Subgroups — C₂×C₁₃×#3208 #15747114

Order 3328.

2822 conjugacy classes of subgroups.

The subgroup lattice has 464 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, complemented
2	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3208	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#492	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#460	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#450	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃	—	2	1	no	—
10	C₂³×D₄×C₁₃	—	2	1	no	—
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
13	C₁₃×#533	—	2	4	no	—
14	C₁₃×#533	C₂²	1	8	yes	complemented
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#127	—	2	1	no	—
18	C₂×C₁₃×#127	—	2	1	no	—
19	C₂×C₁₃×#127	—	2	4	no	—
20	C₂×C₁₃×#127	C₂²	1	2	yes	—
21	C₂×C₁₃×#127	C₂²	1	2	yes	—
22	C₂×C₁₃×#127	C₂²	1	8	yes	—
23	C₂×C₁₃×#125	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#117	—	2	1	no	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#492	C₂²	1	16	yes	complemented
31	C₁₃×#486	C₂²	1	16	yes	complemented
32	C₁₃×#460	C₂²	1	32	yes	complemented
33	C₁₃×#450	C₂²	1	32	yes	complemented
34	C₁₃×#431	C₂²	1	8	yes	complemented
35	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#102	C₂²	1	8	yes	complemented
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
39	C₂⁵×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	8	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	8	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	4	8	no	—
51	C₂²×D₄×C₁₃	—	4	8	no	—
52	C₂²×D₄×C₁₃	—	4	8	no	—
53	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×SD₁₆	—	4	16	no	—
59	C₂×C₁₃×SD₁₆	C₂³	1	32	yes	complemented
60	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
64	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
65	C₁₃×#127	—	2	4	no	—
66	C₁₃×#127	—	2	8	no	—
67	C₁₃×#127	—	2	8	no	—
68	C₁₃×#127	—	2	4	no	—
69	C₁₃×#127	C₂³	1	8	yes	—
70	C₁₃×#127	C₂³	1	8	yes	—
71	C₁₃×#125	—	2	8	no	—
72	C₁₃×C₂²⋊Q₈	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
75	C₄×Q₈×C₁₃	—	2	8	no	—
76	C₄×Q₈×C₁₃	—	2	4	no	—
77	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
78	C₁₃×#117	—	2	8	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₄²×C₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	D₄	1	4	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
94	C₁₃×#102	C₂³	1	32	yes	complemented
95	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
96	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
97	C₂×#3208	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	4	no	—
100	C₂⁴×C₁₃	—	4	8	no	—
101	C₂⁴×C₁₃	—	4	8	no	—
102	C₂⁴×C₁₃	—	4	8	no	—
103	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	8	no	—
107	C₂×Q₈×C₁₃	—	4	4	no	—
108	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	—	2	8	no	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	16	no	—
116	C₂×D₄×C₁₃	—	4	16	no	—
117	C₂×D₄×C₁₃	—	4	8	no	—
118	C₂×D₄×C₁₃	—	4	8	no	—
119	C₂×D₄×C₁₃	—	4	16	no	—
120	C₂×D₄×C₁₃	—	4	32	no	—
121	C₂×D₄×C₁₃	—	4	8	no	—
122	C₂×D₄×C₁₃	—	4	8	no	—
123	C₂×D₄×C₁₃	—	4	32	no	—
124	C₂×D₄×C₁₃	—	4	8	no	—
125	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	SD₁₆	1	8	yes	complemented
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×SD₁₆	—	4	32	no	—
142	C₂×C₈×C₁₃	—	2	8	no	—
143	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₄²×C₁₃	—	2	8	no	—
153	C₄²×C₁₃	C₂×D₄	1	4	yes	—
154	C₄²×C₁₃	C₂×D₄	1	2	yes	—
155	C₄²×C₁₃	C₂×D₄	1	4	yes	—
156	C₄²×C₁₃	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃	C₂⁴	1	2	yes	—
158	C₄²×C₁₃	C₂⁴	1	2	yes	—
159	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic
161	#3208	C₂×C₁₃	1	16	yes	direct product factor
162	C₂×#492	C₂×C₁₃	1	2	yes	complemented
163	C₂×#486	C₂×C₁₃	1	2	yes	complemented
164	C₂×#460	C₂×C₁₃	1	4	yes	complemented
165	C₂×#450	C₂×C₁₃	1	4	yes	complemented
166	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	8	no	—
170	C₂³×C₁₃	—	4	16	no	—
171	C₂³×C₁₃	—	4	16	no	—
172	C₂³×C₁₃	—	4	8	no	—
173	C₂³×C₁₃	—	4	16	no	—
174	C₂³×C₁₃	—	4	8	no	—
175	C₂³×C₁₃	—	4	8	no	—
176	C₂³×C₁₃	—	8	32	no	—
177	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	8	no	—
181	Q₈×C₁₃	—	4	4	no	—
182	Q₈×C₁₃	—	4	8	no	—
183	D₄×C₁₃	—	2	16	no	—
184	D₄×C₁₃	—	4	16	no	—
185	D₄×C₁₃	—	4	16	no	—
186	D₄×C₁₃	—	4	8	no	—
187	D₄×C₁₃	—	4	16	no	—
188	D₄×C₁₃	—	4	16	no	—
189	D₄×C₁₃	—	4	16	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	8	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	4	4	no	—
198	C₂×C₄×C₁₃	—	4	4	no	—
199	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
200	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
201	C₂×C₄×C₁₃	C₂×SD₁₆	1	16	yes	complemented
202	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
210	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
211	C₈×C₁₃	—	2	8	no	—
212	C₂³×D₄	—	2	1	no	—
213	C₂³×D₄	—	2	1	no	—
214	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
215	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
216	#533	—	2	4	no	—
217	#533	C₂²×C₁₃	1	8	yes	complemented
218	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
220	C₂×#127	—	2	1	no	—
221	C₂×#127	—	2	1	no	—
222	C₂×#127	—	2	4	no	—
223	C₂×#127	C₂²×C₁₃	1	2	yes	—
224	C₂×#127	C₂²×C₁₃	1	8	yes	—
225	C₂×#127	C₂²×C₁₃	1	2	yes	—
226	C₂×#125	—	2	1	no	—
227	C₂×C₂²⋊Q₈	—	2	1	no	—
228	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
231	C₂×#117	—	2	1	no	—
232	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
233	#492	C₂²×C₁₃	1	16	yes	complemented
234	#486	C₂²×C₁₃	1	16	yes	complemented
235	#460	C₂²×C₁₃	1	32	yes	complemented
236	#450	C₂²×C₁₃	1	32	yes	complemented
237	#431	C₂²×C₁₃	1	8	yes	complemented
238	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
239	C₂×#102	C₂²×C₁₃	1	8	yes	complemented
240	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
242	C₂²×C₁₃	—	2	2	no	—
243	C₂²×C₁₃	—	2	8	no	—
244	C₂²×C₁₃	—	2	2	no	—
245	C₂²×C₁₃	—	4	8	no	—
246	C₂²×C₁₃	—	4	8	no	—
247	C₂²×C₁₃	—	4	8	no	—
248	C₂²×C₁₃	—	8	32	no	—
249	C₂²×C₁₃	—	8	16	no	—
250	C₂²×C₁₃	#535	1	2	yes	—
251	C₂²×C₁₃	C₂²×SD₁₆	1	4	yes	—
252	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
253	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
254	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	4	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	#535	1	2	yes	—
260	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
261	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
262	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
263	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
264	C₂⁵	—	2	2	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	4	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	8	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	8	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	4	8	no	—
276	C₂²×D₄	—	4	8	no	—
277	C₂²×D₄	—	4	8	no	—
278	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
279	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
280	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
281	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×SD₁₆	—	4	16	no	—
284	C₂×SD₁₆	C₂³×C₁₃	1	32	yes	complemented
285	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
289	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
290	#127	—	2	8	no	—
291	#127	—	2	4	no	—
292	#127	—	2	8	no	—
293	#127	—	2	4	no	—
294	#127	C₂³×C₁₃	1	8	yes	—
295	#127	C₂³×C₁₃	1	8	yes	—
296	#125	—	2	8	no	—
297	C₂²⋊Q₈	—	2	8	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
300	C₄×Q₈	—	2	8	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
303	#117	—	2	8	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₁₃	1	4	yes	—
315	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
318	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
319	#102	C₂³×C₁₃	1	32	yes	complemented
320	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
321	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
322	C₂×C₁₃	—	2	4	no	—
323	C₂×C₁₃	—	8	8	no	—
324	C₂×C₁₃	#3208	1	4	yes	direct product factor
325	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
326	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
327	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
328	C₂⁴	—	2	8	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	4	8	no	—
331	C₂⁴	—	4	8	no	—
332	C₂⁴	—	4	8	no	—
333	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	8	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	16	no	—
346	C₂×D₄	—	4	16	no	—
347	C₂×D₄	—	4	8	no	—
348	C₂×D₄	—	4	8	no	—
349	C₂×D₄	—	4	16	no	—
350	C₂×D₄	—	4	32	no	—
351	C₂×D₄	—	4	8	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	4	32	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	C₁₃×SD₁₆	1	8	yes	complemented
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
371	SD₁₆	—	4	32	no	—
372	C₂×C₈	—	2	8	no	—
373	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₄²	—	2	8	no	—
383	C₄²	C₂×D₄×C₁₃	1	4	yes	—
384	C₄²	C₂×D₄×C₁₃	1	2	yes	—
385	C₄²	C₂×D₄×C₁₃	1	4	yes	—
386	C₄²	C₂×D₄×C₁₃	1	2	yes	—
387	C₄²	C₂⁴×C₁₃	1	2	yes	—
388	C₄²	C₂⁴×C₁₃	1	2	yes	—
389	C₁₃	C₂×#3208	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	4	16	no	—
394	C₂³	—	4	16	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	16	no	—
397	C₂³	—	4	8	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	8	32	no	—
400	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
401	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
402	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
403	Q₈	—	2	8	no	—
404	Q₈	—	4	4	no	—
405	Q₈	—	4	8	no	—
406	D₄	—	2	16	no	—
407	D₄	—	4	16	no	—
408	D₄	—	4	16	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	16	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	16	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
423	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
424	C₂×C₄	C₂×C₁₃×SD₁₆	1	16	yes	complemented
425	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
432	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
433	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
434	C₈	—	2	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	8	32	no	—
442	C₂²	—	8	16	no	—
443	C₂²	C₁₃×#535	1	2	yes	—
444	C₂²	C₂²×C₁₃×SD₁₆	1	4	yes	—
445	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
446	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
447	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	C₁₃×#535	1	2	yes	—
453	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
454	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
455	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
456	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
457	C₂	—	2	4	no	—
458	C₂	—	8	8	no	—
459	C₂	C₁₃×#3208	1	4	yes	direct product factor
460	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
461	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
462	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#127	C₂
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
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3208	C₂	direct (N × H)
4. C₂×C₁₃×#492	C₂	semidirect
5. C₂×C₁₃×#486	C₂	semidirect
6. C₂×C₁₃×#460	C₂	semidirect
7. C₂×C₁₃×#450	C₂	semidirect
8. C₂×C₁₃×#431	C₂	semidirect
12. C₂²×C₁₃×SD₁₆	C₂²	semidirect
14. C₁₃×#533	C₂²	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×#492	C₂²	semidirect
31. C₁₃×#486	C₂²	semidirect
32. C₁₃×#460	C₂²	semidirect
33. C₁₃×#450	C₂²	semidirect
34. C₁₃×#431	C₂²	semidirect
35. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
38. C₂×C₄×C₈×C₁₃	C₂²	semidirect
59. C₂×C₁₃×SD₁₆	C₂³	semidirect
63. C₁₃×C₄⋊Q₈	C₂³	semidirect
64. C₁₃×C₄⋊Q₈	C₂³	semidirect
77. C₄×Q₈×C₁₃	C₂³	semidirect
93. C₁₃×C₄⋊C₈	C₂³	semidirect
94. C₁₃×#102	C₂³	semidirect
96. C₄×C₈×C₁₃	C₂³	semidirect
97. C₂×#3208	C₁₃	direct (N × H)
130. C₂²×C₄×C₁₃	SD₁₆	semidirect
159. C₂×#533	C₂×C₁₃	semidirect
161. #3208	C₂×C₁₃	direct (N × H)
162. C₂×#492	C₂×C₁₃	semidirect
163. C₂×#486	C₂×C₁₃	semidirect
164. C₂×#460	C₂×C₁₃	semidirect
165. C₂×#450	C₂×C₁₃	semidirect
166. C₂×#431	C₂×C₁₃	semidirect
201. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
215. C₂²×SD₁₆	C₂²×C₁₃	semidirect
217. #533	C₂²×C₁₃	semidirect
218. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
219. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
230. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
233. #492	C₂²×C₁₃	semidirect
234. #486	C₂²×C₁₃	semidirect
235. #460	C₂²×C₁₃	semidirect
236. #450	C₂²×C₁₃	semidirect
237. #431	C₂²×C₁₃	semidirect
238. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
239. C₂×#102	C₂²×C₁₃	semidirect
241. C₂×C₄×C₈	C₂²×C₁₃	semidirect
284. C₂×SD₁₆	C₂³×C₁₃	semidirect
288. C₄⋊Q₈	C₂³×C₁₃	semidirect
289. C₄⋊Q₈	C₂³×C₁₃	semidirect
302. C₄×Q₈	C₂³×C₁₃	semidirect
318. C₄⋊C₈	C₂³×C₁₃	semidirect
319. #102	C₂³×C₁₃	semidirect
321. C₄×C₈	C₂³×C₁₃	semidirect
324. C₂×C₁₃	#3208	direct (N × H)
360. C₂²×C₄	C₁₃×SD₁₆	semidirect
389. C₁₃	C₂×#3208	direct (N × H)
424. C₂×C₄	C₂×C₁₃×SD₁₆	semidirect
459. C₂	C₁₃×#3208	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×#127	2
C₁₃×#3208	2
C₂×C₁₃×#492	2
C₂×C₁₃×#486	2
C₂×C₁₃×#460	2
C₂×C₁₃×#450	2
C₂×C₁₃×#431	2
C₂×#3208	13

Subgroups — C2×C13×#3208 #15747114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3208 #15747114