Subgroups — C₂×C₁₃×#1550 #15704046

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 416 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	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1550	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#333	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#332	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×M₁₆	—	2	1	no	—
8	C₂³×C₈×C₁₃	—	2	1	no	—
9	C₁₃×#533	—	2	2	no	—
10	C₁₃×#533	—	2	2	no	—
11	C₁₃×#533	C₄	1	4	yes	—
12	C₁₃×#533	C₂²	1	4	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	C₄	1	2	yes	—
18	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	—
20	C₂×C₁₃×#117	—	2	1	no	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#423	—	2	2	no	—
23	C₁₃×#423	C₂²	1	4	yes	—
24	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
30	C₁₃×#333	C₂²	1	8	yes	complemented
31	C₁₃×#332	C₂²	1	8	yes	complemented
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₂×C₁₃×M₁₆	—	2	4	no	—
38	C₂×C₁₃×M₁₆	—	4	4	no	—
39	C₂²×C₈×C₁₃	—	2	4	no	—
40	C₂²×C₈×C₁₃	—	2	2	no	—
41	C₂²×C₈×C₁₃	—	2	2	no	—
42	C₂²×C₈×C₁₃	—	4	4	no	—
43	C₁₃×C₄⋊Q₈	—	2	1	no	—
44	C₁₃×C₄⋊Q₈	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
48	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
49	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₁₃×#125	—	2	4	no	—
52	C₁₃×#125	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	2	4	no	—
55	C₁₃×C₂²⋊Q₈	—	2	4	no	—
56	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	4	no	—
60	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
61	C₁₃×#117	—	2	4	no	—
62	C₁₃×#117	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×C₄⋊C₈	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
84	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
85	C₂×#1550	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	4	4	no	—
91	C₂×Q₈×C₁₃	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
106	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₁₃×M₁₆	—	4	8	no	—
114	C₂×C₈×C₁₃	—	2	4	no	—
115	C₂×C₈×C₁₃	—	2	4	no	—
116	C₂×C₈×C₁₃	—	4	8	no	—
117	C₂×C₈×C₁₃	—	4	4	no	—
118	C₂×C₈×C₁₃	—	4	4	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	8	no	—
123	C₁₃×C₄⋊C₄	—	2	8	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	8	no	—
130	C₄²×C₁₃	—	2	8	no	—
131	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
142	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
143	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
144	#1550	C₂×C₁₃	1	8	yes	direct product factor
145	C₂×#333	C₂×C₁₃	1	2	yes	complemented
146	C₂×#332	C₂×C₁₃	1	2	yes	complemented
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	#103	1	4	yes	—
150	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	Q₈×C₁₃	—	4	4	no	—
153	Q₈×C₁₃	—	4	4	no	—
154	Q₈×C₁₃	—	4	2	no	—
155	Q₈×C₁₃	—	4	2	no	—
156	Q₈×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	#103	1	8	yes	—
170	C₂×C₄×C₁₃	#103	1	4	yes	—
171	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
180	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₁₃	#137	1	2	yes	—
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₁₃	—	4	4	no	—
187	C₈×C₁₃	—	4	4	no	—
188	C₂²×M₁₆	—	2	1	no	—
189	C₂³×C₈	—	2	1	no	—
190	#533	—	2	2	no	—
191	#533	—	2	2	no	—
192	#533	C₄×C₁₃	1	4	yes	—
193	#533	C₂²×C₁₃	1	4	yes	—
194	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#125	—	2	1	no	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₂²⋊Q₈	C₄×C₁₃	1	2	yes	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×C₄×Q₈	C₄×C₁₃	1	2	yes	—
201	C₂×#117	—	2	1	no	—
202	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
203	#423	—	2	2	no	—
204	#423	C₂²×C₁₃	1	4	yes	—
205	C₂×C₄⋊C₈	—	2	1	no	—
206	C₂×C₄⋊C₈	—	2	2	no	—
207	C₂×C₄⋊C₈	—	2	1	no	—
208	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
211	#333	C₂²×C₁₃	1	8	yes	complemented
212	#332	C₂²×C₁₃	1	8	yes	complemented
213	C₂²×C₁₃	—	2	8	no	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	#413	1	2	yes	—
217	C₂²×C₁₃	C₂×#103	1	4	yes	—
218	C₂²×C₁₃	C₂×#103	1	2	yes	—
219	C₂²×C₁₃	#417	1	2	yes	—
220	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	4	4	no	—
226	C₄×C₁₃	—	4	4	no	—
227	C₄×C₁₃	C₂×#103	1	4	yes	—
228	C₄×C₁₃	C₂×#103	1	2	yes	—
229	C₄×C₁₃	#417	1	2	yes	—
230	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
231	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
232	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	—	4	4	no	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	4	4	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
250	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
252	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
253	#125	—	2	4	no	—
254	#125	—	2	4	no	—
255	C₂²⋊Q₈	—	2	4	no	—
256	C₂²⋊Q₈	—	2	4	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	4	no	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
263	#117	—	2	4	no	—
264	#117	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
275	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₃	1	2	yes	—
278	C₂×C₄²	D₄×C₁₃	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
281	C₄⋊C₈	—	2	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	4	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
286	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
287	C₂×C₁₃	—	2	4	no	—
288	C₂×C₁₃	#1550	1	4	yes	direct product factor
289	C₂×C₁₃	C₂×#413	1	1	yes	characteristic
290	C₂×C₁₃	C₂²×#103	1	1	yes	characteristic
291	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
292	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
307	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
309	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
311	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
312	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
319	M₁₆	—	4	8	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	4	8	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	—	4	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₄²	—	2	8	no	—
337	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
338	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
339	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
340	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
341	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
342	C₄²	C₂×D₄×C₁₃	1	2	yes	—
343	C₄²	C₂×D₄×C₁₃	1	2	yes	—
344	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
347	C₁₃	C₂×#1550	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₁₃×#103	1	4	yes	—
351	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
352	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
353	Q₈	—	4	4	no	—
354	Q₈	—	4	4	no	—
355	Q₈	—	4	4	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	C₁₃×#103	1	8	yes	—
371	C₂×C₄	C₁₃×#103	1	4	yes	—
372	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
374	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
376	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
379	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
380	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
381	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
382	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
383	C₂×C₄	C₁₃×#137	1	2	yes	—
384	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
387	C₈	—	4	4	no	—
388	C₈	—	4	4	no	—
389	C₂²	—	2	8	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	C₁₃×#413	1	2	yes	—
393	C₂²	C₂×C₁₃×#103	1	4	yes	—
394	C₂²	C₂×C₁₃×#103	1	2	yes	—
395	C₂²	C₁₃×#417	1	2	yes	—
396	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	4	no	—
403	C₄	C₂×C₁₃×#103	1	4	yes	—
404	C₄	C₂×C₁₃×#103	1	2	yes	—
405	C₄	C₁₃×#417	1	2	yes	—
406	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
407	C₄	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
408	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
409	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
410	C₂	—	2	4	no	—
411	C₂	C₁₃×#1550	1	4	yes	direct product factor
412	C₂	C₂×C₁₃×#413	1	1	yes	characteristic
413	C₂	C₂²×C₁₃×#103	1	1	yes	characteristic
414	C₂	C₂×C₁₃×#417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
4. C₁₃×#1550	C₂	direct (N × H)
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×#332	C₂	semidirect
30. C₁₃×#333	C₂²	semidirect
31. C₁₃×#332	C₂²	semidirect
85. C₂×#1550	C₁₃	direct (N × H)
144. #1550	C₂×C₁₃	direct (N × H)
145. C₂×#333	C₂×C₁₃	semidirect
146. C₂×#332	C₂×C₁₃	semidirect
211. #333	C₂²×C₁₃	semidirect
212. #332	C₂²×C₁₃	semidirect
288. C₂×C₁₃	#1550	direct (N × H)
347. C₁₃	C₂×#1550	direct (N × H)
411. C₂	C₁₃×#1550	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
C₂×C₁₃×#423	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#1550	2
C₂×C₁₃×#333	2
C₂×C₁₃×#332	2
C₂×#1550	13

Subgroups — C2×C13×#1550 #15704046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1550 #15704046