Subgroups — C₁₃×#60639 #15746978

Order 3328.

3314 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	4	yes	maximal, complemented
2	C₂×C₁₃×#532	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3153	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3152	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3151	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3150	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3147	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	4	yes	—
10	C₁₃×#575	—	2	32	no	—
11	C₂×C₁₃×#137	C₂²	1	16	yes	complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
13	C₂×C₁₃×#135	C₂²	1	16	yes	complemented
14	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
15	C₁₃×#532	—	2	4	no	—
16	C₁₃×#532	—	2	4	no	—
17	C₁₃×#532	C₂²	1	4	yes	—
18	C₁₃×#532	C₂²	1	4	yes	—
19	C₁₃×#532	C₂²	1	4	yes	complemented
20	C₁₃×#532	C₂²	1	4	yes	complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#121	—	2	4	no	—
25	C₂×C₄×D₄×C₁₃	—	2	4	no	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#497	C₂²	1	16	yes	complemented
28	C₁₃×#496	C₂²	1	16	yes	complemented
29	C₁₃×#495	C₂²	1	16	yes	complemented
30	C₁₃×#494	C₂²	1	4	yes	complemented
31	C₁₃×#493	C₂²	1	4	yes	complemented
32	C₁₃×#492	C₂²	1	8	yes	complemented
33	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
34	C₄×C₁₃×M₁₆	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
36	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#41	—	2	4	no	—
38	C₂×C₁₃×#41	—	2	4	no	—
39	C₂×C₁₃×#41	—	2	32	no	—
40	C₂×C₁₃×#41	C₂³	1	8	yes	—
41	C₂×C₁₃×#41	C₂³	1	8	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	—	2	4	no	—
45	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	—	2	4	no	—
47	C₂³×C₄×C₁₃	D₄	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#137	—	2	64	no	—
50	C₁₃×AGL(1,ℤ/8)	—	2	64	no	—
51	C₁₃×#135	—	2	64	no	—
52	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
53	C₂×C₁₃×SD₁₆	C₂³	1	32	yes	—
54	C₂×C₁₃×D₈	C₂³	1	16	yes	—
55	C₂×C₁₃×M₁₆	D₄	1	16	yes	complemented
56	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₁₃×#127	—	2	4	no	—
62	C₁₃×#127	C₂³	1	4	yes	—
63	C₁₃×#127	C₂³	1	4	yes	—
64	C₁₃×#124	—	2	8	no	—
65	C₁₃×#124	C₂³	1	8	yes	—
66	C₁₃×#124	C₂³	1	8	yes	—
67	C₁₃×#121	—	2	8	no	—
68	C₁₃×#121	—	2	8	no	—
69	C₁₃×#121	—	2	8	no	—
70	C₁₃×#121	—	2	8	no	—
71	C₄×D₄×C₁₃	—	2	8	no	—
72	C₄×D₄×C₁₃	—	2	8	no	—
73	C₄×D₄×C₁₃	—	2	8	no	—
74	C₄×D₄×C₁₃	—	2	8	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₄²×C₁₃	D₄	1	4	yes	—
78	C₂×C₄²×C₁₃	D₄	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₁₃×#97	C₂³	1	8	yes	—
84	C₄×C₈×C₁₃	C₂³	1	4	yes	—
85	C₄×C₈×C₁₃	C₂³	1	4	yes	—
86	#60639	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	4	no	—
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₁₃×#41	—	2	32	no	—
90	C₁₃×#41	—	2	32	no	—
91	C₁₃×#41	—	4	16	no	—
92	C₁₃×#41	—	4	16	no	—
93	C₂×Q₈×C₁₃	—	2	4	no	—
94	C₂×Q₈×C₁₃	—	2	16	no	—
95	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
96	C₂×D₄×C₁₃	—	2	8	no	—
97	C₂×D₄×C₁₃	—	2	8	no	—
98	C₂×D₄×C₁₃	—	2	16	no	—
99	C₂×D₄×C₁₃	—	2	8	no	—
100	C₂×D₄×C₁₃	—	2	8	no	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	4	16	no	—
103	C₂×D₄×C₁₃	—	4	16	no	—
104	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	8	no	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	4	16	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×Q₁₆	—	2	32	no	—
120	C₁₃×SD₁₆	—	2	64	no	—
121	C₁₃×D₈	—	2	32	no	—
122	C₁₃×M₁₆	C₂×D₄	1	32	yes	complemented
123	C₂×C₈×C₁₃	C₂×D₄	1	16	yes	complemented
124	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
125	C₁₃×C₄⋊C₄	—	2	8	no	—
126	C₁₃×C₄⋊C₄	—	2	8	no	—
127	C₁₃×C₂²⋊C₄	—	2	16	no	—
128	C₁₃×C₂²⋊C₄	—	2	16	no	—
129	C₄²×C₁₃	C₂×D₄	1	4	yes	—
130	C₄²×C₁₃	C₂×D₄	1	4	yes	—
131	C₄²×C₁₃	C₂×D₄	1	2	yes	—
132	C₄²×C₁₃	C₂×D₄	1	2	yes	—
133	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₄²×C₁₃	C₂⁴	1	2	yes	—
136	C₂×#575	C₂×C₁₃	1	4	yes	complemented
137	C₂×#532	C₂×C₁₃	1	2	yes	complemented
138	#3153	C₂×C₁₃	1	8	yes	complemented
139	#3152	C₂×C₁₃	1	4	yes	complemented
140	#3151	C₂×C₁₃	1	4	yes	complemented
141	#3150	C₂×C₁₃	1	4	yes	complemented
142	#3147	C₂×C₁₃	1	4	yes	complemented
143	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	2	8	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	16	no	—
147	C₂³×C₁₃	—	4	8	no	—
148	C₂³×C₁₃	#127	1	4	yes	—
149	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃	—	2	16	no	—
152	Q₈×C₁₃	—	4	8	no	—
153	D₄×C₁₃	—	2	16	no	—
154	D₄×C₁₃	—	4	16	no	—
155	D₄×C₁₃	—	4	16	no	—
156	D₄×C₁₃	—	4	16	no	—
157	D₄×C₁₃	—	4	8	no	—
158	D₄×C₁₃	—	4	16	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	8	no	—
161	C₂×C₄×C₁₃	—	2	8	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	8	no	—
165	C₂×C₄×C₁₃	—	4	16	no	—
166	C₂×C₄×C₁₃	—	4	16	no	—
167	C₂×C₄×C₁₃	#127	1	8	yes	—
168	C₂×C₄×C₁₃	#127	1	4	yes	—
169	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
177	C₈×C₁₃	C₂²×D₄	1	16	yes	—
178	C₂²×#41	C₂²×C₁₃	1	4	yes	—
179	#575	—	2	32	no	—
180	C₂×#137	C₂²×C₁₃	1	16	yes	complemented
181	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	16	yes	complemented
182	C₂×#135	C₂²×C₁₃	1	16	yes	complemented
183	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
184	#532	—	2	4	no	—
185	#532	—	2	4	no	—
186	#532	C₂²×C₁₃	1	4	yes	—
187	#532	C₂²×C₁₃	1	4	yes	—
188	#532	C₂²×C₁₃	1	4	yes	complemented
189	#532	C₂²×C₁₃	1	4	yes	complemented
190	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
191	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
192	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
193	C₂×#121	—	2	4	no	—
194	C₂×C₄×D₄	—	2	4	no	—
195	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
196	#497	C₂²×C₁₃	1	16	yes	complemented
197	#496	C₂²×C₁₃	1	16	yes	complemented
198	#495	C₂²×C₁₃	1	16	yes	complemented
199	#494	C₂²×C₁₃	1	4	yes	complemented
200	#493	C₂²×C₁₃	1	4	yes	complemented
201	#492	C₂²×C₁₃	1	8	yes	complemented
202	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
203	C₄×M₁₆	C₂²×C₁₃	1	4	yes	complemented
204	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
205	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	4	4	no	—
209	C₂²×C₁₃	—	4	8	no	—
210	C₂²×C₁₃	—	4	16	no	—
211	C₂²×C₁₃	—	8	16	no	—
212	C₂²×C₁₃	C₂×#127	1	4	yes	—
213	C₂²×C₁₃	C₂×#127	1	2	yes	—
214	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	4	no	—
217	C₄×C₁₃	—	4	8	no	—
218	C₄×C₁₃	C₂×#127	1	2	yes	—
219	C₄×C₁₃	C₂×#127	1	4	yes	—
220	C₄×C₁₃	#575	1	4	yes	complemented
221	C₄×C₁₃	C₂³×D₄	1	2	yes	—
222	C₂×#41	—	2	4	no	—
223	C₂×#41	—	2	4	no	—
224	C₂×#41	—	2	32	no	—
225	C₂×#41	C₂³×C₁₃	1	8	yes	—
226	C₂×#41	C₂³×C₁₃	1	8	yes	—
227	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
228	C₂²×D₄	—	2	4	no	—
229	C₂²×D₄	—	2	4	no	—
230	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
231	C₂³×C₄	—	2	4	no	—
232	C₂³×C₄	D₄×C₁₃	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
234	#137	—	2	64	no	—
235	AGL(1,ℤ/8)	—	2	64	no	—
236	#135	—	2	64	no	—
237	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
238	C₂×SD₁₆	C₂³×C₁₃	1	32	yes	—
239	C₂×D₈	C₂³×C₁₃	1	16	yes	—
240	C₂×M₁₆	D₄×C₁₃	1	16	yes	complemented
241	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
245	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
246	#127	—	2	4	no	—
247	#127	C₂³×C₁₃	1	4	yes	—
248	#127	C₂³×C₁₃	1	4	yes	—
249	#124	—	2	8	no	—
250	#124	C₂³×C₁₃	1	8	yes	—
251	#124	C₂³×C₁₃	1	8	yes	—
252	#121	—	2	8	no	—
253	#121	—	2	8	no	—
254	#121	—	2	8	no	—
255	#121	—	2	8	no	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	—	2	8	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₄²	D₄×C₁₃	1	4	yes	—
263	C₂×C₄²	D₄×C₁₃	1	2	yes	—
264	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
268	#97	C₂³×C₁₃	1	8	yes	—
269	C₄×C₈	C₂³×C₁₃	1	4	yes	—
270	C₄×C₈	C₂³×C₁₃	1	4	yes	—
271	C₂×C₁₃	—	2	4	no	—
272	C₂×C₁₃	—	2	2	no	—
273	C₂×C₁₃	—	8	8	no	—
274	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
275	C₂×C₁₃	C₂×#575	1	2	yes	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
278	#41	—	2	32	no	—
279	#41	—	2	32	no	—
280	#41	—	4	16	no	—
281	#41	—	4	16	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	4	16	no	—
292	C₂×D₄	—	4	16	no	—
293	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	16	no	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
308	Q₁₆	—	2	32	no	—
309	SD₁₆	—	2	64	no	—
310	D₈	—	2	32	no	—
311	M₁₆	C₂×D₄×C₁₃	1	32	yes	complemented
312	C₂×C₈	C₂×D₄×C₁₃	1	16	yes	complemented
313	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	16	no	—
317	C₂²⋊C₄	—	2	16	no	—
318	C₄²	C₂×D₄×C₁₃	1	2	yes	—
319	C₄²	C₂×D₄×C₁₃	1	2	yes	—
320	C₄²	C₂×D₄×C₁₃	1	4	yes	—
321	C₄²	C₂×D₄×C₁₃	1	4	yes	—
322	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
323	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
324	C₄²	C₂⁴×C₁₃	1	2	yes	—
325	C₁₃	#60639	1	1	yes	characteristic, direct product factor, Sylow
326	C₂³	—	2	8	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	16	no	—
329	C₂³	—	4	8	no	—
330	C₂³	C₁₃×#127	1	4	yes	—
331	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
332	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
333	Q₈	—	2	16	no	—
334	Q₈	—	4	8	no	—
335	D₄	—	2	16	no	—
336	D₄	—	4	16	no	—
337	D₄	—	4	16	no	—
338	D₄	—	4	16	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	16	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	16	no	—
348	C₂×C₄	—	4	16	no	—
349	C₂×C₄	C₁₃×#127	1	8	yes	—
350	C₂×C₄	C₁₃×#127	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
352	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
356	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
358	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
359	C₈	C₂²×D₄×C₁₃	1	16	yes	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	4	16	no	—
364	C₂²	—	4	8	no	—
365	C₂²	—	8	16	no	—
366	C₂²	C₂×C₁₃×#127	1	4	yes	—
367	C₂²	C₂×C₁₃×#127	1	2	yes	—
368	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	8	no	—
372	C₄	C₂×C₁₃×#127	1	2	yes	—
373	C₄	C₂×C₁₃×#127	1	4	yes	—
374	C₄	C₁₃×#575	1	4	yes	complemented
375	C₄	C₂³×D₄×C₁₃	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	2	2	no	—
378	C₂	—	8	8	no	—
379	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
380	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. C₂×C₁₃×#575	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3153	C₂	semidirect
4. C₁₃×#3152	C₂	semidirect
5. C₁₃×#3151	C₂	semidirect
6. C₁₃×#3150	C₂	semidirect
7. C₁₃×#3147	C₂	semidirect
8. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
11. C₂×C₁₃×#137	C₂²	semidirect
12. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
13. C₂×C₁₃×#135	C₂²	semidirect
19. C₁₃×#532	C₂²	semidirect
20. C₁₃×#532	C₂²	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
27. C₁₃×#497	C₂²	semidirect
28. C₁₃×#496	C₂²	semidirect
29. C₁₃×#495	C₂²	semidirect
30. C₁₃×#494	C₂²	semidirect
31. C₁₃×#493	C₂²	semidirect
32. C₁₃×#492	C₂²	semidirect
33. C₄×C₁₃×M₁₆	C₂²	semidirect
34. C₄×C₁₃×M₁₆	C₂²	semidirect
35. C₂×C₁₃×#97	C₂²	semidirect
36. C₂×C₄×C₈×C₁₃	C₂²	semidirect
55. C₂×C₁₃×M₁₆	D₄	semidirect
86. #60639	C₁₃	direct (N × H)
122. C₁₃×M₁₆	C₂×D₄	semidirect
123. C₂×C₈×C₁₃	C₂×D₄	semidirect
136. C₂×#575	C₂×C₁₃	semidirect
137. C₂×#532	C₂×C₁₃	semidirect
138. #3153	C₂×C₁₃	semidirect
139. #3152	C₂×C₁₃	semidirect
140. #3151	C₂×C₁₃	semidirect
141. #3150	C₂×C₁₃	semidirect
142. #3147	C₂×C₁₃	semidirect
143. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
180. C₂×#137	C₂²×C₁₃	semidirect
181. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
182. C₂×#135	C₂²×C₁₃	semidirect
188. #532	C₂²×C₁₃	semidirect
189. #532	C₂²×C₁₃	semidirect
190. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
191. C₂×#127	C₂²×C₁₃	semidirect
192. C₂×#124	C₂²×C₁₃	semidirect
196. #497	C₂²×C₁₃	semidirect
197. #496	C₂²×C₁₃	semidirect
198. #495	C₂²×C₁₃	semidirect
199. #494	C₂²×C₁₃	semidirect
200. #493	C₂²×C₁₃	semidirect
201. #492	C₂²×C₁₃	semidirect
202. C₄×M₁₆	C₂²×C₁₃	semidirect
203. C₄×M₁₆	C₂²×C₁₃	semidirect
204. C₂×#97	C₂²×C₁₃	semidirect
205. C₂×C₄×C₈	C₂²×C₁₃	semidirect
220. C₄×C₁₃	#575	semidirect
240. C₂×M₁₆	D₄×C₁₃	semidirect
311. M₁₆	C₂×D₄×C₁₃	semidirect
312. C₂×C₈	C₂×D₄×C₁₃	semidirect
325. C₁₃	#60639	direct (N × H)
374. C₄	C₁₃×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#575	2
C₂×C₁₃×#532	2
C₁₃×#3153	2
C₁₃×#3152	2
C₁₃×#3151	2
C₁₃×#3150	2
C₁₃×#3147	2
C₂×C₄×C₁₃×M₁₆	2
#60639	13

Subgroups — C13×#60639 #15746978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60639 #15746978