Subgroups — C₁₃×#24201 #15710540

Order 3328.

1068 conjugacy classes of subgroups.

The subgroup lattice has 504 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	1	yes	maximal, characteristic
2	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2042	C₂	1	2	yes	maximal
6	C₁₃×#2015	C₂	1	2	yes	maximal
7	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1878	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	C₁₃×#556	—	2	4	no	—
15	C₁₃×#556	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	—	2	2	no	—
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#117	—	2	1	no	—
25	C₁₃×#462	—	2	4	no	—
26	C₁₃×#440	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₁₃×#400	—	2	1	no	—
37	C₁₃×#395	—	2	1	no	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#387	—	2	2	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	—	2	4	no	—
51	C₂×C₁₃×Q₁₆	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	—	4	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
61	C₁₃×#126	—	2	16	no	—
62	C₁₃×#124	—	2	4	no	—
63	C₁₃×#124	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	D₄	1	4	yes	—
73	C₁₃×#117	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	2	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#107	—	2	2	no	—
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	4	2	no	—
97	C₁₃×#102	—	2	2	no	—
98	C₁₃×#102	—	4	2	no	—
99	C₁₃×#97	—	2	2	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	2	no	—
103	C₁₃×#95	—	2	2	no	—
104	C₁₃×#95	—	2	2	no	—
105	#24201	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
120	C₂×Q₈×C₁₃	#41	1	2	yes	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	4	4	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×Q₁₆	—	4	8	no	—
140	C₁₃×SD₁₆	—	2	8	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	2	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	#41	1	2	yes	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	4	4	no	—
161	C₁₃×C₄⋊C₄	—	4	2	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₄²×C₁₃	—	2	8	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	4	2	no	—
170	C₄²×C₁₃	C₂×D₄	1	2	yes	—
171	C₄²×C₁₃	C₂×D₄	1	2	yes	—
172	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
173	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
175	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#2042	C₂×C₁₃	1	2	yes	—
177	#2015	C₂×C₁₃	1	2	yes	—
178	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1960	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1878	C₂×C₁₃	1	2	yes	complemented
181	#1863	C₂×C₁₃	1	2	yes	complemented
182	#1804	C₂×C₁₃	1	1	yes	characteristic
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	2	2	no	—
191	Q₈×C₁₃	—	2	4	no	—
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	4	4	no	—
194	Q₈×C₁₃	—	4	2	no	—
195	Q₈×C₁₃	—	4	2	no	—
196	Q₈×C₁₃	—	4	1	no	—
197	Q₈×C₁₃	—	4	1	no	—
198	D₄×C₁₃	—	2	2	no	—
199	D₄×C₁₃	—	2	2	no	—
200	D₄×C₁₃	—	4	1	no	—
201	D₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	#120	1	2	yes	—
224	C₂×C₄×C₁₃	#120	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	4	1	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
235	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
236	#556	—	2	4	no	—
237	#556	—	2	4	no	—
238	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#126	—	2	2	no	—
240	C₂×#124	C₂²×C₁₃	1	2	yes	—
241	C₂×C₂²⋊Q₈	—	2	1	no	—
242	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#117	—	2	1	no	—
247	#462	—	2	4	no	—
248	#440	—	2	4	no	—
249	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×#103	C₂²×C₁₃	1	2	yes	—
252	C₂×#103	C₂²×C₁₃	1	2	yes	—
253	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#103	C₂²×C₁₃	1	2	yes	—
255	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#102	C₂²×C₁₃	1	2	yes	—
257	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
258	#400	—	2	1	no	—
259	#395	—	2	1	no	—
260	#391	C₂²×C₁₃	1	2	yes	—
261	#389	C₂²×C₁₃	1	2	yes	—
262	#387	—	2	2	no	—
263	#382	C₂²×C₁₃	1	1	yes	characteristic
264	#340	C₂²×C₁₃	1	2	yes	—
265	#336	C₂²×C₁₃	1	2	yes	—
266	#336	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	8	2	no	—
271	C₂²×C₁₃	—	8	2	no	—
272	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
273	C₂²×C₁₃	#548	1	1	yes	characteristic
274	C₂²×C₁₃	#550	1	1	yes	characteristic
275	C₂²×C₁₃	#575	1	2	yes	—
276	C₂²×C₁₃	#578	1	2	yes	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	4	4	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	—	8	1	no	—
286	C₄×C₁₃	#525	1	1	yes	characteristic
287	C₄×C₁₃	#537	1	1	yes	characteristic
288	C₄×C₁₃	#546	1	1	yes	characteristic
289	C₄×C₁₃	#547	1	1	yes	characteristic
290	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
292	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂×Q₁₆	—	2	4	no	—
296	C₂×Q₁₆	—	2	4	no	—
297	C₂×Q₁₆	—	4	2	no	—
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	2	no	—
301	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
302	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
306	#126	—	2	16	no	—
307	#124	—	2	4	no	—
308	#124	—	2	4	no	—
309	C₂²⋊Q₈	—	2	8	no	—
310	C₄×Q₈	—	2	4	no	—
311	C₄×Q₈	—	2	4	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₄×Q₈	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	D₄×C₁₃	1	4	yes	—
318	#117	—	2	8	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₄²	—	2	2	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	#107	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	#103	—	2	4	no	—
339	#103	—	2	4	no	—
340	#103	—	2	2	no	—
341	#103	—	4	2	no	—
342	#102	—	2	2	no	—
343	#102	—	4	2	no	—
344	#97	—	2	2	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	2	no	—
350	C₂×C₁₃	—	8	2	no	—
351	C₂×C₁₃	#2407	1	1	yes	characteristic
352	C₂×C₁₃	#3005	1	1	yes	characteristic
353	C₂×C₁₃	#3011	1	1	yes	characteristic
354	C₂×C₁₃	#3377	1	2	yes	—
355	C₂×C₁₃	#3402	1	2	yes	—
356	C₂⁴	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
370	C₂×Q₈	C₁₃×#41	1	2	yes	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
389	Q₁₆	—	4	8	no	—
390	SD₁₆	—	2	8	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	C₁₃×#41	1	2	yes	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₄²	—	2	8	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	4	2	no	—
420	C₄²	C₂×D₄×C₁₃	1	2	yes	—
421	C₄²	C₂×D₄×C₁₃	1	2	yes	—
422	C₁₃	#24201	1	1	yes	characteristic, direct product factor, Sylow
423	C₂³	—	2	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	2	4	no	—
432	Q₈	—	2	4	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	4	1	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	C₁₃×#120	1	2	yes	—
464	C₂×C₄	C₁₃×#120	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
468	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
469	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
480	C₂²	C₁₃×#548	1	1	yes	characteristic
481	C₂²	C₁₃×#550	1	1	yes	characteristic
482	C₂²	C₁₃×#575	1	2	yes	—
483	C₂²	C₁₃×#578	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₄	—	8	1	no	—
493	C₄	C₁₃×#525	1	1	yes	characteristic
494	C₄	C₁₃×#537	1	1	yes	characteristic
495	C₄	C₁₃×#546	1	1	yes	characteristic
496	C₄	C₁₃×#547	1	1	yes	characteristic
497	C₂	—	8	2	no	—
498	C₂	C₁₃×#2407	1	1	yes	characteristic
499	C₂	C₁₃×#3005	1	1	yes	characteristic
500	C₂	C₁₃×#3011	1	1	yes	characteristic
501	C₂	C₁₃×#3377	1	2	yes	—
502	C₂	C₁₃×#3402	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
2. C₂×C₁₃×#462	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
7. C₁₃×#1985	C₂	semidirect
8. C₁₃×#1960	C₂	semidirect
9. C₁₃×#1878	C₂	semidirect
10. C₁₃×#1863	C₂	semidirect
105. #24201	C₁₃	direct (N × H)
173. C₂×#462	C₂×C₁₃	semidirect
175. #2581	C₂×C₁₃	semidirect
178. #1985	C₂×C₁₃	semidirect
179. #1960	C₂×C₁₃	semidirect
180. #1878	C₂×C₁₃	semidirect
181. #1863	C₂×C₁₃	semidirect
422. C₁₃	#24201	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
C₂×C₁₃×#462	2
C₂×C₁₃×#440	2
C₁₃×#2581	2
C₁₃×#2042	2
C₁₃×#2015	2
C₁₃×#1985	2
C₁₃×#1960	2
C₁₃×#1878	2
C₁₃×#1863	2
C₁₃×#1804	2
#24201	13

Subgroups — C13×#24201 #15710540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24201 #15710540