Subgroups — C₁₃×#23944 #15710283

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#452	C₂	1	2	yes	maximal
3	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1878	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₁₃×#541	—	2	8	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	—	2	2	no	—
18	C₂×C₁₃×#125	—	2	2	no	—
19	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₁₃×#452	—	2	8	no	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	1	yes	characteristic
31	C₁₃×#391	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#386	—	2	2	no	—
35	C₁₃×#380	—	2	2	no	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	4	2	no	—
45	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×Q₁₆	—	2	4	no	—
53	C₂×C₁₃×Q₁₆	—	2	4	no	—
54	C₂×C₁₃×Q₁₆	—	4	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	4	no	—
56	C₂×C₁₃×SD₁₆	—	2	4	no	—
57	C₂×C₁₃×SD₁₆	—	4	2	no	—
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×#126	—	2	16	no	—
62	C₁₃×#125	—	2	16	no	—
63	C₁₃×#125	—	2	4	no	—
64	C₁₃×C₂²⋊Q₈	—	2	4	no	—
65	C₁₃×C₂²⋊Q₈	D₄	1	8	yes	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₁₃×#117	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#103	—	2	4	no	—
87	C₁₃×#103	—	4	2	no	—
88	C₁₃×#103	—	4	2	no	—
89	C₁₃×#102	—	2	4	no	—
90	C₁₃×C₂²⋊C₈	—	2	4	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	#23944	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	1	no	—
95	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₁₃×#41	—	4	8	no	—
97	C₁₃×#41	—	4	8	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
107	C₂×Q₈×C₁₃	#41	1	2	yes	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	#41	1	2	yes	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	8	2	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	4	8	no	—
134	C₁₃×SD₁₆	—	4	8	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
151	C₁₃×C₂²⋊C₄	—	2	8	no	—
152	C₁₃×C₂²⋊C₄	—	2	4	no	—
153	C₁₃×C₂²⋊C₄	—	8	2	no	—
154	C₁₃×C₂²⋊C₄	—	8	2	no	—
155	C₄²×C₁₃	—	2	8	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂×#452	C₂×C₁₃	1	2	yes	—
160	#2311	C₂×C₁₃	1	1	yes	characteristic
161	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1880	C₂×C₁₃	1	2	yes	complemented
166	#1878	C₂×C₁₃	1	2	yes	complemented
167	#1872	C₂×C₁₃	1	2	yes	complemented
168	#1818	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	#120	1	2	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	4	no	—
181	Q₈×C₁₃	—	2	4	no	—
182	Q₈×C₁₃	—	2	4	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	2	4	no	—
187	D₄×C₁₃	—	4	8	no	—
188	D₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	8	4	no	—
214	C₂×C₄×C₁₃	#120	1	2	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
219	C₈×C₁₃	—	4	2	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
223	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
224	#541	—	2	8	no	—
225	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#126	—	2	2	no	—
227	C₂×#125	—	2	2	no	—
228	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
231	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#452	—	2	8	no	—
234	C₂×#103	C₂²×C₁₃	1	2	yes	—
235	C₂×#103	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#102	C₂²×C₁₃	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
239	#391	C₂²×C₁₃	1	1	yes	characteristic
240	#391	C₂²×C₁₃	1	1	yes	characteristic
241	#390	C₂²×C₁₃	1	1	yes	characteristic
242	#390	C₂²×C₁₃	1	1	yes	characteristic
243	#386	—	2	2	no	—
244	#380	—	2	2	no	—
245	#340	C₂²×C₁₃	1	2	yes	—
246	#340	C₂²×C₁₃	1	2	yes	—
247	#336	C₂²×C₁₃	1	2	yes	—
248	#336	C₂²×C₁₃	1	1	yes	characteristic
249	#336	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	1	no	—
254	C₂²×C₁₃	—	4	1	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	8	1	no	—
258	C₂²×C₁₃	—	8	1	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
261	C₂²×C₁₃	#525	1	1	yes	characteristic
262	C₂²×C₁₃	#535	1	1	yes	characteristic
263	C₂²×C₁₃	#577	1	2	yes	—
264	C₂²×C₁₃	#578	1	2	yes	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	—	8	1	no	—
272	C₄×C₁₃	—	8	1	no	—
273	C₄×C₁₃	#546	1	2	yes	—
274	C₄×C₁₃	#546	1	2	yes	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	4	2	no	—
279	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
280	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×Q₁₆	—	2	4	no	—
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×Q₁₆	—	4	2	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×SD₁₆	—	4	2	no	—
292	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
293	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
294	C₄⋊Q₈	—	2	4	no	—
295	#126	—	2	16	no	—
296	#125	—	2	16	no	—
297	#125	—	2	4	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	D₄×C₁₃	1	8	yes	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	#117	—	2	4	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	4	2	no	—
309	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	#103	—	2	4	no	—
321	#103	—	4	2	no	—
322	#103	—	4	2	no	—
323	#102	—	2	4	no	—
324	C₂²⋊C₈	—	2	4	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	C₂×C₁₃	—	4	2	no	—
328	C₂×C₁₃	—	8	2	no	—
329	C₂×C₁₃	#2404	1	1	yes	characteristic
330	C₂×C₁₃	#3013	1	2	yes	—
331	C₂×C₁₃	#3120	1	2	yes	—
332	C₂×C₁₃	#3222	1	1	yes	characteristic
333	C₂×C₁₃	#3223	1	1	yes	characteristic
334	C₂⁴	—	2	1	no	—
335	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
336	#41	—	4	8	no	—
337	#41	—	4	8	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
347	C₂×Q₈	C₁₃×#41	1	2	yes	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	C₁₃×#41	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
373	Q₁₆	—	4	8	no	—
374	SD₁₆	—	4	8	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	2	8	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₁₃	#23944	1	1	yes	characteristic, direct product factor, Sylow
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	C₁₃×#120	1	2	yes	—
409	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	Q₈	—	2	4	no	—
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	C₁₃×#120	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
446	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
448	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
449	C₈	—	4	2	no	—
450	C₈	—	4	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
462	C₂²	C₁₃×#525	1	1	yes	characteristic
463	C₂²	C₁₃×#535	1	1	yes	characteristic
464	C₂²	C₁₃×#577	1	2	yes	—
465	C₂²	C₁₃×#578	1	2	yes	—
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	1	no	—
474	C₄	C₁₃×#546	1	2	yes	—
475	C₄	C₁₃×#546	1	2	yes	—
476	C₂	—	4	2	no	—
477	C₂	—	8	2	no	—
478	C₂	C₁₃×#2404	1	1	yes	characteristic
479	C₂	C₁₃×#3013	1	2	yes	—
480	C₂	C₁₃×#3120	1	2	yes	—
481	C₂	C₁₃×#3222	1	1	yes	characteristic
482	C₂	C₁₃×#3223	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#541	C₂	semidirect
4. C₁₃×#2026	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#2016	C₂	semidirect
7. C₁₃×#2013	C₂	semidirect
8. C₁₃×#1880	C₂	semidirect
9. C₁₃×#1878	C₂	semidirect
10. C₁₃×#1872	C₂	semidirect
11. C₁₃×#1818	C₂	semidirect
93. #23944	C₁₃	direct (N × H)
158. C₂×#541	C₂×C₁₃	semidirect
161. #2026	C₂×C₁₃	semidirect
162. #2025	C₂×C₁₃	semidirect
163. #2016	C₂×C₁₃	semidirect
164. #2013	C₂×C₁₃	semidirect
165. #1880	C₂×C₁₃	semidirect
166. #1878	C₂×C₁₃	semidirect
167. #1872	C₂×C₁₃	semidirect
168. #1818	C₂×C₁₃	semidirect
398. C₁₃	#23944	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×#541	2
C₂×C₁₃×#452	2
C₁₃×#2311	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#2016	2
C₁₃×#2013	2
C₁₃×#1880	2
C₁₃×#1878	2
C₁₃×#1872	2
C₁₃×#1818	2
#23944	13

Subgroups — C13×#23944 #15710283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23944 #15710283