Subgroups — C₂×C₁₃×#3165 #15747000

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 410 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	1	yes	maximal, characteristic
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3165	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#500	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#498	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#428	C₂	1	4	yes	maximal
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	—	2	1	no	—
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₁₃×#533	—	2	4	no	—
12	C₁₃×#533	C₂²	1	8	yes	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
26	C₂×C₁₃×#117	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#501	C₂²	1	32	yes	complemented
31	C₁₃×#500	C₂²	1	16	yes	complemented
32	C₁₃×#498	C₂²	1	16	yes	complemented
33	C₁₃×#428	C₂²	1	32	yes	—
34	C₂×C₁₃×#107	C₂²	1	8	yes	—
35	C₂×C₁₃×#106	C₂²	1	8	yes	—
36	C₄×C₁₃×M₁₆	C₂²	1	8	yes	—
37	C₂×C₁₃×#97	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	—	2	8	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	—	2	2	no	—
44	C₂²×Q₈×C₁₃	—	4	8	no	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	Q₈	1	16	yes	complemented
50	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
52	C₁₃×C₄⋊Q₈	—	2	8	no	—
53	C₁₃×C₄⋊Q₈	—	2	8	no	—
54	C₁₃×C₄⋊Q₈	—	2	4	no	—
55	C₁₃×C₄⋊Q₈	—	2	4	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
62	C₁₃×#125	—	2	4	no	—
63	C₁₃×#125	C₂³	1	8	yes	—
64	C₁₃×C₂²⋊Q₈	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₄×Q₈×C₁₃	—	2	8	no	—
67	C₄×Q₈×C₁₃	—	2	8	no	—
68	C₁₃×#117	—	2	4	no	—
69	C₁₃×#117	C₂³	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	2	no	—
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	D₄	1	4	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
91	C₁₃×#107	C₂³	1	32	yes	—
92	C₁₃×#106	C₂³	1	32	yes	—
93	C₁₃×#97	C₂³	1	8	yes	—
94	C₄×C₈×C₁₃	C₂³	1	8	yes	—
95	C₂×#3165	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	4	8	no	—
102	C₂×Q₈×C₁₃	—	4	32	no	—
103	C₂×Q₈×C₁₃	—	4	4	no	—
104	C₂×Q₈×C₁₃	—	4	8	no	—
105	C₂×Q₈×C₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	4	8	no	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₁₃×M₁₆	C₂×Q₈	1	32	yes	complemented
125	C₂×C₈×C₁₃	C₂×Q₈	1	16	yes	complemented
126	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
138	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
139	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
140	C₁₃×C₂²⋊C₄	—	2	8	no	—
141	C₄²×C₁₃	—	2	8	no	—
142	C₄²×C₁₃	C₂×D₄	1	4	yes	—
143	C₄²×C₁₃	C₂×D₄	1	4	yes	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃	C₂⁴	1	2	yes	—
147	C₄²×C₁₃	C₂⁴	1	2	yes	—
148	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
149	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
150	#3165	C₂×C₁₃	1	16	yes	direct product factor
151	C₂×#501	C₂×C₁₃	1	4	yes	complemented
152	C₂×#500	C₂×C₁₃	1	2	yes	complemented
153	C₂×#498	C₂×C₁₃	1	2	yes	complemented
154	C₂×#428	C₂×C₁₃	1	4	yes	—
155	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	C₄⋊Q₈	1	4	yes	—
159	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
160	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₁₃	—	4	16	no	—
162	Q₈×C₁₃	—	4	8	no	—
163	Q₈×C₁₃	—	4	16	no	—
164	Q₈×C₁₃	—	4	8	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	8	no	—
168	C₂×C₄×C₁₃	—	2	8	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	—	4	16	no	—
173	C₂×C₄×C₁₃	—	4	8	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
177	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
178	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
179	C₂×C₄×C₁₃	#137	1	4	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
187	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
188	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
189	C₈×C₁₃	C₂²×Q₈	1	16	yes	complemented
190	C₂³×Q₈	—	2	1	no	—
191	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
192	#533	—	2	4	no	—
193	#533	C₂²×C₁₃	1	8	yes	—
194	C₂×C₄⋊Q₈	—	2	1	no	—
195	C₂×C₄⋊Q₈	—	2	1	no	—
196	C₂×C₄⋊Q₈	—	2	4	no	—
197	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	—
202	C₂×#125	C₂²×C₁₃	1	2	yes	—
203	C₂×C₂²⋊Q₈	—	2	1	no	—
204	C₂×C₂²⋊Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	—	2	1	no	—
207	C₂×#117	C₂²×C₁₃	1	2	yes	—
208	C₂²×C₄⋊C₄	—	2	1	no	—
209	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
211	#501	C₂²×C₁₃	1	32	yes	complemented
212	#500	C₂²×C₁₃	1	16	yes	complemented
213	#498	C₂²×C₁₃	1	16	yes	complemented
214	#428	C₂²×C₁₃	1	32	yes	—
215	C₂×#107	C₂²×C₁₃	1	8	yes	—
216	C₂×#106	C₂²×C₁₃	1	8	yes	—
217	C₄×M₁₆	C₂²×C₁₃	1	8	yes	—
218	C₂×#97	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₁₃	—	2	8	no	—
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
224	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
225	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
226	C₂²×C₁₃	C₂×#137	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	—	4	8	no	—
231	C₄×C₁₃	—	4	4	no	—
232	C₄×C₁₃	—	4	4	no	—
233	C₄×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
234	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
235	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
236	C₄×C₁₃	C₂×#137	1	4	yes	—
237	C₄×C₁₃	C₂³×Q₈	1	2	yes	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	—	2	8	no	—
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	4	8	no	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂×M₁₆	Q₈×C₁₃	1	16	yes	complemented
249	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
250	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
251	C₄⋊Q₈	—	2	8	no	—
252	C₄⋊Q₈	—	2	8	no	—
253	C₄⋊Q₈	—	2	4	no	—
254	C₄⋊Q₈	—	2	4	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
258	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
259	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
260	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
261	#125	—	2	4	no	—
262	#125	C₂³×C₁₃	1	8	yes	—
263	C₂²⋊Q₈	—	2	8	no	—
264	C₂²⋊Q₈	—	2	8	no	—
265	C₄×Q₈	—	2	8	no	—
266	C₄×Q₈	—	2	8	no	—
267	#117	—	2	4	no	—
268	#117	C₂³×C₁₃	1	8	yes	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	8	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₁₃	1	4	yes	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
290	#107	C₂³×C₁₃	1	32	yes	—
291	#106	C₂³×C₁₃	1	32	yes	—
292	#97	C₂³×C₁₃	1	8	yes	—
293	C₄×C₈	C₂³×C₁₃	1	8	yes	—
294	C₂×C₁₃	—	2	4	no	—
295	C₂×C₁₃	#3165	1	4	yes	direct product factor
296	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
297	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
299	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	4	8	no	—
305	C₂×Q₈	—	4	32	no	—
306	C₂×Q₈	—	4	8	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	—	4	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	4	8	no	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
327	M₁₆	C₂×Q₈×C₁₃	1	32	yes	complemented
328	C₂×C₈	C₂×Q₈×C₁₃	1	16	yes	complemented
329	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
341	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
342	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₄²	—	2	8	no	—
345	C₄²	C₂×D₄×C₁₃	1	4	yes	—
346	C₄²	C₂×D₄×C₁₃	1	4	yes	—
347	C₄²	C₂×D₄×C₁₃	1	2	yes	—
348	C₄²	C₂×D₄×C₁₃	1	2	yes	—
349	C₄²	C₂⁴×C₁₃	1	2	yes	—
350	C₄²	C₂⁴×C₁₃	1	2	yes	—
351	C₁₃	C₂×#3165	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₁₃×C₄⋊Q₈	1	4	yes	—
355	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
356	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
357	Q₈	—	4	16	no	—
358	Q₈	—	4	16	no	—
359	Q₈	—	4	8	no	—
360	Q₈	—	4	8	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	C₁₃×C₄⋊Q₈	1	8	yes	—
373	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
374	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
375	C₂×C₄	C₁₃×#137	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
378	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
379	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
384	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
385	C₈	C₂²×Q₈×C₁₃	1	16	yes	complemented
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	8	no	—
389	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
390	C₂²	C₂×C₁₃×C₄⋊Q₈	1	2	yes	—
391	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
392	C₂²	C₂×C₁₃×#137	1	2	yes	—
393	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	8	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
400	C₄	C₂×C₁₃×C₄⋊Q₈	1	2	yes	—
401	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
402	C₄	C₂×C₁₃×#137	1	4	yes	—
403	C₄	C₂³×Q₈×C₁₃	1	2	yes	—
404	C₂	—	2	4	no	—
405	C₂	C₁₃×#3165	1	4	yes	direct product factor
406	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
407	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#3165	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#500	C₂	semidirect
6. C₂×C₁₃×#498	C₂	semidirect
30. C₁₃×#501	C₂²	semidirect
31. C₁₃×#500	C₂²	semidirect
32. C₁₃×#498	C₂²	semidirect
49. C₂×C₁₃×M₁₆	Q₈	semidirect
95. C₂×#3165	C₁₃	direct (N × H)
124. C₁₃×M₁₆	C₂×Q₈	semidirect
125. C₂×C₈×C₁₃	C₂×Q₈	semidirect
150. #3165	C₂×C₁₃	direct (N × H)
151. C₂×#501	C₂×C₁₃	semidirect
152. C₂×#500	C₂×C₁₃	semidirect
153. C₂×#498	C₂×C₁₃	semidirect
189. C₈×C₁₃	C₂²×Q₈	semidirect
211. #501	C₂²×C₁₃	semidirect
212. #500	C₂²×C₁₃	semidirect
213. #498	C₂²×C₁₃	semidirect
248. C₂×M₁₆	Q₈×C₁₃	semidirect
295. C₂×C₁₃	#3165	direct (N × H)
327. M₁₆	C₂×Q₈×C₁₃	semidirect
328. C₂×C₈	C₂×Q₈×C₁₃	semidirect
351. C₁₃	C₂×#3165	direct (N × H)
385. C₈	C₂²×Q₈×C₁₃	semidirect
405. C₂	C₁₃×#3165	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
C₂²×C₁₃×C₄⋊Q₈	2
C₁₃×#3165	2
C₂×C₁₃×#501	2
C₂×C₁₃×#500	2
C₂×C₁₃×#498	2
C₂×C₁₃×#428	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#3165	13

Subgroups — C2×C13×#3165 #15747000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3165 #15747000