Subgroups — C₁₃×#25568 #15711907

Order 3328.

1190 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2000	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1873	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
11	C₁₃×#555	—	2	4	no	—
12	C₁₃×#555	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	—	2	2	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	—	2	1	no	—
22	C₂×C₁₃×#117	C₂²	1	2	yes	—
23	C₁₃×#487	—	2	4	no	—
24	C₁₃×#461	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#399	—	2	2	no	—
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#384	—	2	1	no	—
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	4	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂×C₁₃×SD₁₆	—	2	4	no	—
45	C₂×C₁₃×SD₁₆	—	4	4	no	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
52	C₁₃×#124	—	2	16	no	—
53	C₁₃×C₂²⋊Q₈	—	2	8	no	—
54	C₁₃×C₂²⋊Q₈	—	4	4	no	—
55	C₁₃×#121	—	2	8	no	—
56	C₁₃×#121	—	2	4	no	—
57	C₁₃×#121	—	2	4	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	D₄	1	4	yes	—
62	C₁₃×#117	—	2	8	no	—
63	C₁₃×#117	—	2	4	no	—
64	C₁₃×#117	—	2	4	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	8	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×C₂²⋊C₈	—	4	4	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	#25568	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	1	no	—
90	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₁₃	—	2	4	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	8	2	no	—
97	C₂×D₄×C₁₃	—	2	8	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	8	4	no	—
105	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×SD₁₆	—	4	8	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	8	no	—
133	C₁₃×C₄⋊C₄	—	4	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
137	C₁₃×C₄⋊C₄	#41	1	4	yes	—
138	C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₁₃×C₂²⋊C₄	—	2	8	no	—
140	C₁₃×C₂²⋊C₄	—	2	4	no	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	8	no	—
143	C₄²×C₁₃	—	2	8	no	—
144	C₄²×C₁₃	—	4	2	no	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×#555	C₂×C₁₃	1	1	yes	characteristic
148	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2542	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2000	C₂×C₁₃	1	4	yes	complemented
152	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1873	C₂×C₁₃	1	4	yes	complemented
155	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	4	4	no	—
170	Q₈×C₁₃	—	8	4	no	—
171	D₄×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	4	4	no	—
175	D₄×C₁₃	—	8	8	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	4	no	—
190	C₂×C₄×C₁₃	—	4	8	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	#120	1	2	yes	—
194	C₂×C₄×C₁₃	#120	1	2	yes	—
195	C₂×C₄×C₁₃	#135	1	2	yes	—
196	C₂×C₄×C₁₃	#137	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
200	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	2	no	—
203	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
204	#555	—	2	4	no	—
205	#555	—	2	4	no	—
206	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#124	—	2	2	no	—
209	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
210	C₂×#121	—	2	1	no	—
211	C₂×#121	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#117	—	2	1	no	—
215	C₂×#117	C₂²×C₁₃	1	2	yes	—
216	#487	—	2	4	no	—
217	#461	—	2	4	no	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#103	C₂²×C₁₃	1	4	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
223	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
224	#399	—	2	2	no	—
225	#390	—	2	1	no	—
226	#384	—	2	1	no	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
228	#340	C₂²×C₁₃	1	2	yes	—
229	#340	C₂²×C₁₃	1	4	yes	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	4	2	no	—
232	C₂²×C₁₃	—	4	2	no	—
233	C₂²×C₁₃	—	4	2	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
241	C₂²×C₁₃	#546	1	2	yes	—
242	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
244	C₂²×C₁₃	#577	1	2	yes	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	#452	1	4	yes	—
252	C₄×C₁₃	#532	1	1	yes	characteristic
253	C₄×C₁₃	#535	1	1	yes	characteristic
254	C₄×C₁₃	#550	1	2	yes	—
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	—	4	4	no	—
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
270	#124	—	2	16	no	—
271	C₂²⋊Q₈	—	2	8	no	—
272	C₂²⋊Q₈	—	4	4	no	—
273	#121	—	2	8	no	—
274	#121	—	2	4	no	—
275	#121	—	2	4	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	D₄×C₁₃	1	4	yes	—
280	#117	—	2	8	no	—
281	#117	—	2	4	no	—
282	#117	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	4	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	4	no	—
295	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	C₄⋊C₈	—	2	2	no	—
300	#103	—	2	4	no	—
301	#103	—	2	8	no	—
302	#102	—	2	4	no	—
303	C₂²⋊C₈	—	4	4	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	1	no	—
306	C₂×C₁₃	—	8	2	no	—
307	C₂×C₁₃	—	8	2	no	—
308	C₂×C₁₃	#2431	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
310	C₂×C₁₃	#3009	1	1	yes	characteristic
311	C₂×C₁₃	#3303	1	2	yes	—
312	C₂×C₁₃	#3329	1	2	yes	—
313	C₂⁴	—	2	1	no	—
314	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×D₄	—	2	8	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	8	4	no	—
329	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
345	SD₁₆	—	4	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	8	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
361	C₄⋊C₄	C₁₃×#41	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	4	8	no	—
367	C₄²	—	2	8	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×D₄×C₁₃	1	2	yes	—
370	C₄²	C₂×D₄×C₁₃	1	2	yes	—
371	C₁₃	#25568	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	8	4	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	C₁₃×#120	1	2	yes	—
410	C₂×C₄	C₁₃×#120	1	2	yes	—
411	C₂×C₄	C₁₃×#135	1	2	yes	—
412	C₂×C₄	C₁₃×#137	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
416	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
430	C₂²	C₁₃×#546	1	2	yes	—
431	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
432	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
433	C₂²	C₁₃×#577	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	2	no	—
440	C₄	C₁₃×#452	1	4	yes	—
441	C₄	C₁₃×#532	1	1	yes	characteristic
442	C₄	C₁₃×#535	1	1	yes	characteristic
443	C₄	C₁₃×#550	1	2	yes	—
444	C₂	—	8	2	no	—
445	C₂	—	8	2	no	—
446	C₂	C₁₃×#2431	1	1	yes	characteristic
447	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
448	C₂	C₁₃×#3009	1	1	yes	characteristic
449	C₂	C₁₃×#3303	1	2	yes	—
450	C₂	C₁₃×#3329	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#555	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#487	C₂	semidirect
3. C₂×C₁₃×#461	C₂	semidirect
4. C₁₃×#2542	C₂	semidirect
5. C₁₃×#2000	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
7. C₁₃×#1954	C₂	semidirect
8. C₁₃×#1873	C₂	semidirect
9. C₄×C₁₃×#102	C₂	semidirect
88. #25568	C₁₃	direct (N × H)
148. C₂×#487	C₂×C₁₃	semidirect
149. C₂×#461	C₂×C₁₃	semidirect
150. #2542	C₂×C₁₃	semidirect
151. #2000	C₂×C₁₃	semidirect
152. #1987	C₂×C₁₃	semidirect
153. #1954	C₂×C₁₃	semidirect
154. #1873	C₂×C₁₃	semidirect
155. C₄×#102	C₂×C₁₃	semidirect
371. C₁₃	#25568	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×#555	2
C₂×C₁₃×#487	2
C₂×C₁₃×#461	2
C₁₃×#2542	2
C₁₃×#2000	2
C₁₃×#1987	2
C₁₃×#1954	2
C₁₃×#1873	2
C₄×C₁₃×#102	2
#25568	13

Subgroups — C13×#25568 #15711907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25568 #15711907