Subgroups — #3539×C₂₆₉ #46808646

Order 34432.

1050 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#560×C₂₆₉	C₂	1	4	yes	maximal, complemented
2	#553×C₂₆₉	C₂	1	2	yes	maximal, complemented
3	#553×C₂₆₉	C₂	1	4	yes	maximal, complemented
4	#552×C₂₆₉	C₂	1	2	yes	maximal, complemented
5	#550×C₂₆₉	C₂	1	2	yes	maximal, complemented
6	#547×C₂₆₉	C₂	1	2	yes	maximal, complemented
7	#541×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#540×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#540×C₂₆₉	C₂	1	4	yes	maximal, complemented
10	#539×C₂₆₉	C₂	1	4	yes	maximal, complemented
11	#537×C₂₆₉	C₂	1	2	yes	maximal, complemented
12	#525×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#525×C₂₆₉	C₂	1	2	yes	maximal, complemented
14	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
15	C₂×#41×C₂₆₉	C₂²	1	2	yes	—
16	C₂×#41×C₂₆₉	C₂²	1	2	yes	complemented
17	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
19	#127×C₂₆₉	C₂²	1	4	yes	—
20	#127×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
21	#126×C₂₆₉	C₂²	1	4	yes	—
22	#126×C₂₆₉	C₂²	1	4	yes	—
23	#126×C₂₆₉	C₂²	1	4	yes	complemented
24	#125×C₂₆₉	C₂²	1	4	yes	complemented
25	#125×C₂₆₉	C₂²	1	4	yes	complemented
26	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
27	#125×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
28	#123×C₂₆₉	C₂²	1	4	yes	—
29	#123×C₂₆₉	C₂²	1	2	yes	—
30	#123×C₂₆₉	C₂²	1	4	yes	—
31	#123×C₂₆₉	C₂²	1	4	yes	—
32	#123×C₂₆₉	C₂²	1	4	yes	—
33	#123×C₂₆₉	C₂²	1	4	yes	complemented
34	#123×C₂₆₉	C₂²	1	4	yes	complemented
35	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	—
37	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	—
38	C₂²⋊Q₈×C₂₆₉	C₂²	1	4	yes	complemented
39	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	complemented
40	#121×C₂₆₉	C₂²	1	2	yes	—
41	#121×C₂₆₉	C₂²	1	2	yes	—
42	#121×C₂₆₉	C₂²	1	2	yes	—
43	#121×C₂₆₉	C₂²	1	4	yes	—
44	#121×C₂₆₉	C₂²	1	4	yes	—
45	#121×C₂₆₉	C₂²	1	4	yes	—
46	#121×C₂₆₉	C₂²	1	4	yes	—
47	#121×C₂₆₉	C₂²	1	4	yes	—
48	#121×C₂₆₉	C₂²	1	4	yes	—
49	#121×C₂₆₉	C₂²	1	4	yes	complemented
50	#121×C₂₆₉	C₂²	1	2	yes	complemented
51	#121×C₂₆₉	C₂²	1	4	yes	complemented
52	#120×C₂₆₉	C₂²	1	2	yes	—
53	#120×C₂₆₉	C₂²	1	4	yes	—
54	C₄×Q₈×C₂₆₉	C₂²	1	2	yes	complemented
55	C₄×D₄×C₂₆₉	C₂²	1	4	yes	—
56	C₄×D₄×C₂₆₉	C₂²	1	2	yes	—
57	C₄×D₄×C₂₆₉	C₂²	1	2	yes	—
58	C₄×D₄×C₂₆₉	C₂²	1	4	yes	—
59	C₄×D₄×C₂₆₉	C₂²	1	4	yes	complemented
60	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
61	C₄×D₄×C₂₆₉	C₂²	1	4	yes	complemented
62	#117×C₂₆₉	C₂²	1	1	yes	characteristic
63	#117×C₂₆₉	C₂²	1	2	yes	—
64	#117×C₂₆₉	C₂²	1	4	yes	complemented
65	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
66	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	4	yes	complemented
67	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
68	#41×C₂₆₉	—	4	2	no	—
69	#41×C₂₆₉	—	4	4	no	—
70	#41×C₂₆₉	—	4	4	no	—
71	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
72	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
73	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
74	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
75	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
76	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
77	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
78	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
79	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
80	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
81	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
82	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₂₆₉	C₂³	1	4	yes	—
84	C₂²×C₄×C₂₆₉	—	4	2	no	—
85	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
86	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
87	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
89	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
90	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
91	C₂²×C₄×C₂₆₉	C₂³	1	4	yes	—
92	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
94	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
95	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
96	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
97	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
98	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
99	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
100	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
101	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
102	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
103	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
104	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
105	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
106	C₄⋊C₄×C₂₆₉	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
108	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
109	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
111	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
113	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
114	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
115	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₂₆₉	C₂³	1	4	yes	—
120	C₄²×C₂₆₉	C₂³	1	4	yes	—
121	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
122	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
123	C₄²×C₂₆₉	C₂³	1	4	yes	—
124	C₂³×C₂₆₉	—	4	1	no	—
125	C₂³×C₂₆₉	—	4	2	no	—
126	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
127	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
128	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
129	C₂³×C₂₆₉	C₂⁴	1	4	yes	—
130	Q₈×C₂₆₉	—	2	4	no	—
131	Q₈×C₂₆₉	—	4	1	no	—
132	D₄×C₂₆₉	—	2	4	no	—
133	D₄×C₂₆₉	—	4	2	no	—
134	D₄×C₂₆₉	—	4	4	no	—
135	D₄×C₂₆₉	—	4	4	no	—
136	D₄×C₂₆₉	—	4	4	no	—
137	D₄×C₂₆₉	—	4	2	no	—
138	D₄×C₂₆₉	—	4	4	no	—
139	D₄×C₂₆₉	—	4	2	no	—
140	D₄×C₂₆₉	—	4	1	no	—
141	D₄×C₂₆₉	—	4	4	no	—
142	D₄×C₂₆₉	—	4	4	no	—
143	C₂×C₄×C₂₆₉	—	2	4	no	—
144	C₂×C₄×C₂₆₉	—	2	2	no	—
145	C₂×C₄×C₂₆₉	—	2	4	no	—
146	C₂×C₄×C₂₆₉	—	4	1	no	—
147	C₂×C₄×C₂₆₉	—	4	2	no	—
148	C₂×C₄×C₂₆₉	—	4	4	no	—
149	C₂×C₄×C₂₆₉	—	4	4	no	—
150	C₂×C₄×C₂₆₉	—	4	4	no	—
151	C₂×C₄×C₂₆₉	—	4	4	no	—
152	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
154	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
155	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
156	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
157	C₂×C₄×C₂₆₉	C₂⁴	1	4	yes	—
158	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₂₆₉	—	2	2	no	—
162	C₂²×C₂₆₉	—	2	1	no	—
163	C₂²×C₂₆₉	—	2	2	no	—
164	C₂²×C₂₆₉	—	2	4	no	—
165	C₂²×C₂₆₉	—	2	2	no	—
166	C₂²×C₂₆₉	—	2	4	no	—
167	C₂²×C₂₆₉	—	2	2	no	—
168	C₂²×C₂₆₉	—	2	4	no	—
169	C₂²×C₂₆₉	—	2	2	no	—
170	C₂²×C₂₆₉	—	2	2	no	—
171	C₂²×C₂₆₉	—	2	2	no	—
172	C₂²×C₂₆₉	—	4	4	no	—
173	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
174	C₄×C₂₆₉	—	2	2	no	—
175	C₄×C₂₆₉	—	2	1	no	—
176	C₄×C₂₆₉	—	2	2	no	—
177	C₄×C₂₆₉	—	2	4	no	—
178	C₄×C₂₆₉	—	2	2	no	—
179	C₄×C₂₆₉	—	2	4	no	—
180	C₄×C₂₆₉	—	2	4	no	—
181	C₄×C₂₆₉	—	2	2	no	—
182	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₂₆₉	—	4	2	no	—
184	C₂×C₂₆₉	—	4	4	no	—
185	C₂×C₂₆₉	—	4	2	no	—
186	C₂×C₂₆₉	—	4	1	no	—
187	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₂₆₉	#585	1	2	yes	—
189	C₂₆₉	#3539	1	1	yes	characteristic, direct product factor, Sylow
190	#3539	C₂₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	#560	C₂×C₂₆₉	1	4	yes	complemented
192	#553	C₂×C₂₆₉	1	2	yes	complemented
193	#553	C₂×C₂₆₉	1	4	yes	complemented
194	#552	C₂×C₂₆₉	1	2	yes	complemented
195	#550	C₂×C₂₆₉	1	2	yes	complemented
196	#547	C₂×C₂₆₉	1	2	yes	complemented
197	#541	C₂×C₂₆₉	1	1	yes	characteristic, complemented
198	#540	C₂×C₂₆₉	1	1	yes	characteristic, complemented
199	#540	C₂×C₂₆₉	1	4	yes	complemented
200	#539	C₂×C₂₆₉	1	4	yes	complemented
201	#537	C₂×C₂₆₉	1	2	yes	complemented
202	#525	C₂×C₂₆₉	1	1	yes	characteristic, complemented
203	#525	C₂×C₂₆₉	1	2	yes	complemented
204	C₂×#41	C₂²×C₂₆₉	1	1	yes	characteristic
205	C₂×#41	C₂²×C₂₆₉	1	2	yes	—
206	C₂×#41	C₂²×C₂₆₉	1	2	yes	complemented
207	C₂³×C₄	C₂²×C₂₆₉	1	1	yes	characteristic
208	C₄⋊Q₈	C₂²×C₂₆₉	1	1	yes	characteristic, complemented
209	#127	C₂²×C₂₆₉	1	4	yes	—
210	#127	C₂²×C₂₆₉	1	1	yes	characteristic, complemented
211	#126	C₂²×C₂₆₉	1	4	yes	—
212	#126	C₂²×C₂₆₉	1	4	yes	—
213	#126	C₂²×C₂₆₉	1	4	yes	complemented
214	#125	C₂²×C₂₆₉	1	4	yes	complemented
215	#125	C₂²×C₂₆₉	1	4	yes	complemented
216	#125	C₂²×C₂₆₉	1	1	yes	characteristic, complemented
217	#125	C₂²×C₂₆₉	1	1	yes	characteristic, complemented
218	#123	C₂²×C₂₆₉	1	4	yes	—
219	#123	C₂²×C₂₆₉	1	2	yes	—
220	#123	C₂²×C₂₆₉	1	4	yes	—
221	#123	C₂²×C₂₆₉	1	4	yes	—
222	#123	C₂²×C₂₆₉	1	4	yes	—
223	#123	C₂²×C₂₆₉	1	4	yes	complemented
224	#123	C₂²×C₂₆₉	1	4	yes	complemented
225	C₂²⋊Q₈	C₂²×C₂₆₉	1	2	yes	—
226	C₂²⋊Q₈	C₂²×C₂₆₉	1	2	yes	—
227	C₂²⋊Q₈	C₂²×C₂₆₉	1	2	yes	—
228	C₂²⋊Q₈	C₂²×C₂₆₉	1	4	yes	complemented
229	C₂²⋊Q₈	C₂²×C₂₆₉	1	2	yes	complemented
230	#121	C₂²×C₂₆₉	1	2	yes	—
231	#121	C₂²×C₂₆₉	1	2	yes	—
232	#121	C₂²×C₂₆₉	1	2	yes	—
233	#121	C₂²×C₂₆₉	1	4	yes	—
234	#121	C₂²×C₂₆₉	1	4	yes	—
235	#121	C₂²×C₂₆₉	1	4	yes	—
236	#121	C₂²×C₂₆₉	1	4	yes	—
237	#121	C₂²×C₂₆₉	1	4	yes	—
238	#121	C₂²×C₂₆₉	1	4	yes	—
239	#121	C₂²×C₂₆₉	1	4	yes	complemented
240	#121	C₂²×C₂₆₉	1	2	yes	complemented
241	#121	C₂²×C₂₆₉	1	4	yes	complemented
242	#120	C₂²×C₂₆₉	1	2	yes	—
243	#120	C₂²×C₂₆₉	1	4	yes	—
244	C₄×Q₈	C₂²×C₂₆₉	1	2	yes	complemented
245	C₄×D₄	C₂²×C₂₆₉	1	4	yes	—
246	C₄×D₄	C₂²×C₂₆₉	1	2	yes	—
247	C₄×D₄	C₂²×C₂₆₉	1	2	yes	—
248	C₄×D₄	C₂²×C₂₆₉	1	4	yes	—
249	C₄×D₄	C₂²×C₂₆₉	1	4	yes	complemented
250	C₄×D₄	C₂²×C₂₆₉	1	2	yes	complemented
251	C₄×D₄	C₂²×C₂₆₉	1	4	yes	complemented
252	#117	C₂²×C₂₆₉	1	1	yes	characteristic
253	#117	C₂²×C₂₆₉	1	2	yes	—
254	#117	C₂²×C₂₆₉	1	4	yes	complemented
255	C₂×C₄⋊C₄	C₂²×C₂₆₉	1	2	yes	complemented
256	C₂×C₄⋊C₄	C₂²×C₂₆₉	1	4	yes	complemented
257	C₂⁴	C₂³×C₂₆₉	1	1	yes	characteristic
258	#41	—	4	2	no	—
259	#41	—	4	4	no	—
260	#41	—	4	4	no	—
261	C₂×Q₈	C₂³×C₂₆₉	1	2	yes	—
262	C₂×Q₈	C₂³×C₂₆₉	1	1	yes	characteristic
263	C₂×D₄	C₂³×C₂₆₉	1	2	yes	—
264	C₂×D₄	C₂³×C₂₆₉	1	2	yes	—
265	C₂×D₄	C₂³×C₂₆₉	1	4	yes	—
266	C₂×D₄	C₂³×C₂₆₉	1	4	yes	—
267	C₂×D₄	C₂³×C₂₆₉	1	2	yes	—
268	C₂×D₄	C₂³×C₂₆₉	1	4	yes	—
269	C₂×D₄	C₂³×C₂₆₉	1	4	yes	—
270	C₂×D₄	C₂³×C₂₆₉	1	2	yes	—
271	C₂×D₄	C₂³×C₂₆₉	1	4	yes	—
272	C₂×D₄	C₂³×C₂₆₉	1	1	yes	characteristic
273	C₂×D₄	C₂³×C₂₆₉	1	4	yes	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	C₂³×C₂₆₉	1	2	yes	—
276	C₂²×C₄	C₂³×C₂₆₉	1	2	yes	—
277	C₂²×C₄	C₂³×C₂₆₉	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₂₆₉	1	4	yes	—
279	C₂²×C₄	C₂³×C₂₆₉	1	4	yes	—
280	C₂²×C₄	C₂³×C₂₆₉	1	4	yes	—
281	C₂²×C₄	C₂³×C₂₆₉	1	4	yes	—
282	C₂²×C₄	C₂³×C₂₆₉	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₂₆₉	1	2	yes	—
284	C₄⋊C₄	C₂³×C₂₆₉	1	2	yes	—
285	C₄⋊C₄	C₂³×C₂₆₉	1	2	yes	—
286	C₄⋊C₄	C₂³×C₂₆₉	1	2	yes	—
287	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
288	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
289	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
290	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
291	C₄⋊C₄	C₂³×C₂₆₉	1	2	yes	—
292	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
293	C₄⋊C₄	C₂³×C₂₆₉	1	2	yes	—
294	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
295	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
296	C₄⋊C₄	C₂³×C₂₆₉	1	4	yes	—
297	C₂²⋊C₄	C₂³×C₂₆₉	1	2	yes	—
298	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
299	C₂²⋊C₄	C₂³×C₂₆₉	1	2	yes	—
300	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
301	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
302	C₂²⋊C₄	C₂³×C₂₆₉	1	2	yes	—
303	C₂²⋊C₄	C₂³×C₂₆₉	1	2	yes	—
304	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
306	C₂²⋊C₄	C₂³×C₂₆₉	1	2	yes	—
307	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
308	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
309	C₂²⋊C₄	C₂³×C₂₆₉	1	4	yes	—
310	C₄²	C₂³×C₂₆₉	1	4	yes	—
311	C₄²	C₂³×C₂₆₉	1	1	yes	characteristic
312	C₄²	C₂³×C₂₆₉	1	1	yes	characteristic
313	C₄²	C₂³×C₂₆₉	1	4	yes	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	C₂⁴×C₂₆₉	1	1	yes	characteristic
317	C₂³	C₂⁴×C₂₆₉	1	2	yes	—
318	C₂³	C₂⁴×C₂₆₉	1	2	yes	—
319	C₂³	C₂⁴×C₂₆₉	1	4	yes	—
320	Q₈	—	2	4	no	—
321	Q₈	—	4	1	no	—
322	D₄	—	2	4	no	—
323	D₄	—	4	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	C₂⁴×C₂₆₉	1	2	yes	—
343	C₂×C₄	C₂⁴×C₂₆₉	1	4	yes	—
344	C₂×C₄	C₂⁴×C₂₆₉	1	2	yes	—
345	C₂×C₄	C₂⁴×C₂₆₉	1	4	yes	—
346	C₂×C₄	C₂⁴×C₂₆₉	1	2	yes	—
347	C₂×C₄	C₂⁴×C₂₆₉	1	4	yes	—
348	C₂×C₄	C₂⁴×C₂₆₉	1	2	yes	—
349	C₂×C₄	C₂⁴×C₂₆₉	1	1	yes	characteristic
350	C₂×C₄	C₂⁴×C₂₆₉	1	1	yes	characteristic
351	C₂²	—	2	2	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	C₂⁵×C₂₆₉	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	2	no	—
372	C₄	H(5,𝔽₂)×C₂₆₉	1	2	yes	—
373	C₂	—	4	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	4	2	no	—
376	C₂	—	4	4	no	—
377	C₂	C₂×H(5,𝔽₂)×C₂₆₉	1	1	yes	characteristic
378	C₂	#585×C₂₆₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₆₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₆₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₆₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #560×C₂₆₉	C₂	semidirect
2. #553×C₂₆₉	C₂	semidirect
3. #553×C₂₆₉	C₂	semidirect
4. #552×C₂₆₉	C₂	semidirect
5. #550×C₂₆₉	C₂	semidirect
6. #547×C₂₆₉	C₂	semidirect
7. #541×C₂₆₉	C₂	semidirect
8. #540×C₂₆₉	C₂	semidirect
9. #540×C₂₆₉	C₂	semidirect
10. #539×C₂₆₉	C₂	semidirect
11. #537×C₂₆₉	C₂	semidirect
12. #525×C₂₆₉	C₂	semidirect
13. #525×C₂₆₉	C₂	semidirect
16. C₂×#41×C₂₆₉	C₂²	semidirect
18. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
20. #127×C₂₆₉	C₂²	semidirect
23. #126×C₂₆₉	C₂²	semidirect
24. #125×C₂₆₉	C₂²	semidirect
25. #125×C₂₆₉	C₂²	semidirect
26. #125×C₂₆₉	C₂²	semidirect
27. #125×C₂₆₉	C₂²	semidirect
33. #123×C₂₆₉	C₂²	semidirect
34. #123×C₂₆₉	C₂²	semidirect
38. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
39. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
49. #121×C₂₆₉	C₂²	semidirect
50. #121×C₂₆₉	C₂²	semidirect
51. #121×C₂₆₉	C₂²	semidirect
54. C₄×Q₈×C₂₆₉	C₂²	semidirect
59. C₄×D₄×C₂₆₉	C₂²	semidirect
60. C₄×D₄×C₂₆₉	C₂²	semidirect
61. C₄×D₄×C₂₆₉	C₂²	semidirect
64. #117×C₂₆₉	C₂²	semidirect
65. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
66. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
189. C₂₆₉	#3539	direct (N × H)
190. #3539	C₂₆₉	direct (N × H)
191. #560	C₂×C₂₆₉	semidirect
192. #553	C₂×C₂₆₉	semidirect
193. #553	C₂×C₂₆₉	semidirect
194. #552	C₂×C₂₆₉	semidirect
195. #550	C₂×C₂₆₉	semidirect
196. #547	C₂×C₂₆₉	semidirect
197. #541	C₂×C₂₆₉	semidirect
198. #540	C₂×C₂₆₉	semidirect
199. #540	C₂×C₂₆₉	semidirect
200. #539	C₂×C₂₆₉	semidirect
201. #537	C₂×C₂₆₉	semidirect
202. #525	C₂×C₂₆₉	semidirect
203. #525	C₂×C₂₆₉	semidirect
206. C₂×#41	C₂²×C₂₆₉	semidirect
208. C₄⋊Q₈	C₂²×C₂₆₉	semidirect
210. #127	C₂²×C₂₆₉	semidirect
213. #126	C₂²×C₂₆₉	semidirect
214. #125	C₂²×C₂₆₉	semidirect
215. #125	C₂²×C₂₆₉	semidirect
216. #125	C₂²×C₂₆₉	semidirect
217. #125	C₂²×C₂₆₉	semidirect
223. #123	C₂²×C₂₆₉	semidirect
224. #123	C₂²×C₂₆₉	semidirect
228. C₂²⋊Q₈	C₂²×C₂₆₉	semidirect
229. C₂²⋊Q₈	C₂²×C₂₆₉	semidirect
239. #121	C₂²×C₂₆₉	semidirect
240. #121	C₂²×C₂₆₉	semidirect
241. #121	C₂²×C₂₆₉	semidirect
244. C₄×Q₈	C₂²×C₂₆₉	semidirect
249. C₄×D₄	C₂²×C₂₆₉	semidirect
250. C₄×D₄	C₂²×C₂₆₉	semidirect
251. C₄×D₄	C₂²×C₂₆₉	semidirect
254. #117	C₂²×C₂₆₉	semidirect
255. C₂×C₄⋊C₄	C₂²×C₂₆₉	semidirect
256. C₂×C₄⋊C₄	C₂²×C₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#560×C₂₆₉	2
#553×C₂₆₉	2
#552×C₂₆₉	2
#550×C₂₆₉	2
#547×C₂₆₉	2
#541×C₂₆₉	2
#540×C₂₆₉	2
#539×C₂₆₉	2
#537×C₂₆₉	2
#525×C₂₆₉	2
#3539	269

Subgroups — #3539×C269 #46808646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3539×C₂₆₉ #46808646