Subgroups — C₂×C₁₃×#3393 #15747728

Order 3328.

1958 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3393	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#495	C₂	1	2	yes	maximal
4	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#464	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₁₃×#556	—	2	8	no	—
15	C₁₃×#556	C₂²	1	16	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#126	—	2	4	no	—
18	C₂×C₁₃×#124	C₂²	1	4	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₁₃×#117	—	2	2	no	—
24	C₁₃×#495	C₂²	1	16	yes	—
25	C₁₃×#494	C₂²	1	8	yes	complemented
26	C₁₃×#464	C₂²	1	32	yes	complemented
27	C₁₃×#461	C₂²	1	16	yes	complemented
28	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
29	C₄×C₁₃×Q₁₆	C₂²	1	16	yes	complemented
30	C₄×C₁₃×D₈	C₂²	1	8	yes	—
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	C₂²	1	4	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
40	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂×C₁₃×Q₁₆	—	2	8	no	—
43	C₂×C₁₃×Q₁₆	—	4	4	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
45	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
46	C₂×C₁₃×SD₁₆	—	4	8	no	—
47	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
48	C₂×C₁₃×D₈	—	2	4	no	—
49	C₂×C₁₃×D₈	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
55	C₁₃×#126	—	2	32	no	—
56	C₁₃×#124	—	2	8	no	—
57	C₁₃×#124	C₂³	1	16	yes	—
58	C₁₃×C₂²⋊Q₈	—	2	16	no	—
59	C₄×Q₈×C₁₃	—	2	8	no	—
60	C₄×Q₈×C₁₃	D₄	1	4	yes	—
61	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
62	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	C₂³	1	8	yes	—
65	C₁₃×#117	—	2	16	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₄²×C₁₃	—	2	4	no	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#107	C₂³	1	4	yes	—
79	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
80	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
81	C₁₃×#103	C₂³	1	16	yes	—
82	C₁₃×#102	C₂³	1	8	yes	—
83	C₄×C₈×C₁₃	C₂³	1	4	yes	—
84	C₄×C₈×C₁₃	C₂³	1	8	yes	—
85	C₂×#3393	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	4	no	—
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	—	2	8	no	—
91	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
92	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	4	no	—
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₃	—	4	8	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₁₃×Q₁₆	—	2	16	no	—
107	C₁₃×Q₁₆	—	4	8	no	—
108	C₁₃×SD₁₆	—	4	16	no	—
109	C₁₃×D₈	—	2	8	no	—
110	C₂×C₈×C₁₃	—	2	4	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	#41	1	4	yes	—
113	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
114	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
115	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	16	no	—
118	C₁₃×C₄⋊C₄	—	2	8	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
121	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
122	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
123	C₁₃×C₂²⋊C₄	—	2	16	no	—
124	C₁₃×C₂²⋊C₄	—	2	8	no	—
125	C₁₃×C₂²⋊C₄	—	2	16	no	—
126	C₄²×C₁₃	—	2	16	no	—
127	C₄²×C₁₃	C₂×D₄	1	2	yes	—
128	C₄²×C₁₃	C₂×D₄	1	4	yes	—
129	C₄²×C₁₃	C₂⁴	1	2	yes	—
130	C₄²×C₁₃	C₂⁴	1	4	yes	—
131	C₂×#556	C₂×C₁₃	1	2	yes	complemented
132	#3393	C₂×C₁₃	1	16	yes	direct product factor
133	C₂×#495	C₂×C₁₃	1	2	yes	—
134	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂×#464	C₂×C₁₃	1	4	yes	complemented
136	C₂×#461	C₂×C₁₃	1	2	yes	complemented
137	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
139	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
140	C₂³×C₁₃	—	2	4	no	—
141	C₂³×C₁₃	—	4	4	no	—
142	C₂³×C₁₃	—	4	4	no	—
143	C₂³×C₁₃	—	4	4	no	—
144	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₃	—	2	8	no	—
146	Q₈×C₁₃	—	2	8	no	—
147	Q₈×C₁₃	—	2	8	no	—
148	Q₈×C₁₃	—	4	8	no	—
149	D₄×C₁₃	—	2	4	no	—
150	D₄×C₁₃	—	2	4	no	—
151	D₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	8	no	—
157	C₂×C₄×C₁₃	—	4	8	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	16	no	—
160	C₂×C₄×C₁₃	#135	1	4	yes	—
161	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
164	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
167	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
169	C₈×C₁₃	—	2	4	no	—
170	C₈×C₁₃	—	2	2	no	—
171	C₈×C₁₃	C₂×#41	1	4	yes	—
172	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
173	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
174	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
175	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
176	#556	—	2	8	no	—
177	#556	C₂²×C₁₃	1	16	yes	complemented
178	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
179	C₂×#126	—	2	4	no	—
180	C₂×#124	C₂²×C₁₃	1	4	yes	—
181	C₂×C₂²⋊Q₈	—	2	2	no	—
182	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
183	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
185	C₂×#117	—	2	2	no	—
186	#495	C₂²×C₁₃	1	16	yes	—
187	#494	C₂²×C₁₃	1	8	yes	complemented
188	#464	C₂²×C₁₃	1	32	yes	complemented
189	#461	C₂²×C₁₃	1	16	yes	complemented
190	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
191	C₄×Q₁₆	C₂²×C₁₃	1	16	yes	complemented
192	C₄×D₈	C₂²×C₁₃	1	8	yes	—
193	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
196	C₂×#103	C₂²×C₁₃	1	4	yes	—
197	C₂×#102	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
200	C₂²×C₁₃	—	4	4	no	—
201	C₂²×C₁₃	—	4	4	no	—
202	C₂²×C₁₃	—	4	4	no	—
203	C₂²×C₁₃	—	8	8	no	—
204	C₂²×C₁₃	#550	1	2	yes	—
205	C₂²×C₁₃	C₂×#135	1	2	yes	—
206	C₂²×C₁₃	#578	1	2	yes	—
207	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
208	C₄×C₁₃	—	2	4	no	—
209	C₄×C₁₃	—	2	4	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	4	8	no	—
212	C₄×C₁₃	—	4	4	no	—
213	C₄×C₁₃	#550	1	2	yes	—
214	C₄×C₁₃	C₂×#135	1	4	yes	—
215	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
216	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
218	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
219	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂×Q₁₆	—	2	8	no	—
222	C₂×Q₁₆	—	4	4	no	—
223	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
224	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
225	C₂×SD₁₆	—	4	8	no	—
226	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
227	C₂×D₈	—	2	4	no	—
228	C₂×D₈	C₂³×C₁₃	1	4	yes	—
229	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
232	C₄⋊Q₈	—	2	4	no	—
233	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
234	#126	—	2	32	no	—
235	#124	—	2	8	no	—
236	#124	C₂³×C₁₃	1	16	yes	—
237	C₂²⋊Q₈	—	2	16	no	—
238	C₄×Q₈	—	2	8	no	—
239	C₄×Q₈	D₄×C₁₃	1	4	yes	—
240	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
241	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
242	C₄×D₄	—	2	4	no	—
243	C₄×D₄	C₂³×C₁₃	1	8	yes	—
244	#117	—	2	16	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
257	#107	C₂³×C₁₃	1	4	yes	—
258	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
259	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
260	#103	C₂³×C₁₃	1	16	yes	—
261	#102	C₂³×C₁₃	1	8	yes	—
262	C₄×C₈	C₂³×C₁₃	1	4	yes	—
263	C₄×C₈	C₂³×C₁₃	1	8	yes	—
264	C₂×C₁₃	—	8	4	no	—
265	C₂×C₁₃	#3393	1	4	yes	direct product factor
266	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
267	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
268	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
269	C₂⁴	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	8	no	—
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
275	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	4	8	no	—
284	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
289	Q₁₆	—	2	16	no	—
290	Q₁₆	—	4	8	no	—
291	SD₁₆	—	4	16	no	—
292	D₈	—	2	8	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	C₁₃×#41	1	4	yes	—
296	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
297	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
298	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	16	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
304	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
305	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
306	C₂²⋊C₄	—	2	16	no	—
307	C₂²⋊C₄	—	2	8	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₄²	—	2	16	no	—
310	C₄²	C₂×D₄×C₁₃	1	2	yes	—
311	C₄²	C₂×D₄×C₁₃	1	4	yes	—
312	C₄²	C₂⁴×C₁₃	1	2	yes	—
313	C₄²	C₂⁴×C₁₃	1	4	yes	—
314	C₁₃	C₂×#3393	1	1	yes	characteristic, direct product factor, Sylow
315	C₂³	—	2	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	2	8	no	—
323	Q₈	—	4	8	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	C₁₃×#135	1	4	yes	—
336	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
341	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
342	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	2	2	no	—
346	C₈	C₂×C₁₃×#41	1	4	yes	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	8	8	no	—
351	C₂²	C₁₃×#550	1	2	yes	—
352	C₂²	C₂×C₁₃×#135	1	2	yes	—
353	C₂²	C₁₃×#578	1	2	yes	—
354	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	8	no	—
360	C₄	C₁₃×#550	1	2	yes	—
361	C₄	C₂×C₁₃×#135	1	4	yes	—
362	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
363	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂	—	8	4	no	—
365	C₂	C₁₃×#3393	1	4	yes	direct product factor
366	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
367	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
368	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#556	C₂	semidirect
2. C₁₃×#3393	C₂	direct (N × H)
4. C₂×C₁₃×#494	C₂	semidirect
5. C₂×C₁₃×#464	C₂	semidirect
6. C₂×C₁₃×#461	C₂	semidirect
7. C₂×C₈×Q₈×C₁₃	C₂	semidirect
8. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
15. C₁₃×#556	C₂²	semidirect
25. C₁₃×#494	C₂²	semidirect
26. C₁₃×#464	C₂²	semidirect
27. C₁₃×#461	C₂²	semidirect
28. C₈×Q₈×C₁₃	C₂²	semidirect
29. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₂×#3393	C₁₃	direct (N × H)
131. C₂×#556	C₂×C₁₃	semidirect
132. #3393	C₂×C₁₃	direct (N × H)
134. C₂×#494	C₂×C₁₃	semidirect
135. C₂×#464	C₂×C₁₃	semidirect
136. C₂×#461	C₂×C₁₃	semidirect
137. C₂×C₈×Q₈	C₂×C₁₃	semidirect
138. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
177. #556	C₂²×C₁₃	semidirect
187. #494	C₂²×C₁₃	semidirect
188. #464	C₂²×C₁₃	semidirect
189. #461	C₂²×C₁₃	semidirect
190. C₈×Q₈	C₂²×C₁₃	semidirect
191. C₄×Q₁₆	C₂²×C₁₃	semidirect
265. C₂×C₁₃	#3393	direct (N × H)
314. C₁₃	C₂×#3393	direct (N × H)
365. C₂	C₁₃×#3393	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×#556	2
C₁₃×#3393	2
C₂×C₁₃×#495	2
C₂×C₁₃×#494	2
C₂×C₁₃×#464	2
C₂×C₁₃×#461	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂×#3393	13

Subgroups — C2×C13×#3393 #15747728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3393 #15747728