Subgroups — C₁₃×#24630 #15710969

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2055	C₂	1	2	yes	maximal
6	C₁₃×#2013	C₂	1	2	yes	maximal
7	C₁₃×#1981	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₁₃×#461	—	2	4	no	—
20	C₄×C₁₃×SD₁₆	—	2	4	no	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#398	—	2	2	no	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#389	—	2	1	no	—
35	C₁₃×#389	—	2	1	no	—
36	C₁₃×#388	—	2	2	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#380	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	2	2	no	—
51	C₂×C₁₃×SD₁₆	—	4	2	no	—
52	C₂×C₁₃×SD₁₆	—	4	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	4	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	D₄	1	4	yes	—
64	C₁₃×#117	—	4	4	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	4	2	no	—
87	C₁₃×#103	—	2	4	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×#103	—	4	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₄×C₈×C₁₃	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	D₄	1	2	yes	—
98	#24630	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×SD₁₆	—	2	8	no	—
132	C₁₃×SD₁₆	—	4	8	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	#41	1	2	yes	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	4	4	no	—
149	C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	—	8	1	no	—
155	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
156	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
157	C₁₃×C₂²⋊C₄	—	2	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₁₃×C₂²⋊C₄	—	8	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	2	no	—
163	C₄²×C₁₃	—	4	4	no	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	#41	1	2	yes	—
166	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
167	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
168	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#2354	C₂×C₁₃	1	1	yes	characteristic
170	#2055	C₂×C₁₃	1	2	yes	—
171	#2013	C₂×C₁₃	1	2	yes	—
172	#1981	C₂×C₁₃	1	2	yes	complemented
173	#1956	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1927	C₂×C₁₃	1	2	yes	complemented
176	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	2	no	—
186	Q₈×C₁₃	—	2	2	no	—
187	Q₈×C₁₃	—	4	1	no	—
188	Q₈×C₁₃	—	4	1	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	Q₈×C₁₃	—	4	2	no	—
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	2	2	no	—
194	D₄×C₁₃	—	2	2	no	—
195	D₄×C₁₃	—	4	1	no	—
196	D₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	8	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	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	1	no	—
220	C₂×C₄×C₁₃	#121	1	2	yes	—
221	C₂×C₄×C₁₃	#121	1	2	yes	—
222	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
223	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₁₃	#137	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	4	1	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#117	—	2	1	no	—
241	#461	—	2	4	no	—
242	C₄×SD₁₆	—	2	4	no	—
243	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
246	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#103	C₂²×C₁₃	1	2	yes	—
248	C₂×#103	C₂²×C₁₃	1	2	yes	—
249	C₂×#103	C₂²×C₁₃	1	2	yes	—
250	C₂×#103	C₂²×C₁₃	1	2	yes	—
251	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
253	#398	—	2	2	no	—
254	#391	C₂²×C₁₃	1	2	yes	—
255	#390	C₂²×C₁₃	1	2	yes	—
256	#389	—	2	1	no	—
257	#389	—	2	1	no	—
258	#388	—	2	2	no	—
259	#384	C₂²×C₁₃	1	1	yes	characteristic
260	#380	—	2	1	no	—
261	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	#340	C₂²×C₁₃	1	2	yes	—
264	#336	C₂²×C₁₃	1	2	yes	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	8	1	no	—
269	C₂²×C₁₃	—	8	1	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
273	C₂²×C₁₃	#546	1	1	yes	characteristic
274	C₂²×C₁₃	#550	1	1	yes	characteristic
275	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
276	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
277	C₂²×C₁₃	#577	1	1	yes	characteristic
278	C₂²×C₁₃	#578	1	1	yes	characteristic
279	C₄×C₁₃	—	2	4	no	—
280	C₄×C₁₃	—	2	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	2	no	—
286	C₄×C₁₃	—	8	1	no	—
287	C₄×C₁₃	#461	1	4	yes	—
288	C₄×C₁₃	#525	1	1	yes	characteristic
289	C₄×C₁₃	#535	1	1	yes	characteristic
290	C₄×C₁₃	#553	1	1	yes	characteristic
291	C₄×C₁₃	#555	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
293	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	4	2	no	—
301	C₂×SD₁₆	—	4	2	no	—
302	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	4	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	D₄×C₁₃	1	4	yes	—
313	#117	—	4	4	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
333	#106	—	2	2	no	—
334	C₄⋊C₈	—	2	2	no	—
335	C₄⋊C₈	—	4	2	no	—
336	#103	—	2	4	no	—
337	#103	—	2	2	no	—
338	#103	—	2	4	no	—
339	#103	—	4	2	no	—
340	#103	—	4	2	no	—
341	#102	—	2	2	no	—
342	C₄×C₈	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	#95	D₄×C₁₃	1	2	yes	—
347	C₂×C₁₃	—	8	2	no	—
348	C₂×C₁₃	#2414	1	1	yes	characteristic
349	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
350	C₂×C₁₃	#3046	1	1	yes	characteristic
351	C₂×C₁₃	#3298	1	1	yes	characteristic
352	C₂×C₁₃	#3329	1	1	yes	characteristic
353	C₂×C₁₃	#3392	1	1	yes	characteristic
354	C₂×C₁₃	#3398	1	1	yes	characteristic
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	C₁₃×#41	1	2	yes	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
387	SD₁₆	—	2	8	no	—
388	SD₁₆	—	4	8	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₁₃×#41	1	2	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	—	4	4	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	8	1	no	—
411	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
412	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	4	4	no	—
415	C₂²⋊C₄	—	8	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	4	2	no	—
419	C₄²	—	4	4	no	—
420	C₄²	C₂×D₄×C₁₃	1	2	yes	—
421	C₄²	C₁₃×#41	1	2	yes	—
422	C₁₃	#24630	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	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	1	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	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	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	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	C₁₃×#121	1	2	yes	—
467	C₂×C₄	C₁₃×#121	1	2	yes	—
468	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
469	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
470	C₂×C₄	C₁₃×#137	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
475	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	4	1	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
488	C₂²	C₁₃×#546	1	1	yes	characteristic
489	C₂²	C₁₃×#550	1	1	yes	characteristic
490	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
491	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
492	C₂²	C₁₃×#577	1	1	yes	characteristic
493	C₂²	C₁₃×#578	1	1	yes	characteristic
494	C₄	—	2	4	no	—
495	C₄	—	2	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	2	no	—
501	C₄	—	8	2	no	—
502	C₄	C₁₃×#461	1	4	yes	—
503	C₄	C₁₃×#525	1	1	yes	characteristic
504	C₄	C₁₃×#535	1	1	yes	characteristic
505	C₄	C₁₃×#553	1	1	yes	characteristic
506	C₄	C₁₃×#555	1	1	yes	characteristic
507	C₂	—	8	2	no	—
508	C₂	C₁₃×#2414	1	1	yes	characteristic
509	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
510	C₂	C₁₃×#3046	1	1	yes	characteristic
511	C₂	C₁₃×#3298	1	1	yes	characteristic
512	C₂	C₁₃×#3329	1	1	yes	characteristic
513	C₂	C₁₃×#3392	1	1	yes	characteristic
514	C₂	C₁₃×#3398	1	1	yes	characteristic

	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2546	C₂	semidirect
7. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1956	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1927	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
98. #24630	C₁₃	direct (N × H)
155. C₁₃×C₄⋊C₄	SD₁₆	semidirect
168. #2546	C₂×C₁₃	semidirect
172. #1981	C₂×C₁₃	semidirect
173. #1956	C₂×C₁₃	semidirect
174. #1939	C₂×C₁₃	semidirect
175. #1927	C₂×C₁₃	semidirect
176. #1803	C₂×C₁₃	semidirect
411. C₄⋊C₄	C₁₃×SD₁₆	semidirect
422. C₁₃	#24630	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×#461	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2546	2
C₁₃×#2354	2
C₁₃×#2055	2
C₁₃×#2013	2
C₁₃×#1981	2
C₁₃×#1956	2
C₁₃×#1939	2
C₁₃×#1927	2
C₁₃×#1803	2
#24630	13

Subgroups — C13×#24630 #15710969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24630 #15710969