Subgroups — #46824490

Order 34432.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771337	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771314	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771313	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771302	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771301	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771298	C₂	1	2	yes	maximal, complemented
7	#31771281	C₂	1	2	yes	maximal, complemented
8	#31771278	C₂	1	2	yes	maximal, complemented
9	#31771243	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771242	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771150	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771141	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771134	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771132	C₂	1	2	yes	maximal, complemented
16	#31771115	C₂	1	2	yes	maximal, complemented
17	#31771111	C₂	1	2	yes	maximal, complemented
18	#41×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#16864401	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#22575413	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864401	C₂²	1	1	yes	characteristic
25	C₂×#16864401	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
27	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
28	C₂³×Dic₂₆₉	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₂₆₉	C₂²	1	2	yes	complemented
30	#22575452	C₂²	1	1	yes	characteristic, complemented
31	#22575449	C₂²	1	1	yes	characteristic
32	#22575448	C₂²	1	2	yes	complemented
33	#22575448	C₂²	1	2	yes	complemented
34	#22575446	C₂²	1	2	yes	complemented
35	#22575446	C₂²	1	2	yes	complemented
36	#22575445	C₂²	1	1	yes	characteristic, complemented
37	#22575444	C₂²	1	1	yes	characteristic, complemented
38	#22575443	C₂²	1	2	yes	complemented
39	#22575442	C₂²	1	1	yes	characteristic, complemented
40	#22575439	C₂²	1	2	yes	complemented
41	#22575439	C₂²	1	2	yes	complemented
42	#22575437	C₂²	1	2	yes	complemented
43	#22575437	C₂²	1	2	yes	complemented
44	#22575436	C₂²	1	2	yes	complemented
45	#22575435	C₂²	1	2	yes	complemented
46	#22575435	C₂²	1	2	yes	complemented
47	#22575435	C₂²	1	2	yes	complemented
48	#22575434	C₂²	1	2	yes	complemented
49	#22575433	C₂²	1	2	yes	complemented
50	#22575432	C₂²	1	2	yes	complemented
51	#22575430	C₂²	1	2	yes	complemented
52	#22575430	C₂²	1	2	yes	complemented
53	#22575430	C₂²	1	2	yes	complemented
54	#22575429	C₂²	1	1	yes	characteristic, complemented
55	#22575427	C₂²	1	1	yes	characteristic
56	#22575427	C₂²	1	1	yes	characteristic, complemented
57	#22575425	C₂²	1	2	yes	—
58	#22575425	C₂²	1	2	yes	complemented
59	#22575425	C₂²	1	2	yes	complemented
60	#22575425	C₂²	1	2	yes	complemented
61	#22575424	C₂²	1	1	yes	characteristic
62	#22575424	C₂²	1	2	yes	complemented
63	#22575422	C₂²	1	2	yes	—
64	#22575421	C₂²	1	2	yes	—
65	#22575421	C₂²	1	2	yes	complemented
66	Q₈×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
67	Q₈×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
69	#22575418	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
72	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
73	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
74	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
76	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
77	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
79	D₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₂₆₉	C₂²	1	2	yes	complemented
81	#22575415	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
85	#22575413	C₂²	1	2	yes	—
86	#22575413	C₂²	1	1	yes	characteristic
87	#22575413	C₂²	1	2	yes	complemented
88	#22575413	C₂²	1	2	yes	complemented
89	#22575413	C₂²	1	2	yes	complemented
90	#22575413	C₂²	1	2	yes	complemented
91	#22575413	C₂²	1	2	yes	complemented
92	#22575413	C₂²	1	2	yes	complemented
93	#22575413	C₂²	1	2	yes	complemented
94	#22575413	C₂²	1	1	yes	characteristic, complemented
95	#22575412	C₂²	1	2	yes	complemented
96	#22575412	C₂²	1	1	yes	characteristic, complemented
97	#22575411	C₂²	1	2	yes	complemented
98	#22575411	C₂²	1	1	yes	characteristic, complemented
99	#22575409	C₂²	1	1	yes	characteristic, complemented
100	#22575409	C₂²	1	1	yes	characteristic, complemented
101	#22575409	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
103	C₂×#16864381	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₂²⋊Dic₂₆₉	C₂²	1	2	yes	complemented
106	C₂×#16864379	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
108	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Dic₂₆₉	C₂²	1	2	yes	complemented
111	C₄²×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₂₆₉	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
114	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₂₆₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
118	#121×C₂₆₉	C₂²	1	2	yes	complemented
119	#120×C₂₆₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
123	C₂³×D₂₆₉	C₂³	1	2	yes	—
124	#16864401	—	2	4	no	—
125	#16864401	—	4	4	no	—
126	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₅₃₈	C₂³	1	2	yes	—
128	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₂₆₉	—	2	8	no	—
130	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
138	D₄×D₂₆₉	—	2	4	no	—
139	C₂²×Dic₂₆₉	—	4	4	no	—
140	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
142	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
144	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
145	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
146	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
147	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
148	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
149	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
150	C₂×C₄×D₂₆₉	—	4	4	no	—
151	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
155	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
156	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
157	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
160	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
162	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
164	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
165	#16864381	C₂³	1	2	yes	—
166	#16864381	C₂³	1	1	yes	characteristic
167	#16864381	C₂³	1	2	yes	—
168	#16864381	C₂³	1	2	yes	—
169	#16864381	C₂³	1	2	yes	—
170	#16864381	C₂³	1	1	yes	characteristic
171	#16864381	C₂³	1	1	yes	characteristic
172	#16864381	C₂³	1	1	yes	characteristic
173	#16864381	C₂³	1	2	yes	—
174	#16864381	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
184	#16864379	C₂³	1	2	yes	—
185	#16864379	C₂³	1	2	yes	—
186	#16864379	C₂³	1	1	yes	characteristic
187	#16864379	C₂³	1	2	yes	—
188	#16864379	C₂³	1	2	yes	—
189	#16864379	C₂³	1	2	yes	—
190	#16864379	C₂³	1	1	yes	characteristic
191	#16864379	C₂³	1	2	yes	—
192	#16864379	C₂³	1	2	yes	—
193	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₂₆₉	C₂³	1	2	yes	—
199	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₆₉	C₂³	1	2	yes	—
202	C₄×Dic₂₆₉	C₂³	1	2	yes	—
203	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
205	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
206	#41×C₂₆₉	—	2	4	no	—
207	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₂₆₉	—	2	4	no	—
209	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
210	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
211	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
214	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
216	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
229	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
230	C₂²×D₂₆₉	—	2	4	no	—
231	C₂²×D₂₆₉	—	2	4	no	—
232	C₂²×D₂₆₉	—	4	2	no	—
233	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
234	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
235	Dic₅₃₈	—	2	2	no	—
236	Dic₅₃₈	—	4	2	no	—
237	D₁₀₇₆	—	2	2	no	—
238	C₂²⋊D₂₆₉	—	2	4	no	—
239	C₂²⋊D₂₆₉	—	2	4	no	—
240	C₂²⋊D₂₆₉	—	2	4	no	—
241	C₂²⋊D₂₆₉	—	2	2	no	—
242	C₂²⋊D₂₆₉	—	2	4	no	—
243	C₂²⋊D₂₆₉	—	4	2	no	—
244	C₂²⋊D₂₆₉	—	4	2	no	—
245	C₂²⋊D₂₆₉	#41	1	4	yes	complemented
246	C₂×Dic₂₆₉	—	2	2	no	—
247	C₂×Dic₂₆₉	—	2	4	no	—
248	C₂×Dic₂₆₉	—	2	2	no	—
249	C₂×Dic₂₆₉	—	2	4	no	—
250	C₂×Dic₂₆₉	—	2	2	no	—
251	C₂×Dic₂₆₉	—	2	4	no	—
252	C₂×Dic₂₆₉	—	2	2	no	—
253	C₂×Dic₂₆₉	—	4	2	no	—
254	C₂×Dic₂₆₉	—	4	2	no	—
255	C₂×Dic₂₆₉	—	4	2	no	—
256	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
260	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
261	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
264	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
266	C₄×D₂₆₉	—	2	2	no	—
267	C₄×D₂₆₉	—	2	2	no	—
268	C₄×D₂₆₉	—	2	2	no	—
269	C₄×D₂₆₉	—	2	4	no	—
270	C₄×D₂₆₉	—	4	2	no	—
271	C₄×D₂₆₉	—	4	2	no	—
272	C₂³×C₂₆₉	—	2	4	no	—
273	C₂³×C₂₆₉	—	2	4	no	—
274	C₂³×C₂₆₉	—	4	2	no	—
275	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
276	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
277	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
278	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
279	Q₈×C₂₆₉	—	2	2	no	—
280	D₄×C₂₆₉	—	2	4	no	—
281	D₄×C₂₆₉	—	2	4	no	—
282	D₄×C₂₆₉	—	2	2	no	—
283	D₄×C₂₆₉	—	2	2	no	—
284	D₄×C₂₆₉	—	4	2	no	—
285	D₄×C₂₆₉	#41	1	4	yes	complemented
286	C₂×C₄×C₂₆₉	—	2	4	no	—
287	C₂×C₄×C₂₆₉	—	2	2	no	—
288	C₂×C₄×C₂₆₉	—	2	2	no	—
289	C₂×C₄×C₂₆₉	—	4	2	no	—
290	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
291	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
293	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
295	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₂₆₉	—	2	1	no	—
298	C₂²×C₂₆₉	—	2	2	no	—
299	C₂²×C₂₆₉	—	2	2	no	—
300	C₂²×C₂₆₉	—	2	1	no	—
301	C₂²×C₂₆₉	—	2	1	no	—
302	C₂²×C₂₆₉	—	2	2	no	—
303	C₂²×C₂₆₉	—	2	1	no	—
304	C₂²×C₂₆₉	—	2	2	no	—
305	C₂²×C₂₆₉	—	2	1	no	—
306	C₂²×C₂₆₉	—	2	2	no	—
307	C₂²×C₂₆₉	—	4	8	no	—
308	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
309	C₂²×C₂₆₉	C₂×#41	1	4	yes	—
310	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
311	C₂×D₂₆₉	—	2	1	no	—
312	C₂×D₂₆₉	—	2	1	no	—
313	C₂×D₂₆₉	—	2	2	no	—
314	C₂×D₂₆₉	—	2	2	no	—
315	C₂×D₂₆₉	—	2	2	no	—
316	C₂×D₂₆₉	—	4	8	no	—
317	C₂×D₂₆₉	C₂×#41	1	2	yes	—
318	C₄×C₂₆₉	—	2	1	no	—
319	C₄×C₂₆₉	—	2	1	no	—
320	C₄×C₂₆₉	—	2	2	no	—
321	C₄×C₂₆₉	—	2	1	no	—
322	C₄×C₂₆₉	—	2	1	no	—
323	C₄×C₂₆₉	—	2	2	no	—
324	C₄×C₂₆₉	C₂×#41	1	2	yes	—
325	Dic₂₆₉	—	2	1	no	—
326	Dic₂₆₉	—	2	1	no	—
327	Dic₂₆₉	—	2	2	no	—
328	Dic₂₆₉	—	2	1	no	—
329	Dic₂₆₉	—	2	2	no	—
330	Dic₂₆₉	—	2	1	no	—
331	Dic₂₆₉	—	2	2	no	—
332	Dic₂₆₉	—	2	1	no	—
333	Dic₂₆₉	C₂×#41	1	2	yes	—
334	Dic₂₆₉	H(5,𝔽₂)	1	2	yes	—
335	C₂×C₂₆₉	—	2	4	no	—
336	C₂×C₂₆₉	—	2	2	no	—
337	C₂×C₂₆₉	—	4	1	no	—
338	C₂×C₂₆₉	—	4	2	no	—
339	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
340	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
341	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	D₂₆₉	—	2	2	no	—
343	D₂₆₉	—	4	2	no	—
344	C₂₆₉	#3481	1	1	yes	characteristic, complemented, Sylow
345	#3481	—	269	1	no	maximal, Sylow
346	#559	—	269	1	no	—
347	#554	—	269	1	no	—
348	#554	—	269	1	no	—
349	#553	—	269	2	no	—
350	#553	—	269	1	no	—
351	#553	—	269	1	no	—
352	#551	—	269	2	no	—
353	#551	—	269	2	no	—
354	#546	—	269	1	no	—
355	#546	—	269	2	no	—
356	#546	D₂₆₉	1	1	yes	characteristic, complemented
357	D₄²	—	269	1	no	—
358	#532	—	269	1	no	—
359	#529	—	269	1	no	—
360	#529	—	269	2	no	—
361	#529	—	269	1	no	—
362	#525	—	269	2	no	—
363	#525	—	269	2	no	—
364	C₄×#41	—	269	1	no	—
365	C₄×#41	—	269	1	no	—
366	C₂×C₄×D₄	—	269	1	no	—
367	C₂×C₄×D₄	—	269	1	no	—
368	C₂×C₄×D₄	—	269	2	no	—
369	C₂×#41	—	269	1	no	—
370	C₂×#41	—	269	2	no	—
371	C₂×#41	C₂×D₂₆₉	1	1	yes	characteristic
372	C₂²×D₄	—	269	2	no	—
373	C₂²×D₄	—	269	1	no	—
374	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
375	C₂³×C₄	—	269	2	no	—
376	C₂³×C₄	—	269	2	no	—
377	C₄⋊Q₈	—	269	1	no	—
378	#127	—	269	1	no	—
379	#126	—	269	2	no	—
380	#126	—	269	2	no	—
381	#126	—	269	2	no	—
382	#126	—	269	2	no	—
383	#125	—	269	2	no	—
384	#125	—	269	1	no	—
385	#125	—	269	1	no	—
386	#124	—	269	1	no	—
387	#124	—	269	2	no	—
388	#124	—	269	2	no	—
389	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
390	#123	—	269	2	no	—
391	#123	—	269	2	no	—
392	#123	—	269	2	no	—
393	#123	—	269	2	no	—
394	#123	—	269	2	no	—
395	#123	—	269	2	no	—
396	#123	—	269	2	no	—
397	#123	C₂×D₂₆₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	269	1	no	—
399	C₂²⋊Q₈	—	269	2	no	—
400	C₂²⋊Q₈	—	269	2	no	—
401	C₂²⋊Q₈	—	269	2	no	—
402	C₂²⋊Q₈	—	269	2	no	—
403	C₂²⋊Q₈	—	269	2	no	—
404	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
405	#121	—	269	2	no	—
406	#121	—	269	2	no	—
407	#121	—	269	2	no	—
408	#121	—	269	1	no	—
409	#121	—	269	2	no	—
410	#121	—	269	2	no	—
411	#121	—	269	1	no	—
412	#121	—	269	1	no	—
413	#121	C₂×D₂₆₉	1	2	yes	complemented
414	#121	C₂×D₂₆₉	1	1	yes	characteristic, complemented
415	#120	—	269	2	no	—
416	#120	—	269	2	no	—
417	#120	—	269	2	no	—
418	#120	C₂×D₂₆₉	1	2	yes	complemented
419	C₄×Q₈	—	269	1	no	—
420	C₄×Q₈	—	269	1	no	—
421	C₄×Q₈	—	269	1	no	—
422	C₄×Q₈	—	269	1	no	—
423	C₄×D₄	—	269	1	no	—
424	C₄×D₄	—	269	2	no	—
425	C₄×D₄	—	269	1	no	—
426	C₄×D₄	—	269	1	no	—
427	C₄×D₄	—	269	2	no	—
428	C₄×D₄	—	269	1	no	—
429	C₄×D₄	—	269	2	no	—
430	C₄×D₄	—	269	1	no	—
431	C₄×D₄	—	269	1	no	—
432	C₄×D₄	—	269	2	no	—
433	C₄×D₄	—	269	2	no	—
434	C₄×D₄	—	269	1	no	—
435	C₄×D₄	—	269	1	no	—
436	C₄×D₄	—	269	1	no	—
437	C₄×D₄	—	269	1	no	—
438	C₄×D₄	—	269	2	no	—
439	C₄×D₄	—	269	2	no	—
440	C₄×D₄	—	269	2	no	—
441	C₄×D₄	—	269	2	no	—
442	C₄×D₄	—	269	2	no	—
443	C₄×D₄	—	269	2	no	—
444	C₄×D₄	—	269	2	no	—
445	C₄×D₄	—	269	2	no	—
446	C₄×D₄	—	269	1	no	—
447	C₄×D₄	—	269	1	no	—
448	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
449	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
450	#117	—	269	2	no	—
451	#117	—	269	1	no	—
452	#117	—	269	1	no	—
453	#117	—	269	2	no	—
454	#117	—	269	1	no	—
455	#117	—	269	1	no	—
456	#117	—	269	2	no	—
457	C₂×C₄⋊C₄	—	269	2	no	—
458	C₂×C₄⋊C₄	—	269	1	no	—
459	C₂×C₄⋊C₄	—	269	1	no	—
460	C₂×C₂²⋊C₄	—	269	2	no	—
461	C₂×C₂²⋊C₄	—	269	2	no	—
462	C₂×C₂²⋊C₄	—	269	2	no	—
463	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
464	C₂×C₄²	—	269	1	no	—
465	C₂×C₄²	—	269	2	no	—
466	C₂×C₄²	—	269	1	no	—
467	C₂×C₄²	—	269	1	no	—
468	C₂⁴	—	269	2	no	—
469	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
470	#41	—	2	4	no	—
471	#41	—	538	4	no	—
472	#41	—	1076	4	no	—
473	C₂×Q₈	—	269	1	no	—
474	C₂×Q₈	—	269	2	no	—
475	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	269	1	no	—
478	C₂×D₄	—	269	1	no	—
479	C₂×D₄	—	269	2	no	—
480	C₂×D₄	—	269	2	no	—
481	C₂×D₄	—	269	2	no	—
482	C₂×D₄	—	269	2	no	—
483	C₂×D₄	—	269	2	no	—
484	C₂×D₄	—	269	2	no	—
485	C₂×D₄	—	269	1	no	—
486	C₂×D₄	—	538	8	no	—
487	C₂×D₄	—	538	4	no	—
488	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
489	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
490	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
492	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
493	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
494	C₂²×C₄	—	269	1	no	—
495	C₂²×C₄	—	269	2	no	—
496	C₂²×C₄	—	269	1	no	—
497	C₂²×C₄	—	269	1	no	—
498	C₂²×C₄	—	269	2	no	—
499	C₂²×C₄	—	269	1	no	—
500	C₂²×C₄	—	269	2	no	—
501	C₂²×C₄	—	269	2	no	—
502	C₂²×C₄	—	269	2	no	—
503	C₂²×C₄	—	269	2	no	—
504	C₂²×C₄	—	269	1	no	—
505	C₂²×C₄	—	269	1	no	—
506	C₂²×C₄	—	269	1	no	—
507	C₂²×C₄	—	269	2	no	—
508	C₂²×C₄	—	269	2	no	—
509	C₂²×C₄	—	269	2	no	—
510	C₂²×C₄	—	1076	4	no	—
511	C₂²×C₄	—	1076	4	no	—
512	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
513	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
516	C₄⋊C₄	—	269	1	no	—
517	C₄⋊C₄	—	269	1	no	—
518	C₄⋊C₄	—	269	2	no	—
519	C₄⋊C₄	—	269	1	no	—
520	C₄⋊C₄	—	269	2	no	—
521	C₄⋊C₄	—	269	2	no	—
522	C₄⋊C₄	—	269	2	no	—
523	C₄⋊C₄	—	269	2	no	—
524	C₄⋊C₄	—	269	1	no	—
525	C₄⋊C₄	—	269	1	no	—
526	C₄⋊C₄	—	269	1	no	—
527	C₄⋊C₄	—	269	2	no	—
528	C₄⋊C₄	—	269	1	no	—
529	C₄⋊C₄	—	269	1	no	—
530	C₄⋊C₄	—	269	2	no	—
531	C₄⋊C₄	—	269	2	no	—
532	C₄⋊C₄	—	269	2	no	—
533	C₄⋊C₄	—	269	2	no	—
534	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
537	C₂²⋊C₄	—	269	2	no	—
538	C₂²⋊C₄	—	269	2	no	—
539	C₂²⋊C₄	—	269	2	no	—
540	C₂²⋊C₄	—	269	2	no	—
541	C₂²⋊C₄	—	269	1	no	—
542	C₂²⋊C₄	—	269	2	no	—
543	C₂²⋊C₄	—	269	2	no	—
544	C₂²⋊C₄	—	269	1	no	—
545	C₂²⋊C₄	—	269	2	no	—
546	C₂²⋊C₄	—	269	1	no	—
547	C₂²⋊C₄	—	269	2	no	—
548	C₂²⋊C₄	—	269	2	no	—
549	C₂²⋊C₄	—	269	2	no	—
550	C₂²⋊C₄	—	269	2	no	—
551	C₂²⋊C₄	—	269	2	no	—
552	C₂²⋊C₄	—	269	1	no	—
553	C₂²⋊C₄	—	269	2	no	—
554	C₂²⋊C₄	—	269	2	no	—
555	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
562	C₄²	—	269	1	no	—
563	C₄²	—	269	1	no	—
564	C₄²	—	269	1	no	—
565	C₄²	—	269	1	no	—
566	C₄²	—	269	2	no	—
567	C₄²	—	269	1	no	—
568	C₄²	—	269	1	no	—
569	C₄²	—	269	1	no	—
570	C₄²	—	269	2	no	—
571	C₄²	—	269	2	no	—
572	C₄²	—	269	1	no	—
573	C₄²	—	269	1	no	—
574	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	269	1	no	—
579	C₂³	—	269	2	no	—
580	C₂³	—	538	4	no	—
581	C₂³	—	538	4	no	—
582	C₂³	—	1076	2	no	—
583	C₂³	C₂³×D₂₆₉	1	2	yes	—
584	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
585	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
586	C₂³	C₂³×D₂₆₉	1	2	yes	—
587	Q₈	—	2	2	no	—
588	Q₈	—	538	2	no	—
589	Q₈	—	1076	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	269	4	no	—
596	D₄	—	538	4	no	—
597	D₄	—	538	4	no	—
598	D₄	—	538	2	no	—
599	D₄	—	538	4	no	—
600	D₄	—	538	4	no	—
601	D₄	—	538	2	no	—
602	D₄	—	1076	2	no	—
603	D₄	—	1076	2	no	—
604	D₄	#16864401	1	4	yes	complemented
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	269	1	no	—
610	C₂×C₄	—	269	1	no	—
611	C₂×C₄	—	269	1	no	—
612	C₂×C₄	—	269	1	no	—
613	C₂×C₄	—	269	2	no	—
614	C₂×C₄	—	269	1	no	—
615	C₂×C₄	—	269	2	no	—
616	C₂×C₄	—	269	1	no	—
617	C₂×C₄	—	269	1	no	—
618	C₂×C₄	—	269	2	no	—
619	C₂×C₄	—	538	2	no	—
620	C₂×C₄	—	538	4	no	—
621	C₂×C₄	—	538	2	no	—
622	C₂×C₄	—	538	4	no	—
623	C₂×C₄	—	538	2	no	—
624	C₂×C₄	—	538	4	no	—
625	C₂×C₄	—	538	4	no	—
626	C₂×C₄	—	538	2	no	—
627	C₂×C₄	—	538	2	no	—
628	C₂×C₄	—	538	2	no	—
629	C₂×C₄	—	538	2	no	—
630	C₂×C₄	—	1076	2	no	—
631	C₂×C₄	—	1076	2	no	—
632	C₂×C₄	—	1076	2	no	—
633	C₂×C₄	—	1076	2	no	—
634	C₂×C₄	—	1076	2	no	—
635	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
637	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
641	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	4	8	no	—
653	C₂²	—	269	2	no	—
654	C₂²	—	538	1	no	—
655	C₂²	—	538	1	no	—
656	C₂²	—	538	2	no	—
657	C₂²	—	538	2	no	—
658	C₂²	—	538	2	no	—
659	C₂²	—	1076	8	no	—
660	C₂²	#41×D₂₆₉	1	2	yes	—
661	C₂²	C₂×#16864401	1	4	yes	—
662	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	269	2	no	—
670	C₄	—	269	2	no	—
671	C₄	—	538	1	no	—
672	C₄	—	538	2	no	—
673	C₄	—	538	1	no	—
674	C₄	—	538	1	no	—
675	C₄	—	538	2	no	—
676	C₄	—	538	1	no	—
677	C₄	—	538	2	no	—
678	C₄	—	538	1	no	—
679	C₄	C₂×#16864401	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	538	2	no	—
685	C₂	—	1076	2	no	—
686	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
687	C₂	C₂²×#16864401	1	1	yes	characteristic
688	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#546×C₂₆₉	C₂
hypercenter	#546	D₂₆₉
hypocenter	C₂₆₉	#3481
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #31771337	C₂	semidirect
2. #31771314	C₂	semidirect
3. #31771313	C₂	semidirect
4. #31771302	C₂	semidirect
5. #31771301	C₂	semidirect
6. #31771298	C₂	semidirect
7. #31771281	C₂	semidirect
8. #31771278	C₂	semidirect
9. #31771243	C₂	semidirect
10. #31771242	C₂	semidirect
11. D₄×C₂²⋊D₂₆₉	C₂	semidirect
12. #31771150	C₂	semidirect
13. #31771141	C₂	semidirect
14. #31771134	C₂	semidirect
15. #31771132	C₂	semidirect
16. #31771115	C₂	semidirect
17. #31771111	C₂	semidirect
18. #41×Dic₂₆₉	C₂	semidirect
19. C₄×#16864401	C₂	semidirect
20. C₂×D₄×Dic₂₆₉	C₂	semidirect
21. C₂×#22575413	C₂	semidirect
22. C₄×D₄×D₂₆₉	C₂	semidirect
23. #546×C₂₆₉	C₂	semidirect
25. C₂×#16864401	C₂²	semidirect
28. C₂³×Dic₂₆₉	C₂²	semidirect
29. C₂²×C₄×D₂₆₉	C₂²	semidirect
30. #22575452	C₂²	semidirect
32. #22575448	C₂²	semidirect
33. #22575448	C₂²	semidirect
34. #22575446	C₂²	semidirect
35. #22575446	C₂²	semidirect
36. #22575445	C₂²	semidirect
37. #22575444	C₂²	semidirect
38. #22575443	C₂²	semidirect
39. #22575442	C₂²	semidirect
40. #22575439	C₂²	semidirect
41. #22575439	C₂²	semidirect
42. #22575437	C₂²	semidirect
43. #22575437	C₂²	semidirect
44. #22575436	C₂²	semidirect
45. #22575435	C₂²	semidirect
46. #22575435	C₂²	semidirect
47. #22575435	C₂²	semidirect
48. #22575434	C₂²	semidirect
49. #22575433	C₂²	semidirect
50. #22575432	C₂²	semidirect
51. #22575430	C₂²	semidirect
52. #22575430	C₂²	semidirect
53. #22575430	C₂²	semidirect
54. #22575429	C₂²	semidirect
56. #22575427	C₂²	semidirect
58. #22575425	C₂²	semidirect
59. #22575425	C₂²	semidirect
60. #22575425	C₂²	semidirect
62. #22575424	C₂²	semidirect
65. #22575421	C₂²	semidirect
66. Q₈×Dic₂₆₉	C₂²	semidirect
67. Q₈×Dic₂₆₉	C₂²	semidirect
68. C₄×Dic₅₃₈	C₂²	semidirect
69. #22575418	C₂²	semidirect
70. C₄×D₁₀₇₆	C₂²	semidirect
74. D₄×Dic₂₆₉	C₂²	semidirect
75. D₄×Dic₂₆₉	C₂²	semidirect
76. D₄×Dic₂₆₉	C₂²	semidirect
77. D₄×Dic₂₆₉	C₂²	semidirect
78. D₄×Dic₂₆₉	C₂²	semidirect
79. D₄×Dic₂₆₉	C₂²	semidirect
80. D₄×Dic₂₆₉	C₂²	semidirect
81. #22575415	C₂²	semidirect
83. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
84. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
87. #22575413	C₂²	semidirect
88. #22575413	C₂²	semidirect
89. #22575413	C₂²	semidirect
90. #22575413	C₂²	semidirect
91. #22575413	C₂²	semidirect
92. #22575413	C₂²	semidirect
93. #22575413	C₂²	semidirect
94. #22575413	C₂²	semidirect
95. #22575412	C₂²	semidirect
96. #22575412	C₂²	semidirect
97. #22575411	C₂²	semidirect
98. #22575411	C₂²	semidirect
99. #22575409	C₂²	semidirect
100. #22575409	C₂²	semidirect
101. #22575409	C₂²	semidirect
102. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
103. C₂×#16864381	C₂²	semidirect
104. C₄⋊C₄×D₂₆₉	C₂²	semidirect
105. C₂×C₂²⋊Dic₂₆₉	C₂²	semidirect
106. C₂×#16864379	C₂²	semidirect
107. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
108. C₂×C₄×Dic₂₆₉	C₂²	semidirect
109. C₂×C₄×Dic₂₆₉	C₂²	semidirect
110. C₂×C₄×Dic₂₆₉	C₂²	semidirect
111. C₄²×D₂₆₉	C₂²	semidirect
114. #124×C₂₆₉	C₂²	semidirect
115. #123×C₂₆₉	C₂²	semidirect
116. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
117. #121×C₂₆₉	C₂²	semidirect
118. #121×C₂₆₉	C₂²	semidirect
119. #120×C₂₆₉	C₂²	semidirect
121. C₄×D₄×C₂₆₉	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
245. C₂²⋊D₂₆₉	#41	semidirect
285. D₄×C₂₆₉	#41	semidirect
344. C₂₆₉	#3481	semidirect
356. #546	D₂₆₉	semidirect
389. #124	C₂×D₂₆₉	semidirect
397. #123	C₂×D₂₆₉	semidirect
404. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
413. #121	C₂×D₂₆₉	semidirect
414. #121	C₂×D₂₆₉	semidirect
418. #120	C₂×D₂₆₉	semidirect
449. C₄×D₄	C₂×D₂₆₉	semidirect
463. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
604. D₄	#16864401	semidirect

Maximal subgroups

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

subgroup	index
#31771337	2
#31771314	2
#31771313	2
#31771302	2
#31771301	2
#31771298	2
#31771281	2
#31771278	2
#31771243	2
#31771242	2
D₄×C₂²⋊D₂₆₉	2
#31771150	2
#31771141	2
#31771134	2
#31771132	2
#31771115	2
#31771111	2
#41×Dic₂₆₉	2
C₄×#16864401	2
C₂×D₄×Dic₂₆₉	2
C₂×#22575413	2
C₄×D₄×D₂₆₉	2
#546×C₂₆₉	2
#3481	269