Subgroups — C₁₃×#25884 #15712223

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2035	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1787	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
11	D₄×Q₈×C₁₃	—	2	4	no	—
12	D₄×Q₈×C₁₃	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#124	—	2	1	no	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#487	—	2	4	no	—
23	C₁₃×#475	—	2	4	no	—
24	C₂×C₁₃×#106	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	4	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	4	yes	—
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#397	—	2	2	no	—
33	C₁₃×#391	—	2	1	no	—
34	C₁₃×#380	C₂²	1	4	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	4	no	—
38	C₂²×Q₈×C₁₃	—	2	4	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×Q₈×C₁₃	—	2	8	no	—
42	C₂²×Q₈×C₁₃	—	4	4	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₁₃×C₄⋊Q₈	—	2	8	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
55	C₁₃×#124	—	4	4	no	—
56	C₁₃×C₂²⋊Q₈	—	2	16	no	—
57	C₁₃×C₂²⋊Q₈	—	2	4	no	—
58	C₁₃×C₂²⋊Q₈	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	D₄	1	4	yes	—
61	C₄×D₄×C₁₃	—	2	8	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#106	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	8	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	4	4	no	—
85	C₁₃×C₂²⋊C₈	—	4	4	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	4	no	—
89	#25884	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₁₃	—	2	8	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	4	8	no	—
98	C₂×Q₈×C₁₃	—	4	16	no	—
99	C₂×Q₈×C₁₃	—	4	8	no	—
100	C₂×Q₈×C₁₃	—	4	8	no	—
101	C₂×Q₈×C₁₃	—	4	2	no	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₁₃	#41	1	4	yes	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	SD₁₆	1	4	yes	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	4	8	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	4	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	2	8	no	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	8	no	—
145	C₄²×C₁₃	—	2	4	no	—
146	C₄²×C₁₃	—	4	2	no	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
150	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2547	C₂×C₁₃	1	1	yes	characteristic
153	#2035	C₂×C₁₃	1	4	yes	complemented
154	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1954	C₂×C₁₃	1	1	yes	characteristic
156	#1787	C₂×C₁₃	1	4	yes	complemented
157	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
163	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	2	no	—
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	2	8	no	—
167	Q₈×C₁₃	—	4	16	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	4	2	no	—
170	Q₈×C₁₃	—	8	4	no	—
171	Q₈×C₁₃	#124	1	4	yes	complemented
172	D₄×C₁₃	—	2	8	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	4	16	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	4	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	#120	1	2	yes	—
193	C₂×C₄×C₁₃	#120	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₁₃	#137	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
199	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
200	C₈×C₁₃	—	4	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
203	D₄×Q₈	—	2	4	no	—
204	D₄×Q₈	—	2	4	no	—
205	C₂×C₄⋊Q₈	—	2	1	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	1	no	—
209	C₂×C₂²⋊Q₈	—	2	2	no	—
210	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄×D₄	—	2	1	no	—
213	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	#487	—	2	4	no	—
215	#475	—	2	4	no	—
216	C₂×#106	C₂²×C₁₃	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	4	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#103	C₂²×C₁₃	1	4	yes	—
222	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
223	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
224	#397	—	2	2	no	—
225	#391	—	2	1	no	—
226	#380	C₂²×C₁₃	1	4	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
228	#340	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₁₃	—	2	4	no	—
230	C₂²×C₁₃	—	2	8	no	—
231	C₂²×C₁₃	—	4	4	no	—
232	C₂²×C₁₃	—	4	2	no	—
233	C₂²×C₁₃	—	4	2	no	—
234	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
235	C₂²×C₁₃	#546	1	2	yes	—
236	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
237	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
238	C₂²×C₁₃	#578	1	2	yes	—
239	C₄×C₁₃	—	2	4	no	—
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	—	4	2	no	—
242	C₄×C₁₃	—	4	4	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	—	8	2	no	—
246	C₄×C₁₃	#448	1	4	yes	—
247	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
248	C₄×C₁₃	#535	1	1	yes	characteristic
249	C₄×C₁₃	#546	1	2	yes	—
250	C₂²×Q₈	—	2	4	no	—
251	C₂²×Q₈	—	2	4	no	—
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×Q₈	—	2	8	no	—
255	C₂²×Q₈	—	4	4	no	—
256	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
257	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
263	C₄⋊Q₈	—	2	8	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
268	#124	—	4	4	no	—
269	C₂²⋊Q₈	—	2	16	no	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	D₄×C₁₃	1	4	yes	—
274	C₄×D₄	—	2	8	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	#106	—	2	4	no	—
293	C₄⋊C₈	—	2	2	no	—
294	#103	—	2	4	no	—
295	#103	—	2	8	no	—
296	#103	—	2	4	no	—
297	#103	—	4	4	no	—
298	C₂²⋊C₈	—	4	4	no	—
299	C₄×C₈	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	4	no	—
302	C₂×C₁₃	—	4	4	no	—
303	C₂×C₁₃	#2435	1	1	yes	characteristic
304	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
305	C₂×C₁₃	#3011	1	1	yes	characteristic
306	C₂×C₁₃	#3298	1	2	yes	—
307	C₂×C₁₃	#3328	1	2	yes	—
308	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
309	C₂×Q₈	—	2	8	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	4	8	no	—
316	C₂×Q₈	—	4	16	no	—
317	C₂×Q₈	—	4	8	no	—
318	C₂×Q₈	—	4	8	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
323	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
324	C₂×Q₈	C₁₃×#41	1	4	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₁₃×SD₁₆	1	4	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	8	no	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	4	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	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	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	4	8	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	4	2	no	—
365	C₄²	C₂×D₄×C₁₃	1	2	yes	—
366	C₄²	C₂×D₄×C₁₃	1	2	yes	—
367	C₁₃	#25884	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	4	no	—
372	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
373	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	2	8	no	—
377	Q₈	—	4	16	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	8	4	no	—
381	Q₈	C₁₃×#124	1	4	yes	complemented
382	D₄	—	2	8	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	16	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	C₁₃×#120	1	2	yes	—
403	C₂×C₄	C₁₃×#120	1	2	yes	—
404	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
405	C₂×C₄	C₁₃×#137	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
409	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
418	C₂²	C₁₃×#546	1	2	yes	—
419	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
420	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
421	C₂²	C₁₃×#578	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₁₃×#448	1	4	yes	—
430	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
431	C₄	C₁₃×#535	1	1	yes	characteristic
432	C₄	C₁₃×#546	1	2	yes	—
433	C₂	—	4	4	no	—
434	C₂	C₁₃×#2435	1	1	yes	characteristic
435	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
436	C₂	C₁₃×#3011	1	1	yes	characteristic
437	C₂	C₁₃×#3298	1	2	yes	—
438	C₂	C₁₃×#3328	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
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×#475	C₂	semidirect
5. C₁₃×#2035	C₂	semidirect
6. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1787	C₂	semidirect
9. C₄×C₁₃×#103	C₂	semidirect
89. #25884	C₁₃	direct (N × H)
150. C₂×#487	C₂×C₁₃	semidirect
151. C₂×#475	C₂×C₁₃	semidirect
153. #2035	C₂×C₁₃	semidirect
154. #1981	C₂×C₁₃	semidirect
156. #1787	C₂×C₁₃	semidirect
157. C₄×#103	C₂×C₁₃	semidirect
171. Q₈×C₁₃	#124	semidirect
367. C₁₃	#25884	direct (N × H)
381. Q₈	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#487	2
C₂×C₁₃×#475	2
C₁₃×#2547	2
C₁₃×#2035	2
C₁₃×#1981	2
C₁₃×#1954	2
C₁₃×#1787	2
C₄×C₁₃×#103	2
#25884	13

Subgroups — C13×#25884 #15712223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25884 #15712223