Subgroups — C₁₃×#61259 #15747598

Order 3328.

1866 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3492	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3345	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3337	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3335	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3092	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#554	—	2	2	no	—
20	C₁₃×#554	C₂²	1	4	yes	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	C₂²	1	4	yes	—
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#552	C₂²	1	4	yes	—
25	C₁₃×#547	—	2	2	no	—
26	C₁₃×#547	C₂²	1	4	yes	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#539	—	2	4	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#525	—	2	4	no	—
31	C₁₃×#525	C₂²	1	2	yes	—
32	C₁₃×#525	C₂²	1	1	yes	characteristic
33	C₁₃×#520	C₂²	1	2	yes	—
34	C₁₃×#520	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₁₃×#501	C₂²	1	4	yes	complemented
37	C₁₃×#499	C₂²	1	2	yes	complemented
38	C₁₃×#498	C₂²	1	2	yes	complemented
39	C₁₃×#485	C₂²	1	4	yes	complemented
40	C₁₃×#484	C₂²	1	4	yes	—
41	C₁₃×#483	C₂²	1	4	yes	—
42	C₁₃×#483	C₂²	1	4	yes	complemented
43	C₁₃×#482	C₂²	1	4	yes	complemented
44	C₁₃×#481	C₂²	1	4	yes	—
45	C₁₃×#481	C₂²	1	4	yes	complemented
46	C₁₃×#480	C₂²	1	4	yes	—
47	C₁₃×#479	C₂²	1	4	yes	complemented
48	C₁₃×#478	C₂²	1	4	yes	complemented
49	C₁₃×#476	C₂²	1	4	yes	complemented
50	C₁₃×#475	C₂²	1	4	yes	complemented
51	C₁₃×#470	C₂²	1	2	yes	complemented
52	C₁₃×#469	C₂²	1	2	yes	complemented
53	C₁₃×#467	C₂²	1	2	yes	—
54	C₁₃×#466	C₂²	1	2	yes	—
55	C₁₃×#465	C₂²	1	2	yes	—
56	C₁₃×#465	C₂²	1	2	yes	—
57	C₁₃×#465	C₂²	1	4	yes	complemented
58	C₁₃×#442	C₂²	1	2	yes	complemented
59	C₁₃×#441	C₂²	1	2	yes	complemented
60	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
61	C₁₃×#435	C₂²	1	4	yes	—
62	C₈×D₄×C₁₃	C₂²	1	4	yes	—
63	C₁₃×#428	C₂²	1	2	yes	—
64	C₁₃×#428	C₂²	1	2	yes	—
65	C₁₃×#428	C₂²	1	4	yes	complemented
66	C₁₃×#427	C₂²	1	1	yes	characteristic
67	C₁₃×#427	C₂²	1	2	yes	complemented
68	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#106	C₂²	1	4	yes	—
70	C₂×C₁₃×#106	C₂²	1	2	yes	—
71	C₂×C₁₃×#106	C₂²	1	4	yes	—
72	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
74	C₁₃×#424	C₂²	1	1	yes	characteristic
75	C₁₃×#417	C₂²	1	2	yes	—
76	C₁₃×#417	C₂²	1	2	yes	—
77	C₁₃×#416	C₂²	1	2	yes	—
78	C₁₃×#408	C₂²	1	1	yes	characteristic
79	C₁₃×#407	C₂²	1	1	yes	characteristic
80	C₁₃×#405	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#41	—	2	4	no	—
82	C₂×C₁₃×#41	C₂³	1	2	yes	—
83	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	—	2	2	no	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#135	—	2	4	no	—
87	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
89	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
90	C₁₃×#131	—	2	4	no	—
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	—	2	4	no	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×#126	—	2	4	no	—
103	C₁₃×#126	—	2	4	no	—
104	C₁₃×#125	—	2	4	no	—
105	C₁₃×#125	—	2	4	no	—
106	C₁₃×#125	—	2	2	no	—
107	C₁₃×#125	C₂³	1	4	yes	—
108	C₁₃×#123	—	2	4	no	—
109	C₁₃×#123	—	2	2	no	—
110	C₁₃×#123	—	2	4	no	—
111	C₁₃×#123	—	2	4	no	—
112	C₁₃×#123	—	2	4	no	—
113	C₁₃×#123	D₄	1	2	yes	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	4	no	—
116	C₁₃×C₂²⋊Q₈	—	2	4	no	—
117	C₁₃×C₂²⋊Q₈	—	2	4	no	—
118	C₁₃×C₂²⋊Q₈	—	2	4	no	—
119	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×#121	—	2	4	no	—
124	C₁₃×#121	—	2	4	no	—
125	C₁₃×#121	—	2	2	no	—
126	C₁₃×#121	D₄	1	2	yes	—
127	C₁₃×#121	C₂³	1	2	yes	—
128	C₁₃×#121	C₂³	1	2	yes	—
129	C₁₃×#121	C₂³	1	4	yes	—
130	C₁₃×#120	—	2	2	no	—
131	C₁₃×#120	D₄	1	2	yes	—
132	C₄×Q₈×C₁₃	—	2	2	no	—
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×D₄×C₁₃	—	2	4	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	4	no	—
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	4	no	—
140	C₄×D₄×C₁₃	—	2	4	no	—
141	C₄×D₄×C₁₃	C₂³	1	4	yes	—
142	C₄×D₄×C₁₃	C₂³	1	4	yes	—
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	4	no	—
145	C₁₃×#117	C₂³	1	2	yes	—
146	C₁₃×#117	C₂³	1	4	yes	—
147	C₁₃×#117	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
157	C₁₃×#107	C₂³	1	2	yes	—
158	C₁₃×#107	C₂³	1	4	yes	—
159	C₁₃×#107	C₂³	1	4	yes	—
160	C₁₃×#106	C₂³	1	2	yes	—
161	C₁₃×#106	C₂³	1	2	yes	—
162	C₁₃×#106	C₂³	1	2	yes	—
163	C₁₃×#106	C₂³	1	2	yes	—
164	C₁₃×#106	C₂³	1	4	yes	—
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	1	yes	characteristic
167	C₁₃×#106	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	1	yes	characteristic
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₃×#103	C₂³	1	2	yes	—
172	C₁₃×#103	C₂³	1	2	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#102	C₂³	1	2	yes	—
176	C₁₃×#102	C₂³	1	2	yes	—
177	C₁₃×#102	C₂³	1	4	yes	—
178	C₁₃×#102	C₂³	1	4	yes	—
179	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#97	C₂³	1	2	yes	—
182	C₄×C₈×C₁₃	C₂³	1	2	yes	—
183	#61259	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×#41	—	2	2	no	—
186	C₁₃×#41	—	2	2	no	—
187	C₁₃×#41	—	2	4	no	—
188	C₁₃×#41	—	2	4	no	—
189	C₁₃×#41	—	8	8	no	—
190	C₂×Q₈×C₁₃	—	2	4	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
200	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	8	4	no	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₁₃×Q₁₆	—	2	2	no	—
217	C₁₃×SD₁₆	—	2	4	no	—
218	C₁₃×D₈	—	2	2	no	—
219	C₁₃×M₁₆	—	2	2	no	—
220	C₁₃×M₁₆	—	2	2	no	—
221	C₁₃×M₁₆	—	2	4	no	—
222	C₂×C₈×C₁₃	—	2	2	no	—
223	C₂×C₈×C₁₃	—	2	4	no	—
224	C₂×C₈×C₁₃	—	2	4	no	—
225	C₂×C₈×C₁₃	—	2	4	no	—
226	C₂×C₈×C₁₃	#41	1	4	yes	complemented
227	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
230	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
245	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
246	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
247	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
248	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
249	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	2	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₁₃×C₂²⋊C₄	—	2	2	no	—
259	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
260	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	2	no	—
265	C₄²×C₁₃	C₂⁴	1	2	yes	—
266	#3492	C₂×C₁₃	1	2	yes	complemented
267	#3345	C₂×C₁₃	1	4	yes	complemented
268	#3344	C₂×C₁₃	1	4	yes	complemented
269	#3337	C₂×C₁₃	1	4	yes	complemented
270	#3335	C₂×C₁₃	1	4	yes	complemented
271	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3099	C₂×C₁₃	1	2	yes	complemented
273	#3092	C₂×C₁₃	1	2	yes	complemented
274	#3084	C₂×C₁₃	1	2	yes	complemented
275	#3060	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2912	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	4	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
285	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	Q₈×C₁₃	—	2	2	no	—
288	Q₈×C₁₃	—	2	2	no	—
289	Q₈×C₁₃	—	2	2	no	—
290	Q₈×C₁₃	—	8	4	no	—
291	D₄×C₁₃	—	2	4	no	—
292	D₄×C₁₃	—	2	8	no	—
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	2	no	—
295	D₄×C₁₃	—	2	2	no	—
296	D₄×C₁₃	—	4	4	no	—
297	D₄×C₁₃	—	4	4	no	—
298	D₄×C₁₃	—	4	4	no	—
299	D₄×C₁₃	—	8	4	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	4	8	no	—
312	C₂×C₄×C₁₃	—	4	4	no	—
313	C₂×C₄×C₁₃	—	8	4	no	—
314	C₂×C₄×C₁₃	—	8	2	no	—
315	C₂×C₄×C₁₃	—	8	4	no	—
316	C₂×C₄×C₁₃	—	8	2	no	—
317	C₂×C₄×C₁₃	—	8	4	no	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
323	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
324	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
325	C₈×C₁₃	—	2	2	no	—
326	C₈×C₁₃	—	2	2	no	—
327	C₈×C₁₃	—	2	2	no	—
328	C₈×C₁₃	C₂×#41	1	2	yes	—
329	C₈×C₁₃	C₂×#41	1	2	yes	—
330	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
332	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
333	#554	—	2	2	no	—
334	#554	C₂²×C₁₃	1	4	yes	—
335	#553	—	2	2	no	—
336	#553	C₂²×C₁₃	1	4	yes	—
337	#552	—	2	2	no	—
338	#552	C₂²×C₁₃	1	4	yes	—
339	#547	—	2	2	no	—
340	#547	C₂²×C₁₃	1	4	yes	—
341	#544	C₂²×C₁₃	1	2	yes	—
342	#539	—	2	4	no	—
343	#537	C₂²×C₁₃	1	2	yes	—
344	#525	—	2	4	no	—
345	#525	C₂²×C₁₃	1	2	yes	—
346	#525	C₂²×C₁₃	1	1	yes	characteristic
347	#520	C₂²×C₁₃	1	2	yes	—
348	#520	C₂²×C₁₃	1	2	yes	—
349	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
350	#501	C₂²×C₁₃	1	4	yes	complemented
351	#499	C₂²×C₁₃	1	2	yes	complemented
352	#498	C₂²×C₁₃	1	2	yes	complemented
353	#485	C₂²×C₁₃	1	4	yes	complemented
354	#484	C₂²×C₁₃	1	4	yes	—
355	#483	C₂²×C₁₃	1	4	yes	—
356	#483	C₂²×C₁₃	1	4	yes	complemented
357	#482	C₂²×C₁₃	1	4	yes	complemented
358	#481	C₂²×C₁₃	1	4	yes	—
359	#481	C₂²×C₁₃	1	4	yes	complemented
360	#480	C₂²×C₁₃	1	4	yes	—
361	#479	C₂²×C₁₃	1	4	yes	complemented
362	#478	C₂²×C₁₃	1	4	yes	complemented
363	#476	C₂²×C₁₃	1	4	yes	complemented
364	#475	C₂²×C₁₃	1	4	yes	complemented
365	#470	C₂²×C₁₃	1	2	yes	complemented
366	#469	C₂²×C₁₃	1	2	yes	complemented
367	#467	C₂²×C₁₃	1	2	yes	—
368	#466	C₂²×C₁₃	1	2	yes	—
369	#465	C₂²×C₁₃	1	2	yes	—
370	#465	C₂²×C₁₃	1	2	yes	—
371	#465	C₂²×C₁₃	1	4	yes	complemented
372	#442	C₂²×C₁₃	1	2	yes	complemented
373	#441	C₂²×C₁₃	1	2	yes	complemented
374	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
375	#435	C₂²×C₁₃	1	4	yes	—
376	C₈×D₄	C₂²×C₁₃	1	4	yes	—
377	#428	C₂²×C₁₃	1	2	yes	—
378	#428	C₂²×C₁₃	1	2	yes	—
379	#428	C₂²×C₁₃	1	4	yes	complemented
380	#427	C₂²×C₁₃	1	1	yes	characteristic
381	#427	C₂²×C₁₃	1	2	yes	complemented
382	C₂×#106	C₂²×C₁₃	1	4	yes	—
383	C₂×#106	C₂²×C₁₃	1	2	yes	—
384	C₂×#106	C₂²×C₁₃	1	4	yes	—
385	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
388	#424	C₂²×C₁₃	1	1	yes	characteristic
389	#417	C₂²×C₁₃	1	2	yes	—
390	#417	C₂²×C₁₃	1	2	yes	—
391	#416	C₂²×C₁₃	1	2	yes	—
392	#408	C₂²×C₁₃	1	1	yes	characteristic
393	#407	C₂²×C₁₃	1	1	yes	characteristic
394	#405	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×C₁₃	—	2	8	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	2	2	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	4	2	no	—
402	C₂²×C₁₃	—	4	2	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	#547	1	2	yes	—
405	C₂²×C₁₃	#577	1	4	yes	—
406	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
407	C₄×C₁₃	—	2	2	no	—
408	C₄×C₁₃	—	2	2	no	—
409	C₄×C₁₃	—	2	4	no	—
410	C₄×C₁₃	—	4	2	no	—
411	C₄×C₁₃	—	4	4	no	—
412	C₄×C₁₃	—	4	4	no	—
413	C₄×C₁₃	—	4	2	no	—
414	C₄×C₁₃	—	4	2	no	—
415	C₄×C₁₃	#547	1	2	yes	—
416	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
417	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂×#41	—	2	4	no	—
419	C₂×#41	C₂³×C₁₃	1	2	yes	—
420	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
421	C₂³×C₄	—	2	2	no	—
422	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
423	#135	—	2	4	no	—
424	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
426	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
427	#131	—	2	4	no	—
428	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
430	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	—	2	4	no	—
432	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
434	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
435	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
436	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₄⋊Q₈	—	2	2	no	—
438	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
439	#126	—	2	4	no	—
440	#126	—	2	4	no	—
441	#125	—	2	4	no	—
442	#125	—	2	4	no	—
443	#125	—	2	2	no	—
444	#125	C₂³×C₁₃	1	4	yes	—
445	#123	—	2	4	no	—
446	#123	—	2	2	no	—
447	#123	—	2	4	no	—
448	#123	—	2	4	no	—
449	#123	—	2	4	no	—
450	#123	D₄×C₁₃	1	2	yes	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	4	no	—
453	C₂²⋊Q₈	—	2	4	no	—
454	C₂²⋊Q₈	—	2	4	no	—
455	C₂²⋊Q₈	—	2	4	no	—
456	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
457	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
458	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
459	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
460	#121	—	2	4	no	—
461	#121	—	2	4	no	—
462	#121	—	2	2	no	—
463	#121	D₄×C₁₃	1	2	yes	—
464	#121	C₂³×C₁₃	1	2	yes	—
465	#121	C₂³×C₁₃	1	2	yes	—
466	#121	C₂³×C₁₃	1	4	yes	—
467	#120	—	2	2	no	—
468	#120	D₄×C₁₃	1	2	yes	—
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	C₂³×C₁₃	1	4	yes	—
479	C₄×D₄	C₂³×C₁₃	1	4	yes	—
480	#117	—	2	2	no	—
481	#117	—	2	4	no	—
482	#117	C₂³×C₁₃	1	2	yes	—
483	#117	C₂³×C₁₃	1	4	yes	—
484	#117	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	—	2	2	no	—
486	C₂×C₄⋊C₄	—	2	2	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
494	#107	C₂³×C₁₃	1	2	yes	—
495	#107	C₂³×C₁₃	1	4	yes	—
496	#107	C₂³×C₁₃	1	4	yes	—
497	#106	C₂³×C₁₃	1	2	yes	—
498	#106	C₂³×C₁₃	1	2	yes	—
499	#106	C₂³×C₁₃	1	2	yes	—
500	#106	C₂³×C₁₃	1	2	yes	—
501	#106	C₂³×C₁₃	1	4	yes	—
502	#106	C₂³×C₁₃	1	4	yes	—
503	#106	C₂³×C₁₃	1	1	yes	characteristic
504	#106	C₂³×C₁₃	1	4	yes	—
505	#106	C₂³×C₁₃	1	1	yes	characteristic
506	#106	C₂³×C₁₃	1	4	yes	—
507	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
508	#103	C₂³×C₁₃	1	2	yes	—
509	#103	C₂³×C₁₃	1	2	yes	—
510	#103	C₂³×C₁₃	1	4	yes	—
511	#103	C₂³×C₁₃	1	4	yes	—
512	#102	C₂³×C₁₃	1	2	yes	—
513	#102	C₂³×C₁₃	1	2	yes	—
514	#102	C₂³×C₁₃	1	4	yes	—
515	#102	C₂³×C₁₃	1	4	yes	—
516	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
517	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
518	#97	C₂³×C₁₃	1	2	yes	—
519	C₄×C₈	C₂³×C₁₃	1	2	yes	—
520	C₂×C₁₃	—	2	2	no	—
521	C₂×C₁₃	—	2	4	no	—
522	C₂×C₁₃	—	4	2	no	—
523	C₂×C₁₃	—	8	2	no	—
524	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
525	C₂×C₁₃	C₂×#577	1	2	yes	—
526	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
527	#41	—	2	2	no	—
528	#41	—	2	2	no	—
529	#41	—	2	4	no	—
530	#41	—	2	4	no	—
531	#41	—	8	8	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
540	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
542	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	8	4	no	—
553	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
554	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
558	Q₁₆	—	2	2	no	—
559	SD₁₆	—	2	4	no	—
560	D₈	—	2	2	no	—
561	M₁₆	—	2	2	no	—
562	M₁₆	—	2	2	no	—
563	M₁₆	—	2	4	no	—
564	C₂×C₈	—	2	2	no	—
565	C₂×C₈	—	2	4	no	—
566	C₂×C₈	—	2	4	no	—
567	C₂×C₈	—	2	4	no	—
568	C₂×C₈	C₁₃×#41	1	4	yes	complemented
569	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
570	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
571	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
572	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
573	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
587	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
588	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
589	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
590	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
591	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
602	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
603	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	2	no	—
607	C₄²	C₂⁴×C₁₃	1	2	yes	—
608	C₁₃	#61259	1	1	yes	characteristic, direct product factor, Sylow
609	C₂³	—	2	2	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	2	2	no	—
612	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
613	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
614	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	2	no	—
617	Q₈	—	2	2	no	—
618	Q₈	—	8	4	no	—
619	D₄	—	2	4	no	—
620	D₄	—	2	8	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	4	4	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	4	no	—
627	D₄	—	8	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	4	8	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	8	4	no	—
642	C₂×C₄	—	8	2	no	—
643	C₂×C₄	—	8	4	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	—	8	4	no	—
646	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
651	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
652	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
653	C₈	—	2	2	no	—
654	C₈	—	2	2	no	—
655	C₈	—	2	2	no	—
656	C₈	C₂×C₁₃×#41	1	2	yes	—
657	C₈	C₂×C₁₃×#41	1	2	yes	—
658	C₂²	—	2	8	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	C₁₃×#547	1	2	yes	—
668	C₂²	C₁₃×#577	1	4	yes	—
669	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
670	C₄	—	2	4	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	4	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	2	no	—
678	C₄	C₁₃×#547	1	2	yes	—
679	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
680	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂	—	2	2	no	—
682	C₂	—	2	4	no	—
683	C₂	—	4	2	no	—
684	C₂	—	8	2	no	—
685	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
686	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3492	C₂	semidirect
2. C₁₃×#3345	C₂	semidirect
3. C₁₃×#3344	C₂	semidirect
4. C₁₃×#3337	C₂	semidirect
5. C₁₃×#3335	C₂	semidirect
6. C₁₃×#3163	C₂	semidirect
7. C₁₃×#3099	C₂	semidirect
8. C₁₃×#3092	C₂	semidirect
9. C₁₃×#3084	C₂	semidirect
10. C₁₃×#3060	C₂	semidirect
11. C₁₃×#3050	C₂	semidirect
12. C₁₃×#2952	C₂	semidirect
13. C₁₃×#2929	C₂	semidirect
14. C₁₃×#2912	C₂	semidirect
15. C₂²×C₁₃×#106	C₂	semidirect
36. C₁₃×#501	C₂²	semidirect
37. C₁₃×#499	C₂²	semidirect
38. C₁₃×#498	C₂²	semidirect
39. C₁₃×#485	C₂²	semidirect
42. C₁₃×#483	C₂²	semidirect
43. C₁₃×#482	C₂²	semidirect
45. C₁₃×#481	C₂²	semidirect
47. C₁₃×#479	C₂²	semidirect
48. C₁₃×#478	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
50. C₁₃×#475	C₂²	semidirect
51. C₁₃×#470	C₂²	semidirect
52. C₁₃×#469	C₂²	semidirect
57. C₁₃×#465	C₂²	semidirect
58. C₁₃×#442	C₂²	semidirect
59. C₁₃×#441	C₂²	semidirect
60. C₄×C₁₃×SD₁₆	C₂²	semidirect
65. C₁₃×#428	C₂²	semidirect
67. C₁₃×#427	C₂²	semidirect
73. C₂×C₁₃×#106	C₂²	semidirect
183. #61259	C₁₃	direct (N × H)
226. C₂×C₈×C₁₃	#41	semidirect
266. #3492	C₂×C₁₃	semidirect
267. #3345	C₂×C₁₃	semidirect
268. #3344	C₂×C₁₃	semidirect
269. #3337	C₂×C₁₃	semidirect
270. #3335	C₂×C₁₃	semidirect
271. #3163	C₂×C₁₃	semidirect
272. #3099	C₂×C₁₃	semidirect
273. #3092	C₂×C₁₃	semidirect
274. #3084	C₂×C₁₃	semidirect
275. #3060	C₂×C₁₃	semidirect
276. #3050	C₂×C₁₃	semidirect
277. #2952	C₂×C₁₃	semidirect
278. #2929	C₂×C₁₃	semidirect
279. #2912	C₂×C₁₃	semidirect
280. C₂²×#106	C₂×C₁₃	semidirect
350. #501	C₂²×C₁₃	semidirect
351. #499	C₂²×C₁₃	semidirect
352. #498	C₂²×C₁₃	semidirect
353. #485	C₂²×C₁₃	semidirect
356. #483	C₂²×C₁₃	semidirect
357. #482	C₂²×C₁₃	semidirect
359. #481	C₂²×C₁₃	semidirect
361. #479	C₂²×C₁₃	semidirect
362. #478	C₂²×C₁₃	semidirect
363. #476	C₂²×C₁₃	semidirect
364. #475	C₂²×C₁₃	semidirect
365. #470	C₂²×C₁₃	semidirect
366. #469	C₂²×C₁₃	semidirect
371. #465	C₂²×C₁₃	semidirect
372. #442	C₂²×C₁₃	semidirect
373. #441	C₂²×C₁₃	semidirect
374. C₄×SD₁₆	C₂²×C₁₃	semidirect
379. #428	C₂²×C₁₃	semidirect
381. #427	C₂²×C₁₃	semidirect
387. C₂×#106	C₂²×C₁₃	semidirect
568. C₂×C₈	C₁₃×#41	semidirect
608. C₁₃	#61259	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3492	2
C₁₃×#3345	2
C₁₃×#3344	2
C₁₃×#3337	2
C₁₃×#3335	2
C₁₃×#3163	2
C₁₃×#3099	2
C₁₃×#3092	2
C₁₃×#3084	2
C₁₃×#3060	2
C₁₃×#3050	2
C₁₃×#2952	2
C₁₃×#2929	2
C₁₃×#2912	2
C₂²×C₁₃×#106	2
#61259	13

Subgroups — C13×#61259 #15747598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61259 #15747598