Subgroups — C₁₃×#26252 #15712591

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2447	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#495	—	2	4	no	—
18	C₄×C₁₃×D₈	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#397	—	2	2	no	—
30	C₁₃×#397	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#385	—	2	2	no	—
36	C₁₃×#381	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	—	2	2	no	—
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	—	2	4	no	—
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	4	2	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	D₄	1	4	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#124	—	2	4	no	—
58	C₁₃×#124	—	4	2	no	—
59	C₄×D₄×C₁₃	—	2	4	no	—
60	C₄×D₄×C₁₃	—	4	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×#103	—	4	2	no	—
78	C₁₃×#103	—	4	2	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	4	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₄×C₈×C₁₃	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	#26252	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	8	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×Q₁₆	—	4	4	no	—
119	C₁₃×SD₁₆	—	4	8	no	—
120	C₁₃×D₈	—	2	8	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₃	#41	1	2	yes	—
131	C₂×C₈×C₁₃	#41	1	2	yes	—
132	C₂×C₈×C₁₃	#41	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	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	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	—	4	4	no	—
141	C₁₃×C₂²⋊C₄	—	4	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₂×#495	C₂×C₁₃	1	1	yes	characteristic
152	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
153	#2447	C₂×C₁₃	1	2	yes	complemented
154	#2055	C₂×C₁₃	1	2	yes	complemented
155	#2042	C₂×C₁₃	1	2	yes	complemented
156	#1970	C₂×C₁₃	1	1	yes	characteristic
157	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1877	C₂×C₁₃	1	2	yes	complemented
161	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	4	2	no	—
171	Q₈×C₁₃	—	4	2	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	2	4	no	—
175	D₄×C₁₃	—	2	4	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	8	8	no	—
204	C₂×C₄×C₁₃	#135	1	2	yes	—
205	C₂×C₄×C₁₃	#135	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	#123	1	4	yes	—
216	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
218	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#124	C₂²×C₁₃	1	2	yes	—
220	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
221	#495	—	2	4	no	—
222	C₄×D₈	—	2	4	no	—
223	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#103	C₂²×C₁₃	1	2	yes	—
227	C₂×#103	C₂²×C₁₃	1	2	yes	—
228	C₂×#102	C₂²×C₁₃	1	2	yes	—
229	C₂×#102	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
233	#397	—	2	2	no	—
234	#397	—	2	2	no	—
235	#391	C₂²×C₁₃	1	2	yes	—
236	#391	C₂²×C₁₃	1	2	yes	—
237	#390	C₂²×C₁₃	1	2	yes	—
238	#389	C₂²×C₁₃	1	2	yes	—
239	#385	—	2	2	no	—
240	#381	—	2	2	no	—
241	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	#340	C₂²×C₁₃	1	2	yes	—
243	#336	C₂²×C₁₃	1	1	yes	characteristic
244	#336	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	#532	1	1	yes	characteristic
253	C₂²×C₁₃	D₄²	1	1	yes	characteristic
254	C₂²×C₁₃	#550	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
257	C₂²×C₁₃	#576	1	1	yes	characteristic
258	C₂²×C₁₃	#578	1	1	yes	characteristic
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	4	1	no	—
262	C₄×C₁₃	—	4	1	no	—
263	C₄×C₁₃	—	4	1	no	—
264	C₄×C₁₃	—	4	1	no	—
265	C₄×C₁₃	—	8	2	no	—
266	C₄×C₁₃	—	8	2	no	—
267	C₄×C₁₃	—	8	2	no	—
268	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
269	C₄×C₁₃	#540	1	1	yes	characteristic
270	C₄×C₁₃	#546	1	1	yes	characteristic
271	C₄×C₁₃	#559	1	1	yes	characteristic
272	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
274	C₂³×C₄	—	2	2	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	2	4	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂×SD₁₆	—	4	2	no	—
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	D₄×C₁₃	1	4	yes	—
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	#124	—	2	4	no	—
289	#124	—	4	2	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	4	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	#107	—	2	2	no	—
306	#107	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#103	—	4	2	no	—
309	#103	—	4	2	no	—
310	#102	—	2	4	no	—
311	#102	—	4	2	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	D₄×C₁₃	1	1	yes	characteristic
321	#95	D₄×C₁₃	1	1	yes	characteristic
322	C₂×C₁₃	—	8	4	no	—
323	C₂×C₁₃	#2445	1	1	yes	characteristic
324	C₂×C₁₃	#3168	1	1	yes	characteristic
325	C₂×C₁₃	#3175	1	1	yes	characteristic
326	C₂×C₁₃	#3280	1	1	yes	characteristic
327	C₂×C₁₃	#3283	1	1	yes	characteristic
328	C₂×C₁₃	#3393	1	1	yes	characteristic
329	C₂×C₁₃	#3396	1	1	yes	characteristic
330	C₂⁴	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
356	Q₁₆	—	4	4	no	—
357	SD₁₆	—	4	8	no	—
358	D₈	—	2	8	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
368	C₂×C₈	C₁₃×#41	1	2	yes	—
369	C₂×C₈	C₁₃×#41	1	2	yes	—
370	C₂×C₈	C₁₃×#41	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	8	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₁₃	#26252	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	C₁₃×#135	1	2	yes	—
433	C₂×C₄	C₁₃×#135	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
437	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
438	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	1	no	—
443	C₈	C₁₃×#123	1	4	yes	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	C₁₃×#532	1	1	yes	characteristic
452	C₂²	D₄²×C₁₃	1	1	yes	characteristic
453	C₂²	C₁₃×#550	1	1	yes	characteristic
454	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
455	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
456	C₂²	C₁₃×#576	1	1	yes	characteristic
457	C₂²	C₁₃×#578	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	2	no	—
467	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
468	C₄	C₁₃×#540	1	1	yes	characteristic
469	C₄	C₁₃×#546	1	1	yes	characteristic
470	C₄	C₁₃×#559	1	1	yes	characteristic
471	C₂	—	8	4	no	—
472	C₂	C₁₃×#2445	1	1	yes	characteristic
473	C₂	C₁₃×#3168	1	1	yes	characteristic
474	C₂	C₁₃×#3175	1	1	yes	characteristic
475	C₂	C₁₃×#3280	1	1	yes	characteristic
476	C₂	C₁₃×#3283	1	1	yes	characteristic
477	C₂	C₁₃×#3393	1	1	yes	characteristic
478	C₂	C₁₃×#3396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
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×#2447	C₂	semidirect
4. C₁₃×#2055	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
7. C₁₃×#1969	C₂	semidirect
8. C₁₃×#1969	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1877	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
91. #26252	C₁₃	direct (N × H)
153. #2447	C₂×C₁₃	semidirect
154. #2055	C₂×C₁₃	semidirect
155. #2042	C₂×C₁₃	semidirect
157. #1969	C₂×C₁₃	semidirect
158. #1969	C₂×C₁₃	semidirect
159. #1942	C₂×C₁₃	semidirect
160. #1877	C₂×C₁₃	semidirect
161. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
389. C₁₃	#26252	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×#495	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2447	2
C₁₃×#2055	2
C₁₃×#2042	2
C₁₃×#1970	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1877	2
C₈×C₁₃×C₄⋊C₄	2
#26252	13

Subgroups — C13×#26252 #15712591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26252 #15712591