Subgroups — C₁₃×#60676 #15747015

Order 3328.

1998 conjugacy classes of subgroups.

The subgroup lattice has 400 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×#3172	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3171	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3135	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3054	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₃×#135	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#135	C₂²	1	4	yes	—
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#533	C₂²	1	4	yes	—
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#532	C₂²	1	2	yes	—
15	C₁₃×#532	C₂²	1	4	yes	—
16	C₁₃×#529	—	2	4	no	—
17	C₁₃×#529	—	2	4	no	—
18	C₁₃×#529	C₂²	1	8	yes	—
19	C₁₃×#525	—	2	4	no	—
20	C₁₃×#525	C₂²	1	4	yes	—
21	C₄×C₁₃×#41	—	2	4	no	—
22	C₄×C₁₃×#41	C₂²	1	4	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#501	C₂²	1	8	yes	complemented
25	C₁₃×#497	C₂²	1	4	yes	complemented
26	C₁₃×#496	C₂²	1	4	yes	complemented
27	C₁₃×#491	C₂²	1	4	yes	complemented
28	C₁₃×#490	C₂²	1	4	yes	complemented
29	C₁₃×#489	C₂²	1	8	yes	complemented
30	C₁₃×#470	C₂²	1	8	yes	—
31	C₁₃×#469	C₂²	1	8	yes	—
32	C₁₃×#468	C₂²	1	16	yes	—
33	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
34	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
35	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
36	C₁₃×#427	C₂²	1	4	yes	—
37	C₁₃×#416	C₂²	1	8	yes	—
38	C₄×C₁₃×M₁₆	C₂²	1	8	yes	—
39	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
42	C₂×C₁₃×#41	—	2	4	no	—
43	C₂×C₁₃×#41	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	D₄	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×#135	—	2	16	no	—
47	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
48	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
49	C₂×C₁₃×D₈	C₂³	1	4	yes	—
50	C₂×C₁₃×M₁₆	—	2	8	no	—
51	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
56	C₁₃×#127	C₂³	1	2	yes	—
57	C₁₃×#126	—	2	8	no	—
58	C₁₃×#125	—	2	4	no	—
59	C₁₃×#125	C₂³	1	4	yes	—
60	C₁₃×#124	—	2	4	no	—
61	C₁₃×#124	C₂³	1	4	yes	—
62	C₁₃×#123	—	2	8	no	—
63	C₁₃×#123	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	4	no	—
65	C₁₃×C₂²⋊Q₈	—	2	4	no	—
66	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
67	C₁₃×#121	—	2	4	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#121	C₂³	1	8	yes	—
70	C₁₃×#120	—	2	4	no	—
71	C₄×Q₈×C₁₃	—	2	4	no	—
72	C₄×Q₈×C₁₃	—	2	4	no	—
73	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
74	C₄×D₄×C₁₃	—	2	8	no	—
75	C₄×D₄×C₁₃	—	2	8	no	—
76	C₄×D₄×C₁₃	—	2	8	no	—
77	C₄×D₄×C₁₃	—	2	4	no	—
78	C₄×D₄×C₁₃	—	2	4	no	—
79	C₄×D₄×C₁₃	C₂³	1	8	yes	—
80	C₁₃×#117	—	2	4	no	—
81	C₁₃×#117	—	2	8	no	—
82	C₁₃×#117	—	2	4	no	—
83	C₁₃×#117	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	D₄	1	2	yes	—
86	C₂×C₄²×C₁₃	D₄	1	2	yes	—
87	C₂×C₄²×C₁₃	D₄	1	2	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#107	C₂³	1	8	yes	—
92	C₁₃×#106	C₂³	1	8	yes	—
93	C₁₃×#103	C₂³	1	16	yes	—
94	C₁₃×#102	C₂³	1	16	yes	—
95	C₁₃×#97	C₂³	1	4	yes	—
96	C₁₃×#97	C₂³	1	4	yes	—
97	C₄×C₈×C₁₃	C₂³	1	8	yes	—
98	#60676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₁₃×#41	—	2	16	no	—
101	C₁₃×#41	—	4	16	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	8	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	4	4	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×Q₁₆	—	2	8	no	—
121	C₁₃×SD₁₆	—	2	16	no	—
122	C₁₃×D₈	—	2	8	no	—
123	C₁₃×M₁₆	—	2	16	no	—
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	#41	1	8	yes	complemented
126	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
127	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
134	C₁₃×C₂²⋊C₄	—	2	8	no	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₄²×C₁₃	—	2	8	no	—
140	C₄²×C₁₃	—	2	4	no	—
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂×D₄	1	4	yes	—
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃	C₂×D₄	1	4	yes	—
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂⁴	1	2	yes	—
147	C₄²×C₁₃	C₂⁴	1	2	yes	—
148	#3444	C₂×C₁₃	1	2	yes	complemented
149	#3172	C₂×C₁₃	1	8	yes	complemented
150	#3171	C₂×C₁₃	1	8	yes	complemented
151	#3162	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#3135	C₂×C₁₃	1	2	yes	complemented
154	#3054	C₂×C₁₃	1	4	yes	complemented
155	C₄×#135	C₂×C₁₃	1	4	yes	complemented
156	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	8	no	—
163	Q₈×C₁₃	—	4	8	no	—
164	D₄×C₁₃	—	2	8	no	—
165	D₄×C₁₃	—	4	8	no	—
166	D₄×C₁₃	—	4	16	no	—
167	D₄×C₁₃	—	4	8	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	8	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	8	no	—
178	C₂×C₄×C₁₃	—	4	16	no	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
185	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
186	C₈×C₁₃	—	2	4	no	—
187	C₈×C₁₃	C₂×#41	1	8	yes	—
188	C₂×#135	C₂²×C₁₃	1	4	yes	—
189	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
190	#533	C₂²×C₁₃	1	4	yes	—
191	#533	C₂²×C₁₃	1	2	yes	—
192	#532	C₂²×C₁₃	1	2	yes	—
193	#532	C₂²×C₁₃	1	4	yes	—
194	#529	—	2	4	no	—
195	#529	—	2	4	no	—
196	#529	C₂²×C₁₃	1	8	yes	—
197	#525	—	2	4	no	—
198	#525	C₂²×C₁₃	1	4	yes	—
199	C₄×#41	—	2	4	no	—
200	C₄×#41	C₂²×C₁₃	1	4	yes	—
201	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
202	#501	C₂²×C₁₃	1	8	yes	complemented
203	#497	C₂²×C₁₃	1	4	yes	complemented
204	#496	C₂²×C₁₃	1	4	yes	complemented
205	#491	C₂²×C₁₃	1	4	yes	complemented
206	#490	C₂²×C₁₃	1	4	yes	complemented
207	#489	C₂²×C₁₃	1	8	yes	complemented
208	#470	C₂²×C₁₃	1	8	yes	—
209	#469	C₂²×C₁₃	1	8	yes	—
210	#468	C₂²×C₁₃	1	16	yes	—
211	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
212	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
213	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
214	#427	C₂²×C₁₃	1	4	yes	—
215	#416	C₂²×C₁₃	1	8	yes	—
216	C₄×M₁₆	C₂²×C₁₃	1	8	yes	—
217	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	—	4	4	no	—
225	C₂²×C₁₃	—	4	8	no	—
226	C₂²×C₁₃	#532	1	2	yes	—
227	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	4	8	no	—
233	C₄×C₁₃	#532	1	2	yes	—
234	C₄×C₁₃	#575	1	4	yes	—
235	C₄×C₁₃	C₂²×#41	1	2	yes	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	C₂³×C₁₃	1	4	yes	—
238	C₂³×C₄	D₄×C₁₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
240	#135	—	2	16	no	—
241	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
242	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
243	C₂×D₈	C₂³×C₁₃	1	4	yes	—
244	C₂×M₁₆	—	2	8	no	—
245	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
246	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
248	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
249	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
250	#127	C₂³×C₁₃	1	2	yes	—
251	#126	—	2	8	no	—
252	#125	—	2	4	no	—
253	#125	C₂³×C₁₃	1	4	yes	—
254	#124	—	2	4	no	—
255	#124	C₂³×C₁₃	1	4	yes	—
256	#123	—	2	8	no	—
257	#123	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
261	#121	—	2	4	no	—
262	#121	—	2	4	no	—
263	#121	C₂³×C₁₃	1	8	yes	—
264	#120	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
268	C₄×D₄	—	2	8	no	—
269	C₄×D₄	—	2	8	no	—
270	C₄×D₄	—	2	8	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	C₂³×C₁₃	1	8	yes	—
274	#117	—	2	4	no	—
275	#117	—	2	8	no	—
276	#117	—	2	4	no	—
277	#117	C₂³×C₁₃	1	4	yes	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	D₄×C₁₃	1	2	yes	—
280	C₂×C₄²	D₄×C₁₃	1	2	yes	—
281	C₂×C₄²	D₄×C₁₃	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
284	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
285	#107	C₂³×C₁₃	1	8	yes	—
286	#106	C₂³×C₁₃	1	8	yes	—
287	#103	C₂³×C₁₃	1	16	yes	—
288	#102	C₂³×C₁₃	1	16	yes	—
289	#97	C₂³×C₁₃	1	4	yes	—
290	#97	C₂³×C₁₃	1	4	yes	—
291	C₄×C₈	C₂³×C₁₃	1	8	yes	—
292	C₂×C₁₃	—	2	2	no	—
293	C₂×C₁₃	—	4	2	no	—
294	C₂×C₁₃	—	8	4	no	—
295	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
296	C₂×C₁₃	C₂×#575	1	2	yes	—
297	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
298	#41	—	2	16	no	—
299	#41	—	4	16	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
316	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
318	Q₁₆	—	2	8	no	—
319	SD₁₆	—	2	16	no	—
320	D₈	—	2	8	no	—
321	M₁₆	—	2	16	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	C₁₃×#41	1	8	yes	complemented
324	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
325	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₄²	—	2	8	no	—
338	C₄²	—	2	4	no	—
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₁₃	1	4	yes	—
342	C₄²	C₂×D₄×C₁₃	1	2	yes	—
343	C₄²	C₂×D₄×C₁₃	1	4	yes	—
344	C₄²	C₂⁴×C₁₃	1	2	yes	—
345	C₄²	C₂⁴×C₁₃	1	2	yes	—
346	C₁₃	#60676	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	2	no	—
350	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
351	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	Q₈	—	2	8	no	—
353	Q₈	—	4	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	16	no	—
357	D₄	—	4	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
371	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
374	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
375	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
376	C₈	—	2	4	no	—
377	C₈	C₂×C₁₃×#41	1	8	yes	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	8	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₁₃×#532	1	2	yes	—
385	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	8	no	—
390	C₄	—	4	4	no	—
391	C₄	C₁₃×#532	1	2	yes	—
392	C₄	C₁₃×#575	1	4	yes	—
393	C₄	C₂²×C₁₃×#41	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	4	2	no	—
396	C₂	—	8	4	no	—
397	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
398	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×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×#3172	C₂	semidirect
3. C₁₃×#3171	C₂	semidirect
4. C₁₃×#3162	C₂	semidirect
5. C₁₃×#3150	C₂	semidirect
6. C₁₃×#3135	C₂	semidirect
7. C₁₃×#3054	C₂	semidirect
8. C₄×C₁₃×#135	C₂	semidirect
9. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
24. C₁₃×#501	C₂²	semidirect
25. C₁₃×#497	C₂²	semidirect
26. C₁₃×#496	C₂²	semidirect
27. C₁₃×#491	C₂²	semidirect
28. C₁₃×#490	C₂²	semidirect
29. C₁₃×#489	C₂²	semidirect
33. C₄×C₁₃×Q₁₆	C₂²	semidirect
34. C₄×C₁₃×SD₁₆	C₂²	semidirect
35. C₄×C₁₃×D₈	C₂²	semidirect
98. #60676	C₁₃	direct (N × H)
125. C₂×C₈×C₁₃	#41	semidirect
148. #3444	C₂×C₁₃	semidirect
149. #3172	C₂×C₁₃	semidirect
150. #3171	C₂×C₁₃	semidirect
151. #3162	C₂×C₁₃	semidirect
152. #3150	C₂×C₁₃	semidirect
153. #3135	C₂×C₁₃	semidirect
154. #3054	C₂×C₁₃	semidirect
155. C₄×#135	C₂×C₁₃	semidirect
156. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
202. #501	C₂²×C₁₃	semidirect
203. #497	C₂²×C₁₃	semidirect
204. #496	C₂²×C₁₃	semidirect
205. #491	C₂²×C₁₃	semidirect
206. #490	C₂²×C₁₃	semidirect
207. #489	C₂²×C₁₃	semidirect
211. C₄×Q₁₆	C₂²×C₁₃	semidirect
212. C₄×SD₁₆	C₂²×C₁₃	semidirect
213. C₄×D₈	C₂²×C₁₃	semidirect
323. C₂×C₈	C₁₃×#41	semidirect
346. C₁₃	#60676	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×#3172	2
C₁₃×#3171	2
C₁₃×#3162	2
C₁₃×#3150	2
C₁₃×#3135	2
C₁₃×#3054	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×M₁₆	2
#60676	13

Subgroups — C13×#60676 #15747015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60676 #15747015