Subgroups — #13128510

Order 1664.

1522 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88257	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719534	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719429	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719361	C₂	1	2	yes	maximal, complemented
9	#11719360	C₂	1	2	yes	maximal, complemented
10	#11719359	C₂	1	2	yes	maximal, complemented
11	#11719353	C₂	1	2	yes	maximal, complemented
12	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719334	C₂	1	1	yes	maximal, characteristic, complemented
15	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719315	C₂	1	2	yes	maximal, complemented
17	#11719302	C₂	1	2	yes	maximal, complemented
18	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#88150	C₂	1	2	yes	maximal, complemented
23	#11719212	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
26	#88257	—	2	8	no	—
27	#41×D₁₃	—	2	8	no	—
28	C₂×#6131	C₂²	1	1	yes	characteristic
29	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
30	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#6129	C₂²	1	2	yes	—
33	C₂×#6129	C₂²	1	1	yes	characteristic
34	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
35	C₂×#6129	C₂²	1	2	yes	complemented
36	C₂×#6129	C₂²	1	2	yes	complemented
37	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₁₃	C₂²	1	2	yes	—
39	C₂×#6127	C₂²	1	2	yes	—
40	C₂×#6127	C₂²	1	1	yes	characteristic
41	C₂×#6127	C₂²	1	2	yes	complemented
42	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
44	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
45	C₂²×Dic₂₆	C₂²	1	2	yes	complemented
46	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#123	C₂²	1	2	yes	complemented
49	C₁₃×#123	C₂²	1	2	yes	complemented
50	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#121	C₂²	1	2	yes	complemented
53	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
56	#88201	C₂²	1	1	yes	characteristic, complemented
57	#88200	C₂²	1	1	yes	characteristic
58	#88200	C₂²	1	1	yes	characteristic, complemented
59	#88198	C₂²	1	1	yes	characteristic, complemented
60	#88193	C₂²	1	1	yes	characteristic, complemented
61	#88193	C₂²	1	2	yes	complemented
62	#88193	C₂²	1	2	yes	complemented
63	#88193	C₂²	1	2	yes	complemented
64	#88191	C₂²	1	1	yes	characteristic
65	#88191	C₂²	1	2	yes	—
66	#88189	C₂²	1	2	yes	complemented
67	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
68	#88184	C₂²	1	2	yes	complemented
69	#88184	C₂²	1	1	yes	characteristic, complemented
70	#88183	C₂²	1	2	yes	complemented
71	#88183	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₂×#6103	C₂²	1	2	yes	—
76	C₂×#6103	C₂²	1	2	yes	—
77	#88178	C₂²	1	1	yes	characteristic, complemented
78	C₂×#6101	C₂²	1	2	yes	complemented
79	C₂×#6101	C₂²	1	2	yes	complemented
80	#88151	C₂²	1	1	yes	characteristic
81	#88150	C₂²	1	2	yes	—
82	#88150	C₂²	1	1	yes	characteristic
83	#88150	C₂²	1	2	yes	—
84	#88150	C₂²	1	2	yes	—
85	#88150	C₂²	1	2	yes	complemented
86	#88150	C₂²	1	2	yes	complemented
87	#88150	C₂²	1	2	yes	complemented
88	#88150	C₂²	1	2	yes	complemented
89	#88150	C₂²	1	2	yes	complemented
90	#88150	C₂²	1	2	yes	complemented
91	#88149	C₂²	1	2	yes	complemented
92	#88149	C₂²	1	1	yes	characteristic, complemented
93	#88148	C₂²	1	2	yes	complemented
94	#88148	C₂²	1	2	yes	complemented
95	#88148	C₂²	1	1	yes	characteristic, complemented
96	#88147	C₂²	1	2	yes	—
97	#88147	C₂²	1	2	yes	complemented
98	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
99	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
100	#88142	C₂²	1	2	yes	complemented
101	#88142	C₂²	1	2	yes	complemented
102	#88141	C₂²	1	1	yes	characteristic, complemented
103	#88140	C₂²	1	2	yes	complemented
104	#88139	C₂²	1	2	yes	complemented
105	#88139	C₂²	1	2	yes	complemented
106	#88138	C₂²	1	1	yes	characteristic
107	#88138	C₂²	1	2	yes	complemented
108	#88138	C₂²	1	2	yes	complemented
109	#88138	C₂²	1	2	yes	complemented
110	#88137	C₂²	1	1	yes	characteristic, complemented
111	#88136	C₂²	1	1	yes	characteristic
112	#88136	C₂²	1	2	yes	—
113	#88135	C₂²	1	2	yes	—
114	#88135	C₂²	1	2	yes	complemented
115	#88135	C₂²	1	2	yes	complemented
116	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
117	#88132	C₂²	1	1	yes	characteristic, complemented
118	#88132	C₂²	1	2	yes	complemented
119	#88132	C₂²	1	2	yes	complemented
120	#88131	C₂²	1	2	yes	complemented
121	#88129	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₅₂	C₂²	1	1	yes	characteristic
123	#88126	C₂²	1	1	yes	characteristic, complemented
124	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
125	C₂³×D₁₃	C₂³	1	1	yes	characteristic
126	C₂³×D₁₃	C₂³	1	2	yes	—
127	C₁₃×#41	—	2	4	no	—
128	C₁₃×#41	—	2	4	no	—
129	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂×D₄×C₁₃	C₂³	1	2	yes	—
133	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₃	C₂³	1	2	yes	—
151	C₂²×Dic₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₃	C₂³	1	2	yes	—
153	C₂²×Dic₁₃	C₂³	1	2	yes	—
154	#6131	—	2	4	no	—
155	Q₈×D₁₃	—	2	4	no	—
156	Q₈×D₁₃	—	2	4	no	—
157	Q₈×D₁₃	—	2	4	no	—
158	#6129	—	2	4	no	—
159	#6129	—	2	8	no	—
160	#6129	—	2	8	no	—
161	#6129	—	2	8	no	—
162	#6129	D₄	1	8	yes	complemented
163	D₄×D₁₃	—	2	4	no	—
164	D₄×D₁₃	—	2	8	no	—
165	#6127	—	2	8	no	—
166	#6127	—	2	8	no	—
167	#6127	—	2	4	no	—
168	#6127	—	2	4	no	—
169	C₂×D₅₂	C₂³	1	1	yes	characteristic
170	C₂×D₅₂	C₂³	1	1	yes	characteristic
171	C₂×D₅₂	C₂³	1	1	yes	characteristic
172	C₂×D₅₂	C₂³	1	2	yes	—
173	C₂×D₅₂	C₂³	1	2	yes	—
174	C₂×C₄×D₁₃	—	2	8	no	—
175	C₂×C₄×D₁₃	—	2	4	no	—
176	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₁₃	C₂³	1	2	yes	—
179	C₂×C₄×D₁₃	C₂³	1	2	yes	—
180	C₂×C₄×D₁₃	C₂³	1	2	yes	—
181	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₁₃	C₂³	1	2	yes	—
184	C₂×C₄×D₁₃	C₂³	1	2	yes	—
185	C₂×C₄×D₁₃	C₂³	1	2	yes	—
186	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
187	C₂×Dic₂₆	—	2	8	no	—
188	C₂×Dic₂₆	—	2	4	no	—
189	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
190	C₂×Dic₂₆	C₂³	1	2	yes	—
191	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
192	C₂×Dic₂₆	C₂³	1	2	yes	—
193	C₂×Dic₂₆	C₂³	1	2	yes	—
194	C₂×Dic₂₆	C₂³	1	2	yes	—
195	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
209	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
210	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
211	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	#6103	C₂³	1	1	yes	characteristic
213	#6103	C₂³	1	1	yes	characteristic
214	#6103	C₂³	1	1	yes	characteristic
215	#6103	C₂³	1	1	yes	characteristic
216	#6103	C₂³	1	2	yes	—
217	#6103	C₂³	1	2	yes	—
218	#6103	C₂³	1	2	yes	—
219	#6103	C₂³	1	2	yes	—
220	#6103	C₂³	1	1	yes	characteristic
221	#6103	C₂³	1	1	yes	characteristic
222	#6103	C₂³	1	2	yes	—
223	#6103	C₂³	1	2	yes	—
224	#6103	C₂³	1	2	yes	—
225	#6103	C₂³	1	2	yes	—
226	#6103	C₂³	1	2	yes	—
227	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₁₃	C₂³	1	2	yes	—
230	#6101	C₂³	1	2	yes	—
231	#6101	C₂³	1	1	yes	characteristic
232	#6101	C₂³	1	1	yes	characteristic
233	#6101	C₂³	1	2	yes	—
234	#6101	C₂³	1	2	yes	—
235	#6101	C₂³	1	1	yes	characteristic
236	#6101	C₂³	1	2	yes	—
237	#6101	C₂³	1	2	yes	—
238	#6101	C₂³	1	2	yes	—
239	#6101	C₂³	1	2	yes	—
240	#6101	C₂³	1	1	yes	characteristic
241	#6101	C₂³	1	2	yes	—
242	C₄×Dic₁₃	C₂³	1	2	yes	—
243	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
244	C₄×Dic₁₃	C₂³	1	2	yes	—
245	#3489	—	13	1	no	maximal, Sylow
246	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂³×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×D₁₃	—	2	4	no	—
250	C₂²×D₁₃	—	2	2	no	—
251	C₂²×D₁₃	—	2	2	no	—
252	C₂²×D₁₃	—	2	4	no	—
253	C₂²×D₁₃	—	4	1	no	—
254	C₂²×D₁₃	—	4	2	no	—
255	C₂²×D₁₃	C₂⁴	1	2	yes	—
256	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
259	Q₈×C₁₃	—	2	2	no	—
260	Q₈×C₁₃	—	2	2	no	—
261	D₄×C₁₃	—	2	4	no	—
262	D₄×C₁₃	—	2	4	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	C₂×D₄	1	4	yes	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²⋊D₁₃	—	2	4	no	—
279	C₂²⋊D₁₃	—	2	4	no	—
280	C₂²⋊D₁₃	—	2	2	no	—
281	C₂²⋊D₁₃	—	2	2	no	—
282	C₂²⋊D₁₃	—	2	4	no	—
283	C₂²⋊D₁₃	—	2	2	no	—
284	C₂²⋊D₁₃	—	4	2	no	—
285	C₂²⋊D₁₃	—	4	1	no	—
286	C₂²⋊D₁₃	C₂×D₄	1	8	yes	—
287	C₂×Dic₁₃	—	2	4	no	—
288	C₂×Dic₁₃	—	2	4	no	—
289	C₂×Dic₁₃	—	2	2	no	—
290	C₂×Dic₁₃	—	4	2	no	—
291	C₂×Dic₁₃	C₂×D₄	1	8	yes	—
292	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₁₃	C₂⁴	1	2	yes	—
295	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₁₃	C₂⁴	1	2	yes	—
297	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
298	C₂×Dic₁₃	C₂⁴	1	2	yes	—
299	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
300	D₅₂	—	2	2	no	—
301	D₅₂	—	2	4	no	—
302	D₅₂	—	2	2	no	—
303	D₅₂	—	2	2	no	—
304	D₅₂	—	4	2	no	—
305	C₄×D₁₃	—	2	2	no	—
306	C₄×D₁₃	—	2	4	no	—
307	C₄×D₁₃	—	2	2	no	—
308	C₄×D₁₃	—	2	2	no	—
309	C₄×D₁₃	—	2	2	no	—
310	C₄×D₁₃	—	2	4	no	—
311	C₄×D₁₃	—	2	4	no	—
312	C₄×D₁₃	—	2	4	no	—
313	C₄×D₁₃	—	2	4	no	—
314	C₄×D₁₃	—	4	2	no	—
315	C₄×D₁₃	C₂×D₄	1	4	yes	—
316	Dic₂₆	—	2	2	no	—
317	Dic₂₆	—	2	4	no	—
318	Dic₂₆	—	2	2	no	—
319	Dic₂₆	—	2	4	no	—
320	Dic₂₆	—	2	4	no	—
321	Dic₂₆	—	2	4	no	—
322	Dic₂₆	C₂×D₄	1	4	yes	—
323	C₂×2₋¹⁺⁴	—	13	1	no	—
324	C₂²×#41	—	13	1	no	—
325	D₄×Q₈	—	13	1	no	—
326	D₄×Q₈	—	13	1	no	—
327	#548	—	13	1	no	—
328	#548	—	13	1	no	—
329	#547	—	13	1	no	—
330	#547	—	13	2	no	—
331	#547	—	13	2	no	—
332	#547	D₁₃	1	1	yes	characteristic, complemented
333	#546	—	13	1	no	—
334	#546	—	13	2	no	—
335	#546	—	13	2	no	—
336	#546	—	13	1	no	—
337	#537	—	13	1	no	—
338	#537	—	13	2	no	—
339	#536	—	13	1	no	—
340	#536	—	13	2	no	—
341	#525	—	13	2	no	—
342	#525	—	13	1	no	—
343	C₂×C₂²⋊Q₈	—	13	1	no	—
344	C₂×C₂²⋊Q₈	—	13	2	no	—
345	#520	—	13	1	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	2	1	no	—
349	C₂²×C₁₃	—	2	1	no	—
350	C₂²×C₁₃	—	2	1	no	—
351	C₂²×C₁₃	—	2	1	no	—
352	C₂²×C₁₃	—	2	1	no	—
353	C₂²×C₁₃	—	2	1	no	—
354	C₂²×C₁₃	C₂²×D₄	1	4	yes	—
355	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
356	C₂×D₁₃	—	2	1	no	—
357	C₂×D₁₃	—	2	1	no	—
358	C₂×D₁₃	—	2	1	no	—
359	C₂×D₁₃	—	2	1	no	—
360	C₂×D₁₃	—	2	1	no	—
361	C₂×D₁₃	—	2	2	no	—
362	C₂×D₁₃	—	2	1	no	—
363	C₂×D₁₃	—	2	2	no	—
364	C₂×D₁₃	—	2	1	no	—
365	C₂×D₁₃	—	2	2	no	—
366	C₂×D₁₃	—	4	4	no	—
367	C₂×D₁₃	—	4	8	no	—
368	C₂×D₁₃	C₂²×D₄	1	2	yes	—
369	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	complemented
370	C₄×C₁₃	—	2	1	no	—
371	C₄×C₁₃	—	2	2	no	—
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	2	1	no	—
374	C₄×C₁₃	—	2	1	no	—
375	C₄×C₁₃	—	2	2	no	—
376	C₄×C₁₃	—	2	1	no	—
377	C₄×C₁₃	C₂²×D₄	1	2	yes	—
378	Dic₁₃	—	2	2	no	—
379	Dic₁₃	—	2	1	no	—
380	Dic₁₃	—	2	1	no	—
381	Dic₁₃	—	2	1	no	—
382	Dic₁₃	—	2	2	no	—
383	Dic₁₃	—	2	1	no	—
384	Dic₁₃	C₂²×D₄	1	4	yes	—
385	Dic₁₃	C₂²×D₄	1	2	yes	—
386	2₋¹⁺⁴	—	26	8	no	—
387	C₂×#41	—	13	1	no	—
388	C₂×#41	—	13	1	no	—
389	C₂×#41	—	13	2	no	—
390	C₂×#41	—	13	2	no	—
391	C₂×#41	—	13	1	no	—
392	C₂×#41	—	13	2	no	—
393	C₂×#41	—	13	1	no	—
394	C₂×#41	—	13	2	no	—
395	C₂×#41	—	13	2	no	—
396	C₂×#41	—	13	1	no	—
397	C₂×#41	—	26	8	no	—
398	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
399	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
400	C₂²×Q₈	—	13	1	no	—
401	C₂²×Q₈	—	13	1	no	—
402	C₂²×Q₈	—	13	1	no	—
403	C₂²×Q₈	—	13	2	no	—
404	C₂²×Q₈	—	13	1	no	—
405	C₂²×D₄	—	13	2	no	—
406	C₂²×D₄	—	13	1	no	—
407	C₂³×C₄	—	13	2	no	—
408	C₂³×C₄	—	13	1	no	—
409	C₄⋊Q₈	—	13	1	no	—
410	C₄⋊Q₈	—	13	2	no	—
411	C₄⋊Q₈	—	13	2	no	—
412	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
413	#124	—	13	1	no	—
414	#124	—	13	2	no	—
415	#124	—	13	2	no	—
416	#124	—	13	1	no	—
417	#123	—	13	2	no	—
418	#123	—	13	2	no	—
419	#123	—	13	2	no	—
420	#123	—	13	1	no	—
421	#123	—	13	2	no	—
422	#123	—	13	2	no	—
423	#123	—	13	1	no	—
424	#123	—	13	2	no	—
425	#123	C₂×D₁₃	1	2	yes	complemented
426	#123	C₂×D₁₃	1	2	yes	complemented
427	C₂²⋊Q₈	—	13	1	no	—
428	C₂²⋊Q₈	—	13	1	no	—
429	C₂²⋊Q₈	—	13	1	no	—
430	C₂²⋊Q₈	—	13	2	no	—
431	C₂²⋊Q₈	—	13	1	no	—
432	C₂²⋊Q₈	—	13	2	no	—
433	C₂²⋊Q₈	—	13	2	no	—
434	C₂²⋊Q₈	—	13	2	no	—
435	C₂²⋊Q₈	—	13	2	no	—
436	C₂²⋊Q₈	—	13	1	no	—
437	C₂²⋊Q₈	—	13	2	no	—
438	C₂²⋊Q₈	—	13	2	no	—
439	C₂²⋊Q₈	—	13	2	no	—
440	C₂²⋊Q₈	—	13	2	no	—
441	C₂²⋊Q₈	—	13	2	no	—
442	C₂²⋊Q₈	—	13	1	no	—
443	C₂²⋊Q₈	—	13	2	no	—
444	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
445	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
446	#121	—	13	1	no	—
447	#121	—	13	2	no	—
448	#121	—	13	2	no	—
449	#121	—	13	2	no	—
450	#121	—	13	2	no	—
451	#121	—	13	1	no	—
452	#121	—	13	2	no	—
453	#121	—	13	1	no	—
454	#121	—	13	1	no	—
455	#121	—	13	2	no	—
456	#121	—	13	2	no	—
457	#121	—	13	2	no	—
458	#121	C₂×D₁₃	1	2	yes	complemented
459	#120	—	13	2	no	—
460	#120	—	13	1	no	—
461	#120	—	13	1	no	—
462	#120	—	13	2	no	—
463	C₄×Q₈	—	13	1	no	—
464	C₄×Q₈	—	13	1	no	—
465	C₄×D₄	—	13	1	no	—
466	C₄×D₄	—	13	2	no	—
467	C₄×D₄	—	13	1	no	—
468	C₄×D₄	—	13	1	no	—
469	C₄×D₄	—	13	2	no	—
470	C₄×D₄	—	13	2	no	—
471	C₄×D₄	—	13	2	no	—
472	C₄×D₄	—	13	2	no	—
473	C₄×D₄	—	13	2	no	—
474	C₄×D₄	—	13	1	no	—
475	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
476	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
477	#117	—	13	2	no	—
478	#117	—	13	1	no	—
479	C₂×C₄⋊C₄	—	13	2	no	—
480	C₂×C₄⋊C₄	—	13	2	no	—
481	C₂×C₄⋊C₄	—	13	1	no	—
482	C₂×C₄⋊C₄	—	13	2	no	—
483	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
484	C₂×C₂²⋊C₄	—	13	2	no	—
485	C₂×C₂²⋊C₄	—	13	2	no	—
486	C₂×C₂²⋊C₄	—	13	2	no	—
487	C₂×C₁₃	—	2	4	no	—
488	C₂×C₁₃	—	4	1	no	—
489	C₂×C₁₃	—	4	1	no	—
490	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
491	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
492	C₂×C₁₃	#585	1	1	yes	characteristic
493	D₁₃	—	2	2	no	—
494	D₁₃	—	2	2	no	—
495	D₁₃	—	4	1	no	—
496	D₁₃	—	4	2	no	—
497	C₂⁴	—	13	1	no	—
498	C₂⁴	—	13	2	no	—
499	#41	—	2	4	no	—
500	#41	—	2	4	no	—
501	#41	—	13	8	no	—
502	#41	—	26	4	no	—
503	#41	—	26	8	no	—
504	#41	—	26	8	no	—
505	#41	—	26	4	no	—
506	#41	—	26	8	no	—
507	#41	—	26	8	no	—
508	#41	—	26	4	no	—
509	#41	—	26	8	no	—
510	#41	—	26	4	no	—
511	C₂×Q₈	—	13	1	no	—
512	C₂×Q₈	—	13	2	no	—
513	C₂×Q₈	—	13	1	no	—
514	C₂×Q₈	—	13	2	no	—
515	C₂×Q₈	—	13	2	no	—
516	C₂×Q₈	—	13	1	no	—
517	C₂×Q₈	—	13	2	no	—
518	C₂×Q₈	—	26	8	no	—
519	C₂×Q₈	—	26	4	no	—
520	C₂×Q₈	—	26	4	no	—
521	C₂×Q₈	—	26	4	no	—
522	C₂×Q₈	—	26	4	no	—
523	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
524	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
525	C₂×D₄	—	13	2	no	—
526	C₂×D₄	—	13	1	no	—
527	C₂×D₄	—	13	1	no	—
528	C₂×D₄	—	13	2	no	—
529	C₂×D₄	—	13	1	no	—
530	C₂×D₄	—	13	2	no	—
531	C₂×D₄	—	13	2	no	—
532	C₂×D₄	—	13	2	no	—
533	C₂×D₄	—	13	1	no	—
534	C₂×D₄	—	13	1	no	—
535	C₂×D₄	—	13	1	no	—
536	C₂×D₄	—	13	2	no	—
537	C₂×D₄	—	13	1	no	—
538	C₂×D₄	—	13	2	no	—
539	C₂×D₄	—	26	8	no	—
540	C₂×D₄	—	26	4	no	—
541	C₂×D₄	C₂²×D₁₃	1	2	yes	—
542	C₂×D₄	C₂²×D₁₃	1	2	yes	—
543	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂²×C₄	—	13	2	no	—
546	C₂²×C₄	—	13	1	no	—
547	C₂²×C₄	—	13	2	no	—
548	C₂²×C₄	—	13	2	no	—
549	C₂²×C₄	—	13	1	no	—
550	C₂²×C₄	—	13	2	no	—
551	C₂²×C₄	—	13	2	no	—
552	C₂²×C₄	—	13	1	no	—
553	C₂²×C₄	—	13	2	no	—
554	C₂²×C₄	—	13	1	no	—
555	C₂²×C₄	—	13	2	no	—
556	C₂²×C₄	—	13	1	no	—
557	C₂²×C₄	—	13	2	no	—
558	C₂²×C₄	—	13	1	no	—
559	C₂²×C₄	—	13	2	no	—
560	C₂²×C₄	—	13	2	no	—
561	C₂²×C₄	—	26	8	no	—
562	C₂²×C₄	—	26	4	no	—
563	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
564	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
565	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
568	C₄⋊C₄	—	13	2	no	—
569	C₄⋊C₄	—	13	1	no	—
570	C₄⋊C₄	—	13	1	no	—
571	C₄⋊C₄	—	13	2	no	—
572	C₄⋊C₄	—	13	2	no	—
573	C₄⋊C₄	—	13	2	no	—
574	C₄⋊C₄	—	13	1	no	—
575	C₄⋊C₄	—	13	2	no	—
576	C₄⋊C₄	—	13	2	no	—
577	C₄⋊C₄	—	13	2	no	—
578	C₄⋊C₄	—	13	2	no	—
579	C₄⋊C₄	—	13	1	no	—
580	C₄⋊C₄	—	13	2	no	—
581	C₄⋊C₄	—	13	1	no	—
582	C₄⋊C₄	—	13	1	no	—
583	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
584	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
585	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
586	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
587	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
588	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
589	C₂²⋊C₄	—	13	2	no	—
590	C₂²⋊C₄	—	13	2	no	—
591	C₂²⋊C₄	—	13	1	no	—
592	C₂²⋊C₄	—	13	1	no	—
593	C₂²⋊C₄	—	13	2	no	—
594	C₂²⋊C₄	—	13	1	no	—
595	C₂²⋊C₄	—	13	2	no	—
596	C₂²⋊C₄	—	13	1	no	—
597	C₂²⋊C₄	—	13	2	no	—
598	C₂²⋊C₄	—	13	2	no	—
599	C₂²⋊C₄	—	13	2	no	—
600	C₂²⋊C₄	—	13	2	no	—
601	C₂²⋊C₄	—	13	1	no	—
602	C₂²⋊C₄	—	13	1	no	—
603	C₂²⋊C₄	—	13	1	no	—
604	C₂²⋊C₄	—	13	2	no	—
605	C₂²⋊C₄	—	13	2	no	—
606	C₂²⋊C₄	—	13	2	no	—
607	C₂²⋊C₄	—	13	1	no	—
608	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
609	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
610	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
611	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
612	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
613	C₄²	—	13	2	no	—
614	C₄²	—	13	2	no	—
615	C₄²	—	13	1	no	—
616	C₄²	C₂²×D₁₃	1	1	yes	characteristic
617	C₁₃	#3489	1	1	yes	characteristic, complemented, Sylow
618	C₂³	—	13	1	no	—
619	C₂³	—	13	1	no	—
620	C₂³	—	13	2	no	—
621	C₂³	—	13	1	no	—
622	C₂³	—	26	2	no	—
623	C₂³	—	26	4	no	—
624	C₂³	—	26	2	no	—
625	C₂³	—	26	4	no	—
626	C₂³	—	52	2	no	—
627	C₂³	—	52	1	no	—
628	C₂³	C₂³×D₁₃	1	1	yes	characteristic
629	C₂³	C₂³×D₁₃	1	1	yes	characteristic
630	C₂³	C₂³×D₁₃	1	2	yes	—
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	13	4	no	—
634	Q₈	—	26	2	no	—
635	Q₈	—	26	4	no	—
636	Q₈	—	26	4	no	—
637	Q₈	—	26	4	no	—
638	Q₈	—	26	4	no	—
639	Q₈	—	26	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	4	1	no	—
643	D₄	—	13	8	no	—
644	D₄	—	26	2	no	—
645	D₄	—	26	4	no	—
646	D₄	—	26	2	no	—
647	D₄	—	26	4	no	—
648	D₄	—	26	2	no	—
649	D₄	—	26	2	no	—
650	D₄	—	26	2	no	—
651	D₄	—	26	4	no	—
652	D₄	—	26	4	no	—
653	D₄	—	26	2	no	—
654	D₄	—	52	2	no	—
655	D₄	—	52	2	no	—
656	D₄	—	52	1	no	—
657	D₄	D₄×D₁₃	1	4	yes	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	13	8	no	—
664	C₂×C₄	—	13	2	no	—
665	C₂×C₄	—	13	1	no	—
666	C₂×C₄	—	13	4	no	—
667	C₂×C₄	—	13	1	no	—
668	C₂×C₄	—	13	2	no	—
669	C₂×C₄	—	13	1	no	—
670	C₂×C₄	—	13	2	no	—
671	C₂×C₄	—	13	1	no	—
672	C₂×C₄	—	13	1	no	—
673	C₂×C₄	—	26	2	no	—
674	C₂×C₄	—	26	4	no	—
675	C₂×C₄	—	26	4	no	—
676	C₂×C₄	—	26	4	no	—
677	C₂×C₄	—	26	4	no	—
678	C₂×C₄	—	26	2	no	—
679	C₂×C₄	—	26	4	no	—
680	C₂×C₄	—	26	2	no	—
681	C₂×C₄	—	26	4	no	—
682	C₂×C₄	—	26	4	no	—
683	C₂×C₄	—	26	2	no	—
684	C₂×C₄	—	26	2	no	—
685	C₂×C₄	—	52	2	no	—
686	C₂×C₄	—	52	2	no	—
687	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
688	C₂×C₄	C₂³×D₁₃	1	2	yes	—
689	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
690	C₂×C₄	C₂³×D₁₃	1	2	yes	—
691	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
692	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
693	C₂×C₄	C₂³×D₁₃	1	2	yes	—
694	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	13	2	no	—
704	C₂²	—	13	2	no	—
705	C₂²	—	26	1	no	—
706	C₂²	—	26	1	no	—
707	C₂²	—	26	1	no	—
708	C₂²	—	26	1	no	—
709	C₂²	—	26	1	no	—
710	C₂²	—	26	2	no	—
711	C₂²	—	26	1	no	—
712	C₂²	—	26	2	no	—
713	C₂²	—	26	1	no	—
714	C₂²	—	26	2	no	—
715	C₂²	—	52	8	no	—
716	C₂²	—	52	4	no	—
717	C₂²	C₂×D₄×D₁₃	1	4	yes	—
718	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	1	no	—
726	C₄	—	13	2	no	—
727	C₄	—	13	4	no	—
728	C₄	—	26	1	no	—
729	C₄	—	26	2	no	—
730	C₄	—	26	1	no	—
731	C₄	—	26	2	no	—
732	C₄	—	26	1	no	—
733	C₄	—	26	1	no	—
734	C₄	C₂×D₄×D₁₃	1	2	yes	—
735	C₂	—	2	4	no	—
736	C₂	—	4	1	no	—
737	C₂	—	4	1	no	—
738	C₂	—	26	2	no	—
739	C₂	—	26	2	no	—
740	C₂	—	52	2	no	—
741	C₂	—	52	1	no	—
742	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic
743	C₂	#11719648	1	1	yes	characteristic
744	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#547	C₂
hypercenter	#547	D₁₃
hypocenter	C₁₃	#3489
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#88257	C₂	semidirect
2. C₂×#41×D₁₃	C₂	semidirect
3. C₁₃×#547	C₂	semidirect
4. #11719534	C₂	semidirect
5. #11719529	C₂	semidirect
6. #11719432	C₂	semidirect
7. #11719429	C₂	semidirect
8. #11719361	C₂	semidirect
9. #11719360	C₂	semidirect
10. #11719359	C₂	semidirect
11. #11719353	C₂	semidirect
12. #11719338	C₂	semidirect
13. #11719337	C₂	semidirect
14. #11719334	C₂	semidirect
15. D₁₃×C₂²⋊Q₈	C₂	semidirect
16. #11719315	C₂	semidirect
17. #11719302	C₂	semidirect
18. #11719259	C₂	semidirect
19. #11719257	C₂	semidirect
20. #11719252	C₂	semidirect
21. #11719251	C₂	semidirect
22. C₂×#88150	C₂	semidirect
23. #11719212	C₂	semidirect
25. C₂×C₁₃×#41	C₂²	semidirect
30. C₂×Q₈×D₁₃	C₂²	semidirect
31. C₂×Q₈×D₁₃	C₂²	semidirect
34. C₂×#6129	C₂²	semidirect
35. C₂×#6129	C₂²	semidirect
36. C₂×#6129	C₂²	semidirect
41. C₂×#6127	C₂²	semidirect
42. C₂×#6127	C₂²	semidirect
45. C₂²×Dic₂₆	C₂²	semidirect
46. C₂²×Dic₂₆	C₂²	semidirect
47. C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#123	C₂²	semidirect
49. C₁₃×#123	C₂²	semidirect
50. C₁₃×C₂²⋊Q₈	C₂²	semidirect
51. C₁₃×C₂²⋊Q₈	C₂²	semidirect
52. C₁₃×#121	C₂²	semidirect
53. C₄×D₄×C₁₃	C₂²	semidirect
54. C₄×D₄×C₁₃	C₂²	semidirect
55. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
56. #88201	C₂²	semidirect
58. #88200	C₂²	semidirect
59. #88198	C₂²	semidirect
60. #88193	C₂²	semidirect
61. #88193	C₂²	semidirect
62. #88193	C₂²	semidirect
63. #88193	C₂²	semidirect
66. #88189	C₂²	semidirect
67. D₄×Dic₁₃	C₂²	semidirect
68. #88184	C₂²	semidirect
69. #88184	C₂²	semidirect
70. #88183	C₂²	semidirect
71. #88183	C₂²	semidirect
73. C₄×C₂²⋊D₁₃	C₂²	semidirect
74. C₄×C₂²⋊D₁₃	C₂²	semidirect
77. #88178	C₂²	semidirect
78. C₂×#6101	C₂²	semidirect
79. C₂×#6101	C₂²	semidirect
85. #88150	C₂²	semidirect
86. #88150	C₂²	semidirect
87. #88150	C₂²	semidirect
88. #88150	C₂²	semidirect
89. #88150	C₂²	semidirect
90. #88150	C₂²	semidirect
91. #88149	C₂²	semidirect
92. #88149	C₂²	semidirect
93. #88148	C₂²	semidirect
94. #88148	C₂²	semidirect
95. #88148	C₂²	semidirect
97. #88147	C₂²	semidirect
98. C₄⋊C₄×D₁₃	C₂²	semidirect
99. C₄⋊C₄×D₁₃	C₂²	semidirect
100. #88142	C₂²	semidirect
101. #88142	C₂²	semidirect
102. #88141	C₂²	semidirect
103. #88140	C₂²	semidirect
104. #88139	C₂²	semidirect
105. #88139	C₂²	semidirect
107. #88138	C₂²	semidirect
108. #88138	C₂²	semidirect
109. #88138	C₂²	semidirect
110. #88137	C₂²	semidirect
114. #88135	C₂²	semidirect
115. #88135	C₂²	semidirect
117. #88132	C₂²	semidirect
118. #88132	C₂²	semidirect
119. #88132	C₂²	semidirect
120. #88131	C₂²	semidirect
121. #88129	C₂²	semidirect
123. #88126	C₂²	semidirect
124. C₄×Dic₂₆	C₂²	semidirect
162. #6129	D₄	semidirect
332. #547	D₁₃	semidirect
369. C₂×D₁₃	2₋¹⁺⁴	semidirect
399. C₂×#41	C₂×D₁₃	semidirect
412. C₄⋊Q₈	C₂×D₁₃	semidirect
425. #123	C₂×D₁₃	semidirect
426. #123	C₂×D₁₃	semidirect
444. C₂²⋊Q₈	C₂×D₁₃	semidirect
445. C₂²⋊Q₈	C₂×D₁₃	semidirect
458. #121	C₂×D₁₃	semidirect
475. C₄×D₄	C₂×D₁₃	semidirect
476. C₄×D₄	C₂×D₁₃	semidirect
483. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
617. C₁₃	#3489	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88257	2
C₂×#41×D₁₃	2
C₁₃×#547	2
#11719534	2
#11719529	2
#11719432	2
#11719429	2
#11719361	2
#11719360	2
#11719359	2
#11719353	2
#11719338	2
#11719337	2
#11719334	2
D₁₃×C₂²⋊Q₈	2
#11719315	2
#11719302	2
#11719259	2
#11719257	2
#11719252	2
#11719251	2
C₂×#88150	2
#11719212	2
#3489	13