Subgroups — #46825110

Order 34432.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771352	C₂	1	2	yes	maximal, complemented
2	#31771349	C₂	1	2	yes	maximal, complemented
3	#31771316	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771315	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771267	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771263	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771260	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771258	C₂	1	1	yes	maximal, characteristic, complemented
9	#31771250	C₂	1	1	yes	maximal, characteristic, complemented
10	#31771248	C₂	1	1	yes	maximal, characteristic, complemented
11	#31771248	C₂	1	2	yes	maximal, complemented
12	#31771247	C₂	1	2	yes	maximal, complemented
13	#31771230	C₂	1	2	yes	maximal, complemented
14	#31771226	C₂	1	1	yes	maximal, characteristic, complemented
15	#31771196	C₂	1	2	yes	maximal, complemented
16	#31771194	C₂	1	2	yes	maximal, complemented
17	#31771185	C₂	1	2	yes	maximal, complemented
18	#31771185	C₂	1	1	yes	maximal, characteristic, complemented
19	#31771184	C₂	1	1	yes	maximal, characteristic, complemented
20	#31771117	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²⋊Q₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864403	C₂²	1	2	yes	complemented
25	C₂×#16864403	C₂²	1	1	yes	characteristic, complemented
26	C₂×#16864402	C₂²	1	1	yes	characteristic, complemented
27	C₂×#16864402	C₂²	1	2	yes	complemented
28	C₂×#16864401	C₂²	1	1	yes	characteristic, complemented
29	C₂×Q₈×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₄×D₂₆₉	C₂²	1	2	yes	—
31	C₂×D₄×D₂₆₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
33	#22575453	C₂²	1	1	yes	characteristic, complemented
34	#22575448	C₂²	1	2	yes	complemented
35	#22575445	C₂²	1	2	yes	complemented
36	#22575444	C₂²	1	2	yes	complemented
37	#22575441	C₂²	1	2	yes	complemented
38	#22575441	C₂²	1	1	yes	characteristic, complemented
39	#22575439	C₂²	1	2	yes	complemented
40	#22575439	C₂²	1	2	yes	complemented
41	#22575438	C₂²	1	2	yes	complemented
42	#22575438	C₂²	1	2	yes	complemented
43	#22575437	C₂²	1	2	yes	complemented
44	#22575437	C₂²	1	1	yes	characteristic, complemented
45	#22575437	C₂²	1	1	yes	characteristic, complemented
46	#22575435	C₂²	1	2	yes	complemented
47	#22575435	C₂²	1	2	yes	complemented
48	#22575435	C₂²	1	2	yes	complemented
49	#22575435	C₂²	1	2	yes	complemented
50	#22575433	C₂²	1	1	yes	characteristic
51	#22575433	C₂²	1	1	yes	characteristic
52	#22575433	C₂²	1	1	yes	characteristic, complemented
53	#22575433	C₂²	1	1	yes	characteristic, complemented
54	#22575433	C₂²	1	2	yes	complemented
55	#22575432	C₂²	1	1	yes	characteristic, complemented
56	#22575432	C₂²	1	2	yes	complemented
57	#22575431	C₂²	1	2	yes	—
58	#22575431	C₂²	1	2	yes	—
59	#22575431	C₂²	1	2	yes	complemented
60	#22575431	C₂²	1	2	yes	complemented
61	#22575431	C₂²	1	2	yes	complemented
62	#22575430	C₂²	1	2	yes	complemented
63	#22575430	C₂²	1	2	yes	complemented
64	#22575430	C₂²	1	2	yes	complemented
65	#22575429	C₂²	1	2	yes	—
66	#22575429	C₂²	1	1	yes	characteristic
67	#22575429	C₂²	1	1	yes	characteristic, complemented
68	#22575429	C₂²	1	2	yes	complemented
69	#22575429	C₂²	1	2	yes	complemented
70	#22575428	C₂²	1	1	yes	characteristic
71	#22575428	C₂²	1	1	yes	characteristic
72	#22575428	C₂²	1	2	yes	complemented
73	#22575428	C₂²	1	1	yes	characteristic, complemented
74	#22575428	C₂²	1	2	yes	complemented
75	#22575428	C₂²	1	1	yes	characteristic, complemented
76	#22575427	C₂²	1	1	yes	characteristic
77	#22575427	C₂²	1	2	yes	complemented
78	#22575426	C₂²	1	2	yes	—
79	#22575426	C₂²	1	2	yes	complemented
80	#22575426	C₂²	1	2	yes	complemented
81	#22575426	C₂²	1	2	yes	complemented
82	#22575426	C₂²	1	2	yes	complemented
83	#22575426	C₂²	1	2	yes	complemented
84	#22575425	C₂²	1	2	yes	—
85	#22575425	C₂²	1	2	yes	complemented
86	#22575424	C₂²	1	1	yes	characteristic
87	#22575424	C₂²	1	1	yes	characteristic, complemented
88	#22575424	C₂²	1	2	yes	complemented
89	#22575423	C₂²	1	2	yes	—
90	#22575423	C₂²	1	2	yes	—
91	#22575423	C₂²	1	1	yes	characteristic
92	#22575423	C₂²	1	1	yes	characteristic
93	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₁₀₇₆	C₂²	1	2	yes	—
95	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
96	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic
97	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
98	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
99	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
101	#22575415	C₂²	1	2	yes	—
102	#22575413	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₂₆₉	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×#16864379	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₂₆₉	C₂²	1	2	yes	complemented
114	#124×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
115	#124×C₂₆₉	C₂²	1	2	yes	complemented
116	#123×C₂₆₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₂₆₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₂₆₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
122	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
124	C₂³×D₂₆₉	C₂³	1	2	yes	—
125	#16864403	—	4	2	no	—
126	#16864403	—	4	4	no	—
127	#16864402	—	4	2	no	—
128	#16864402	—	4	4	no	—
129	#16864401	—	4	2	no	—
130	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₅₃₈	C₂³	1	2	yes	—
132	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
133	C₂×Dic₅₃₈	C₂³	1	2	yes	—
134	Q₈×D₂₆₉	—	4	2	no	—
135	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
136	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
137	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
138	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
139	C₂×D₁₀₇₆	C₂³	1	2	yes	—
140	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
141	C₂×D₁₀₇₆	C₂³	1	2	yes	—
142	C₂×D₁₀₇₆	C₂³	1	2	yes	—
143	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
151	D₄×D₂₆₉	—	4	2	no	—
152	D₄×D₂₆₉	—	4	4	no	—
153	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
154	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₂₆₉	—	4	2	no	—
156	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
157	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
163	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
164	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
165	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
166	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
168	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
169	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
172	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
175	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
176	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
178	#16864381	C₂³	1	2	yes	—
179	#16864381	C₂³	1	2	yes	—
180	#16864381	C₂³	1	2	yes	—
181	#16864381	C₂³	1	2	yes	—
182	#16864381	C₂³	1	2	yes	—
183	#16864381	C₂³	1	2	yes	—
184	#16864381	C₂³	1	2	yes	—
185	#16864381	C₂³	1	2	yes	—
186	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
189	#16864379	C₂³	1	1	yes	characteristic
190	#16864379	C₂³	1	2	yes	—
191	#16864379	C₂³	1	2	yes	—
192	#16864379	C₂³	1	2	yes	—
193	#16864379	C₂³	1	2	yes	—
194	#16864379	C₂³	1	1	yes	characteristic
195	#16864379	C₂³	1	2	yes	—
196	#16864379	C₂³	1	2	yes	—
197	#16864379	C₂³	1	1	yes	characteristic
198	#16864379	C₂³	1	2	yes	—
199	#16864379	C₂³	1	1	yes	characteristic
200	#16864379	C₂³	1	2	yes	—
201	#16864379	C₂³	1	1	yes	characteristic
202	#16864379	C₂³	1	1	yes	characteristic
203	#16864379	C₂³	1	2	yes	—
204	#16864379	C₂³	1	2	yes	—
205	#16864379	C₂³	1	1	yes	characteristic
206	#16864379	C₂³	1	1	yes	characteristic
207	C₄×Dic₂₆₉	C₂³	1	2	yes	—
208	C₂×Q₈×C₂₆₉	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₂₆₉	C₂³	1	2	yes	—
210	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
220	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
228	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
229	C₄²×C₂₆₉	C₂³	1	2	yes	—
230	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
231	C₂²×D₂₆₉	—	2	2	no	—
232	C₂²×D₂₆₉	—	2	2	no	—
233	C₂²×D₂₆₉	—	2	4	no	—
234	C₂²×D₂₆₉	—	4	1	no	—
235	C₂²×D₂₆₉	—	4	2	no	—
236	C₂²×D₂₆₉	—	4	2	no	—
237	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
238	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
240	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
242	Dic₅₃₈	—	2	2	no	—
243	Dic₅₃₈	—	4	2	no	—
244	Dic₅₃₈	—	4	1	no	—
245	Dic₅₃₈	—	4	2	no	—
246	D₁₀₇₆	—	2	4	no	—
247	D₁₀₇₆	—	2	2	no	—
248	D₁₀₇₆	—	2	2	no	—
249	D₁₀₇₆	—	2	2	no	—
250	D₁₀₇₆	—	2	2	no	—
251	D₁₀₇₆	—	2	2	no	—
252	D₁₀₇₆	—	4	1	no	—
253	D₁₀₇₆	—	4	2	no	—
254	D₁₀₇₆	—	4	2	no	—
255	C₂²⋊D₂₆₉	—	2	4	no	—
256	C₂²⋊D₂₆₉	—	4	2	no	—
257	C₂²⋊D₂₆₉	—	4	2	no	—
258	C₂²⋊D₂₆₉	—	4	2	no	—
259	C₂²⋊D₂₆₉	—	4	1	no	—
260	C₂²⋊D₂₆₉	—	4	2	no	—
261	C₂²⋊D₂₆₉	—	4	1	no	—
262	C₂×Dic₂₆₉	—	4	1	no	—
263	C₂×Dic₂₆₉	—	4	2	no	—
264	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
265	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
266	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
269	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
271	C₄×D₂₆₉	—	2	4	no	—
272	C₄×D₂₆₉	—	2	2	no	—
273	C₄×D₂₆₉	—	2	2	no	—
274	C₄×D₂₆₉	—	2	2	no	—
275	C₄×D₂₆₉	—	2	2	no	—
276	C₄×D₂₆₉	—	4	1	no	—
277	C₄×D₂₆₉	—	4	1	no	—
278	C₄×D₂₆₉	—	4	2	no	—
279	C₄×D₂₆₉	—	4	2	no	—
280	C₄×D₂₆₉	—	4	2	no	—
281	C₄×D₂₆₉	—	4	2	no	—
282	C₄×D₂₆₉	—	4	2	no	—
283	C₄×D₂₆₉	—	4	2	no	—
284	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
285	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
286	Q₈×C₂₆₉	—	2	2	no	—
287	Q₈×C₂₆₉	—	4	2	no	—
288	D₄×C₂₆₉	—	2	2	no	—
289	D₄×C₂₆₉	—	4	2	no	—
290	C₂×C₄×C₂₆₉	—	2	2	no	—
291	C₂×C₄×C₂₆₉	—	4	2	no	—
292	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
298	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
300	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
301	C₂²×C₂₆₉	—	2	1	no	—
302	C₂²×C₂₆₉	—	2	2	no	—
303	C₂²×C₂₆₉	—	2	2	no	—
304	C₂²×C₂₆₉	—	2	1	no	—
305	C₂²×C₂₆₉	—	2	1	no	—
306	C₂²×C₂₆₉	—	2	2	no	—
307	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
308	C₂×D₂₆₉	—	2	1	no	—
309	C₂×D₂₆₉	—	2	1	no	—
310	C₂×D₂₆₉	—	2	1	no	—
311	C₂×D₂₆₉	—	2	1	no	—
312	C₂×D₂₆₉	—	2	1	no	—
313	C₂×D₂₆₉	—	2	1	no	—
314	C₂×D₂₆₉	—	2	1	no	—
315	C₂×D₂₆₉	—	2	1	no	—
316	C₂×D₂₆₉	—	2	2	no	—
317	C₂×D₂₆₉	—	2	2	no	—
318	C₂×D₂₆₉	—	2	1	no	—
319	C₂×D₂₆₉	—	2	1	no	—
320	C₂×D₂₆₉	—	2	2	no	—
321	C₂×D₂₆₉	—	4	4	no	—
322	C₂×D₂₆₉	—	8	4	no	—
323	C₂×D₂₆₉	H(5,𝔽₂)	1	2	yes	—
324	C₂×D₂₆₉	2₋¹⁺⁴	1	2	yes	—
325	C₄×C₂₆₉	—	2	1	no	—
326	C₄×C₂₆₉	—	2	1	no	—
327	C₄×C₂₆₉	—	2	2	no	—
328	C₄×C₂₆₉	—	2	2	no	—
329	C₄×C₂₆₉	—	2	2	no	—
330	C₄×C₂₆₉	—	2	1	no	—
331	C₄×C₂₆₉	—	2	1	no	—
332	C₄×C₂₆₉	—	2	1	no	—
333	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
334	Dic₂₆₉	—	2	2	no	—
335	Dic₂₆₉	—	2	1	no	—
336	Dic₂₆₉	—	2	1	no	—
337	Dic₂₆₉	—	2	1	no	—
338	Dic₂₆₉	—	2	1	no	—
339	Dic₂₆₉	—	2	2	no	—
340	Dic₂₆₉	—	2	2	no	—
341	C₂×C₂₆₉	—	4	1	no	—
342	C₂×C₂₆₉	—	4	2	no	—
343	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₂₆₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	D₂₆₉	—	2	2	no	—
347	D₂₆₉	—	2	2	no	—
348	D₂₆₉	—	4	1	no	—
349	D₂₆₉	—	4	1	no	—
350	D₂₆₉	—	4	2	no	—
351	C₂₆₉	#3536	1	1	yes	characteristic, complemented, Sylow
352	#3536	—	269	1	no	maximal, Sylow
353	#562	—	269	2	no	—
354	#562	—	269	2	no	—
355	#554	—	269	1	no	—
356	#554	—	269	1	no	—
357	#548	—	269	1	no	—
358	#548	—	269	1	no	—
359	#547	—	269	1	no	—
360	#547	—	269	1	no	—
361	#546	—	269	2	no	—
362	#546	—	269	1	no	—
363	#546	—	269	2	no	—
364	#546	—	269	1	no	—
365	#543	—	269	2	no	—
366	#542	—	269	1	no	—
367	#542	D₂₆₉	1	1	yes	characteristic, complemented
368	#539	—	269	2	no	—
369	#538	—	269	2	no	—
370	#537	—	269	2	no	—
371	#537	—	269	1	no	—
372	#537	—	269	1	no	—
373	#525	—	269	1	no	—
374	C₂×C₂²⋊Q₈	—	269	1	no	—
375	C₂×#121	—	269	1	no	—
376	C₂×#41	—	269	2	no	—
377	C₂×#41	—	269	1	no	—
378	C₂×#41	—	269	1	no	—
379	C₂×#41	—	269	1	no	—
380	C₂×#41	—	269	2	no	—
381	C₂²×Q₈	—	269	1	no	—
382	C₂²×D₄	—	269	1	no	—
383	C₂²×D₄	—	269	2	no	—
384	C₂³×C₄	—	269	1	no	—
385	C₄⋊Q₈	—	269	1	no	—
386	C₄⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
387	#126	—	269	2	no	—
388	#126	C₂×D₂₆₉	1	2	yes	complemented
389	#125	—	269	2	no	—
390	#125	—	269	2	no	—
391	#124	—	269	2	no	—
392	#124	—	269	2	no	—
393	#124	—	269	2	no	—
394	#124	—	269	1	no	—
395	#124	C₂×D₂₆₉	1	1	yes	characteristic, complemented
396	#124	C₂×D₂₆₉	1	2	yes	complemented
397	#123	—	269	2	no	—
398	#123	—	269	2	no	—
399	#123	—	269	1	no	—
400	#123	—	269	1	no	—
401	#123	—	269	2	no	—
402	#123	—	269	2	no	—
403	#123	—	269	2	no	—
404	#123	—	269	2	no	—
405	#123	—	269	2	no	—
406	#123	C₂×D₂₆₉	1	2	yes	complemented
407	C₂²⋊Q₈	—	269	1	no	—
408	C₂²⋊Q₈	—	269	1	no	—
409	C₂²⋊Q₈	—	269	2	no	—
410	C₂²⋊Q₈	—	269	2	no	—
411	C₂²⋊Q₈	—	269	2	no	—
412	C₂²⋊Q₈	—	269	1	no	—
413	C₂²⋊Q₈	—	269	2	no	—
414	C₂²⋊Q₈	—	269	2	no	—
415	C₂²⋊Q₈	—	269	1	no	—
416	C₂²⋊Q₈	—	269	1	no	—
417	C₂²⋊Q₈	—	269	1	no	—
418	C₂²⋊Q₈	—	269	2	no	—
419	C₂²⋊Q₈	—	269	2	no	—
420	C₂²⋊Q₈	—	269	1	no	—
421	C₂²⋊Q₈	—	269	2	no	—
422	C₂²⋊Q₈	—	269	2	no	—
423	C₂²⋊Q₈	—	269	2	no	—
424	C₂²⋊Q₈	—	269	2	no	—
425	C₂²⋊Q₈	—	269	2	no	—
426	C₂²⋊Q₈	—	269	2	no	—
427	C₂²⋊Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
428	C₂²⋊Q₈	C₂×D₂₆₉	1	2	yes	complemented
429	#121	—	269	1	no	—
430	#121	—	269	2	no	—
431	#121	—	269	1	no	—
432	#121	—	269	2	no	—
433	#121	—	269	2	no	—
434	#121	—	269	1	no	—
435	#121	—	269	2	no	—
436	#121	—	269	1	no	—
437	#121	—	269	1	no	—
438	#121	—	269	1	no	—
439	#121	—	269	2	no	—
440	#121	—	269	1	no	—
441	#121	—	269	2	no	—
442	#121	—	269	2	no	—
443	#121	—	269	2	no	—
444	#121	—	269	2	no	—
445	#121	—	269	2	no	—
446	#121	—	269	2	no	—
447	#121	—	269	2	no	—
448	#121	C₂×D₂₆₉	1	1	yes	characteristic
449	#120	—	269	1	no	—
450	#120	—	269	1	no	—
451	#120	—	269	2	no	—
452	#120	—	269	2	no	—
453	C₄×Q₈	—	269	1	no	—
454	C₄×Q₈	C₂×D₂₆₉	1	1	yes	characteristic, complemented
455	C₄×D₄	—	269	2	no	—
456	C₄×D₄	—	269	2	no	—
457	C₄×D₄	—	269	1	no	—
458	C₄×D₄	—	269	1	no	—
459	C₄×D₄	—	269	1	no	—
460	C₄×D₄	—	269	1	no	—
461	C₄×D₄	—	269	2	no	—
462	C₄×D₄	—	269	2	no	—
463	C₄×D₄	—	269	1	no	—
464	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
465	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
466	C₂×C₄⋊C₄	—	269	1	no	—
467	C₂×C₄⋊C₄	—	269	2	no	—
468	C₂×C₄⋊C₄	—	269	1	no	—
469	C₂×C₄⋊C₄	—	269	1	no	—
470	C₂×C₄⋊C₄	—	269	1	no	—
471	C₂×C₂²⋊C₄	—	269	2	no	—
472	C₂×C₂²⋊C₄	—	269	2	no	—
473	C₂×C₂²⋊C₄	—	269	2	no	—
474	C₂×C₂²⋊C₄	—	269	2	no	—
475	C₂⁴	—	269	1	no	—
476	C₂⁴	—	269	2	no	—
477	#41	—	1076	2	no	—
478	#41	—	1076	4	no	—
479	#41	—	1076	2	no	—
480	#41	—	1076	4	no	—
481	#41	—	1076	2	no	—
482	C₂×Q₈	—	269	1	no	—
483	C₂×Q₈	—	269	1	no	—
484	C₂×Q₈	—	269	2	no	—
485	C₂×Q₈	—	269	2	no	—
486	C₂×Q₈	—	1076	2	no	—
487	C₂×Q₈	C₂²×D₂₆₉	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₂₆₉	1	2	yes	—
489	C₂×D₄	—	269	2	no	—
490	C₂×D₄	—	269	1	no	—
491	C₂×D₄	—	269	1	no	—
492	C₂×D₄	—	269	2	no	—
493	C₂×D₄	—	269	2	no	—
494	C₂×D₄	—	269	2	no	—
495	C₂×D₄	—	269	2	no	—
496	C₂×D₄	—	269	1	no	—
497	C₂×D₄	—	269	1	no	—
498	C₂×D₄	—	269	1	no	—
499	C₂×D₄	—	269	1	no	—
500	C₂×D₄	—	269	2	no	—
501	C₂×D₄	—	269	1	no	—
502	C₂×D₄	—	269	2	no	—
503	C₂×D₄	—	269	2	no	—
504	C₂×D₄	—	269	1	no	—
505	C₂×D₄	—	1076	2	no	—
506	C₂×D₄	—	1076	4	no	—
507	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
509	C₂²×C₄	—	269	2	no	—
510	C₂²×C₄	—	269	1	no	—
511	C₂²×C₄	—	269	2	no	—
512	C₂²×C₄	—	269	1	no	—
513	C₂²×C₄	—	269	1	no	—
514	C₂²×C₄	—	269	1	no	—
515	C₂²×C₄	—	269	1	no	—
516	C₂²×C₄	—	269	1	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	1	no	—
522	C₂²×C₄	—	269	2	no	—
523	C₂²×C₄	—	269	2	no	—
524	C₂²×C₄	—	1076	2	no	—
525	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
527	C₄⋊C₄	—	269	1	no	—
528	C₄⋊C₄	—	269	1	no	—
529	C₄⋊C₄	—	269	2	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	—	269	2	no	—
535	C₄⋊C₄	—	269	2	no	—
536	C₄⋊C₄	—	269	2	no	—
537	C₄⋊C₄	—	269	2	no	—
538	C₄⋊C₄	—	269	1	no	—
539	C₄⋊C₄	—	269	1	no	—
540	C₄⋊C₄	—	269	1	no	—
541	C₄⋊C₄	—	269	1	no	—
542	C₄⋊C₄	—	269	2	no	—
543	C₄⋊C₄	—	269	2	no	—
544	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
547	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
550	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
551	C₂²⋊C₄	—	269	2	no	—
552	C₂²⋊C₄	—	269	2	no	—
553	C₂²⋊C₄	—	269	2	no	—
554	C₂²⋊C₄	—	269	2	no	—
555	C₂²⋊C₄	—	269	1	no	—
556	C₂²⋊C₄	—	269	1	no	—
557	C₂²⋊C₄	—	269	2	no	—
558	C₂²⋊C₄	—	269	2	no	—
559	C₂²⋊C₄	—	269	2	no	—
560	C₂²⋊C₄	—	269	2	no	—
561	C₂²⋊C₄	—	269	2	no	—
562	C₂²⋊C₄	—	269	1	no	—
563	C₂²⋊C₄	—	269	1	no	—
564	C₂²⋊C₄	—	269	2	no	—
565	C₂²⋊C₄	—	269	2	no	—
566	C₂²⋊C₄	—	269	1	no	—
567	C₂²⋊C₄	—	269	1	no	—
568	C₂²⋊C₄	—	269	2	no	—
569	C₂²⋊C₄	—	269	2	no	—
570	C₂²⋊C₄	—	269	1	no	—
571	C₂²⋊C₄	—	269	1	no	—
572	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
577	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
578	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
579	C₄²	—	269	2	no	—
580	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
581	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
582	C₄²	C₂²×D₂₆₉	1	2	yes	—
583	C₂³	—	269	1	no	—
584	C₂³	—	269	1	no	—
585	C₂³	—	269	2	no	—
586	C₂³	—	269	1	no	—
587	C₂³	—	269	1	no	—
588	C₂³	—	538	2	no	—
589	C₂³	—	538	2	no	—
590	C₂³	—	538	4	no	—
591	C₂³	—	1076	1	no	—
592	C₂³	—	1076	2	no	—
593	C₂³	—	1076	2	no	—
594	C₂³	C₂³×D₂₆₉	1	2	yes	—
595	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	538	2	no	—
599	Q₈	—	1076	2	no	—
600	Q₈	—	1076	2	no	—
601	Q₈	—	1076	1	no	—
602	D₄	—	2	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	538	4	no	—
605	D₄	—	538	2	no	—
606	D₄	—	538	2	no	—
607	D₄	—	538	2	no	—
608	D₄	—	538	2	no	—
609	D₄	—	538	4	no	—
610	D₄	—	538	2	no	—
611	D₄	—	1076	2	no	—
612	D₄	—	1076	1	no	—
613	D₄	—	1076	2	no	—
614	D₄	—	1076	2	no	—
615	D₄	—	1076	2	no	—
616	D₄	—	1076	2	no	—
617	D₄	—	1076	1	no	—
618	D₄	—	1076	1	no	—
619	D₄	—	1076	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	269	2	no	—
623	C₂×C₄	—	269	2	no	—
624	C₂×C₄	—	269	1	no	—
625	C₂×C₄	—	269	2	no	—
626	C₂×C₄	—	269	1	no	—
627	C₂×C₄	—	269	1	no	—
628	C₂×C₄	—	269	1	no	—
629	C₂×C₄	—	538	4	no	—
630	C₂×C₄	—	538	2	no	—
631	C₂×C₄	—	538	2	no	—
632	C₂×C₄	—	538	2	no	—
633	C₂×C₄	—	538	2	no	—
634	C₂×C₄	—	1076	1	no	—
635	C₂×C₄	—	1076	1	no	—
636	C₂×C₄	—	1076	2	no	—
637	C₂×C₄	—	1076	2	no	—
638	C₂×C₄	—	1076	2	no	—
639	C₂×C₄	—	1076	2	no	—
640	C₂×C₄	—	1076	2	no	—
641	C₂×C₄	—	1076	2	no	—
642	C₂×C₄	—	1076	1	no	—
643	C₂×C₄	—	1076	2	no	—
644	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
645	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
649	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
650	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
651	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
653	C₂²	—	2	2	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	269	2	no	—
660	C₂²	—	269	2	no	—
661	C₂²	—	538	1	no	—
662	C₂²	—	538	1	no	—
663	C₂²	—	538	1	no	—
664	C₂²	—	538	1	no	—
665	C₂²	—	538	1	no	—
666	C₂²	—	538	1	no	—
667	C₂²	—	538	2	no	—
668	C₂²	—	538	1	no	—
669	C₂²	—	538	1	no	—
670	C₂²	—	538	2	no	—
671	C₂²	—	538	1	no	—
672	C₂²	—	538	1	no	—
673	C₂²	—	538	2	no	—
674	C₂²	—	1076	4	no	—
675	C₂²	—	2152	4	no	—
676	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	538	2	no	—
686	C₄	—	538	2	no	—
687	C₄	—	538	1	no	—
688	C₄	—	538	1	no	—
689	C₄	—	538	1	no	—
690	C₄	—	538	1	no	—
691	C₄	—	538	2	no	—
692	C₄	#22575499	1	2	yes	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	538	2	no	—
696	C₂	—	538	2	no	—
697	C₂	—	1076	2	no	—
698	C₂	—	1076	1	no	—
699	C₂	—	1076	1	no	—
700	C₂	H(5,𝔽₂)×D₂₆₉	1	1	yes	characteristic
701	C₂	C₂×#22575499	1	1	yes	characteristic
702	C₂	2₋¹⁺⁴×D₂₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	#542×C₂₆₉	C₂
hypercenter	#542	D₂₆₉
hypocenter	C₂₆₉	#3536
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #31771352	C₂	semidirect
2. #31771349	C₂	semidirect
3. #31771316	C₂	semidirect
4. #31771315	C₂	semidirect
5. #31771267	C₂	semidirect
6. #31771263	C₂	semidirect
7. #31771260	C₂	semidirect
8. #31771258	C₂	semidirect
9. #31771250	C₂	semidirect
10. #31771248	C₂	semidirect
11. #31771248	C₂	semidirect
12. #31771247	C₂	semidirect
13. #31771230	C₂	semidirect
14. #31771226	C₂	semidirect
15. #31771196	C₂	semidirect
16. #31771194	C₂	semidirect
17. #31771185	C₂	semidirect
18. #31771185	C₂	semidirect
19. #31771184	C₂	semidirect
20. #31771117	C₂	semidirect
21. C₂²⋊Q₈×D₂₆₉	C₂	semidirect
22. #121×D₂₆₉	C₂	semidirect
23. #542×C₂₆₉	C₂	semidirect
24. C₂×#16864403	C₂²	semidirect
25. C₂×#16864403	C₂²	semidirect
26. C₂×#16864402	C₂²	semidirect
27. C₂×#16864402	C₂²	semidirect
28. C₂×#16864401	C₂²	semidirect
29. C₂×Q₈×D₂₆₉	C₂²	semidirect
33. #22575453	C₂²	semidirect
34. #22575448	C₂²	semidirect
35. #22575445	C₂²	semidirect
36. #22575444	C₂²	semidirect
37. #22575441	C₂²	semidirect
38. #22575441	C₂²	semidirect
39. #22575439	C₂²	semidirect
40. #22575439	C₂²	semidirect
41. #22575438	C₂²	semidirect
42. #22575438	C₂²	semidirect
43. #22575437	C₂²	semidirect
44. #22575437	C₂²	semidirect
45. #22575437	C₂²	semidirect
46. #22575435	C₂²	semidirect
47. #22575435	C₂²	semidirect
48. #22575435	C₂²	semidirect
49. #22575435	C₂²	semidirect
52. #22575433	C₂²	semidirect
53. #22575433	C₂²	semidirect
54. #22575433	C₂²	semidirect
55. #22575432	C₂²	semidirect
56. #22575432	C₂²	semidirect
59. #22575431	C₂²	semidirect
60. #22575431	C₂²	semidirect
61. #22575431	C₂²	semidirect
62. #22575430	C₂²	semidirect
63. #22575430	C₂²	semidirect
64. #22575430	C₂²	semidirect
67. #22575429	C₂²	semidirect
68. #22575429	C₂²	semidirect
69. #22575429	C₂²	semidirect
72. #22575428	C₂²	semidirect
73. #22575428	C₂²	semidirect
74. #22575428	C₂²	semidirect
75. #22575428	C₂²	semidirect
77. #22575427	C₂²	semidirect
79. #22575426	C₂²	semidirect
80. #22575426	C₂²	semidirect
81. #22575426	C₂²	semidirect
82. #22575426	C₂²	semidirect
83. #22575426	C₂²	semidirect
85. #22575425	C₂²	semidirect
87. #22575424	C₂²	semidirect
88. #22575424	C₂²	semidirect
93. C₄×Dic₅₃₈	C₂²	semidirect
97. C₄×D₁₀₇₆	C₂²	semidirect
98. C₄×D₁₀₇₆	C₂²	semidirect
99. C₄×D₁₀₇₆	C₂²	semidirect
100. C₄×D₁₀₇₆	C₂²	semidirect
102. #22575413	C₂²	semidirect
104. C₄⋊C₄×D₂₆₉	C₂²	semidirect
105. C₄⋊C₄×D₂₆₉	C₂²	semidirect
106. C₄⋊C₄×D₂₆₉	C₂²	semidirect
107. C₄⋊C₄×D₂₆₉	C₂²	semidirect
112. C₄⋊Q₈×C₂₆₉	C₂²	semidirect
113. #126×C₂₆₉	C₂²	semidirect
114. #124×C₂₆₉	C₂²	semidirect
115. #124×C₂₆₉	C₂²	semidirect
116. #123×C₂₆₉	C₂²	semidirect
117. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
118. C₂²⋊Q₈×C₂₆₉	C₂²	semidirect
120. C₄×Q₈×C₂₆₉	C₂²	semidirect
121. C₄×D₄×C₂₆₉	C₂²	semidirect
122. #117×C₂₆₉	C₂²	semidirect
351. C₂₆₉	#3536	semidirect
367. #542	D₂₆₉	semidirect
386. C₄⋊Q₈	C₂×D₂₆₉	semidirect
388. #126	C₂×D₂₆₉	semidirect
395. #124	C₂×D₂₆₉	semidirect
396. #124	C₂×D₂₆₉	semidirect
406. #123	C₂×D₂₆₉	semidirect
427. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
428. C₂²⋊Q₈	C₂×D₂₆₉	semidirect
454. C₄×Q₈	C₂×D₂₆₉	semidirect
464. C₄×D₄	C₂×D₂₆₉	semidirect
465. #117	C₂×D₂₆₉	semidirect

Maximal subgroups

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

subgroup	index
#31771352	2
#31771349	2
#31771316	2
#31771315	2
#31771267	2
#31771263	2
#31771260	2
#31771258	2
#31771250	2
#31771248	2
#31771247	2
#31771230	2
#31771226	2
#31771196	2
#31771194	2
#31771185	2
#31771184	2
#31771117	2
C₂²⋊Q₈×D₂₆₉	2
#121×D₂₆₉	2
#542×C₂₆₉	2
#3536	269