Subgroups — C₁₃×#25056 #15711395

Order 3328.

766 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2093	C₂	1	2	yes	maximal
4	C₁₃×#2083	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1925	C₂	1	2	yes	maximal
8	C₁₃×#1918	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#107	C₂²	1	2	yes	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#396	—	2	2	no	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#389	—	2	2	no	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#384	C₂²	1	1	yes	characteristic
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#384	C₂²	1	2	yes	—
32	C₁₃×#380	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×C₂²⋊Q₈	—	4	4	no	—
48	C₄×Q₈×C₁₃	—	2	2	no	—
49	C₄×Q₈×C₁₃	—	2	2	no	—
50	C₄×Q₈×C₁₃	—	4	4	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	4	no	—
75	C₁₃×#107	—	4	2	no	—
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#102	—	2	2	no	—
79	C₁₃×#102	—	4	2	no	—
80	C₁₃×#102	Q₈	1	4	yes	complemented
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	2	no	—
85	#25056	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	D₈	1	4	yes	—
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	2	1	no	—
92	C₂×D₄×C₁₃	—	2	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₁₃	#41	1	2	yes	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₄⋊C₄	—	4	2	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	—	8	1	no	—
134	C₁₃×C₄⋊C₄	—	8	1	no	—
135	C₁₃×C₄⋊C₄	—	8	2	no	—
136	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	4	4	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	#41	1	2	yes	—
145	C₄²×C₁₃	#41	1	2	yes	—
146	#2538	C₂×C₁₃	1	1	yes	characteristic
147	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2093	C₂×C₁₃	1	2	yes	—
149	#2083	C₂×C₁₃	1	2	yes	complemented
150	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1925	C₂×C₁₃	1	2	yes	—
153	#1918	C₂×C₁₃	1	2	yes	complemented
154	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1802	C₂×C₁₃	1	1	yes	characteristic
156	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	8	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	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	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	8	4	no	—
193	C₂×C₄×C₁₃	#123	1	2	yes	—
194	C₂×C₄×C₁₃	#123	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
196	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₁₃	#137	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	4	2	no	—
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂×C₄×Q₈	—	2	1	no	—
209	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#107	C₂²×C₁₃	1	2	yes	—
212	C₂×#107	C₂²×C₁₃	1	2	yes	—
213	C₂×#107	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#396	—	2	2	no	—
220	#390	C₂²×C₁₃	1	2	yes	—
221	#389	—	2	1	no	—
222	#389	—	2	2	no	—
223	#389	C₂²×C₁₃	1	2	yes	—
224	#384	C₂²×C₁₃	1	1	yes	characteristic
225	#384	C₂²×C₁₃	1	2	yes	—
226	#384	C₂²×C₁₃	1	1	yes	characteristic
227	#380	—	2	1	no	—
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	1	yes	characteristic
232	#340	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#336	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	8	1	no	—
240	C₂²×C₁₃	—	8	1	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
244	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
245	C₂²×C₁₃	#550	1	1	yes	characteristic
246	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
248	C₂²×C₁₃	#576	1	1	yes	characteristic
249	C₂²×C₁₃	#578	1	1	yes	characteristic
250	C₄×C₁₃	—	2	4	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	8	1	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	#480	1	4	yes	—
259	C₄×C₁₃	#533	1	1	yes	characteristic
260	C₄×C₁₃	#542	1	1	yes	characteristic
261	C₄×C₁₃	#552	1	1	yes	characteristic
262	C₄×C₁₃	#554	1	1	yes	characteristic
263	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
264	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²⋊Q₈	—	4	4	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	4	4	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	#107	—	2	4	no	—
297	#107	—	4	2	no	—
298	#107	—	4	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	4	2	no	—
302	#102	Q₈×C₁₃	1	4	yes	complemented
303	C₄×C₈	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	2	no	—
307	C₂×C₁₃	—	8	2	no	—
308	C₂×C₁₃	#2423	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
310	C₂×C₁₃	#3098	1	1	yes	characteristic
311	C₂×C₁₃	Q₈×D₈	1	1	yes	characteristic
312	C₂×C₁₃	#3385	1	1	yes	characteristic
313	C₂×C₁₃	#3391	1	1	yes	characteristic
314	C₂×C₁₃	#3398	1	1	yes	characteristic
315	C₂⁴	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	C₁₃×D₈	1	4	yes	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
346	C₂×C₈	C₁₃×#41	1	2	yes	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	8	1	no	—
363	C₄⋊C₄	—	8	1	no	—
364	C₄⋊C₄	—	8	2	no	—
365	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	4	4	no	—
372	C₄²	—	4	2	no	—
373	C₄²	C₁₃×#41	1	2	yes	—
374	C₄²	C₁₃×#41	1	2	yes	—
375	C₁₃	#25056	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	8	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	8	4	no	—
412	C₂×C₄	C₁₃×#123	1	2	yes	—
413	C₂×C₄	C₁₃×#123	1	2	yes	—
414	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
415	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
416	C₂×C₄	C₁₃×#137	1	2	yes	—
417	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
434	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
435	C₂²	C₁₃×#550	1	1	yes	characteristic
436	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
437	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
438	C₂²	C₁₃×#576	1	1	yes	characteristic
439	C₂²	C₁₃×#578	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	C₁₃×#480	1	4	yes	—
449	C₄	C₁₃×#533	1	1	yes	characteristic
450	C₄	C₁₃×#542	1	1	yes	characteristic
451	C₄	C₁₃×#552	1	1	yes	characteristic
452	C₄	C₁₃×#554	1	1	yes	characteristic
453	C₂	—	8	2	no	—
454	C₂	C₁₃×#2423	1	1	yes	characteristic
455	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
456	C₂	C₁₃×#3098	1	1	yes	characteristic
457	C₂	Q₈×C₁₃×D₈	1	1	yes	characteristic
458	C₂	C₁₃×#3385	1	1	yes	characteristic
459	C₂	C₁₃×#3391	1	1	yes	characteristic
460	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
4. C₁₃×#2083	C₂	semidirect
5. C₁₃×#1984	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
8. C₁₃×#1918	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
80. C₁₃×#102	Q₈	semidirect
85. #25056	C₁₃	direct (N × H)
147. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
149. #2083	C₂×C₁₃	semidirect
150. #1984	C₂×C₁₃	semidirect
151. #1947	C₂×C₁₃	semidirect
153. #1918	C₂×C₁₃	semidirect
154. #1845	C₂×C₁₃	semidirect
302. #102	Q₈×C₁₃	semidirect
375. C₁₃	#25056	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2538	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2093	2
C₁₃×#2083	2
C₁₃×#1984	2
C₁₃×#1947	2
C₁₃×#1925	2
C₁₃×#1918	2
C₁₃×#1845	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#25056	13

Subgroups — C13×#25056 #15711395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25056 #15711395