Subgroups — #46824917

Order 34432.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771320	C₂	1	1	yes	maximal, characteristic, complemented
2	#31771312	C₂	1	1	yes	maximal, characteristic, complemented
3	#31771303	C₂	1	2	yes	maximal, complemented
4	#31771301	C₂	1	2	yes	maximal, complemented
5	#31771276	C₂	1	1	yes	maximal, characteristic, complemented
6	#31771251	C₂	1	2	yes	maximal, complemented
7	#31771245	C₂	1	4	yes	maximal, complemented
8	D₄×D₁₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₂²⋊D₂₆₉	C₂	1	2	yes	maximal, complemented
10	#31771206	C₂	1	2	yes	maximal, complemented
11	#31771188	C₂	1	4	yes	maximal, complemented
12	#31771155	C₂	1	1	yes	maximal, characteristic, complemented
13	#31771139	C₂	1	1	yes	maximal, characteristic, complemented
14	#31771116	C₂	1	2	yes	maximal, complemented
15	C₂×#22575427	C₂	1	2	yes	maximal, complemented
16	#31771077	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16864402	C₂²	1	2	yes	complemented
19	C₂×#16864402	C₂²	1	2	yes	complemented
20	C₂²×D₁₀₇₆	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
22	C₂×D₄×D₂₆₉	C₂²	1	2	yes	—
23	#22575453	C₂²	1	1	yes	characteristic, complemented
24	#22575450	C₂²	1	1	yes	characteristic, complemented
25	#22575449	C₂²	1	2	yes	complemented
26	#22575448	C₂²	1	4	yes	complemented
27	#22575447	C₂²	1	2	yes	complemented
28	#22575445	C₂²	1	1	yes	characteristic, complemented
29	#22575444	C₂²	1	2	yes	complemented
30	#22575441	C₂²	1	1	yes	characteristic, complemented
31	#22575441	C₂²	1	2	yes	complemented
32	#22575439	C₂²	1	4	yes	complemented
33	#22575438	C₂²	1	4	yes	complemented
34	#22575436	C₂²	1	2	yes	complemented
35	#22575436	C₂²	1	4	yes	complemented
36	#22575435	C₂²	1	4	yes	complemented
37	#22575432	C₂²	1	1	yes	characteristic, complemented
38	#22575432	C₂²	1	2	yes	complemented
39	#22575430	C₂²	1	4	yes	complemented
40	#22575428	C₂²	1	2	yes	complemented
41	#22575427	C₂²	1	1	yes	characteristic
42	#22575427	C₂²	1	2	yes	complemented
43	#22575427	C₂²	1	2	yes	complemented
44	#22575427	C₂²	1	4	yes	complemented
45	#22575427	C₂²	1	2	yes	complemented
46	#22575427	C₂²	1	4	yes	complemented
47	#22575427	C₂²	1	2	yes	complemented
48	#22575427	C₂²	1	2	yes	complemented
49	#22575426	C₂²	1	4	yes	complemented
50	#22575426	C₂²	1	4	yes	complemented
51	#22575425	C₂²	1	4	yes	complemented
52	#22575424	C₂²	1	2	yes	complemented
53	#22575423	C₂²	1	4	yes	complemented
54	#22575422	C₂²	1	4	yes	complemented
55	#22575421	C₂²	1	4	yes	complemented
56	C₄×Dic₅₃₈	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₁₀₇₆	C₂²	1	1	yes	characteristic, complemented
58	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
59	C₄×D₁₀₇₆	C₂²	1	2	yes	complemented
60	D₄×Dic₂₆₉	C₂²	1	2	yes	—
61	#22575415	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₂₆₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊D₂₆₉	C₂²	1	4	yes	complemented
65	#22575413	C₂²	1	4	yes	complemented
66	#22575412	C₂²	1	2	yes	complemented
67	#22575411	C₂²	1	2	yes	complemented
68	#22575410	C₂²	1	2	yes	complemented
69	C₂×C₄⋊Dic₂₆₉	C₂²	1	2	yes	complemented
70	C₂×#16864379	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₂₆₉	C₂²	1	4	yes	complemented
72	C₂²×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₂₆₉	C₂²	1	2	yes	complemented
74	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
77	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×D₄×C₂₆₉	C₂²	1	2	yes	complemented
79	C₄×D₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄⋊C₄×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊C₄×C₂₆₉	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₂₆₉	C₂³	1	4	yes	—
84	#16864402	—	4	4	no	—
85	#16864402	—	4	4	no	—
86	C₂×Dic₅₃₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₅₃₈	C₂³	1	2	yes	—
88	C₂×D₁₀₇₆	—	4	4	no	—
89	C₂×D₁₀₇₆	C₂³	1	2	yes	—
90	C₂×D₁₀₇₆	C₂³	1	1	yes	characteristic
91	C₂×D₁₀₇₆	C₂³	1	2	yes	—
92	C₂×D₁₀₇₆	C₂³	1	2	yes	—
93	C₂×D₁₀₇₆	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₂₆₉	—	4	8	no	—
95	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₂₆₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₂₆₉	C₂³	1	4	yes	—
101	D₄×D₂₆₉	—	2	8	no	—
102	C₂²×Dic₂₆₉	C₂³	1	4	yes	—
103	C₂×C₄×D₂₆₉	C₂³	1	2	yes	—
104	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
105	C₂×C₄×D₂₆₉	C₂³	1	4	yes	—
106	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
108	C₄⋊Dic₂₆₉	C₂³	1	4	yes	—
109	C₄⋊Dic₂₆₉	C₂³	1	2	yes	—
110	C₄⋊Dic₂₆₉	C₂³	1	1	yes	characteristic
111	#16864381	C₂³	1	2	yes	—
112	#16864381	C₂³	1	2	yes	—
113	#16864381	C₂³	1	2	yes	—
114	#16864381	C₂³	1	4	yes	—
115	#16864381	C₂³	1	2	yes	—
116	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₂₆₉	C₂³	1	4	yes	—
118	C₂²⋊Dic₂₆₉	C₂³	1	2	yes	—
119	#16864379	C₂³	1	2	yes	—
120	#16864379	C₂³	1	4	yes	—
121	#16864379	C₂³	1	2	yes	—
122	#16864379	C₂³	1	4	yes	—
123	#16864379	C₂³	1	4	yes	—
124	#16864379	C₂³	1	2	yes	—
125	#16864379	C₂³	1	4	yes	—
126	#16864379	C₂³	1	4	yes	—
127	#16864379	C₂³	1	2	yes	—
128	C₄×Dic₂₆₉	C₂³	1	2	yes	—
129	C₄×Dic₂₆₉	C₂³	1	4	yes	—
130	C₂⁴×C₂₆₉	C₂³	1	2	yes	—
131	C₂×D₄×C₂₆₉	—	2	4	no	—
132	C₂×D₄×C₂₆₉	C₂³	1	2	yes	—
133	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₂₆₉	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₂₆₉	—	4	4	no	—
136	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
138	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
142	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
143	C₂²×C₄×C₂₆₉	C₂³	1	2	yes	—
144	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₂₆₉	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₂₆₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₂₆₉	C₂³	1	2	yes	—
151	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
152	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
153	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
154	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
155	C₂²×D₂₆₉	—	2	8	no	—
156	C₂²×D₂₆₉	—	4	4	no	—
157	C₂²×D₂₆₉	—	4	4	no	—
158	C₂²×D₂₆₉	C₂⁴	1	2	yes	—
159	C₂²×D₂₆₉	C₂⁴	1	4	yes	—
160	Dic₅₃₈	—	2	2	no	—
161	Dic₅₃₈	—	4	2	no	—
162	D₁₀₇₆	—	2	4	no	—
163	D₁₀₇₆	—	2	2	no	—
164	D₁₀₇₆	—	2	4	no	—
165	D₁₀₇₆	—	4	4	no	—
166	D₁₀₇₆	—	4	2	no	—
167	C₂²⋊D₂₆₉	—	2	8	no	—
168	C₂²⋊D₂₆₉	—	2	4	no	—
169	C₂²⋊D₂₆₉	—	2	8	no	—
170	C₂²⋊D₂₆₉	—	4	4	no	—
171	C₂²⋊D₂₆₉	—	4	4	no	—
172	C₂²⋊D₂₆₉	—	4	4	no	—
173	C₂×Dic₂₆₉	—	4	4	no	—
174	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
175	C₂×Dic₂₆₉	C₂⁴	1	4	yes	—
176	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
177	C₂×Dic₂₆₉	C₂⁴	1	2	yes	—
178	C₄×D₂₆₉	—	2	4	no	—
179	C₄×D₂₆₉	—	4	4	no	—
180	C₄×D₂₆₉	—	4	4	no	—
181	C₂³×C₂₆₉	—	2	4	no	—
182	C₂³×C₂₆₉	—	2	4	no	—
183	C₂³×C₂₆₉	—	4	2	no	—
184	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
185	C₂³×C₂₆₉	C₂⁴	1	2	yes	—
186	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
187	D₄×C₂₆₉	—	2	4	no	—
188	D₄×C₂₆₉	—	2	2	no	—
189	D₄×C₂₆₉	#41	1	4	yes	complemented
190	C₂×C₄×C₂₆₉	—	2	2	no	—
191	C₂×C₄×C₂₆₉	—	2	2	no	—
192	C₂×C₄×C₂₆₉	—	2	2	no	—
193	C₂×C₄×C₂₆₉	—	2	4	no	—
194	C₂×C₄×C₂₆₉	—	2	4	no	—
195	C₂×C₄×C₂₆₉	—	4	2	no	—
196	C₂×C₄×C₂₆₉	—	4	2	no	—
197	C₂×C₄×C₂₆₉	—	4	2	no	—
198	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
200	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
201	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
202	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
203	C₂×C₄×C₂₆₉	C₂⁴	1	2	yes	—
204	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
205	C₂×C₄×C₂₆₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₂₆₉	—	2	1	no	—
207	C₂²×C₂₆₉	—	2	1	no	—
208	C₂²×C₂₆₉	—	2	2	no	—
209	C₂²×C₂₆₉	—	2	2	no	—
210	C₂²×C₂₆₉	—	2	2	no	—
211	C₂²×C₂₆₉	—	2	2	no	—
212	C₂²×C₂₆₉	—	2	2	no	—
213	C₂²×C₂₆₉	—	4	8	no	—
214	C₂²×C₂₆₉	C₂×#41	1	4	yes	—
215	C₂²×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
216	C₂²×C₂₆₉	C₂⁵	1	1	yes	characteristic
217	C₂×D₂₆₉	—	2	2	no	—
218	C₂×D₂₆₉	—	2	4	no	—
219	C₂×D₂₆₉	—	2	4	no	—
220	C₂×D₂₆₉	—	2	4	no	—
221	C₂×D₂₆₉	—	2	2	no	—
222	C₂×D₂₆₉	—	2	2	no	—
223	C₂×D₂₆₉	—	8	8	no	—
224	C₄×C₂₆₉	—	2	1	no	—
225	C₄×C₂₆₉	—	2	1	no	—
226	C₄×C₂₆₉	—	2	2	no	—
227	C₄×C₂₆₉	—	2	2	no	—
228	C₄×C₂₆₉	—	2	1	no	—
229	C₄×C₂₆₉	—	2	1	no	—
230	C₄×C₂₆₉	C₂×#41	1	2	yes	—
231	C₄×C₂₆₉	H(5,𝔽₂)	1	2	yes	—
232	Dic₂₆₉	—	2	2	no	—
233	Dic₂₆₉	—	2	2	no	—
234	Dic₂₆₉	—	2	4	no	—
235	Dic₂₆₉	—	2	2	no	—
236	C₂×C₂₆₉	—	2	4	no	—
237	C₂×C₂₆₉	—	2	2	no	—
238	C₂×C₂₆₉	—	4	2	no	—
239	C₂×C₂₆₉	C₂²×#41	1	1	yes	characteristic
240	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₂₆₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	D₂₆₉	—	4	4	no	—
243	D₂₆₉	—	4	2	no	—
244	C₂₆₉	#3519	1	1	yes	characteristic, complemented, Sylow
245	#3519	—	269	1	no	maximal, Sylow
246	#555	—	269	1	no	—
247	#554	—	269	1	no	—
248	#553	—	269	2	no	—
249	#553	—	269	2	no	—
250	#550	—	269	1	no	—
251	#546	—	269	2	no	—
252	#546	—	269	4	no	—
253	D₄²	—	269	2	no	—
254	D₄²	—	269	1	no	—
255	#540	—	269	2	no	—
256	#538	—	269	4	no	—
257	#532	—	269	1	no	—
258	#529	—	269	1	no	—
259	#525	—	269	2	no	—
260	C₂×#121	—	269	2	no	—
261	#518	—	269	2	no	—
262	C₂×C₄×D₄	D₂₆₉	1	1	yes	characteristic, complemented
263	C₂×#41	—	269	2	no	—
264	C₂×#41	—	269	2	no	—
265	C₂²×D₄	—	269	4	no	—
266	C₂²×D₄	—	269	2	no	—
267	C₂²×D₄	—	269	2	no	—
268	C₂²×D₄	C₂×D₂₆₉	1	1	yes	characteristic
269	C₂³×C₄	C₂×D₂₆₉	1	2	yes	complemented
270	C₄⋊Q₈	—	269	1	no	—
271	#127	—	269	2	no	—
272	#127	—	269	1	no	—
273	#126	—	269	4	no	—
274	#126	—	269	2	no	—
275	#125	—	269	2	no	—
276	#125	—	269	1	no	—
277	#124	—	269	4	no	—
278	#124	—	269	1	no	—
279	#124	—	269	2	no	—
280	#123	—	269	4	no	—
281	#123	—	269	2	no	—
282	#123	—	269	4	no	—
283	#123	—	269	4	no	—
284	C₂²⋊Q₈	—	269	1	no	—
285	C₂²⋊Q₈	—	269	2	no	—
286	C₂²⋊Q₈	—	269	4	no	—
287	#121	—	269	4	no	—
288	#121	—	269	2	no	—
289	#121	—	269	1	no	—
290	#121	—	269	2	no	—
291	#121	—	269	4	no	—
292	#121	—	269	4	no	—
293	#121	—	269	2	no	—
294	#121	—	269	2	no	—
295	#121	—	269	2	no	—
296	#121	—	269	2	no	—
297	#121	—	269	2	no	—
298	#121	—	269	4	no	—
299	#121	—	269	4	no	—
300	#120	—	269	4	no	—
301	#120	—	269	4	no	—
302	#120	—	269	4	no	—
303	C₄×Q₈	—	269	1	no	—
304	C₄×D₄	—	269	2	no	—
305	C₄×D₄	—	269	4	no	—
306	C₄×D₄	—	269	4	no	—
307	C₄×D₄	—	269	2	no	—
308	C₄×D₄	—	269	2	no	—
309	C₄×D₄	—	269	4	no	—
310	C₄×D₄	—	269	2	no	—
311	C₄×D₄	—	269	1	no	—
312	C₄×D₄	—	269	2	no	—
313	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
314	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic
315	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
316	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
317	C₄×D₄	C₂×D₂₆₉	1	2	yes	complemented
318	C₄×D₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
319	#117	—	269	2	no	—
320	#117	—	269	2	no	—
321	#117	—	269	2	no	—
322	C₂×C₄⋊C₄	—	269	2	no	—
323	C₂×C₄⋊C₄	C₂×D₂₆₉	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊C₄	—	269	4	no	—
325	C₂×C₂²⋊C₄	—	269	4	no	—
326	C₂×C₂²⋊C₄	C₂×D₂₆₉	1	2	yes	complemented
327	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic, complemented
328	C₂⁴	—	269	4	no	—
329	C₂⁴	C₂²×D₂₆₉	1	2	yes	—
330	#41	—	1076	4	no	—
331	#41	—	1076	4	no	—
332	C₂×Q₈	—	269	1	no	—
333	C₂×Q₈	—	269	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	269	4	no	—
336	C₂×D₄	—	269	4	no	—
337	C₂×D₄	—	269	2	no	—
338	C₂×D₄	—	269	4	no	—
339	C₂×D₄	—	269	4	no	—
340	C₂×D₄	—	269	4	no	—
341	C₂×D₄	—	269	2	no	—
342	C₂×D₄	—	269	1	no	—
343	C₂×D₄	—	269	2	no	—
344	C₂×D₄	—	269	2	no	—
345	C₂×D₄	—	269	4	no	—
346	C₂×D₄	—	538	8	no	—
347	C₂×D₄	—	1076	4	no	—
348	C₂×D₄	—	1076	8	no	—
349	C₂×D₄	C₂²×D₂₆₉	1	2	yes	—
350	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
351	C₂×D₄	C₂²×D₂₆₉	1	1	yes	characteristic
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	269	4	no	—
354	C₂²×C₄	—	269	2	no	—
355	C₂²×C₄	—	269	4	no	—
356	C₂²×C₄	—	269	4	no	—
357	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
359	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
360	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
361	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
362	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
363	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
364	C₂²×C₄	C₂²×D₂₆₉	1	2	yes	—
365	C₄⋊C₄	—	269	1	no	—
366	C₄⋊C₄	—	269	2	no	—
367	C₄⋊C₄	—	269	4	no	—
368	C₄⋊C₄	—	269	1	no	—
369	C₄⋊C₄	—	269	2	no	—
370	C₄⋊C₄	—	269	2	no	—
371	C₄⋊C₄	—	269	2	no	—
372	C₄⋊C₄	—	269	2	no	—
373	C₄⋊C₄	—	269	4	no	—
374	C₄⋊C₄	—	269	2	no	—
375	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂²×D₂₆₉	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×D₂₆₉	1	2	yes	—
378	C₂²⋊C₄	—	269	4	no	—
379	C₂²⋊C₄	—	269	4	no	—
380	C₂²⋊C₄	—	269	2	no	—
381	C₂²⋊C₄	—	269	2	no	—
382	C₂²⋊C₄	—	269	4	no	—
383	C₂²⋊C₄	—	269	2	no	—
384	C₂²⋊C₄	—	269	4	no	—
385	C₂²⋊C₄	—	269	4	no	—
386	C₂²⋊C₄	—	269	2	no	—
387	C₂²⋊C₄	—	269	2	no	—
388	C₂²⋊C₄	—	269	4	no	—
389	C₂²⋊C₄	—	269	4	no	—
390	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
391	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
392	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₂₆₉	1	2	yes	—
394	C₄²	—	269	4	no	—
395	C₄²	—	269	2	no	—
396	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
397	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
398	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
399	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	269	2	no	—
404	C₂³	—	269	4	no	—
405	C₂³	—	538	8	no	—
406	C₂³	—	1076	4	no	—
407	C₂³	—	1076	4	no	—
408	C₂³	C₂³×D₂₆₉	1	2	yes	—
409	C₂³	C₂³×D₂₆₉	1	2	yes	—
410	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
411	Q₈	—	538	2	no	—
412	Q₈	—	1076	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	538	8	no	—
416	D₄	—	538	4	no	—
417	D₄	—	538	8	no	—
418	D₄	—	538	4	no	—
419	D₄	—	538	2	no	—
420	D₄	—	538	4	no	—
421	D₄	—	1076	4	no	—
422	D₄	—	1076	2	no	—
423	D₄	—	1076	4	no	—
424	D₄	—	1076	4	no	—
425	D₄	—	1076	4	no	—
426	D₄	#16864402	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	269	2	no	—
436	C₂×C₄	—	269	2	no	—
437	C₂×C₄	—	269	4	no	—
438	C₂×C₄	—	269	2	no	—
439	C₂×C₄	—	538	4	no	—
440	C₂×C₄	—	1076	4	no	—
441	C₂×C₄	—	1076	4	no	—
442	C₂×C₄	—	1076	4	no	—
443	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
444	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
445	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₂₆₉	1	2	yes	—
449	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₂₆₉	1	1	yes	characteristic
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	538	2	no	—
460	C₂²	—	538	4	no	—
461	C₂²	—	538	4	no	—
462	C₂²	—	538	2	no	—
463	C₂²	—	538	4	no	—
464	C₂²	—	538	2	no	—
465	C₂²	—	2152	8	no	—
466	C₂²	C₂×#16864402	1	4	yes	—
467	C₂²	#22575499	1	2	yes	—
468	C₂²	C₂⁴×D₂₆₉	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	538	2	no	—
476	C₄	—	538	2	no	—
477	C₄	—	538	2	no	—
478	C₄	—	538	4	no	—
479	C₄	C₂×#16864402	1	2	yes	—
480	C₄	#22575498	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	1076	2	no	—
485	C₂	—	1076	4	no	—
486	C₂	C₂²×#16864402	1	1	yes	characteristic
487	C₂	C₂×#22575498	1	1	yes	characteristic
488	C₂	C₂×#22575499	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₆₉
commutator, socle, cosocle	C₂²×C₂₆₉	C₂⁵
Fitting	C₂×C₄×D₄×C₂₆₉	C₂
hypercenter	C₂×C₄×D₄	D₂₆₉
hypocenter	C₂₆₉	#3519
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #31771320	C₂	semidirect
2. #31771312	C₂	semidirect
3. #31771303	C₂	semidirect
4. #31771301	C₂	semidirect
5. #31771276	C₂	semidirect
6. #31771251	C₂	semidirect
7. #31771245	C₂	semidirect
8. D₄×D₁₀₇₆	C₂	semidirect
9. D₄×C₂²⋊D₂₆₉	C₂	semidirect
10. #31771206	C₂	semidirect
11. #31771188	C₂	semidirect
12. #31771155	C₂	semidirect
13. #31771139	C₂	semidirect
14. #31771116	C₂	semidirect
15. C₂×#22575427	C₂	semidirect
16. #31771077	C₂	semidirect
17. C₂×C₄×D₄×C₂₆₉	C₂	semidirect
18. C₂×#16864402	C₂²	semidirect
19. C₂×#16864402	C₂²	semidirect
20. C₂²×D₁₀₇₆	C₂²	semidirect
21. C₂²×C₂²⋊D₂₆₉	C₂²	semidirect
23. #22575453	C₂²	semidirect
24. #22575450	C₂²	semidirect
25. #22575449	C₂²	semidirect
26. #22575448	C₂²	semidirect
27. #22575447	C₂²	semidirect
28. #22575445	C₂²	semidirect
29. #22575444	C₂²	semidirect
30. #22575441	C₂²	semidirect
31. #22575441	C₂²	semidirect
32. #22575439	C₂²	semidirect
33. #22575438	C₂²	semidirect
34. #22575436	C₂²	semidirect
35. #22575436	C₂²	semidirect
36. #22575435	C₂²	semidirect
37. #22575432	C₂²	semidirect
38. #22575432	C₂²	semidirect
39. #22575430	C₂²	semidirect
40. #22575428	C₂²	semidirect
42. #22575427	C₂²	semidirect
43. #22575427	C₂²	semidirect
44. #22575427	C₂²	semidirect
45. #22575427	C₂²	semidirect
46. #22575427	C₂²	semidirect
47. #22575427	C₂²	semidirect
48. #22575427	C₂²	semidirect
49. #22575426	C₂²	semidirect
50. #22575426	C₂²	semidirect
51. #22575425	C₂²	semidirect
52. #22575424	C₂²	semidirect
53. #22575423	C₂²	semidirect
54. #22575422	C₂²	semidirect
55. #22575421	C₂²	semidirect
56. C₄×Dic₅₃₈	C₂²	semidirect
57. C₄×D₁₀₇₆	C₂²	semidirect
58. C₄×D₁₀₇₆	C₂²	semidirect
59. C₄×D₁₀₇₆	C₂²	semidirect
61. #22575415	C₂²	semidirect
62. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
63. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
64. C₄×C₂²⋊D₂₆₉	C₂²	semidirect
65. #22575413	C₂²	semidirect
66. #22575412	C₂²	semidirect
67. #22575411	C₂²	semidirect
68. #22575410	C₂²	semidirect
69. C₂×C₄⋊Dic₂₆₉	C₂²	semidirect
70. C₂×#16864379	C₂²	semidirect
71. C₂²⋊C₄×D₂₆₉	C₂²	semidirect
73. C₂³×C₄×C₂₆₉	C₂²	semidirect
76. C₄×D₄×C₂₆₉	C₂²	semidirect
77. C₄×D₄×C₂₆₉	C₂²	semidirect
78. C₄×D₄×C₂₆₉	C₂²	semidirect
79. C₄×D₄×C₂₆₉	C₂²	semidirect
80. C₂×C₄⋊C₄×C₂₆₉	C₂²	semidirect
81. C₂×C₂²⋊C₄×C₂₆₉	C₂²	semidirect
82. C₂×C₄²×C₂₆₉	C₂²	semidirect
189. D₄×C₂₆₉	#41	semidirect
244. C₂₆₉	#3519	semidirect
262. C₂×C₄×D₄	D₂₆₉	semidirect
269. C₂³×C₄	C₂×D₂₆₉	semidirect
315. C₄×D₄	C₂×D₂₆₉	semidirect
316. C₄×D₄	C₂×D₂₆₉	semidirect
317. C₄×D₄	C₂×D₂₆₉	semidirect
318. C₄×D₄	C₂×D₂₆₉	semidirect
323. C₂×C₄⋊C₄	C₂×D₂₆₉	semidirect
326. C₂×C₂²⋊C₄	C₂×D₂₆₉	semidirect
327. C₂×C₄²	C₂×D₂₆₉	semidirect
426. D₄	#16864402	semidirect

Maximal subgroups

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

subgroup	index
#31771320	2
#31771312	2
#31771303	2
#31771301	2
#31771276	2
#31771251	2
#31771245	2
D₄×D₁₀₇₆	2
D₄×C₂²⋊D₂₆₉	2
#31771206	2
#31771188	2
#31771155	2
#31771139	2
#31771116	2
C₂×#22575427	2
#31771077	2
C₂×C₄×D₄×C₂₆₉	2
#3519	269