Subgroups — #16771459

Order 3328.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719648	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128516	C₂	1	8	yes	maximal, complemented
3	#13128505	C₂	1	8	yes	maximal, complemented
4	#13128494	C₂	1	2	yes	maximal, complemented
5	#13128487	C₂	1	2	yes	maximal, complemented
6	#13128480	C₂	1	6	yes	maximal, complemented
7	#13128471	C₂	1	6	yes	maximal, complemented
8	#41×C₂²⋊D₁₃	C₂	1	16	yes	maximal, complemented
9	#13128165	C₂	1	6	yes	maximal, complemented
10	C₂×#11719496	C₂	1	6	yes	maximal, complemented
11	#13128039	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	—	2	16	no	—
14	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
18	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
22	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	complemented
23	#11719648	—	2	16	no	—
24	C₂×#88257	C₂²	1	4	yes	complemented
25	C₂×#88256	C₂²	1	4	yes	complemented
26	C₂×#41×D₁₃	C₂²	1	8	yes	complemented
27	C₂×#88254	C₂²	1	2	yes	complemented
28	C₂×#88251	C₂²	1	6	yes	complemented
29	C₂²×#6127	C₂²	1	6	yes	complemented
30	C₂×#88207	C₂²	1	12	yes	complemented
31	#11719539	C₂²	1	16	yes	complemented
32	#11719538	C₂²	1	24	yes	complemented
33	#11719537	C₂²	1	24	yes	complemented
34	#11719536	C₂²	1	16	yes	complemented
35	#11719535	C₂²	1	12	yes	complemented
36	#11719534	C₂²	1	48	yes	complemented
37	#11719533	C₂²	1	24	yes	complemented
38	#11719532	C₂²	1	8	yes	complemented
39	#41×Dic₁₃	C₂²	1	8	yes	complemented
40	#11719530	C₂²	1	12	yes	complemented
41	#11719529	C₂²	1	48	yes	complemented
42	#11719522	C₂²	1	16	yes	complemented
43	#11719521	C₂²	1	12	yes	complemented
44	Q₈×C₂²⋊D₁₃	C₂²	1	16	yes	complemented
45	#11719517	C₂²	1	2	yes	complemented
46	#11719511	C₂²	1	48	yes	complemented
47	#11719510	C₂²	1	12	yes	complemented
48	#11719509	C₂²	1	24	yes	complemented
49	D₄×C₂²⋊D₁₃	C₂²	1	48	yes	complemented
50	#11719503	C₂²	1	6	yes	complemented
51	#11719496	C₂²	1	12	yes	complemented
52	#11719496	C₂²	1	4	yes	complemented
53	#11719496	C₂²	1	24	yes	complemented
54	#11719496	C₂²	1	24	yes	complemented
55	#11719496	C₂²	1	12	yes	complemented
56	#11719496	C₂²	1	12	yes	complemented
57	C₂×#88184	C₂²	1	12	yes	complemented
58	C₂×#88183	C₂²	1	12	yes	complemented
59	C₂×C₄×C₂²⋊D₁₃	C₂²	1	24	yes	complemented
60	C₂×#88180	C₂²	1	6	yes	complemented
61	C₂×#88178	C₂²	1	12	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	3	yes	—
63	C₂×C₁₃×#41	—	2	64	no	—
64	C₂×C₁₃×#41	—	2	64	no	—
65	C₂×C₁₃×#41	—	2	8	no	—
66	C₂×C₁₃×#41	—	2	24	no	—
67	C₂×C₁₃×#41	—	2	24	no	—
68	C₂×C₁₃×#41	D₄	1	16	yes	complemented
69	C₂×C₁₃×#41	C₂³	1	24	yes	—
70	C₂×C₁₃×#41	C₂³	1	12	yes	—
71	C₂×C₁₃×#41	C₂³	1	12	yes	—
72	C₂×C₁₃×#41	C₂³	1	8	yes	—
73	C₂×C₁₃×#41	C₂³	1	4	yes	—
74	C₂×C₁₃×#41	C₂³	1	4	yes	—
75	C₂²×Q₈×C₁₃	—	2	8	no	—
76	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	—	2	24	no	—
80	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
84	C₂³×C₄×C₁₃	—	2	24	no	—
85	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
93	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
94	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
95	#88257	—	2	32	no	—
96	#88256	—	2	32	no	—
97	#41×D₁₃	—	2	64	no	—
98	#88254	—	2	16	no	—
99	C₂×#6131	C₂³	1	8	yes	complemented
100	C₂×Q₈×D₁₃	C₂³	1	8	yes	complemented
101	#88251	—	2	48	no	—
102	C₂×#6129	C₂³	1	24	yes	complemented
103	C₂×D₄×D₁₃	C₂³	1	24	yes	complemented
104	C₂×#6127	—	2	48	no	—
105	C₂×#6127	C₂³	1	4	yes	—
106	C₂×#6127	C₂³	1	12	yes	—
107	C₂×#6127	C₂³	1	12	yes	complemented
108	C₂×#6127	C₂³	1	12	yes	complemented
109	C₂²×D₅₂	C₂³	1	6	yes	complemented
110	C₂²×C₄×D₁₃	C₂³	1	12	yes	complemented
111	C₂²×Dic₂₆	C₂³	1	6	yes	complemented
112	#88207	C₂³	1	8	yes	—
113	#88207	C₂³	1	48	yes	—
114	#88207	C₂³	1	24	yes	—
115	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
116	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
117	#88201	C₂³	1	24	yes	complemented
118	#88200	C₂³	1	48	yes	complemented
119	Q₈×Dic₁₃	C₂³	1	16	yes	complemented
120	#88198	C₂³	1	24	yes	complemented
121	#88194	C₂³	1	24	yes	complemented
122	#88193	C₂³	1	96	yes	complemented
123	#88192	C₂³	1	48	yes	complemented
124	#88191	C₂³	1	48	yes	complemented
125	#88190	C₂³	1	24	yes	complemented
126	#88189	C₂³	1	48	yes	complemented
127	D₄×Dic₁₃	C₂³	1	48	yes	complemented
128	#88184	C₂³	1	8	yes	—
129	#88184	C₂³	1	24	yes	—
130	#88184	C₂³	1	24	yes	complemented
131	#88184	C₂³	1	24	yes	complemented
132	#88183	C₂³	1	8	yes	—
133	#88183	C₂³	1	24	yes	—
134	#88183	C₂³	1	48	yes	complemented
135	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
136	C₄×C₂²⋊D₁₃	C₂³	1	48	yes	—
137	C₄×C₂²⋊D₁₃	C₂³	1	48	yes	complemented
138	C₄×C₂²⋊D₁₃	C₂³	1	48	yes	complemented
139	C₂×#6103	C₂³	1	24	yes	complemented
140	#88180	C₂³	1	4	yes	—
141	#88180	C₂³	1	12	yes	—
142	#88180	C₂³	1	12	yes	complemented
143	#88180	C₂³	1	12	yes	complemented
144	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
145	#88178	C₂³	1	8	yes	—
146	#88178	C₂³	1	24	yes	—
147	#88178	C₂³	1	24	yes	complemented
148	#88178	C₂³	1	24	yes	complemented
149	C₂×#6101	C₂³	1	24	yes	complemented
150	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
151	#62811	—	13	1	no	maximal, Sylow
152	C₂⁴×C₁₃	—	2	12	no	—
153	C₂⁴×C₁₃	—	4	12	no	—
154	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
156	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
157	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
158	C₂³×D₁₃	C₂⁴	1	12	yes	—
159	C₁₃×#41	—	2	32	no	—
160	C₁₃×#41	—	2	96	no	—
161	C₁₃×#41	—	2	48	no	—
162	C₁₃×#41	—	2	48	no	—
163	C₁₃×#41	C₂×D₄	1	32	yes	complemented
164	C₁₃×#41	C₂×D₄	1	32	yes	complemented
165	C₂×Q₈×C₁₃	—	2	32	no	—
166	C₂×Q₈×C₁₃	—	2	12	no	—
167	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
168	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
169	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
170	C₂×D₄×C₁₃	—	2	24	no	—
171	C₂×D₄×C₁₃	—	2	96	no	—
172	C₂×D₄×C₁₃	—	2	12	no	—
173	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
174	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
175	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
176	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
177	C₂²×C₄×C₁₃	—	2	12	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	12	no	—
180	C₂²×C₄×C₁₃	—	2	12	no	—
181	C₂²×C₄×C₁₃	—	2	12	no	—
182	C₂²×C₄×C₁₃	—	2	48	no	—
183	C₂²×C₄×C₁₃	—	2	48	no	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
185	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
198	C₂×C₂²⋊D₁₃	—	2	48	no	—
199	C₂×C₂²⋊D₁₃	—	4	48	no	—
200	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
201	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
202	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
203	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
204	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
205	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
206	#6131	—	2	32	no	—
207	Q₈×D₁₃	—	2	32	no	—
208	#6129	—	2	96	no	—
209	D₄×D₁₃	—	2	96	no	—
210	#6127	—	2	16	no	—
211	#6127	—	2	48	no	—
212	#6127	—	2	48	no	—
213	#6127	—	2	48	no	—
214	C₂×D₅₂	—	2	24	no	—
215	C₂×D₅₂	C₂⁴	1	4	yes	—
216	C₂×D₅₂	C₂⁴	1	12	yes	—
217	C₂×C₄×D₁₃	—	2	48	no	—
218	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
219	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
220	C₂×Dic₂₆	—	2	24	no	—
221	C₂×Dic₂₆	C₂⁴	1	4	yes	—
222	C₂×Dic₂₆	C₂⁴	1	12	yes	—
223	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
224	C₂²⋊Dic₁₃	C₂⁴	1	48	yes	—
225	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
226	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
227	#6103	C₂⁴	1	16	yes	—
228	#6103	C₂⁴	1	48	yes	—
229	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
230	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
231	#6101	C₂⁴	1	16	yes	—
232	#6101	C₂⁴	1	48	yes	—
233	C₄×Dic₁₃	C₂⁴	1	8	yes	—
234	C₄×Dic₁₃	C₂⁴	1	24	yes	—
235	C₂×#585	—	13	1	no	—
236	C₂³×#41	D₁₃	1	1	yes	characteristic, complemented
237	#3489	—	13	8	no	—
238	#3488	—	13	8	no	—
239	#3487	—	13	2	no	—
240	#3486	—	13	2	no	—
241	#3485	—	13	6	no	—
242	#3484	—	13	6	no	—
243	D₄×#41	—	13	16	no	—
244	#3449	—	13	6	no	—
245	C₂×#525	—	13	6	no	—
246	#3428	—	13	1	no	—
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	2	4	no	—
249	C₂³×C₁₃	—	2	24	no	—
250	C₂³×C₁₃	—	2	6	no	—
251	C₂³×C₁₃	—	2	24	no	—
252	C₂³×C₁₃	—	4	6	no	—
253	C₂³×C₁₃	—	4	12	no	—
254	C₂³×C₁₃	—	4	6	no	—
255	C₂³×C₁₃	—	4	48	no	—
256	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
257	C₂³×C₁₃	C₂⁵	1	6	yes	—
258	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
259	C₂³×C₁₃	C₂⁵	1	6	yes	—
260	C₂³×C₁₃	C₂⁵	1	2	yes	—
261	C₂²×D₁₃	—	2	24	no	—
262	C₂²×D₁₃	—	4	24	no	—
263	C₂²×D₁₃	C₂⁵	1	8	yes	—
264	Q₈×C₁₃	—	2	24	no	—
265	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
266	D₄×C₁₃	—	2	48	no	—
267	D₄×C₁₃	—	2	24	no	—
268	D₄×C₁₃	C₂²×D₄	1	48	yes	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	6	no	—
271	C₂×C₄×C₁₃	—	2	24	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	24	no	—
275	C₂×C₄×C₁₃	—	2	24	no	—
276	C₂×C₄×C₁₃	—	2	12	no	—
277	C₂×C₄×C₁₃	—	2	12	no	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
282	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
283	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
284	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
285	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
287	C₂²⋊D₁₃	—	2	16	no	—
288	C₂²⋊D₁₃	—	2	48	no	—
289	C₂²⋊D₁₃	—	2	32	no	—
290	C₂²⋊D₁₃	—	4	48	no	—
291	C₂×Dic₁₃	—	2	24	no	—
292	C₂×Dic₁₃	—	4	24	no	—
293	C₂×Dic₁₃	C₂⁵	1	16	yes	—
294	C₂×Dic₁₃	C₂⁵	1	8	yes	—
295	D₅₂	—	2	8	no	—
296	D₅₂	—	2	24	no	—
297	C₄×D₁₃	—	2	16	no	—
298	C₄×D₁₃	—	2	48	no	—
299	Dic₂₆	—	2	8	no	—
300	Dic₂₆	—	2	24	no	—
301	#585	—	26	16	no	—
302	C₂×2₋¹⁺⁴	—	13	4	no	—
303	C₂×2₋¹⁺⁴	—	13	2	no	—
304	C₂×H(5,𝔽₂)	—	13	4	no	—
305	C₂×H(5,𝔽₂)	—	13	6	no	—
306	C₂²×#41	—	2	16	no	—
307	C₂²×#41	—	13	8	no	—
308	C₂²×#41	—	13	6	no	—
309	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
310	C₂²×#41	C₂×D₁₃	1	3	yes	complemented
311	C₂²×#41	C₂×D₁₃	1	8	yes	complemented
312	C₂²×#41	C₂×D₁₃	1	3	yes	complemented
313	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
314	C₂²×#41	C₂×D₁₃	1	8	yes	complemented
315	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
316	C₂³×D₄	C₂×D₁₃	1	3	yes	complemented
317	C₂⁴×C₄	C₂×D₁₃	1	3	yes	complemented
318	#550	—	13	16	no	—
319	D₄×Q₈	—	13	16	no	—
320	#548	—	13	16	no	—
321	#548	—	13	16	no	—
322	#547	—	13	48	no	—
323	#546	—	13	48	no	—
324	#546	—	13	48	no	—
325	D₄²	—	13	48	no	—
326	#537	—	13	24	no	—
327	#536	—	13	12	no	—
328	#536	—	13	12	no	—
329	#535	—	13	12	no	—
330	#535	—	13	12	no	—
331	#534	—	13	24	no	—
332	#532	—	13	24	no	—
333	#525	—	13	24	no	—
334	#525	—	13	4	no	—
335	#525	—	13	12	no	—
336	#525	—	13	24	no	—
337	#525	—	13	12	no	—
338	#525	—	13	12	no	—
339	#525	—	13	24	no	—
340	C₂×#123	—	13	12	no	—
341	C₂×C₂²⋊Q₈	—	13	12	no	—
342	C₂×#121	—	13	12	no	—
343	C₂×#120	—	13	12	no	—
344	#520	—	13	8	no	—
345	#519	—	13	2	no	—
346	#518	—	13	6	no	—
347	C₄×#41	—	13	8	no	—
348	C₂×C₄×D₄	—	13	24	no	—
349	C₂×#117	—	13	6	no	—
350	C₂²×C₁₃	—	2	8	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	12	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	2	2	no	—
355	C₂²×C₁₃	—	2	6	no	—
356	C₂²×C₁₃	—	2	12	no	—
357	C₂²×C₁₃	—	4	12	no	—
358	C₂²×C₁₃	—	4	48	no	—
359	C₂²×C₁₃	—	4	12	no	—
360	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
361	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
362	C₂²×C₁₃	#585	1	4	yes	complemented
363	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
364	C₂×D₁₃	—	2	8	no	—
365	C₂×D₁₃	—	2	16	no	—
366	C₂×D₁₃	—	8	24	no	—
367	C₄×C₁₃	—	2	2	no	—
368	C₄×C₁₃	—	2	6	no	—
369	C₄×C₁₃	C₂³×D₄	1	2	yes	—
370	C₄×C₁₃	C₂³×D₄	1	12	yes	—
371	C₄×C₁₃	C₂³×D₄	1	2	yes	—
372	Dic₁₃	—	2	8	no	—
373	Dic₁₃	—	2	16	no	—
374	C₂⁵	C₂²×D₁₃	1	3	yes	—
375	2₋¹⁺⁴	—	26	32	no	—
376	2₋¹⁺⁴	—	26	16	no	—
377	H(5,𝔽₂)	—	26	32	no	—
378	H(5,𝔽₂)	—	26	48	no	—
379	C₂×#41	—	2	64	no	—
380	C₂×#41	—	2	64	no	—
381	C₂×#41	—	2	8	no	—
382	C₂×#41	—	2	24	no	—
383	C₂×#41	—	2	24	no	—
384	C₂×#41	—	13	8	no	—
385	C₂×#41	—	13	24	no	—
386	C₂×#41	—	13	4	no	—
387	C₂×#41	—	13	12	no	—
388	C₂×#41	—	13	12	no	—
389	C₂×#41	—	13	12	no	—
390	C₂×#41	—	26	64	no	—
391	C₂×#41	—	26	48	no	—
392	C₂×#41	C₂²⋊D₁₃	1	16	yes	complemented
393	C₂×#41	C₂²×D₁₃	1	12	yes	—
394	C₂×#41	C₂²×D₁₃	1	12	yes	—
395	C₂×#41	C₂²×D₁₃	1	24	yes	—
396	C₂×#41	C₂²×D₁₃	1	8	yes	—
397	C₂×#41	C₂²×D₁₃	1	4	yes	—
398	C₂×#41	C₂²×D₁₃	1	4	yes	—
399	C₂²×Q₈	—	2	8	no	—
400	C₂²×Q₈	—	13	8	no	—
401	C₂²×Q₈	—	13	6	no	—
402	C₂²×Q₈	C₂²×D₁₃	1	3	yes	—
403	C₂²×Q₈	C₂²×D₁₃	1	8	yes	—
404	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
405	C₂²×D₄	—	2	24	no	—
406	C₂²×D₄	—	13	12	no	—
407	C₂²×D₄	—	13	24	no	—
408	C₂²×D₄	—	13	24	no	—
409	C₂²×D₄	—	13	6	no	—
410	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
411	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
412	C₂²×D₄	C₂²×D₁₃	1	24	yes	—
413	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
414	C₂³×C₄	—	2	24	no	—
415	C₂³×C₄	—	13	12	no	—
416	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
417	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
418	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
419	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
420	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
421	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
422	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
423	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
424	C₄⋊Q₈	—	13	24	no	—
425	#127	—	13	24	no	—
426	#124	—	13	24	no	—
427	#124	—	13	24	no	—
428	#123	—	13	48	no	—
429	#123	—	13	8	no	—
430	#123	—	13	24	no	—
431	#123	—	13	48	no	—
432	C₂²⋊Q₈	—	13	48	no	—
433	C₂²⋊Q₈	—	13	8	no	—
434	C₂²⋊Q₈	—	13	24	no	—
435	C₂²⋊Q₈	—	13	24	no	—
436	C₂²⋊Q₈	—	13	24	no	—
437	#121	—	13	48	no	—
438	#121	—	13	96	no	—
439	#121	—	13	8	no	—
440	#121	—	13	24	no	—
441	#121	—	13	24	no	—
442	#121	—	13	24	no	—
443	#120	—	13	8	no	—
444	#120	—	13	24	no	—
445	#120	—	13	48	no	—
446	#120	—	13	48	no	—
447	C₄×Q₈	—	13	16	no	—
448	C₄×D₄	—	13	48	no	—
449	C₄×D₄	—	13	16	no	—
450	C₄×D₄	—	13	48	no	—
451	C₄×D₄	—	13	48	no	—
452	C₄×D₄	—	13	48	no	—
453	#117	—	13	4	no	—
454	#117	—	13	12	no	—
455	#117	—	13	12	no	—
456	#117	—	13	12	no	—
457	C₂×C₄⋊C₄	—	13	12	no	—
458	C₂×C₄⋊C₄	—	13	24	no	—
459	C₂×C₂²⋊C₄	—	13	12	no	—
460	C₂×C₂²⋊C₄	—	13	24	no	—
461	C₂×C₂²⋊C₄	—	13	24	no	—
462	C₂×C₄²	—	13	12	no	—
463	C₂×C₁₃	—	2	12	no	—
464	C₂×C₁₃	—	2	2	no	—
465	C₂×C₁₃	—	2	4	no	—
466	C₂×C₁₃	—	4	6	no	—
467	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
468	C₂×C₁₃	C₂×#585	1	2	yes	—
469	D₁₃	—	4	8	no	—
470	C₂⁴	—	2	12	no	—
471	C₂⁴	—	4	12	no	—
472	C₂⁴	—	13	12	no	—
473	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
474	C₂⁴	C₂³×D₁₃	1	12	yes	—
475	C₂⁴	C₂³×D₁₃	1	3	yes	—
476	C₂⁴	C₂³×D₁₃	1	3	yes	—
477	#41	—	2	32	no	—
478	#41	—	2	96	no	—
479	#41	—	2	48	no	—
480	#41	—	2	48	no	—
481	#41	—	26	32	no	—
482	#41	—	26	96	no	—
483	#41	—	26	16	no	—
484	#41	—	26	48	no	—
485	#41	—	26	48	no	—
486	#41	—	26	48	no	—
487	#41	C₂×C₂²⋊D₁₃	1	32	yes	complemented
488	#41	C₂×C₂²⋊D₁₃	1	32	yes	complemented
489	C₂×Q₈	—	2	32	no	—
490	C₂×Q₈	—	2	12	no	—
491	C₂×Q₈	—	13	4	no	—
492	C₂×Q₈	—	13	12	no	—
493	C₂×Q₈	—	26	32	no	—
494	C₂×Q₈	—	26	24	no	—
495	C₂×Q₈	C₂×C₂²⋊D₁₃	1	8	yes	complemented
496	C₂×Q₈	C₂³×D₁₃	1	12	yes	—
497	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
498	C₂×D₄	—	2	24	no	—
499	C₂×D₄	—	2	96	no	—
500	C₂×D₄	—	2	12	no	—
501	C₂×D₄	—	13	16	no	—
502	C₂×D₄	—	13	8	no	—
503	C₂×D₄	—	13	24	no	—
504	C₂×D₄	—	13	48	no	—
505	C₂×D₄	—	13	4	no	—
506	C₂×D₄	—	13	12	no	—
507	C₂×D₄	—	26	48	no	—
508	C₂×D₄	—	26	96	no	—
509	C₂×D₄	—	26	24	no	—
510	C₂×D₄	—	52	48	no	—
511	C₂×D₄	C₂×C₂²⋊D₁₃	1	24	yes	complemented
512	C₂×D₄	C₂³×D₁₃	1	24	yes	—
513	C₂×D₄	C₂³×D₁₃	1	12	yes	—
514	C₂×D₄	C₂³×D₁₃	1	12	yes	—
515	C₂²×C₄	—	2	12	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	12	no	—
518	C₂²×C₄	—	2	12	no	—
519	C₂²×C₄	—	2	12	no	—
520	C₂²×C₄	—	2	48	no	—
521	C₂²×C₄	—	2	48	no	—
522	C₂²×C₄	—	13	12	no	—
523	C₂²×C₄	—	13	24	no	—
524	C₂²×C₄	—	13	24	no	—
525	C₂²×C₄	—	13	8	no	—
526	C₂²×C₄	—	26	48	no	—
527	C₂²×C₄	C₂×C₂²⋊D₁₃	1	24	yes	complemented
528	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
529	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
530	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
531	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
532	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
533	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
535	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
536	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
537	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
538	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
539	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
540	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
541	C₄⋊C₄	—	13	8	no	—
542	C₄⋊C₄	—	13	16	no	—
543	C₄⋊C₄	—	13	24	no	—
544	C₄⋊C₄	—	13	48	no	—
545	C₂²⋊C₄	—	13	8	no	—
546	C₂²⋊C₄	—	13	16	no	—
547	C₂²⋊C₄	—	13	24	no	—
548	C₂²⋊C₄	—	13	48	no	—
549	C₂²⋊C₄	—	13	16	no	—
550	C₂²⋊C₄	—	13	48	no	—
551	C₄²	—	13	24	no	—
552	C₄²	—	13	8	no	—
553	C₁₃	#62811	1	1	yes	characteristic, complemented, Sylow
554	C₂³	—	2	4	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	24	no	—
557	C₂³	—	2	24	no	—
558	C₂³	—	2	6	no	—
559	C₂³	—	4	6	no	—
560	C₂³	—	4	12	no	—
561	C₂³	—	4	6	no	—
562	C₂³	—	4	48	no	—
563	C₂³	—	13	8	no	—
564	C₂³	—	26	24	no	—
565	C₂³	—	52	24	no	—
566	C₂³	C₂²×C₂²⋊D₁₃	1	12	yes	—
567	C₂³	C₂⁴×D₁₃	1	6	yes	—
568	C₂³	C₂⁴×D₁₃	1	2	yes	—
569	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
570	C₂³	C₂⁴×D₁₃	1	6	yes	—
571	Q₈	—	2	24	no	—
572	Q₈	—	26	8	no	—
573	Q₈	—	26	24	no	—
574	Q₈	C₂²×C₂²⋊D₁₃	1	16	yes	—
575	D₄	—	2	48	no	—
576	D₄	—	2	24	no	—
577	D₄	—	26	32	no	—
578	D₄	—	26	16	no	—
579	D₄	—	26	48	no	—
580	D₄	—	26	8	no	—
581	D₄	—	26	24	no	—
582	D₄	—	52	48	no	—
583	D₄	C₂²×C₂²⋊D₁₃	1	48	yes	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	6	no	—
586	C₂×C₄	—	2	24	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	24	no	—
590	C₂×C₄	—	2	24	no	—
591	C₂×C₄	—	2	12	no	—
592	C₂×C₄	—	2	12	no	—
593	C₂×C₄	—	13	16	no	—
594	C₂×C₄	—	13	8	no	—
595	C₂×C₄	—	26	24	no	—
596	C₂×C₄	—	26	16	no	—
597	C₂×C₄	—	26	48	no	—
598	C₂×C₄	—	52	24	no	—
599	C₂×C₄	C₂²×C₂²⋊D₁₃	1	4	yes	—
600	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
601	C₂×C₄	C₂²×C₂²⋊D₁₃	1	12	yes	—
602	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
603	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
604	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
605	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
606	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
608	C₂²	—	2	8	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	12	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	6	no	—
614	C₂²	—	2	12	no	—
615	C₂²	—	4	12	no	—
616	C₂²	—	4	48	no	—
617	C₂²	—	4	12	no	—
618	C₂²	—	26	8	no	—
619	C₂²	—	26	16	no	—
620	C₂²	—	104	24	no	—
621	C₂²	#11719648	1	4	yes	complemented
622	C₂²	C₂³×C₂²⋊D₁₃	1	2	yes	—
623	C₂²	C₂³×C₂²⋊D₁₃	1	12	yes	—
624	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
625	C₄	—	2	2	no	—
626	C₄	—	2	6	no	—
627	C₄	—	26	8	no	—
628	C₄	—	26	16	no	—
629	C₄	C₂³×C₂²⋊D₁₃	1	2	yes	—
630	C₄	C₂³×C₂²⋊D₁₃	1	2	yes	—
631	C₄	C₂³×C₂²⋊D₁₃	1	12	yes	—
632	C₂	—	2	4	no	—
633	C₂	—	2	2	no	—
634	C₂	—	2	12	no	—
635	C₂	—	4	6	no	—
636	C₂	—	52	8	no	—
637	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
638	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₁₃×#41	C₂
hypercenter	C₂³×#41	D₁₃
hypocenter	C₁₃	#62811
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#11719648	C₂	semidirect
2. #13128516	C₂	semidirect
3. #13128505	C₂	semidirect
4. #13128494	C₂	semidirect
5. #13128487	C₂	semidirect
6. #13128480	C₂	semidirect
7. #13128471	C₂	semidirect
8. #41×C₂²⋊D₁₃	C₂	semidirect
9. #13128165	C₂	semidirect
10. C₂×#11719496	C₂	semidirect
11. #13128039	C₂	semidirect
12. C₂³×C₁₃×#41	C₂	semidirect
15. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₂³×D₄×C₁₃	C₂²	semidirect
22. C₂⁴×C₄×C₁₃	C₂²	semidirect
24. C₂×#88257	C₂²	semidirect
25. C₂×#88256	C₂²	semidirect
26. C₂×#41×D₁₃	C₂²	semidirect
27. C₂×#88254	C₂²	semidirect
28. C₂×#88251	C₂²	semidirect
29. C₂²×#6127	C₂²	semidirect
30. C₂×#88207	C₂²	semidirect
31. #11719539	C₂²	semidirect
32. #11719538	C₂²	semidirect
33. #11719537	C₂²	semidirect
34. #11719536	C₂²	semidirect
35. #11719535	C₂²	semidirect
36. #11719534	C₂²	semidirect
37. #11719533	C₂²	semidirect
38. #11719532	C₂²	semidirect
39. #41×Dic₁₃	C₂²	semidirect
40. #11719530	C₂²	semidirect
41. #11719529	C₂²	semidirect
42. #11719522	C₂²	semidirect
43. #11719521	C₂²	semidirect
44. Q₈×C₂²⋊D₁₃	C₂²	semidirect
45. #11719517	C₂²	semidirect
46. #11719511	C₂²	semidirect
47. #11719510	C₂²	semidirect
48. #11719509	C₂²	semidirect
49. D₄×C₂²⋊D₁₃	C₂²	semidirect
50. #11719503	C₂²	semidirect
51. #11719496	C₂²	semidirect
52. #11719496	C₂²	semidirect
53. #11719496	C₂²	semidirect
54. #11719496	C₂²	semidirect
55. #11719496	C₂²	semidirect
56. #11719496	C₂²	semidirect
57. C₂×#88184	C₂²	semidirect
58. C₂×#88183	C₂²	semidirect
59. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
60. C₂×#88180	C₂²	semidirect
61. C₂×#88178	C₂²	semidirect
68. C₂×C₁₃×#41	D₄	semidirect
99. C₂×#6131	C₂³	semidirect
100. C₂×Q₈×D₁₃	C₂³	semidirect
102. C₂×#6129	C₂³	semidirect
103. C₂×D₄×D₁₃	C₂³	semidirect
107. C₂×#6127	C₂³	semidirect
108. C₂×#6127	C₂³	semidirect
109. C₂²×D₅₂	C₂³	semidirect
110. C₂²×C₄×D₁₃	C₂³	semidirect
111. C₂²×Dic₂₆	C₂³	semidirect
117. #88201	C₂³	semidirect
118. #88200	C₂³	semidirect
119. Q₈×Dic₁₃	C₂³	semidirect
120. #88198	C₂³	semidirect
121. #88194	C₂³	semidirect
122. #88193	C₂³	semidirect
123. #88192	C₂³	semidirect
124. #88191	C₂³	semidirect
125. #88190	C₂³	semidirect
126. #88189	C₂³	semidirect
127. D₄×Dic₁₃	C₂³	semidirect
130. #88184	C₂³	semidirect
131. #88184	C₂³	semidirect
134. #88183	C₂³	semidirect
137. C₄×C₂²⋊D₁₃	C₂³	semidirect
138. C₄×C₂²⋊D₁₃	C₂³	semidirect
139. C₂×#6103	C₂³	semidirect
142. #88180	C₂³	semidirect
143. #88180	C₂³	semidirect
144. C₂×C₄⋊Dic₁₃	C₂³	semidirect
147. #88178	C₂³	semidirect
148. #88178	C₂³	semidirect
149. C₂×#6101	C₂³	semidirect
150. C₂×C₄×Dic₁₃	C₂³	semidirect
163. C₁₃×#41	C₂×D₄	semidirect
164. C₁₃×#41	C₂×D₄	semidirect
167. C₂×Q₈×C₁₃	C₂×D₄	semidirect
173. C₂×D₄×C₁₃	C₂×D₄	semidirect
184. C₂²×C₄×C₁₃	C₂×D₄	semidirect
236. C₂³×#41	D₁₃	semidirect
310. C₂²×#41	C₂×D₁₃	semidirect
311. C₂²×#41	C₂×D₁₃	semidirect
312. C₂²×#41	C₂×D₁₃	semidirect
313. C₂²×#41	C₂×D₁₃	semidirect
314. C₂²×#41	C₂×D₁₃	semidirect
315. C₂³×Q₈	C₂×D₁₃	semidirect
316. C₂³×D₄	C₂×D₁₃	semidirect
317. C₂⁴×C₄	C₂×D₁₃	semidirect
362. C₂²×C₁₃	#585	semidirect
392. C₂×#41	C₂²⋊D₁₃	semidirect
487. #41	C₂×C₂²⋊D₁₃	semidirect
488. #41	C₂×C₂²⋊D₁₃	semidirect
495. C₂×Q₈	C₂×C₂²⋊D₁₃	semidirect
511. C₂×D₄	C₂×C₂²⋊D₁₃	semidirect
527. C₂²×C₄	C₂×C₂²⋊D₁₃	semidirect
553. C₁₃	#62811	semidirect
621. C₂²	#11719648	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719648	2
#13128516	2
#13128505	2
#13128494	2
#13128487	2
#13128480	2
#13128471	2
#41×C₂²⋊D₁₃	2
#13128165	2
C₂×#11719496	2
#13128039	2
C₂³×C₁₃×#41	2
#62811	13