Subgroups — C₁₃×#60971 #15747310

Order 3328.

1780 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	C₂×C₁₃×#533	C₂	1	2	yes	maximal
2	C₁₃×#3255	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3229	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3209	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3195	C₂	1	4	yes	maximal
6	C₁₃×#3185	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3113	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#533	—	2	2	no	—
10	C₁₃×#533	—	2	2	no	—
11	C₁₃×#533	—	2	2	no	—
12	C₁₃×#533	—	2	2	no	—
13	C₁₃×#533	C₂²	1	4	yes	—
14	C₁₃×#533	C₂²	1	4	yes	—
15	C₁₃×#533	C₂²	1	4	yes	—
16	C₁₃×#533	C₂²	1	4	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#125	—	2	2	no	—
20	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
24	C₂×C₁₃×#117	—	2	2	no	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#498	C₂²	1	4	yes	complemented
27	C₁₃×#494	C₂²	1	4	yes	complemented
28	C₁₃×#487	C₂²	1	8	yes	complemented
29	C₁₃×#483	C₂²	1	16	yes	—
30	C₁₃×#475	C₂²	1	16	yes	complemented
31	C₁₃×#470	C₂²	1	16	yes	—
32	C₁₃×#462	C₂²	1	16	yes	complemented
33	C₁₃×#451	C₂²	1	16	yes	—
34	C₁₃×#441	C₂²	1	16	yes	complemented
35	C₁₃×#432	C₂²	1	4	yes	—
36	C₁₃×#431	C₂²	1	4	yes	—
37	C₁₃×#423	C₂²	1	2	yes	—
38	C₁₃×#407	C₂²	1	2	yes	—
39	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₃	—	2	2	no	—
41	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	D₄	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
45	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
46	C₁₃×C₄⋊Q₈	—	2	2	no	—
47	C₁₃×C₄⋊Q₈	—	2	2	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
51	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
52	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
54	C₁₃×#125	—	2	4	no	—
55	C₁₃×#125	—	2	4	no	—
56	C₁₃×#125	—	2	4	no	—
57	C₁₃×#125	—	2	4	no	—
58	C₁₃×C₂²⋊Q₈	—	2	4	no	—
59	C₁₃×C₂²⋊Q₈	—	2	4	no	—
60	C₁₃×C₂²⋊Q₈	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	—	2	4	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
65	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	2	4	no	—
69	C₄×Q₈×C₁₃	—	2	4	no	—
70	C₄×Q₈×C₁₃	—	2	4	no	—
71	C₄×Q₈×C₁₃	—	2	4	no	—
72	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
73	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
74	C₁₃×#117	—	2	4	no	—
75	C₁₃×#117	—	2	4	no	—
76	C₁₃×#117	—	2	4	no	—
77	C₁₃×#117	—	2	4	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
85	C₂×C₄²×C₁₃	—	2	4	no	—
86	C₂×C₄²×C₁₃	D₄	1	2	yes	—
87	C₂×C₄²×C₁₃	D₄	1	2	yes	—
88	C₂×C₄²×C₁₃	D₄	1	2	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#106	C₂³	1	16	yes	—
94	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
95	C₁₃×#103	C₂³	1	32	yes	—
96	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
97	C₁₃×#97	C₂³	1	4	yes	—
98	C₄×C₈×C₁₃	C₂³	1	4	yes	—
99	#60971	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	4	no	—
104	C₂×Q₈×C₁₃	—	4	8	no	—
105	C₂×Q₈×C₁₃	—	4	8	no	—
106	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	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	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×Q₁₆	—	4	16	no	—
122	C₁₃×M₁₆	—	4	4	no	—
123	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
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	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	—	2	8	no	—
138	C₄²×C₁₃	—	2	8	no	—
139	C₄²×C₁₃	—	2	8	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂×D₄	1	2	yes	—
143	C₄²×C₁₃	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₁₃	C₂×D₄	1	2	yes	—
147	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₄²×C₁₃	C₂⁴	1	2	yes	—
150	C₂×#533	C₂×C₁₃	1	2	yes	—
151	#3255	C₂×C₁₃	1	4	yes	complemented
152	#3229	C₂×C₁₃	1	4	yes	complemented
153	#3209	C₂×C₁₃	1	4	yes	complemented
154	#3195	C₂×C₁₃	1	4	yes	—
155	#3185	C₂×C₁₃	1	4	yes	complemented
156	#3113	C₂×C₁₃	1	8	yes	complemented
157	#2920	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
162	Q₈×C₁₃	—	2	16	no	—
163	Q₈×C₁₃	—	4	8	no	—
164	Q₈×C₁₃	—	4	8	no	—
165	Q₈×C₁₃	—	4	8	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	8	no	—
174	C₂×C₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	8	no	—
178	C₂×C₄×C₁₃	—	4	8	no	—
179	C₂×C₄×C₁₃	#137	1	8	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
187	C₈×C₁₃	—	2	8	no	—
188	#533	—	2	2	no	—
189	#533	—	2	2	no	—
190	#533	—	2	2	no	—
191	#533	—	2	2	no	—
192	#533	C₂²×C₁₃	1	4	yes	—
193	#533	C₂²×C₁₃	1	4	yes	—
194	#533	C₂²×C₁₃	1	4	yes	—
195	#533	C₂²×C₁₃	1	4	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×#125	—	2	2	no	—
199	C₂×C₂²⋊Q₈	—	2	2	no	—
200	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
201	C₂×C₄×Q₈	—	2	2	no	—
202	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
203	C₂×#117	—	2	2	no	—
204	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
205	#498	C₂²×C₁₃	1	4	yes	complemented
206	#494	C₂²×C₁₃	1	4	yes	complemented
207	#487	C₂²×C₁₃	1	8	yes	complemented
208	#483	C₂²×C₁₃	1	16	yes	—
209	#475	C₂²×C₁₃	1	16	yes	complemented
210	#470	C₂²×C₁₃	1	16	yes	—
211	#462	C₂²×C₁₃	1	16	yes	complemented
212	#451	C₂²×C₁₃	1	16	yes	—
213	#441	C₂²×C₁₃	1	16	yes	complemented
214	#432	C₂²×C₁₃	1	4	yes	—
215	#431	C₂²×C₁₃	1	4	yes	—
216	#423	C₂²×C₁₃	1	2	yes	—
217	#407	C₂²×C₁₃	1	2	yes	—
218	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	C₂×#137	1	4	yes	—
225	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	4	8	no	—
231	C₄×C₁₃	—	4	8	no	—
232	C₄×C₁₃	C₂×#137	1	4	yes	—
233	C₄×C₁₃	C₂×#137	1	4	yes	—
234	C₄×C₁₃	#585	1	2	yes	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
237	C₂³×C₄	D₄×C₁₃	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
239	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
240	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
246	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
247	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
248	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
249	#125	—	2	4	no	—
250	#125	—	2	4	no	—
251	#125	—	2	4	no	—
252	#125	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	—	2	4	no	—
255	C₂²⋊Q₈	—	2	4	no	—
256	C₂²⋊Q₈	—	2	4	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
260	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	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×Q₈	C₂³×C₁₃	1	8	yes	—
269	#117	—	2	4	no	—
270	#117	—	2	4	no	—
271	#117	—	2	4	no	—
272	#117	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	D₄×C₁₃	1	2	yes	—
282	C₂×C₄²	D₄×C₁₃	1	2	yes	—
283	C₂×C₄²	D₄×C₁₃	1	2	yes	—
284	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	#106	C₂³×C₁₃	1	16	yes	—
289	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
290	#103	C₂³×C₁₃	1	32	yes	—
291	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
292	#97	C₂³×C₁₃	1	4	yes	—
293	C₄×C₈	C₂³×C₁₃	1	4	yes	—
294	C₂×C₁₃	—	2	4	no	—
295	C₂×C₁₃	—	4	1	no	—
296	C₂×C₁₃	#3449	1	1	yes	characteristic
297	C₂×C₁₃	C₂²×#137	1	2	yes	—
298	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	4	8	no	—
303	C₂×Q₈	—	4	8	no	—
304	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	2	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	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
319	Q₁₆	—	4	16	no	—
320	M₁₆	—	4	4	no	—
321	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
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	—	2	8	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₄²	—	2	8	no	—
337	C₄²	—	2	8	no	—
338	C₄²	C₂×D₄×C₁₃	1	2	yes	—
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₃	1	2	yes	—
341	C₄²	C₂×D₄×C₁₃	1	2	yes	—
342	C₄²	C₂×D₄×C₁₃	1	2	yes	—
343	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₁₃	1	2	yes	—
345	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
346	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
347	C₄²	C₂⁴×C₁₃	1	2	yes	—
348	C₁₃	#60971	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	4	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
352	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
353	Q₈	—	2	16	no	—
354	Q₈	—	4	8	no	—
355	Q₈	—	4	8	no	—
356	Q₈	—	4	8	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	C₁₃×#137	1	8	yes	—
371	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
372	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
374	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
377	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
378	C₈	—	2	8	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₂×C₁₃×#137	1	4	yes	—
385	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	8	no	—
391	C₄	—	4	8	no	—
392	C₄	C₂×C₁₃×#137	1	4	yes	—
393	C₄	C₂×C₁₃×#137	1	4	yes	—
394	C₄	C₁₃×#585	1	2	yes	—
395	C₂	—	2	4	no	—
396	C₂	—	4	1	no	—
397	C₂	C₁₃×#3449	1	1	yes	characteristic
398	C₂	C₂²×C₁₃×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3255	C₂	semidirect
3. C₁₃×#3229	C₂	semidirect
4. C₁₃×#3209	C₂	semidirect
6. C₁₃×#3185	C₂	semidirect
7. C₁₃×#3113	C₂	semidirect
26. C₁₃×#498	C₂²	semidirect
27. C₁₃×#494	C₂²	semidirect
28. C₁₃×#487	C₂²	semidirect
30. C₁₃×#475	C₂²	semidirect
32. C₁₃×#462	C₂²	semidirect
34. C₁₃×#441	C₂²	semidirect
99. #60971	C₁₃	direct (N × H)
151. #3255	C₂×C₁₃	semidirect
152. #3229	C₂×C₁₃	semidirect
153. #3209	C₂×C₁₃	semidirect
155. #3185	C₂×C₁₃	semidirect
156. #3113	C₂×C₁₃	semidirect
205. #498	C₂²×C₁₃	semidirect
206. #494	C₂²×C₁₃	semidirect
207. #487	C₂²×C₁₃	semidirect
209. #475	C₂²×C₁₃	semidirect
211. #462	C₂²×C₁₃	semidirect
213. #441	C₂²×C₁₃	semidirect
348. C₁₃	#60971	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₁₃×#3255	2
C₁₃×#3229	2
C₁₃×#3209	2
C₁₃×#3195	2
C₁₃×#3185	2
C₁₃×#3113	2
C₁₃×#2920	2
#60971	13

Subgroups — C13×#60971 #15747310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60971 #15747310