect
153. C₄⋊Dic₂₆₉	C₂³	semidirect
154. #16864381	C₂³	semidirect
155. #16864381	C₂³	semidirect
156. #16864381	C₂³	semidirect
157. #16864381	C₂³	semidirect
158. #16864381	C₂³	semidirect
159. #16864381	C₂³	semidirect
165. C₂²⋊Dic₂₆₉	C₂³	semidirect
166. C₂²⋊Dic₂₆₉	C₂³	semidirect
177. #16864379	C₂³	semidirect
178. #16864379	C₂³	semidirect
179. #16864379	C₂³	semidirect
180. #16864379	C₂³	semidirect
181. C₄×Dic₂₆₉	C₂³	semidirect
182. C₄×Dic₂₆₉	C₂³	semidirect
183. C₄×Dic₂₆₉	C₂³	semidirect
185. C₂×Q₈×C₂₆₉	C₂³	semidirect
189. C₂×D₄×C₂₆₉	C₂³	semidirect
192. C₂²×C₄×C₂₆₉	C₂³	semidirect
193. C₄⋊C₄×C₂₆₉	C₂³	semidirect
194. C₄⋊C₄×C₂₆₉	C₂³	semidirect
195. C₄⋊C₄×C₂₆₉	C₂³	semidirect
196. 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
341. #538	D₂₆₉	semidirect
361. #126	C₂×D₂₆₉	semidirect
365. #124	C₂×D₂₆₉	semidirect
375. #123	C₂×D₂₆₉	semidirect
385. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
394. #121	C₂×D₂₆₉	semidirect
395. #121	C₂×D₂₆₉	semidirect
405. #120	C₂×D₂₆₉	semidirect
417. C₄×D₄	C₂×D₂₆₉	semidirect
435. C₂×C₂²⋊C₄	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
#31771285	2
#31771283	2
#31771280	2
#31771252	2
#31771248	2
#31771247	2
#31771244	2
#31771230	2
#31771193	2
#31771190	2
#31771163	2
#31771118	2
#31771115	2
#31771114	2
#120×D₂₆₉	2
#31771077	2
C₂×C₂²⋊C₄×D₂₆₉	2
#538×C₂₆₉	2
#3490	269