Subgroups — C₁₃×#24327 #15710666

Order 3328.

1146 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1879	C₂	1	2	yes	maximal
10	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₁₃×#554	—	2	4	no	—
14	C₁₃×#554	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₁₃×#476	—	2	4	no	—
26	C₄×C₁₃×D₈	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#396	—	2	2	no	—
36	C₁₃×#390	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#384	C₂²	1	1	yes	characteristic
39	C₁₃×#380	—	2	1	no	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	2	no	—
54	C₂×C₁₃×D₈	Q₈	1	4	yes	complemented
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
60	C₁₃×#125	—	2	4	no	—
61	C₁₃×#125	—	2	4	no	—
62	C₁₃×C₂²⋊Q₈	—	2	8	no	—
63	C₁₃×C₂²⋊Q₈	—	2	16	no	—
64	C₁₃×C₂²⋊Q₈	—	4	4	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	4	no	—
68	C₄×D₄×C₁₃	—	2	4	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	D₄	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#107	—	2	2	no	—
94	C₁₃×#106	—	2	4	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	4	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	2	4	no	—
100	C₄×C₈×C₁₃	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	#24327	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂⁴×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	8	1	no	—
110	C₂×Q₈×C₁₃	—	8	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
121	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
122	C₂×D₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	8	2	no	—
135	C₂²×C₄×C₁₃	—	8	2	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×D₈	—	2	8	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	4	4	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	8	1	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	8	2	no	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
179	#2538	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2059	C₂×C₁₃	1	2	yes	complemented
181	#2025	C₂×C₁₃	1	2	yes	complemented
182	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1879	C₂×C₁₃	1	2	yes	—
185	#1864	C₂×C₁₃	1	2	yes	complemented
186	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	—	4	1	no	—
201	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	8	4	no	—
204	D₄×C₁₃	—	2	2	no	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	8	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	8	8	no	—
234	C₂×C₄×C₁₃	—	8	4	no	—
235	C₂×C₄×C₁₃	#120	1	2	yes	—
236	C₂×C₄×C₁₃	#120	1	2	yes	—
237	C₂×C₄×C₁₃	#135	1	2	yes	—
238	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
245	C₈×C₁₃	—	2	2	no	—
246	C₈×C₁₃	—	4	1	no	—
247	C₈×C₁₃	—	4	2	no	—
248	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
249	#554	—	2	4	no	—
250	#554	—	2	4	no	—
251	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#125	C₂²×C₁₃	1	2	yes	—
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	C₂×C₂²⋊Q₈	—	2	1	no	—
255	C₂×C₂²⋊Q₈	—	2	2	no	—
256	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	—	2	1	no	—
261	#476	—	2	4	no	—
262	C₄×D₈	—	2	4	no	—
263	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#106	C₂²×C₁₃	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#102	C₂²×C₁₃	1	2	yes	—
267	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#102	C₂²×C₁₃	1	2	yes	—
269	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
271	#396	—	2	2	no	—
272	#390	C₂²×C₁₃	1	2	yes	—
273	#389	C₂²×C₁₃	1	2	yes	—
274	#384	C₂²×C₁₃	1	1	yes	characteristic
275	#380	—	2	1	no	—
276	#340	C₂²×C₁₃	1	2	yes	—
277	#340	C₂²×C₁₃	1	2	yes	—
278	#340	C₂²×C₁₃	1	2	yes	—
279	#336	C₂²×C₁₃	1	2	yes	—
280	#336	C₂²×C₁₃	1	2	yes	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	2	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	4	2	no	—
291	C₂²×C₁₃	—	8	1	no	—
292	C₂²×C₁₃	—	8	1	no	—
293	C₂²×C₁₃	—	8	1	no	—
294	C₂²×C₁₃	—	8	1	no	—
295	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
296	C₂²×C₁₃	#548	1	1	yes	characteristic
297	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
298	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
299	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₂²×C₁₃	#576	1	1	yes	characteristic
301	C₂²×C₁₃	#577	1	1	yes	characteristic
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	2	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	—	8	2	no	—
308	C₄×C₁₃	—	8	1	no	—
309	C₄×C₁₃	#449	1	4	yes	—
310	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
311	C₄×C₁₃	#536	1	1	yes	characteristic
312	C₄×C₁₃	#548	1	1	yes	characteristic
313	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
316	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	—	2	1	no	—
321	C₂×D₈	—	2	2	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	Q₈×C₁₃	1	4	yes	complemented
324	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
326	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
329	#125	—	2	4	no	—
330	#125	—	2	4	no	—
331	C₂²⋊Q₈	—	2	8	no	—
332	C₂²⋊Q₈	—	2	16	no	—
333	C₂²⋊Q₈	—	4	4	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	D₄×C₁₃	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	8	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	#107	—	2	2	no	—
363	#106	—	2	4	no	—
364	C₄⋊C₈	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	4	no	—
367	#102	—	2	2	no	—
368	#102	—	2	4	no	—
369	C₄×C₈	—	2	2	no	—
370	#95	—	2	2	no	—
371	C₂×C₁₃	—	4	4	no	—
372	C₂×C₁₃	—	8	2	no	—
373	C₂×C₁₃	#2409	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
375	C₂×C₁₃	#3012	1	1	yes	characteristic
376	C₂×C₁₃	#3360	1	1	yes	characteristic
377	C₂×C₁₃	#3366	1	1	yes	characteristic
378	C₂×C₁₃	#3380	1	1	yes	characteristic
379	C₂×C₁₃	#3384	1	1	yes	characteristic
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	1	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	8	1	no	—
387	C₂×Q₈	—	8	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
398	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
399	C₂×D₄	C₁₃×#41	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	8	2	no	—
412	C₂²×C₄	—	8	2	no	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	D₈	—	2	8	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	8	1	no	—
442	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
443	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	8	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	C₂×D₄×C₁₃	1	2	yes	—
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₁₃	#24327	1	1	yes	characteristic, direct product factor, Sylow
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	Q₈	—	4	4	no	—
470	Q₈	—	8	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	8	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	C₁₃×#120	1	2	yes	—
503	C₂×C₄	C₁₃×#120	1	2	yes	—
504	C₂×C₄	C₁₃×#135	1	2	yes	—
505	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
509	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
510	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
511	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
512	C₈	—	2	2	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	2	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
530	C₂²	C₁₃×#548	1	1	yes	characteristic
531	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
532	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
533	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
534	C₂²	C₁₃×#576	1	1	yes	characteristic
535	C₂²	C₁₃×#577	1	1	yes	characteristic
536	C₄	—	2	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	8	2	no	—
542	C₄	—	8	1	no	—
543	C₄	C₁₃×#449	1	4	yes	—
544	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
545	C₄	C₁₃×#536	1	1	yes	characteristic
546	C₄	C₁₃×#548	1	1	yes	characteristic
547	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
548	C₂	—	4	4	no	—
549	C₂	—	8	2	no	—
550	C₂	C₁₃×#2409	1	1	yes	characteristic
551	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
552	C₂	C₁₃×#3012	1	1	yes	characteristic
553	C₂	C₁₃×#3360	1	1	yes	characteristic
554	C₂	C₁₃×#3366	1	1	yes	characteristic
555	C₂	C₁₃×#3380	1	1	yes	characteristic
556	C₂	C₁₃×#3384	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×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×#554	C₂	semidirect
2. C₂×C₁₃×#476	C₂	semidirect
4. C₁₃×#2538	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1984	C₂	semidirect
10. C₁₃×#1864	C₂	semidirect
11. C₁₃×#1802	C₂	semidirect
54. C₂×C₁₃×D₈	Q₈	semidirect
102. #24327	C₁₃	direct (N × H)
176. C₂×#554	C₂×C₁₃	semidirect
177. C₂×#476	C₂×C₁₃	semidirect
179. #2538	C₂×C₁₃	semidirect
180. #2059	C₂×C₁₃	semidirect
181. #2025	C₂×C₁₃	semidirect
182. #1990	C₂×C₁₃	semidirect
183. #1984	C₂×C₁₃	semidirect
185. #1864	C₂×C₁₃	semidirect
186. #1802	C₂×C₁₃	semidirect
211. D₄×C₁₃	C₂²⋊Q₈	semidirect
323. C₂×D₈	Q₈×C₁₃	semidirect
453. C₁₃	#24327	direct (N × H)
478. D₄	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#554	2
C₂×C₁₃×#476	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2538	2
C₁₃×#2059	2
C₁₃×#2025	2
C₁₃×#1990	2
C₁₃×#1984	2
C₁₃×#1879	2
C₁₃×#1864	2
C₁₃×#1802	2
#24327	13

Subgroups — C13×#24327 #15710666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24327 #15710666