Subgroups — C₁₃×#60693 #15747032

Order 3328.

1998 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3185	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3184	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3183	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3182	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3131	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3054	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2943	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	4	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	4	yes	—
18	C₁₃×#529	—	2	4	no	—
19	C₁₃×#529	—	2	4	no	—
20	C₁₃×#529	C₂²	1	8	yes	—
21	C₁₃×#525	—	2	4	no	—
22	C₁₃×#525	C₂²	1	4	yes	—
23	C₄×C₁₃×#41	—	2	4	no	—
24	C₄×C₁₃×#41	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	2	yes	complemented
27	C₁₃×#499	C₂²	1	4	yes	complemented
28	C₁₃×#498	C₂²	1	2	yes	complemented
29	C₁₃×#495	C₂²	1	4	yes	complemented
30	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#492	C₂²	1	2	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#487	C₂²	1	4	yes	complemented
35	C₁₃×#486	C₂²	1	4	yes	complemented
36	C₁₃×#470	C₂²	1	8	yes	—
37	C₁₃×#469	C₂²	1	8	yes	—
38	C₁₃×#468	C₂²	1	16	yes	—
39	C₁₃×#442	C₂²	1	8	yes	complemented
40	C₁₃×#441	C₂²	1	8	yes	complemented
41	C₁₃×#440	C₂²	1	16	yes	complemented
42	C₁₃×#427	C₂²	1	4	yes	—
43	C₁₃×#416	C₂²	1	8	yes	—
44	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
45	C₄×C₁₃×M₁₆	C₂²	1	4	yes	—
46	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
47	C₂×C₁₃×#97	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#41	—	2	4	no	—
51	C₂×C₁₃×#41	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	D₄	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#135	—	2	16	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
56	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
57	C₂×C₁₃×D₈	C₂³	1	4	yes	—
58	C₂×C₁₃×M₁₆	—	2	8	no	—
59	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
65	C₁₃×#127	C₂³	1	2	yes	—
66	C₁₃×#126	—	2	8	no	—
67	C₁₃×#125	—	2	4	no	—
68	C₁₃×#125	C₂³	1	4	yes	—
69	C₁₃×#124	—	2	4	no	—
70	C₁₃×#124	C₂³	1	4	yes	—
71	C₁₃×#123	—	2	8	no	—
72	C₁₃×#123	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	C₂³	1	8	yes	—
79	C₁₃×#120	—	2	4	no	—
80	C₄×Q₈×C₁₃	—	2	4	no	—
81	C₄×Q₈×C₁₃	—	2	4	no	—
82	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
83	C₄×D₄×C₁₃	—	2	8	no	—
84	C₄×D₄×C₁₃	—	2	8	no	—
85	C₄×D₄×C₁₃	—	2	8	no	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	C₂³	1	8	yes	—
89	C₁₃×#117	—	2	4	no	—
90	C₁₃×#117	—	2	8	no	—
91	C₁₃×#117	—	2	4	no	—
92	C₁₃×#117	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	—	2	4	no	—
94	C₂×C₄²×C₁₃	D₄	1	4	yes	—
95	C₂×C₄²×C₁₃	D₄	1	2	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#107	C₂³	1	8	yes	—
101	C₁₃×#106	C₂³	1	8	yes	—
102	C₁₃×#103	C₂³	1	16	yes	—
103	C₁₃×#102	C₂³	1	16	yes	—
104	C₁₃×#97	C₂³	1	4	yes	—
105	C₁₃×#97	C₂³	1	4	yes	—
106	C₄×C₈×C₁₃	C₂³	1	2	yes	—
107	C₄×C₈×C₁₃	C₂³	1	2	yes	—
108	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₃	C₂³	1	2	yes	—
111	#60693	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₁₃×#41	—	2	16	no	—
114	C₁₃×#41	—	4	16	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	4	4	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	2	8	no	—
134	C₁₃×SD₁₆	—	2	16	no	—
135	C₁₃×D₈	—	2	8	no	—
136	C₁₃×M₁₆	—	2	8	no	—
137	C₁₃×M₁₆	—	2	8	no	—
138	C₂×C₈×C₁₃	—	2	4	no	—
139	C₂×C₈×C₁₃	#41	1	8	yes	complemented
140	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
142	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
149	C₁₃×C₂²⋊C₄	—	2	8	no	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	8	no	—
153	C₁₃×C₂²⋊C₄	—	2	8	no	—
154	C₄²×C₁₃	—	2	8	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	C₂×D₄	1	4	yes	—
157	C₄²×C₁₃	C₂×D₄	1	4	yes	—
158	C₄²×C₁₃	C₂×D₄	1	2	yes	—
159	C₄²×C₁₃	C₂×D₄	1	2	yes	—
160	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₄²×C₁₃	C₂⁴	1	2	yes	—
163	#3444	C₂×C₁₃	1	2	yes	complemented
164	#3185	C₂×C₁₃	1	2	yes	complemented
165	#3184	C₂×C₁₃	1	2	yes	complemented
166	#3183	C₂×C₁₃	1	8	yes	complemented
167	#3182	C₂×C₁₃	1	4	yes	complemented
168	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#3131	C₂×C₁₃	1	2	yes	complemented
171	#3054	C₂×C₁₃	1	4	yes	complemented
172	#2943	C₂×C₁₃	1	4	yes	complemented
173	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	8	no	—
180	Q₈×C₁₃	—	4	8	no	—
181	D₄×C₁₃	—	2	8	no	—
182	D₄×C₁₃	—	4	16	no	—
183	D₄×C₁₃	—	4	8	no	—
184	D₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	—	4	16	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
202	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
203	C₈×C₁₃	—	2	4	no	—
204	C₈×C₁₃	C₂×#41	1	4	yes	—
205	C₈×C₁₃	C₂×#41	1	4	yes	—
206	C₂×#135	C₂²×C₁₃	1	4	yes	—
207	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
208	#533	C₂²×C₁₃	1	4	yes	—
209	#533	C₂²×C₁₃	1	2	yes	—
210	#532	C₂²×C₁₃	1	2	yes	—
211	#532	C₂²×C₁₃	1	4	yes	—
212	#529	—	2	4	no	—
213	#529	—	2	4	no	—
214	#529	C₂²×C₁₃	1	8	yes	—
215	#525	—	2	4	no	—
216	#525	C₂²×C₁₃	1	4	yes	—
217	C₄×#41	—	2	4	no	—
218	C₄×#41	C₂²×C₁₃	1	4	yes	—
219	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
220	#500	C₂²×C₁₃	1	2	yes	complemented
221	#499	C₂²×C₁₃	1	4	yes	complemented
222	#498	C₂²×C₁₃	1	2	yes	complemented
223	#495	C₂²×C₁₃	1	4	yes	complemented
224	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
226	#492	C₂²×C₁₃	1	2	yes	complemented
227	#488	C₂²×C₁₃	1	8	yes	complemented
228	#487	C₂²×C₁₃	1	4	yes	complemented
229	#486	C₂²×C₁₃	1	4	yes	complemented
230	#470	C₂²×C₁₃	1	8	yes	—
231	#469	C₂²×C₁₃	1	8	yes	—
232	#468	C₂²×C₁₃	1	16	yes	—
233	#442	C₂²×C₁₃	1	8	yes	complemented
234	#441	C₂²×C₁₃	1	8	yes	complemented
235	#440	C₂²×C₁₃	1	16	yes	complemented
236	#427	C₂²×C₁₃	1	4	yes	—
237	#416	C₂²×C₁₃	1	8	yes	—
238	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
239	C₄×M₁₆	C₂²×C₁₃	1	4	yes	—
240	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
241	C₂×#97	C₂²×C₁₃	1	2	yes	—
242	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	2	2	no	—
246	C₂²×C₁₃	—	2	4	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	8	no	—
250	C₂²×C₁₃	#532	1	2	yes	—
251	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
252	C₄×C₁₃	—	2	2	no	—
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	—	4	8	no	—
257	C₄×C₁₃	#532	1	2	yes	—
258	C₄×C₁₃	#575	1	4	yes	—
259	C₄×C₁₃	C₂²×#41	1	2	yes	—
260	C₂×#41	—	2	4	no	—
261	C₂×#41	C₂³×C₁₃	1	4	yes	—
262	C₂³×C₄	D₄×C₁₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
264	#135	—	2	16	no	—
265	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
266	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
267	C₂×D₈	C₂³×C₁₃	1	4	yes	—
268	C₂×M₁₆	—	2	8	no	—
269	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
270	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
271	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
273	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
274	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
275	#127	C₂³×C₁₃	1	2	yes	—
276	#126	—	2	8	no	—
277	#125	—	2	4	no	—
278	#125	C₂³×C₁₃	1	4	yes	—
279	#124	—	2	4	no	—
280	#124	C₂³×C₁₃	1	4	yes	—
281	#123	—	2	8	no	—
282	#123	—	2	4	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	C₂³×C₁₃	1	8	yes	—
289	#120	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	8	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	C₂³×C₁₃	1	8	yes	—
299	#117	—	2	4	no	—
300	#117	—	2	8	no	—
301	#117	—	2	4	no	—
302	#117	C₂³×C₁₃	1	4	yes	—
303	C₂×C₄²	—	2	4	no	—
304	C₂×C₄²	D₄×C₁₃	1	4	yes	—
305	C₂×C₄²	D₄×C₁₃	1	2	yes	—
306	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
310	#107	C₂³×C₁₃	1	8	yes	—
311	#106	C₂³×C₁₃	1	8	yes	—
312	#103	C₂³×C₁₃	1	16	yes	—
313	#102	C₂³×C₁₃	1	16	yes	—
314	#97	C₂³×C₁₃	1	4	yes	—
315	#97	C₂³×C₁₃	1	4	yes	—
316	C₄×C₈	C₂³×C₁₃	1	2	yes	—
317	C₄×C₈	C₂³×C₁₃	1	2	yes	—
318	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₁₃	1	2	yes	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	—	4	2	no	—
323	C₂×C₁₃	—	8	4	no	—
324	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
325	C₂×C₁₃	C₂×#575	1	2	yes	—
326	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
327	#41	—	2	16	no	—
328	#41	—	4	16	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
347	Q₁₆	—	2	8	no	—
348	SD₁₆	—	2	16	no	—
349	D₈	—	2	8	no	—
350	M₁₆	—	2	8	no	—
351	M₁₆	—	2	8	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	C₁₃×#41	1	8	yes	complemented
354	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
355	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
356	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₄²	—	2	8	no	—
369	C₄²	—	2	4	no	—
370	C₄²	C₂×D₄×C₁₃	1	2	yes	—
371	C₄²	C₂×D₄×C₁₃	1	4	yes	—
372	C₄²	C₂×D₄×C₁₃	1	2	yes	—
373	C₄²	C₂×D₄×C₁₃	1	4	yes	—
374	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
375	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
376	C₄²	C₂⁴×C₁₃	1	2	yes	—
377	C₁₃	#60693	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	2	no	—
381	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	Q₈	—	2	8	no	—
384	Q₈	—	4	8	no	—
385	D₄	—	2	8	no	—
386	D₄	—	4	16	no	—
387	D₄	—	4	8	no	—
388	D₄	—	4	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
405	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
406	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
407	C₈	—	2	4	no	—
408	C₈	C₂×C₁₃×#41	1	4	yes	—
409	C₈	C₂×C₁₃×#41	1	4	yes	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	4	no	—
416	C₂²	C₁₃×#532	1	2	yes	—
417	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	8	no	—
422	C₄	—	4	4	no	—
423	C₄	C₁₃×#532	1	2	yes	—
424	C₄	C₁₃×#575	1	4	yes	—
425	C₄	C₂²×C₁₃×#41	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	—	8	4	no	—
429	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
430	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3185	C₂	semidirect
3. C₁₃×#3184	C₂	semidirect
4. C₁₃×#3183	C₂	semidirect
5. C₁₃×#3182	C₂	semidirect
6. C₁₃×#3160	C₂	semidirect
7. C₁₃×#3147	C₂	semidirect
8. C₁₃×#3131	C₂	semidirect
9. C₁₃×#3054	C₂	semidirect
10. C₁₃×#2943	C₂	semidirect
11. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
26. C₁₃×#500	C₂²	semidirect
27. C₁₃×#499	C₂²	semidirect
28. C₁₃×#498	C₂²	semidirect
29. C₁₃×#495	C₂²	semidirect
30. C₁₃×#494	C₂²	semidirect
31. C₁₃×#493	C₂²	semidirect
32. C₁₃×#492	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#487	C₂²	semidirect
35. C₁₃×#486	C₂²	semidirect
39. C₁₃×#442	C₂²	semidirect
40. C₁₃×#441	C₂²	semidirect
41. C₁₃×#440	C₂²	semidirect
111. #60693	C₁₃	direct (N × H)
139. C₂×C₈×C₁₃	#41	semidirect
163. #3444	C₂×C₁₃	semidirect
164. #3185	C₂×C₁₃	semidirect
165. #3184	C₂×C₁₃	semidirect
166. #3183	C₂×C₁₃	semidirect
167. #3182	C₂×C₁₃	semidirect
168. #3160	C₂×C₁₃	semidirect
169. #3147	C₂×C₁₃	semidirect
170. #3131	C₂×C₁₃	semidirect
171. #3054	C₂×C₁₃	semidirect
172. #2943	C₂×C₁₃	semidirect
173. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
220. #500	C₂²×C₁₃	semidirect
221. #499	C₂²×C₁₃	semidirect
222. #498	C₂²×C₁₃	semidirect
223. #495	C₂²×C₁₃	semidirect
224. #494	C₂²×C₁₃	semidirect
225. #493	C₂²×C₁₃	semidirect
226. #492	C₂²×C₁₃	semidirect
227. #488	C₂²×C₁₃	semidirect
228. #487	C₂²×C₁₃	semidirect
229. #486	C₂²×C₁₃	semidirect
233. #442	C₂²×C₁₃	semidirect
234. #441	C₂²×C₁₃	semidirect
235. #440	C₂²×C₁₃	semidirect
353. C₂×C₈	C₁₃×#41	semidirect
377. C₁₃	#60693	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×#3444	2
C₁₃×#3185	2
C₁₃×#3184	2
C₁₃×#3183	2
C₁₃×#3182	2
C₁₃×#3160	2
C₁₃×#3147	2
C₁₃×#3131	2
C₁₃×#3054	2
C₁₃×#2943	2
C₂×C₄×C₁₃×M₁₆	2
#60693	13

Subgroups — C13×#60693 #15747032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60693 #15747032