Subgroups — #46825041

Order 34432.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771347	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771346	C₂	1	2	yes	maximal, complemented
3	#31771345	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771279	C₂	1	2	yes	maximal, complemented
5	#31771247	C₂	1	2	yes	maximal, complemented
6	#31771246	C₂	1	2	yes	maximal, complemented
7	#31771245	C₂	1	2	yes	maximal, complemented
8	D₄×D₁₀₇₆	C₂	1	2	yes	maximal, complemented
9	#31771237	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771195	C₂	1	2	yes	maximal, complemented
11	#31771194	C₂	1	2	yes	maximal, complemented
12	#31771188	C₂	1	2	yes	maximal, complemented
13	#31771174	C₂	1	2	yes	maximal, complemented
14	#31771173	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771166	C₂	1	2	yes	maximal, complemented
16	#31771166	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#22575423	C₂	1	2	yes	maximal, complemented
18	#120×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#551×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
22	C₂×#16864402	C₂²	1	2	yes	complemented
23	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
24	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
25	C₂²×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
27	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
29	C₂×D₄×D₂₆₉	C₂²	1	2	yes	complemented
30	#22575450	C₂²	1	1	yes	characteristic, complemented
31	#22575450	C₂²	1	2	yes	complemented
32	#22575449	C₂²	1	1	yes	characteristic, complemented
33	#22575448	C₂²	1	2	yes	complemented
34	#22575448	C₂²	1	2	yes	complemented
35	#22575447	C₂²	1	2	yes	complemented
36	#22575442	C₂²	1	1	yes	characteristic, complemented
37	#22575442	C₂²	1	2	yes	complemented
38	#22575441	C₂²	1	2	yes	complemented
39	#22575441	C₂²	1	2	yes	complemented
40	#22575439	C₂²	1	2	yes	complemented
41	#22575439	C₂²	1	2	yes	complemented
42	#22575438	C₂²	1	2	yes	complemented
43	#22575438	C₂²	1	2	yes	complemented
44	#22575438	C₂²	1	2	yes	complemented
45	#22575438	C₂²	1	2	yes	complemented
46	#22575438	C₂²	1	2	yes	complemented
47	#22575436	C₂²	1	2	yes	complemented
48	#22575436	C₂²	1	1	yes	characteristic, complemented
49	#22575435	C₂²	1	2	yes	complemented
50	#22575431	C₂²	1	2	yes	complemented
51	#22575430	C₂²	1	2	yes	complemented
52	#22575428	C₂²	1	2	yes	complemented
53	#22575428	C₂²	1	2	yes	complemented
54	#22575428	C₂²	1	2	yes	complemented
55	#22575428	C₂²	1	2	yes	complemented
56	#22575428	C₂²	1	2	yes	complemented
57	#22575428	C₂²	1	2	yes	complemented
58	#22575428	C₂²	1	2	yes	complemented
59	#22575427	C₂²	1	2	yes	complemented
60	#22575427	C₂²	1	2	yes	complemented
61	#22575426	C₂²	1	2	yes	complemented
62	#22575426	C₂²	1	2	yes	complemented
63	#22575426	C₂²	1	2	yes	complemented
64	#22575426	C₂²	1	2	yes	complemented
65	#22575426	C₂²	1	2	yes	complemented
66	#22575425	C₂²	1	2	yes	complemented
67	#22575423	C₂²	1	2	yes	—
68	#22575423	C₂²	1	2	yes	complemented
69	#22575423	C₂²	1	2	yes	complemented
70	#22575423	C₂²	1	2	yes	complemented
71	#22575423	C₂²	1	2	yes	complemented
72	#22575423	C₂²	1	2	yes	complemented
73	#22575423	C₂²	1	2	yes	complemented
74	#22575423	C₂²	1	1	yes	characteristic, complemented
75	#22575423	C₂²	1	2	yes	complemented
76	#22575423	C₂²	1	2	yes	complemented
77	#22575423	C₂²	1	2	yes	complemented
78	#22575423	C₂²	1	2	yes	complemented
79	#22575423	C₂²	1	2	yes	complemented
80	#22575423	C₂²	1	1	yes	characteristic, complemented
81	#22575423	C₂²	1	2	yes	complemented
82	#22575422	C₂²	1	1	yes	characteristic, complemented
83	#22575421	C₂²	1	2	yes	complemented
84	#22575421	C₂²	1	1	yes	characteristic, complemented
85	#22575421	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
87	#22575415	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
89	#22575413	C₂²	1	2	yes	complemented
90	#22575413	C₂²	1	2	yes	complemented
91	#22575410	C₂²	1	1	yes	characteristic, complemented
92	C₂×#16864379	C₂²	1	2	yes	complemented
93	C₂×#16864379	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
98	#126×C₂₆₉	C₂²	1	2	yes	complemented
99	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
100	#123×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
101	#123×C₂₆₉	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	complemented
103	#120×C₂₆₉	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
105	#117×C₂₆₉	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
107	C₂³×D₂₆₉	—	4	4	no	—
108	C₂³×D₂₆₉	—	4	2	no	—
109	C₂³×D₂₆₉	C₂³	1	2	yes	—
110	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
111	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
112	C₂³×D₂₆₉	C₂³	1	2	yes	—
113	C₂³×D₂₆₉	C₂³	1	2	yes	—
114	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
115	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic, complemented
116	#16864403	—	4	2	no	—
117	#16864402	—	4	4	no	—
118	C₂×Dic₅₃₈	C₂³	1	2	yes	complemented
119	C₂×D₁₀₇₆	—	4	4	no	—
120	C₂×D₁₀₇₆	—	4	4	no	—
121	C₂×D₁₀₇₆	—	4	2	no	—
122	C₂×D₁₀₇₆	C₂³	1	2	yes	—
123	C₂×D₁₀₇₆	C₂³	1	2	yes	—
124	C₂×D₁₀₇₆	C₂³	1	2	yes	—
125	C₂×D₁₀₇₆	C₂³	1	2	yes	—
126	C₂×D₁₀₇₆	C₂³	1	2	yes	—
127	C₂×D₁₀₇₆	C₂³	1	2	yes	—
128	C₂×D₁₀₇₆	C₂³	1	2	yes	—
129	C₂×D₁₀₇₆	C₂³	1	2	yes	—
130	C₂×D₁₀₇₆	C₂³	1	2	yes	—
131	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
132	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
133	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic, complemented
134	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
135	C₂×D₁₀₇₆	C₂³	1	2	yes	complemented
136	C₂×C₂²⋊D₂₆₉	—	4	4	no	—
137	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	complemented
146	D₄×D₂₆₉	—	4	4	no	—
147	D₄×D₂₆₉	—	4	4	no	—
148	D₄×D₂₆₉	—	4	2	no	—
149	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
150	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
152	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
153	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
154	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
155	C₂×C₄×D₂₆₉	C₂³	1	2	yes	complemented
156	C₄⋊Dic₂₆₉	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	#16864381	C₂³	1	2	yes	complemented
161	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
162	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
163	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic, complemented
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	—
174	#16864379	C₂³	1	2	yes	—
175	#16864379	C₂³	1	2	yes	complemented
176	#16864379	C₂³	1	2	yes	complemented
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	#16864379	C₂³	1	2	yes	complemented
182	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic, 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	1	yes	characteristic
188	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
189	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
190	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
191	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
192	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
193	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
194	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
195	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic, complemented
202	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	complemented
203	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic, complemented
204	C₄²×C₂₆₉	C₂³	1	2	yes	complemented
205	C₂²×D₂₆₉	—	2	4	no	—
206	C₂²×D₂₆₉	—	2	4	no	—
207	C₂²×D₂₆₉	—	2	4	no	—
208	C₂²×D₂₆₉	—	2	2	no	—
209	C₂²×D₂₆₉	—	2	4	no	—
210	C₂²×D₂₆₉	—	2	2	no	—
211	C₂²×D₂₆₉	—	4	2	no	—
212	C₂²×D₂₆₉	—	4	2	no	—
213	C₂²×D₂₆₉	—	4	2	no	—
214	C₂²×D₂₆₉	—	4	2	no	—
215	C₂²×D₂₆₉	—	4	2	no	—
216	C₂²×D₂₆₉	—	4	1	no	—
217	C₂²×D₂₆₉	—	4	2	no	—
218	C₂²×D₂₆₉	—	4	2	no	—
219	C₂²×D₂₆₉	—	4	2	no	—
220	C₂²×D₂₆₉	—	4	2	no	—
221	C₂²×D₂₆₉	—	4	1	no	—
222	C₂²×D₂₆₉	—	4	16	no	—
223	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
224	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
225	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
226	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
227	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
228	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
229	Dic₅₃₈	—	4	2	no	—
230	D₁₀₇₆	—	2	4	no	—
231	D₁₀₇₆	—	2	4	no	—
232	D₁₀₇₆	—	4	2	no	—
233	D₁₀₇₆	—	4	1	no	—
234	D₁₀₇₆	—	4	2	no	—
235	D₁₀₇₆	—	4	2	no	—
236	D₁₀₇₆	—	4	2	no	—
237	D₁₀₇₆	—	4	2	no	—
238	D₁₀₇₆	—	4	2	no	—
239	D₁₀₇₆	—	4	2	no	—
240	D₁₀₇₆	—	4	2	no	—
241	D₁₀₇₆	—	4	2	no	—
242	D₁₀₇₆	—	4	2	no	—
243	D₁₀₇₆	—	4	1	no	—
244	C₂²⋊D₂₆₉	—	2	4	no	—
245	C₂²⋊D₂₆₉	—	2	4	no	—
246	C₂²⋊D₂₆₉	—	2	4	no	—
247	C₂²⋊D₂₆₉	—	4	1	no	—
248	C₂²⋊D₂₆₉	—	4	1	no	—
249	C₂²⋊D₂₆₉	—	4	2	no	—
250	C₂²⋊D₂₆₉	—	4	2	no	—
251	C₂²⋊D₂₆₉	—	4	2	no	—
252	C₂²⋊D₂₆₉	—	4	2	no	—
253	C₂×Dic₂₆₉	—	4	2	no	—
254	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
255	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
256	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
257	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
258	C₄×D₂₆₉	—	2	2	no	—
259	C₄×D₂₆₉	—	4	2	no	—
260	C₄×D₂₆₉	—	4	2	no	—
261	C₄×D₂₆₉	—	4	2	no	—
262	C₄×D₂₆₉	—	4	2	no	—
263	C₄×D₂₆₉	—	4	2	no	—
264	C₂³×C₂₆₉	—	2	4	no	—
265	C₂³×C₂₆₉	—	4	1	no	—
266	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
267	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
268	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
269	Q₈×C₂₆₉	—	4	1	no	—
270	D₄×C₂₆₉	—	2	4	no	—
271	D₄×C₂₆₉	—	4	1	no	—
272	C₂×C₄×C₂₆₉	—	2	4	no	—
273	C₂×C₄×C₂₆₉	—	4	2	no	—
274	C₂×C₄×C₂₆₉	—	4	1	no	—
275	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
276	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
277	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
278	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
280	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
281	C₂²×C₂₆₉	—	2	2	no	—
282	C₂²×C₂₆₉	—	2	2	no	—
283	C₂²×C₂₆₉	—	2	1	no	—
284	C₂²×C₂₆₉	—	2	2	no	—
285	C₂²×C₂₆₉	—	2	1	no	—
286	C₂²×C₂₆₉	—	2	2	no	—
287	C₂²×C₂₆₉	—	4	4	no	—
288	C₂²×C₂₆₉	H(5,𝔽₂)	1	4	yes	—
289	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
290	C₂×D₂₆₉	—	2	2	no	—
291	C₂×D₂₆₉	—	2	2	no	—
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	1	no	—
297	C₂×D₂₆₉	—	2	2	no	—
298	C₂×D₂₆₉	—	2	1	no	—
299	C₂×D₂₆₉	—	2	2	no	—
300	C₂×D₂₆₉	—	2	2	no	—
301	C₂×D₂₆₉	—	2	2	no	—
302	C₂×D₂₆₉	—	2	2	no	—
303	C₂×D₂₆₉	—	2	2	no	—
304	C₂×D₂₆₉	—	4	8	no	—
305	C₂×D₂₆₉	—	4	4	no	—
306	C₂×D₂₆₉	—	4	8	no	—
307	C₂×D₂₆₉	—	4	4	no	—
308	C₂×D₂₆₉	—	8	2	no	—
309	C₂×D₂₆₉	—	8	4	no	—
310	C₂×D₂₆₉	—	8	2	no	—
311	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	—
312	C₄×C₂₆₉	—	2	2	no	—
313	C₄×C₂₆₉	—	2	2	no	—
314	C₄×C₂₆₉	—	2	2	no	—
315	C₄×C₂₆₉	—	2	2	no	—
316	C₄×C₂₆₉	—	2	2	no	—
317	C₄×C₂₆₉	—	2	1	no	—
318	Dic₂₆₉	—	2	1	no	—
319	Dic₂₆₉	—	2	2	no	—
320	Dic₂₆₉	—	2	2	no	—
321	Dic₂₆₉	—	2	2	no	—
322	C₂×C₂₆₉	—	2	4	no	—
323	C₂×C₂₆₉	—	4	1	no	—
324	C₂×C₂₆₉	—	4	1	no	—
325	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	2	yes	—
327	D₂₆₉	—	2	2	no	—
328	D₂₆₉	—	4	2	no	—
329	D₂₆₉	—	4	1	no	—
330	D₂₆₉	—	4	2	no	—
331	D₂₆₉	—	4	1	no	—
332	D₂₆₉	—	4	2	no	—
333	C₂₆₉	#3532	1	1	yes	characteristic, complemented, Sylow
334	#3532	—	269	1	no	maximal, Sylow
335	H(3,𝔽₄)	—	269	1	no	—
336	#560	—	269	2	no	—
337	#560	—	269	1	no	—
338	#551	—	269	2	no	—
339	#551	D₂₆₉	1	1	yes	characteristic, complemented
340	#546	—	269	2	no	—
341	#546	—	269	2	no	—
342	#546	—	269	2	no	—
343	D₄²	—	269	1	no	—
344	D₄²	—	269	2	no	—
345	#538	—	269	2	no	—
346	#538	—	269	2	no	—
347	#538	—	269	2	no	—
348	#535	—	269	1	no	—
349	#535	—	269	2	no	—
350	#534	—	269	2	no	—
351	#534	—	269	1	no	—
352	C₂×#120	—	269	1	no	—
353	C₂×#120	—	269	2	no	—
354	C₂⁵	—	269	1	no	—
355	C₂×#41	—	269	1	no	—
356	C₂×#41	—	269	2	no	—
357	C₂²×D₄	—	269	2	no	—
358	C₂²×D₄	—	269	1	no	—
359	C₂²×D₄	—	269	2	no	—
360	C₂²×D₄	—	269	2	no	—
361	C₂²×D₄	—	269	2	no	—
362	C₂²×D₄	—	269	2	no	—
363	C₂²×D₄	—	269	1	no	—
364	#127	—	269	1	no	—
365	#127	—	269	1	no	—
366	#127	—	269	2	no	—
367	#126	—	269	2	no	—
368	#126	—	269	2	no	—
369	#126	—	269	2	no	—
370	#126	C₂×D₂₆₉	1	2	yes	complemented
371	#124	—	269	1	no	—
372	#124	—	269	2	no	—
373	#124	—	269	2	no	—
374	#124	—	269	2	no	—
375	#124	—	269	2	no	—
376	#124	—	269	2	no	—
377	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
378	#123	—	269	2	no	—
379	#123	—	269	1	no	—
380	#123	—	269	2	no	—
381	#123	—	269	2	no	—
382	#123	—	269	2	no	—
383	#123	—	269	2	no	—
384	#123	—	269	2	no	—
385	#123	—	269	2	no	—
386	#123	C₂×D₂₆₉	1	1	yes	characteristic, complemented
387	#123	C₂×D₂₆₉	1	2	yes	complemented
388	C₂²⋊Q₈	—	269	2	no	—
389	C₂²⋊Q₈	—	269	2	no	—
390	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	complemented
391	#121	—	269	2	no	—
392	#121	—	269	2	no	—
393	#121	—	269	2	no	—
394	#121	—	269	2	no	—
395	#121	—	269	2	no	—
396	#121	—	269	2	no	—
397	#121	—	269	2	no	—
398	#121	—	269	2	no	—
399	#121	—	269	2	no	—
400	#121	—	269	2	no	—
401	#121	—	269	2	no	—
402	#121	—	269	2	no	—
403	#121	—	269	2	no	—
404	#121	—	269	2	no	—
405	#121	—	269	2	no	—
406	#120	—	269	1	no	—
407	#120	—	269	2	no	—
408	#120	—	269	1	no	—
409	#120	—	269	1	no	—
410	#120	—	269	2	no	—
411	#120	—	269	2	no	—
412	#120	—	269	2	no	—
413	#120	—	269	2	no	—
414	#120	—	269	2	no	—
415	#120	—	269	2	no	—
416	#120	—	269	2	no	—
417	#120	—	269	2	no	—
418	#120	—	269	1	no	—
419	#120	—	269	2	no	—
420	#120	—	269	2	no	—
421	#120	—	269	2	no	—
422	#120	—	269	1	no	—
423	#120	—	269	2	no	—
424	#120	—	269	2	no	—
425	#120	C₂×D₂₆₉	1	1	yes	characteristic
426	C₄×D₄	—	269	2	no	—
427	C₄×D₄	—	269	2	no	—
428	C₄×D₄	—	269	2	no	—
429	C₄×D₄	—	269	2	no	—
430	C₄×D₄	—	269	2	no	—
431	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
432	#117	—	269	1	no	—
433	#117	C₂×D₂₆₉	1	2	yes	complemented
434	C₂×C₂²⋊C₄	—	269	2	no	—
435	C₂×C₂²⋊C₄	—	269	2	no	—
436	C₂×C₂²⋊C₄	—	269	1	no	—
437	C₂×C₂²⋊C₄	—	269	2	no	—
438	C₂×C₂²⋊C₄	—	269	2	no	—
439	C₂×C₂²⋊C₄	—	269	1	no	—
440	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
441	C₂⁴	—	269	2	no	—
442	C₂⁴	—	269	1	no	—
443	C₂⁴	—	269	2	no	—
444	C₂⁴	—	269	1	no	—
445	C₂⁴	—	269	2	no	—
446	C₂⁴	—	269	1	no	—
447	C₂⁴	—	269	1	no	—
448	C₂⁴	—	1076	4	no	—
449	C₂⁴	—	1076	2	no	—
450	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
451	#41	—	1076	4	no	—
452	#41	—	1076	2	no	—
453	C₂×Q₈	—	269	2	no	—
454	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
455	C₂×D₄	—	269	2	no	—
456	C₂×D₄	—	269	2	no	—
457	C₂×D₄	—	269	2	no	—
458	C₂×D₄	—	269	1	no	—
459	C₂×D₄	—	269	2	no	—
460	C₂×D₄	—	269	2	no	—
461	C₂×D₄	—	269	1	no	—
462	C₂×D₄	—	269	2	no	—
463	C₂×D₄	—	269	2	no	—
464	C₂×D₄	—	269	2	no	—
465	C₂×D₄	—	269	2	no	—
466	C₂×D₄	—	269	2	no	—
467	C₂×D₄	—	269	2	no	—
468	C₂×D₄	—	269	2	no	—
469	C₂×D₄	—	269	2	no	—
470	C₂×D₄	—	269	2	no	—
471	C₂×D₄	—	269	2	no	—
472	C₂×D₄	—	269	1	no	—
473	C₂×D₄	—	269	2	no	—
474	C₂×D₄	—	269	1	no	—
475	C₂×D₄	—	269	2	no	—
476	C₂×D₄	—	269	2	no	—
477	C₂×D₄	—	269	2	no	—
478	C₂×D₄	—	1076	4	no	—
479	C₂×D₄	—	1076	4	no	—
480	C₂×D₄	—	1076	2	no	—
481	C₂×D₄	—	1076	2	no	—
482	C₂×D₄	—	1076	4	no	—
483	C₂×D₄	—	1076	4	no	—
484	C₂×D₄	—	1076	4	no	—
485	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
486	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
487	C₂²×C₄	—	269	2	no	—
488	C₂²×C₄	—	269	1	no	—
489	C₂²×C₄	—	269	2	no	—
490	C₂²×C₄	—	269	2	no	—
491	C₂²×C₄	—	269	2	no	—
492	C₂²×C₄	—	269	2	no	—
493	C₂²×C₄	—	269	2	no	—
494	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
495	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
496	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
497	C₄⋊C₄	—	269	2	no	—
498	C₄⋊C₄	—	269	2	no	—
499	C₄⋊C₄	—	269	2	no	—
500	C₄⋊C₄	—	269	2	no	—
501	C₄⋊C₄	—	269	2	no	—
502	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
503	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
504	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
505	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
506	C₂²⋊C₄	—	269	2	no	—
507	C₂²⋊C₄	—	269	1	no	—
508	C₂²⋊C₄	—	269	1	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	—	269	2	no	—
526	C₂²⋊C₄	—	269	2	no	—
527	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
534	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	complemented
535	C₄²	—	269	1	no	—
536	C₄²	—	269	2	no	—
537	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic, complemented
538	C₄²	C₂²×D₂₆₉	1	2	yes	complemented
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	269	1	no	—
542	C₂³	—	269	2	no	—
543	C₂³	—	269	1	no	—
544	C₂³	—	269	2	no	—
545	C₂³	—	269	2	no	—
546	C₂³	—	269	1	no	—
547	C₂³	—	538	4	no	—
548	C₂³	—	538	2	no	—
549	C₂³	—	538	2	no	—
550	C₂³	—	538	4	no	—
551	C₂³	—	538	4	no	—
552	C₂³	—	538	4	no	—
553	C₂³	—	1076	2	no	—
554	C₂³	—	1076	2	no	—
555	C₂³	—	1076	2	no	—
556	C₂³	—	1076	1	no	—
557	C₂³	—	1076	2	no	—
558	C₂³	—	1076	2	no	—
559	C₂³	—	1076	2	no	—
560	C₂³	—	1076	2	no	—
561	C₂³	—	1076	1	no	—
562	C₂³	—	1076	2	no	—
563	C₂³	—	1076	2	no	—
564	C₂³	—	1076	16	no	—
565	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
566	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
567	C₂³	C₂³×D₂₆₉	1	2	yes	—
568	Q₈	—	4	1	no	—
569	Q₈	—	1076	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	4	1	no	—
572	D₄	—	538	4	no	—
573	D₄	—	538	4	no	—
574	D₄	—	538	4	no	—
575	D₄	—	538	4	no	—
576	D₄	—	538	4	no	—
577	D₄	—	1076	2	no	—
578	D₄	—	1076	2	no	—
579	D₄	—	1076	2	no	—
580	D₄	—	1076	1	no	—
581	D₄	—	1076	2	no	—
582	D₄	—	1076	2	no	—
583	D₄	—	1076	2	no	—
584	D₄	—	1076	2	no	—
585	D₄	—	1076	2	no	—
586	D₄	—	1076	2	no	—
587	D₄	—	1076	1	no	—
588	D₄	—	1076	2	no	—
589	D₄	—	1076	1	no	—
590	D₄	—	1076	1	no	—
591	D₄	—	1076	2	no	—
592	D₄	—	1076	2	no	—
593	D₄	—	1076	2	no	—
594	D₄	—	1076	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	269	2	no	—
599	C₂×C₄	—	269	2	no	—
600	C₂×C₄	—	269	2	no	—
601	C₂×C₄	—	269	1	no	—
602	C₂×C₄	—	538	2	no	—
603	C₂×C₄	—	1076	2	no	—
604	C₂×C₄	—	1076	2	no	—
605	C₂×C₄	—	1076	2	no	—
606	C₂×C₄	—	1076	2	no	—
607	C₂×C₄	—	1076	2	no	—
608	C₂×C₄	—	1076	2	no	—
609	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
611	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
612	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
613	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
614	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	269	2	no	—
623	C₂²	—	538	2	no	—
624	C₂²	—	538	2	no	—
625	C₂²	—	538	2	no	—
626	C₂²	—	538	1	no	—
627	C₂²	—	538	2	no	—
628	C₂²	—	538	1	no	—
629	C₂²	—	538	2	no	—
630	C₂²	—	538	2	no	—
631	C₂²	—	538	2	no	—
632	C₂²	—	538	2	no	—
633	C₂²	—	538	2	no	—
634	C₂²	—	538	2	no	—
635	C₂²	—	538	2	no	—
636	C₂²	—	538	2	no	—
637	C₂²	—	1076	8	no	—
638	C₂²	—	1076	8	no	—
639	C₂²	—	1076	4	no	—
640	C₂²	—	1076	4	no	—
641	C₂²	—	2152	4	no	—
642	C₂²	—	2152	2	no	—
643	C₂²	—	2152	2	no	—
644	C₂²	#22575499	1	4	yes	—
645	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	538	1	no	—
653	C₄	—	538	2	no	—
654	C₄	—	538	2	no	—
655	C₄	—	538	2	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	538	2	no	—
660	C₂	—	1076	2	no	—
661	C₂	—	1076	1	no	—
662	C₂	—	1076	2	no	—
663	C₂	—	1076	2	no	—
664	C₂	—	1076	1	no	—
665	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
666	C₂	C₂×#22575499	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#551×C₂₆₉	C₂
hypercenter	#551	D₂₆₉
hypocenter	C₂₆₉	#3532
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #31771347	C₂	semidirect
2. #31771346	C₂	semidirect
3. #31771345	C₂	semidirect
4. #31771279	C₂	semidirect
5. #31771247	C₂	semidirect
6. #31771246	C₂	semidirect
7. #31771245	C₂	semidirect
8. D₄×D₁₀₇₆	C₂	semidirect
9. #31771237	C₂	semidirect
10. #31771195	C₂	semidirect
11. #31771194	C₂	semidirect
12. #31771188	C₂	semidirect
13. #31771174	C₂	semidirect
14. #31771173	C₂	semidirect
15. #31771166	C₂	semidirect
16. #31771166	C₂	semidirect
17. C₂×#22575423	C₂	semidirect
18. #120×D₂₆₉	C₂	semidirect
19. #551×C₂₆₉	C₂	semidirect
20. C₂⁴×D₂₆₉	C₂²	semidirect
21. C₂×#16864403	C₂²	semidirect
22. C₂×#16864402	C₂²	semidirect
23. C₂²×D₁₀₇₆	C₂²	semidirect
24. C₂²×D₁₀₇₆	C₂²	semidirect
25. C₂²×D₁₀₇₆	C₂²	semidirect
26. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
27. C₂×D₄×D₂₆₉	C₂²	semidirect
28. C₂×D₄×D₂₆₉	C₂²	semidirect
29. C₂×D₄×D₂₆₉	C₂²	semidirect
30. #22575450	C₂²	semidirect
31. #22575450	C₂²	semidirect
32. #22575449	C₂²	semidirect
33. #22575448	C₂²	semidirect
34. #22575448	C₂²	semidirect
35. #22575447	C₂²	semidirect
36. #22575442	C₂²	semidirect
37. #22575442	C₂²	semidirect
38. #22575441	C₂²	semidirect
39. #22575441	C₂²	semidirect
40. #22575439	C₂²	semidirect
41. #22575439	C₂²	semidirect
42. #22575438	C₂²	semidirect
43. #22575438	C₂²	semidirect
44. #22575438	C₂²	semidirect
45. #22575438	C₂²	semidirect
46. #22575438	C₂²	semidirect
47. #22575436	C₂²	semidirect
48. #22575436	C₂²	semidirect
49. #22575435	C₂²	semidirect
50. #22575431	C₂²	semidirect
51. #22575430	C₂²	semidirect
52. #22575428	C₂²	semidirect
53. #22575428	C₂²	semidirect
54. #22575428	C₂²	semidirect
55. #22575428	C₂²	semidirect
56. #22575428	C₂²	semidirect
57. #22575428	C₂²	semidirect
58. #22575428	C₂²	semidirect
59. #22575427	C₂²	semidirect
60. #22575427	C₂²	semidirect
61. #22575426	C₂²	semidirect
62. #22575426	C₂²	semidirect
63. #22575426	C₂²	semidirect
64. #22575426	C₂²	semidirect
65. #22575426	C₂²	semidirect
66. #22575425	C₂²	semidirect
68. #22575423	C₂²	semidirect
69. #22575423	C₂²	semidirect
70. #22575423	C₂²	semidirect
71. #22575423	C₂²	semidirect
72. #22575423	C₂²	semidirect
73. #22575423	C₂²	semidirect
74. #22575423	C₂²	semidirect
75. #22575423	C₂²	semidirect
76. #22575423	C₂²	semidirect
77. #22575423	C₂²	semidirect
78. #22575423	C₂²	semidirect
79. #22575423	C₂²	semidirect
80. #22575423	C₂²	semidirect
81. #22575423	C₂²	semidirect
82. #22575422	C₂²	semidirect
83. #22575421	C₂²	semidirect
84. #22575421	C₂²	semidirect
85. #22575421	C₂²	semidirect
86. C₄×D₁₀₇₆	C₂²	semidirect
87. #22575415	C₂²	semidirect
88. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
89. #22575413	C₂²	semidirect
90. #22575413	C₂²	semidirect
91. #22575410	C₂²	semidirect
92. C₂×#16864379	C₂²	semidirect
93. C₂×#16864379	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. #123×C₂₆₉	C₂²	semidirect
102. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
104. C₄×D₄×C₂₆₉	C₂²	semidirect
105. #117×C₂₆₉	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
115. C₂³×D₂₆₉	C₂³	semidirect
118. C₂×Dic₅₃₈	C₂³	semidirect
132. C₂×D₁₀₇₆	C₂³	semidirect
133. C₂×D₁₀₇₆	C₂³	semidirect
134. C₂×D₁₀₇₆	C₂³	semidirect
135. C₂×D₁₀₇₆	C₂³	semidirect
145. C₂×C₂²⋊D₂₆₉	C₂³	semidirect
152. C₂×C₄×D₂₆₉	C₂³	semidirect
153. C₂×C₄×D₂₆₉	C₂³	semidirect
154. C₂×C₄×D₂₆₉	C₂³	semidirect
155. C₂×C₄×D₂₆₉	C₂³	semidirect
156. C₄⋊Dic₂₆₉	C₂³	semidirect
157. #16864381	C₂³	semidirect
158. #16864381	C₂³	semidirect
159. #16864381	C₂³	semidirect
160. #16864381	C₂³	semidirect
163. C₂²⋊Dic₂₆₉	C₂³	semidirect
175. #16864379	C₂³	semidirect
176. #16864379	C₂³	semidirect
177. #16864379	C₂³	semidirect
178. #16864379	C₂³	semidirect
179. #16864379	C₂³	semidirect
180. #16864379	C₂³	semidirect
181. #16864379	C₂³	semidirect
182. C₄×Dic₂₆₉	C₂³	semidirect
183. C₄×Dic₂₆₉	C₂³	semidirect
185. C₂×Q₈×C₂₆₉	C₂³	semidirect
190. C₂²×C₄×C₂₆₉	C₂³	semidirect
191. C₄⋊C₄×C₂₆₉	C₂³	semidirect
192. C₄⋊C₄×C₂₆₉	C₂³	semidirect
193. C₄⋊C₄×C₂₆₉	C₂³	semidirect
194. C₄⋊C₄×C₂₆₉	C₂³	semidirect
201. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
202. C₂²⋊C₄×C₂₆₉	C₂³	semidirect
203. C₄²×C₂₆₉	C₂³	semidirect
204. C₄²×C₂₆₉	C₂³	semidirect
333. C₂₆₉	#3532	semidirect
339. #551	D₂₆₉	semidirect
370. #126	C₂×D₂₆₉	semidirect
377. #124	C₂×D₂₆₉	semidirect
386. #123	C₂×D₂₆₉	semidirect
387. #123	C₂×D₂₆₉	semidirect
390. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
431. C₄×D₄	C₂×D₂₆₉	semidirect
433. #117	C₂×D₂₆₉	semidirect
440. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
454. C₂×Q₈	C₂²×D₂₆₉	semidirect
496. C₂²×C₄	C₂²×D₂₆₉	semidirect
502. C₄⋊C₄	C₂²×D₂₆₉	semidirect
503. C₄⋊C₄	C₂²×D₂₆₉	semidirect
504. C₄⋊C₄	C₂²×D₂₆₉	semidirect
505. C₄⋊C₄	C₂²×D₂₆₉	semidirect
533. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
534. C₂²⋊C₄	C₂²×D₂₆₉	semidirect
537. C₄²	C₂²×D₂₆₉	semidirect
538. 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
#31771347	2
#31771346	2
#31771345	2
#31771279	2
#31771247	2
#31771246	2
#31771245	2
D₄×D₁₀₇₆	2
#31771237	2
#31771195	2
#31771194	2
#31771188	2
#31771174	2
#31771173	2
#31771166	2
C₂×#22575423	2
#120×D₂₆₉	2
#551×C₂₆₉	2
#3532	269