Subgroups — #46824439

Order 34432.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771323	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771318	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771310	C₂	1	1	yes	maximal, characteristic, complemented
4	#31771303	C₂	1	1	yes	maximal, characteristic, complemented
5	#31771299	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771294	C₂	1	1	yes	maximal, characteristic, complemented
7	#31771290	C₂	1	1	yes	maximal, characteristic, complemented
8	#31771288	C₂	1	2	yes	maximal, complemented
9	#31771281	C₂	1	2	yes	maximal, complemented
10	#31771279	C₂	1	2	yes	maximal, complemented
11	#31771256	C₂	1	1	yes	maximal, characteristic, complemented
12	#31771245	C₂	1	2	yes	maximal, complemented
13	#31771158	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771139	C₂	1	2	yes	maximal, complemented
15	#31771133	C₂	1	2	yes	maximal, complemented
16	#31771133	C₂	1	2	yes	maximal, complemented
17	#31771117	C₂	1	1	yes	maximal, characteristic, complemented
18	#31771116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#16864402	C₂	1	2	yes	maximal, complemented
20	#31771073	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×C₂²⋊D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#117×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16864402	C₂²	1	2	yes	—
25	C₂×#16864402	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₂₆₉	C₂²	1	1	yes	characteristic
28	#22575452	C₂²	1	1	yes	characteristic, complemented
29	#22575452	C₂²	1	1	yes	characteristic, complemented
30	#22575448	C₂²	1	2	yes	complemented
31	#22575448	C₂²	1	2	yes	complemented
32	#22575447	C₂²	1	2	yes	complemented
33	#22575447	C₂²	1	2	yes	complemented
34	#22575446	C₂²	1	2	yes	complemented
35	#22575446	C₂²	1	2	yes	complemented
36	#22575445	C₂²	1	2	yes	complemented
37	#22575444	C₂²	1	1	yes	characteristic, complemented
38	#22575444	C₂²	1	1	yes	characteristic, complemented
39	#22575443	C₂²	1	2	yes	complemented
40	#22575443	C₂²	1	2	yes	complemented
41	#22575441	C₂²	1	2	yes	complemented
42	#22575439	C₂²	1	2	yes	—
43	#22575439	C₂²	1	2	yes	complemented
44	#22575438	C₂²	1	2	yes	complemented
45	#22575438	C₂²	1	2	yes	complemented
46	#22575437	C₂²	1	2	yes	—
47	#22575436	C₂²	1	2	yes	—
48	#22575436	C₂²	1	2	yes	—
49	#22575436	C₂²	1	2	yes	complemented
50	#22575435	C₂²	1	2	yes	—
51	#22575435	C₂²	1	2	yes	complemented
52	#22575433	C₂²	1	1	yes	characteristic, complemented
53	#22575433	C₂²	1	1	yes	characteristic, complemented
54	#22575432	C₂²	1	2	yes	complemented
55	#22575432	C₂²	1	1	yes	characteristic, complemented
56	#22575432	C₂²	1	1	yes	characteristic, complemented
57	#22575431	C₂²	1	2	yes	complemented
58	#22575431	C₂²	1	2	yes	complemented
59	#22575430	C₂²	1	2	yes	—
60	#22575430	C₂²	1	2	yes	—
61	#22575428	C₂²	1	1	yes	characteristic, complemented
62	#22575428	C₂²	1	1	yes	characteristic, complemented
63	#22575427	C₂²	1	2	yes	—
64	#22575427	C₂²	1	1	yes	characteristic, complemented
65	#22575427	C₂²	1	1	yes	characteristic, complemented
66	#22575426	C₂²	1	2	yes	—
67	#22575426	C₂²	1	2	yes	—
68	#22575423	C₂²	1	2	yes	—
69	#22575422	C₂²	1	2	yes	—
70	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
71	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
72	C₄×Dic₅₃₈	C₂²	1	2	yes	complemented
73	#22575418	C₂²	1	1	yes	characteristic, complemented
74	#22575418	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
76	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
77	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
78	#22575415	C₂²	1	1	yes	characteristic, complemented
79	#22575415	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₂₆₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
92	#22575413	C₂²	1	2	yes	—
93	#22575413	C₂²	1	2	yes	—
94	#22575412	C₂²	1	1	yes	characteristic
95	#22575412	C₂²	1	2	yes	complemented
96	#22575411	C₂²	1	1	yes	characteristic, complemented
97	#22575411	C₂²	1	1	yes	characteristic, complemented
98	#22575410	C₂²	1	2	yes	complemented
99	#22575410	C₂²	1	2	yes	complemented
100	#22575410	C₂²	1	2	yes	complemented
101	#22575410	C₂²	1	2	yes	complemented
102	#22575409	C₂²	1	2	yes	—
103	C₂×#16864381	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₂₆₉	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊Dic₂₆₉	C₂²	1	1	yes	characteristic
107	C₂×#16864379	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₂₆₉	C₂²	1	2	yes	—
109	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
110	C₄²×D₂₆₉	C₂²	1	2	yes	complemented
111	C₄²×D₂₆₉	C₂²	1	2	yes	complemented
112	C₂³×C₄×C₂₆₉	C₂²	1	1	yes	characteristic
113	#117×C₂₆₉	C₂²	1	1	yes	characteristic
114	#117×C₂₆₉	C₂²	1	2	yes	—
115	#117×C₂₆₉	C₂²	1	1	yes	characteristic
116	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
117	#117×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
118	#117×C₂₆₉	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	—
122	C₂×C₄²×C₂₆₉	C₂²	1	2	yes	complemented
123	C₂³×D₂₆₉	C₂³	1	1	yes	characteristic
124	#16864402	—	2	8	no	—
125	#16864402	—	2	4	no	—
126	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₅₃₈	C₂³	1	2	yes	—
128	C₂×Dic₅₃₈	C₂³	1	2	yes	—
129	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
130	C₂×D₁₀₇₆	C₂³	1	2	yes	—
131	C₂×D₁₀₇₆	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₂₆₉	—	2	4	no	—
133	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₆₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
142	C₂²×Dic₂₆₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₂₆₉	—	2	4	no	—
144	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
146	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
147	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
148	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₆₉	C₂³	1	1	yes	characteristic
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	—
153	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
156	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
157	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
158	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
159	#16864381	C₂³	1	2	yes	—
160	#16864381	C₂³	1	2	yes	—
161	#16864381	C₂³	1	1	yes	characteristic
162	#16864381	C₂³	1	1	yes	characteristic
163	#16864381	C₂³	1	1	yes	characteristic
164	#16864381	C₂³	1	1	yes	characteristic
165	#16864381	C₂³	1	2	yes	—
166	#16864381	C₂³	1	2	yes	—
167	#16864381	C₂³	1	2	yes	—
168	#16864381	C₂³	1	2	yes	—
169	#16864381	C₂³	1	2	yes	—
170	#16864381	C₂³	1	2	yes	—
171	#16864381	C₂³	1	2	yes	—
172	#16864381	C₂³	1	2	yes	—
173	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
180	#16864379	C₂³	1	2	yes	—
181	#16864379	C₂³	1	2	yes	—
182	#16864379	C₂³	1	1	yes	characteristic
183	#16864379	C₂³	1	1	yes	characteristic
184	#16864379	C₂³	1	1	yes	characteristic
185	#16864379	C₂³	1	1	yes	characteristic
186	#16864379	C₂³	1	2	yes	—
187	#16864379	C₂³	1	2	yes	—
188	#16864379	C₂³	1	2	yes	—
189	#16864379	C₂³	1	2	yes	—
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	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₂₆₉	C₂³	1	2	yes	—
196	C₄×Dic₂₆₉	C₂³	1	2	yes	—
197	C₄×Dic₂₆₉	C₂³	1	2	yes	—
198	C₄×Dic₂₆₉	C₂³	1	2	yes	—
199	C₄×Dic₂₆₉	C₂³	1	2	yes	—
200	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₂₆₉	C₂³	1	1	yes	characteristic
203	C₂⁴×C₂₆₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₂₆₉	—	2	4	no	—
205	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
207	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
223	C₄²×C₂₆₉	C₂³	1	2	yes	—
224	C₄²×C₂₆₉	C₂³	1	2	yes	—
225	C₄²×C₂₆₉	C₂³	1	2	yes	—
226	C₄²×C₂₆₉	C₂³	1	2	yes	—
227	C₂²×D₂₆₉	—	2	2	no	—
228	C₂²×D₂₆₉	—	2	2	no	—
229	C₂²×D₂₆₉	—	4	1	no	—
230	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
232	C₂²×D₂₆₉	C₂⁴	1	1	yes	characteristic
233	Dic₅₃₈	—	2	2	no	—
234	Dic₅₃₈	—	2	4	no	—
235	Dic₅₃₈	—	4	2	no	—
236	D₁₀₇₆	—	2	4	no	—
237	D₁₀₇₆	—	2	2	no	—
238	D₁₀₇₆	—	4	2	no	—
239	C₂²⋊D₂₆₉	—	2	2	no	—
240	C₂²⋊D₂₆₉	—	2	4	no	—
241	C₂²⋊D₂₆₉	—	2	4	no	—
242	C₂²⋊D₂₆₉	—	2	2	no	—
243	C₂²⋊D₂₆₉	—	2	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	2	no	—
248	C₂×Dic₂₆₉	—	4	1	no	—
249	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
253	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
254	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
255	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₂₆₉	C₂⁴	1	1	yes	characteristic
258	C₄×D₂₆₉	—	2	4	no	—
259	C₄×D₂₆₉	—	2	2	no	—
260	C₄×D₂₆₉	—	2	2	no	—
261	C₄×D₂₆₉	—	2	2	no	—
262	C₄×D₂₆₉	—	2	2	no	—
263	C₄×D₂₆₉	—	2	4	no	—
264	C₄×D₂₆₉	—	2	4	no	—
265	C₄×D₂₆₉	—	4	2	no	—
266	C₄×D₂₆₉	—	4	2	no	—
267	C₂³×C₂₆₉	—	2	2	no	—
268	C₂³×C₂₆₉	—	2	2	no	—
269	C₂³×C₂₆₉	—	4	1	no	—
270	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
271	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
272	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₂₆₉	—	2	2	no	—
274	C₂×C₄×C₂₆₉	—	2	4	no	—
275	C₂×C₄×C₂₆₉	—	2	2	no	—
276	C₂×C₄×C₂₆₉	—	2	2	no	—
277	C₂×C₄×C₂₆₉	—	2	2	no	—
278	C₂×C₄×C₂₆₉	—	2	2	no	—
279	C₂×C₄×C₂₆₉	—	4	2	no	—
280	C₂×C₄×C₂₆₉	#41	1	4	yes	complemented
281	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
283	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
284	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
285	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
286	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₂₆₉	—	2	1	no	—
290	C₂²×C₂₆₉	—	2	1	no	—
291	C₂²×C₂₆₉	—	2	1	no	—
292	C₂²×C₂₆₉	—	2	1	no	—
293	C₂²×C₂₆₉	—	2	1	no	—
294	C₂²×C₂₆₉	—	2	1	no	—
295	C₂²×C₂₆₉	—	2	1	no	—
296	C₂²×C₂₆₉	—	4	4	no	—
297	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
298	C₂²×C₂₆₉	C₂×#41	1	2	yes	—
299	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
300	C₂×D₂₆₉	—	2	1	no	—
301	C₂×D₂₆₉	—	2	1	no	—
302	C₂×D₂₆₉	—	2	1	no	—
303	C₂×D₂₆₉	—	2	2	no	—
304	C₂×D₂₆₉	—	2	2	no	—
305	C₂×D₂₆₉	—	2	1	no	—
306	C₂×D₂₆₉	—	2	2	no	—
307	C₂×D₂₆₉	—	2	1	no	—
308	C₂×D₂₆₉	—	4	4	no	—
309	C₂×D₂₆₉	C₂×#41	1	2	yes	—
310	C₄×C₂₆₉	—	2	1	no	—
311	C₄×C₂₆₉	—	2	1	no	—
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	C₂×#41	1	2	yes	—
317	C₄×C₂₆₉	C₂×#41	1	2	yes	—
318	Dic₂₆₉	—	2	1	no	—
319	Dic₂₆₉	—	2	1	no	—
320	Dic₂₆₉	—	2	2	no	—
321	Dic₂₆₉	—	2	2	no	—
322	Dic₂₆₉	—	2	1	no	—
323	Dic₂₆₉	—	2	1	no	—
324	Dic₂₆₉	—	2	2	no	—
325	Dic₂₆₉	—	2	1	no	—
326	Dic₂₆₉	C₂×#41	1	2	yes	—
327	C₂×C₂₆₉	—	2	2	no	—
328	C₂×C₂₆₉	—	2	2	no	—
329	C₂×C₂₆₉	—	4	1	no	—
330	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
331	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
332	C₂×C₂₆₉	#585	1	1	yes	characteristic
333	D₂₆₉	—	2	2	no	—
334	D₂₆₉	—	4	2	no	—
335	D₂₆₉	—	4	1	no	—
336	C₂₆₉	#3475	1	1	yes	characteristic, complemented, Sylow
337	#3475	—	269	1	no	maximal, Sylow
338	#556	—	269	1	no	—
339	#555	—	269	1	no	—
340	#554	—	269	1	no	—
341	#553	—	269	1	no	—
342	#553	—	269	1	no	—
343	#552	—	269	2	no	—
344	#552	—	269	1	no	—
345	#552	—	269	1	no	—
346	#551	—	269	2	no	—
347	#551	—	269	2	no	—
348	#547	—	269	1	no	—
349	#546	—	269	2	no	—
350	#533	—	269	1	no	—
351	#529	—	269	2	no	—
352	#529	—	269	2	no	—
353	#529	—	269	2	no	—
354	#525	—	269	1	no	—
355	#525	—	269	1	no	—
356	C₄×#41	—	269	1	no	—
357	C₄×#41	—	269	2	no	—
358	C₂×C₄×D₄	—	269	1	no	—
359	C₂×#117	—	269	1	no	—
360	C₂×#117	D₂₆₉	1	1	yes	characteristic, complemented
361	C₂×#41	—	269	1	no	—
362	C₂×#41	—	269	2	no	—
363	C₂²×D₄	—	269	1	no	—
364	C₂³×C₄	—	269	1	no	—
365	C₂³×C₄	C₂×D₂₆₉	1	1	yes	characteristic
366	C₄⋊Q₈	—	269	1	no	—
367	C₄⋊Q₈	—	269	1	no	—
368	#126	—	269	2	no	—
369	#126	—	269	2	no	—
370	#126	—	269	2	no	—
371	#126	—	269	2	no	—
372	#126	—	269	2	no	—
373	#126	—	269	2	no	—
374	#125	—	269	2	no	—
375	#125	—	269	2	no	—
376	#125	—	269	1	no	—
377	#125	—	269	1	no	—
378	#125	—	269	2	no	—
379	#124	—	269	2	no	—
380	#124	—	269	2	no	—
381	#124	—	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	—	269	2	no	—
387	#123	—	269	2	no	—
388	#123	—	269	2	no	—
389	#123	—	269	2	no	—
390	C₂²⋊Q₈	—	269	1	no	—
391	C₂²⋊Q₈	—	269	1	no	—
392	C₂²⋊Q₈	—	269	2	no	—
393	C₂²⋊Q₈	—	269	1	no	—
394	C₂²⋊Q₈	—	269	1	no	—
395	C₂²⋊Q₈	—	269	2	no	—
396	C₂²⋊Q₈	—	269	2	no	—
397	C₂²⋊Q₈	—	269	2	no	—
398	C₂²⋊Q₈	—	269	2	no	—
399	#121	—	269	1	no	—
400	#121	—	269	1	no	—
401	#121	—	269	2	no	—
402	#121	—	269	1	no	—
403	#121	—	269	1	no	—
404	#121	—	269	2	no	—
405	#121	—	269	2	no	—
406	#120	—	269	2	no	—
407	#120	—	269	2	no	—
408	C₄×Q₈	—	269	1	no	—
409	C₄×Q₈	—	269	1	no	—
410	C₄×Q₈	—	269	2	no	—
411	C₄×Q₈	—	269	2	no	—
412	C₄×Q₈	—	269	2	no	—
413	C₄×D₄	—	269	1	no	—
414	C₄×D₄	—	269	1	no	—
415	C₄×D₄	—	269	1	no	—
416	C₄×D₄	—	269	1	no	—
417	C₄×D₄	—	269	1	no	—
418	C₄×D₄	—	269	1	no	—
419	C₄×D₄	—	269	1	no	—
420	C₄×D₄	—	269	1	no	—
421	C₄×D₄	—	269	2	no	—
422	C₄×D₄	—	269	2	no	—
423	C₄×D₄	—	269	2	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	2	no	—
429	C₄×D₄	—	269	2	no	—
430	C₄×D₄	—	269	2	no	—
431	C₄×D₄	—	269	2	no	—
432	#117	—	269	1	no	—
433	#117	—	269	2	no	—
434	#117	—	269	1	no	—
435	#117	—	269	1	no	—
436	#117	—	269	2	no	—
437	#117	—	269	2	no	—
438	#117	—	269	2	no	—
439	#117	—	269	2	no	—
440	#117	—	269	2	no	—
441	#117	C₂×D₂₆₉	1	1	yes	characteristic
442	#117	C₂×D₂₆₉	1	1	yes	characteristic
443	#117	C₂×D₂₆₉	1	2	yes	—
444	#117	C₂×D₂₆₉	1	2	yes	complemented
445	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
446	#117	C₂×D₂₆₉	1	1	yes	characteristic, complemented
447	C₂×C₄⋊C₄	—	269	1	no	—
448	C₂×C₄⋊C₄	—	269	1	no	—
449	C₂×C₄⋊C₄	—	269	1	no	—
450	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
451	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
452	C₂×C₂²⋊C₄	—	269	1	no	—
453	C₂×C₂²⋊C₄	—	269	1	no	—
454	C₂×C₂²⋊C₄	—	269	2	no	—
455	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	—
456	C₂×C₄²	—	269	1	no	—
457	C₂×C₄²	—	269	2	no	—
458	C₂×C₄²	—	269	2	no	—
459	C₂×C₄²	C₂×D₂₆₉	1	2	yes	complemented
460	C₂⁴	—	269	1	no	—
461	C₂⁴	C₂²×D₂₆₉	1	1	yes	characteristic
462	#41	—	538	8	no	—
463	#41	—	538	4	no	—
464	C₂×Q₈	—	269	1	no	—
465	C₂×Q₈	—	269	2	no	—
466	C₂×Q₈	—	269	2	no	—
467	C₂×D₄	—	269	1	no	—
468	C₂×D₄	—	269	2	no	—
469	C₂×D₄	—	269	2	no	—
470	C₂×D₄	—	269	1	no	—
471	C₂×D₄	—	269	1	no	—
472	C₂×D₄	—	269	1	no	—
473	C₂×D₄	—	269	2	no	—
474	C₂×D₄	—	269	2	no	—
475	C₂×D₄	—	269	1	no	—
476	C₂×D₄	—	269	2	no	—
477	C₂×D₄	—	538	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	269	1	no	—
480	C₂²×C₄	—	269	1	no	—
481	C₂²×C₄	—	269	1	no	—
482	C₂²×C₄	—	269	2	no	—
483	C₂²×C₄	—	269	2	no	—
484	C₂²×C₄	—	269	1	no	—
485	C₂²×C₄	—	269	1	no	—
486	C₂²×C₄	—	269	1	no	—
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	—	538	4	no	—
492	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
493	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
499	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
500	C₄⋊C₄	—	269	1	no	—
501	C₄⋊C₄	—	269	1	no	—
502	C₄⋊C₄	—	269	1	no	—
503	C₄⋊C₄	—	269	2	no	—
504	C₄⋊C₄	—	269	2	no	—
505	C₄⋊C₄	—	269	1	no	—
506	C₄⋊C₄	—	269	1	no	—
507	C₄⋊C₄	—	269	1	no	—
508	C₄⋊C₄	—	269	2	no	—
509	C₄⋊C₄	—	269	2	no	—
510	C₄⋊C₄	—	269	2	no	—
511	C₄⋊C₄	—	269	2	no	—
512	C₄⋊C₄	—	269	2	no	—
513	C₄⋊C₄	—	269	2	no	—
514	C₄⋊C₄	—	269	2	no	—
515	C₄⋊C₄	—	269	2	no	—
516	C₄⋊C₄	—	269	2	no	—
517	C₄⋊C₄	—	269	2	no	—
518	C₄⋊C₄	—	269	2	no	—
519	C₄⋊C₄	—	269	2	no	—
520	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
525	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
526	C₂²⋊C₄	—	269	1	no	—
527	C₂²⋊C₄	—	269	2	no	—
528	C₂²⋊C₄	—	269	1	no	—
529	C₂²⋊C₄	—	269	1	no	—
530	C₂²⋊C₄	—	269	1	no	—
531	C₂²⋊C₄	—	269	2	no	—
532	C₂²⋊C₄	—	269	2	no	—
533	C₂²⋊C₄	—	269	1	no	—
534	C₂²⋊C₄	—	269	2	no	—
535	C₂²⋊C₄	—	269	2	no	—
536	C₂²⋊C₄	—	269	1	no	—
537	C₂²⋊C₄	—	269	1	no	—
538	C₂²⋊C₄	—	269	1	no	—
539	C₂²⋊C₄	—	269	2	no	—
540	C₂²⋊C₄	—	269	2	no	—
541	C₂²⋊C₄	—	269	2	no	—
542	C₂²⋊C₄	—	269	2	no	—
543	C₂²⋊C₄	—	269	2	no	—
544	C₂²⋊C₄	—	269	2	no	—
545	C₂²⋊C₄	—	269	2	no	—
546	C₂²⋊C₄	—	269	2	no	—
547	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
551	C₄²	—	269	2	no	—
552	C₄²	—	269	2	no	—
553	C₄²	—	269	2	no	—
554	C₄²	—	269	1	no	—
555	C₄²	—	269	1	no	—
556	C₄²	—	269	2	no	—
557	C₄²	—	269	1	no	—
558	C₄²	—	269	1	no	—
559	C₄²	—	269	2	no	—
560	C₄²	C₂²×D₂₆₉	1	2	yes	—
561	C₄²	C₂²×D₂₆₉	1	2	yes	—
562	C₄²	C₂²×D₂₆₉	1	2	yes	—
563	C₄²	C₂²×D₂₆₉	1	2	yes	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	269	1	no	—
568	C₂³	—	269	1	no	—
569	C₂³	—	269	2	no	—
570	C₂³	—	538	2	no	—
571	C₂³	—	538	2	no	—
572	C₂³	—	1076	1	no	—
573	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
574	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
575	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
576	Q₈	—	538	4	no	—
577	Q₈	—	538	2	no	—
578	Q₈	—	1076	2	no	—
579	D₄	—	269	4	no	—
580	D₄	—	538	4	no	—
581	D₄	—	538	2	no	—
582	D₄	—	538	2	no	—
583	D₄	—	538	2	no	—
584	D₄	—	538	4	no	—
585	D₄	—	538	4	no	—
586	D₄	—	538	2	no	—
587	D₄	—	1076	2	no	—
588	D₄	—	1076	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	269	1	no	—
597	C₂×C₄	—	269	1	no	—
598	C₂×C₄	—	269	1	no	—
599	C₂×C₄	—	269	1	no	—
600	C₂×C₄	—	269	2	no	—
601	C₂×C₄	—	269	2	no	—
602	C₂×C₄	—	269	2	no	—
603	C₂×C₄	—	269	1	no	—
604	C₂×C₄	—	269	1	no	—
605	C₂×C₄	—	538	4	no	—
606	C₂×C₄	—	538	4	no	—
607	C₂×C₄	—	538	2	no	—
608	C₂×C₄	—	538	2	no	—
609	C₂×C₄	—	538	2	no	—
610	C₂×C₄	—	538	2	no	—
611	C₂×C₄	—	538	2	no	—
612	C₂×C₄	—	538	2	no	—
613	C₂×C₄	—	538	4	no	—
614	C₂×C₄	—	1076	2	no	—
615	C₂×C₄	—	1076	2	no	—
616	C₂×C₄	—	1076	1	no	—
617	C₂×C₄	#16864402	1	4	yes	complemented
618	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
619	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
620	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
622	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
623	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	269	2	no	—
635	C₂²	—	538	1	no	—
636	C₂²	—	538	1	no	—
637	C₂²	—	538	2	no	—
638	C₂²	—	538	1	no	—
639	C₂²	—	538	1	no	—
640	C₂²	—	538	2	no	—
641	C₂²	—	538	2	no	—
642	C₂²	—	538	1	no	—
643	C₂²	—	1076	4	no	—
644	C₂²	#41×D₂₆₉	1	2	yes	—
645	C₂²	C₂×#16864402	1	2	yes	—
646	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	269	2	no	—
654	C₄	—	538	1	no	—
655	C₄	—	538	2	no	—
656	C₄	—	538	1	no	—
657	C₄	—	538	1	no	—
658	C₄	—	538	2	no	—
659	C₄	—	538	1	no	—
660	C₄	—	538	2	no	—
661	C₄	—	538	1	no	—
662	C₄	C₂×#16864402	1	2	yes	—
663	C₄	C₂×#16864402	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	2	2	no	—
666	C₂	—	4	1	no	—
667	C₂	—	538	2	no	—
668	C₂	—	1076	1	no	—
669	C₂	—	1076	2	no	—
670	C₂	C₂×#41×D₂₆₉	1	1	yes	characteristic
671	C₂	C₂²×#16864402	1	1	yes	characteristic
672	C₂	#31771441	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Frattini	C₂²	C₂⁴×D₂₆₉
Fitting	C₂×#117×C₂₆₉	C₂
hypercenter	C₂×#117	D₂₆₉
hypocenter	C₂₆₉	#3475
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #31771323	C₂	semidirect
2. #31771318	C₂	semidirect
3. #31771310	C₂	semidirect
4. #31771303	C₂	semidirect
5. #31771299	C₂	semidirect
6. #31771294	C₂	semidirect
7. #31771290	C₂	semidirect
8. #31771288	C₂	semidirect
9. #31771281	C₂	semidirect
10. #31771279	C₂	semidirect
11. #31771256	C₂	semidirect
12. #31771245	C₂	semidirect
13. #31771158	C₂	semidirect
14. #31771139	C₂	semidirect
15. #31771133	C₂	semidirect
16. #31771133	C₂	semidirect
17. #31771117	C₂	semidirect
18. #31771116	C₂	semidirect
19. C₄×#16864402	C₂	semidirect
20. #31771073	C₂	semidirect
21. C₂×C₄×C₂²⋊D₂₆₉	C₂	semidirect
22. #117×D₂₆₉	C₂	semidirect
23. C₂×#117×C₂₆₉	C₂	semidirect
28. #22575452	C₂²	semidirect
29. #22575452	C₂²	semidirect
30. #22575448	C₂²	semidirect
31. #22575448	C₂²	semidirect
32. #22575447	C₂²	semidirect
33. #22575447	C₂²	semidirect
34. #22575446	C₂²	semidirect
35. #22575446	C₂²	semidirect
36. #22575445	C₂²	semidirect
37. #22575444	C₂²	semidirect
38. #22575444	C₂²	semidirect
39. #22575443	C₂²	semidirect
40. #22575443	C₂²	semidirect
41. #22575441	C₂²	semidirect
43. #22575439	C₂²	semidirect
44. #22575438	C₂²	semidirect
45. #22575438	C₂²	semidirect
49. #22575436	C₂²	semidirect
51. #22575435	C₂²	semidirect
52. #22575433	C₂²	semidirect
53. #22575433	C₂²	semidirect
54. #22575432	C₂²	semidirect
55. #22575432	C₂²	semidirect
56. #22575432	C₂²	semidirect
57. #22575431	C₂²	semidirect
58. #22575431	C₂²	semidirect
61. #22575428	C₂²	semidirect
62. #22575428	C₂²	semidirect
64. #22575427	C₂²	semidirect
65. #22575427	C₂²	semidirect
70. C₄×Dic₅₃₈	C₂²	semidirect
71. C₄×Dic₅₃₈	C₂²	semidirect
72. C₄×Dic₅₃₈	C₂²	semidirect
73. #22575418	C₂²	semidirect
74. #22575418	C₂²	semidirect
75. C₄×D₁₀₇₆	C₂²	semidirect
76. C₄×D₁₀₇₆	C₂²	semidirect
77. C₄×D₁₀₇₆	C₂²	semidirect
78. #22575415	C₂²	semidirect
79. #22575415	C₂²	semidirect
89. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
90. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
91. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
95. #22575412	C₂²	semidirect
96. #22575411	C₂²	semidirect
97. #22575411	C₂²	semidirect
98. #22575410	C₂²	semidirect
99. #22575410	C₂²	semidirect
100. #22575410	C₂²	semidirect
101. #22575410	C₂²	semidirect
104. C₄⋊C₄×D₂₆₉	C₂²	semidirect
105. C₄⋊C₄×D₂₆₉	C₂²	semidirect
110. C₄²×D₂₆₉	C₂²	semidirect
111. C₄²×D₂₆₉	C₂²	semidirect
116. #117×C₂₆₉	C₂²	semidirect
117. #117×C₂₆₉	C₂²	semidirect
118. #117×C₂₆₉	C₂²	semidirect
119. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
120. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
122. C₂×C₄²×C₂₆₉	C₂²	semidirect
245. C₂²⋊D₂₆₉	#41	semidirect
280. C₂×C₄×C₂₆₉	#41	semidirect
336. C₂₆₉	#3475	semidirect
360. C₂×#117	D₂₆₉	semidirect
444. #117	C₂×D₂₆₉	semidirect
445. #117	C₂×D₂₆₉	semidirect
446. #117	C₂×D₂₆₉	semidirect
450. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
451. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
459. C₂×C₄²	C₂×D₂₆₉	semidirect
617. C₂×C₄	#16864402	semidirect

Maximal subgroups

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

subgroup	index
#31771323	2
#31771318	2
#31771310	2
#31771303	2
#31771299	2
#31771294	2
#31771290	2
#31771288	2
#31771281	2
#31771279	2
#31771256	2
#31771245	2
#31771158	2
#31771139	2
#31771133	2
#31771117	2
#31771116	2
C₄×#16864402	2
#31771073	2
C₂×C₄×C₂²⋊D₂₆₉	2
#117×D₂₆₉	2
C₂×#117×C₂₆₉	2
#3475	269