Subgroups — C₁₃×#25942 #15712281

Order 3328.

1054 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×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	2	yes	maximal
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1880	C₂	1	2	yes	maximal
10	C₁₃×#1878	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	Q₈²×C₁₃	—	2	4	no	—
15	Q₈²×C₁₃	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
17	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#489	—	2	4	no	—
26	C₁₃×#464	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#397	—	2	1	no	—
35	C₁₃×#393	—	2	1	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#388	—	2	2	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	4	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	4	no	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	—	2	16	no	—
59	C₁₃×C₄⋊Q₈	—	2	8	no	—
60	C₁₃×C₄⋊Q₈	—	2	4	no	—
61	C₁₃×C₄⋊Q₈	—	2	4	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
64	C₁₃×#124	—	2	2	no	—
65	C₁₃×#124	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	8	no	—
67	C₄×Q₈×C₁₃	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	2	4	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	D₄	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₄²×C₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#97	—	2	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	#25942	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	8	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	8	1	no	—
114	C₂×Q₈×C₁₃	—	8	1	no	—
115	C₂×Q₈×C₁₃	—	8	2	no	—
116	C₂×Q₈×C₁₃	—	8	2	no	—
117	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×Q₈×C₁₃	#41	1	4	yes	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₁₃×Q₁₆	—	4	4	no	—
134	C₁₃×SD₁₆	—	4	4	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	8	2	no	—
158	C₄²×C₁₃	—	2	8	no	—
159	C₄²×C₁₃	—	2	4	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	8	1	no	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂×#489	C₂×C₁₃	1	1	yes	characteristic
167	C₂×#464	C₂×C₁₃	1	1	yes	characteristic
168	#2592	C₂×C₁₃	1	1	yes	characteristic
169	#2024	C₂×C₁₃	1	2	yes	complemented
170	#2023	C₂×C₁₃	1	2	yes	—
171	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1880	C₂×C₁₃	1	2	yes	—
174	#1878	C₂×C₁₃	1	2	yes	complemented
175	#1763	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	8	no	—
183	Q₈×C₁₃	—	2	2	no	—
184	Q₈×C₁₃	—	2	4	no	—
185	Q₈×C₁₃	—	4	1	no	—
186	Q₈×C₁₃	—	4	1	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	Q₈×C₁₃	—	8	4	no	—
189	Q₈×C₁₃	—	8	8	no	—
190	Q₈×C₁₃	#124	1	4	yes	—
191	D₄×C₁₃	—	4	1	no	—
192	D₄×C₁₃	—	4	1	no	—
193	D₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	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	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	#120	1	2	yes	—
216	C₂×C₄×C₁₃	#120	1	2	yes	—
217	C₂×C₄×C₁₃	#137	1	4	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
221	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
222	C₈×C₁₃	—	4	1	no	—
223	C₈×C₁₃	—	4	1	no	—
224	C₈×C₁₃	—	4	2	no	—
225	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
227	Q₈²	—	2	4	no	—
228	Q₈²	—	2	4	no	—
229	C₂×C₄⋊Q₈	—	2	2	no	—
230	C₂×C₄⋊Q₈	—	2	1	no	—
231	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄×Q₈	—	2	1	no	—
235	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
238	#489	—	2	4	no	—
239	#464	—	2	4	no	—
240	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#103	C₂²×C₁₃	1	2	yes	—
242	C₂×#103	C₂²×C₁₃	1	2	yes	—
243	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#102	C₂²×C₁₃	1	2	yes	—
245	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
247	#397	—	2	1	no	—
248	#393	—	2	1	no	—
249	#391	C₂²×C₁₃	1	2	yes	—
250	#390	C₂²×C₁₃	1	2	yes	—
251	#388	—	2	2	no	—
252	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	#340	C₂²×C₁₃	1	2	yes	—
254	#340	C₂²×C₁₃	1	2	yes	—
255	#340	C₂²×C₁₃	1	2	yes	—
256	#336	C₂²×C₁₃	1	2	yes	—
257	#336	C₂²×C₁₃	1	2	yes	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	—	8	1	no	—
261	C₂²×C₁₃	—	8	1	no	—
262	C₂²×C₁₃	—	8	1	no	—
263	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
264	C₂²×C₁₃	#548	1	2	yes	—
265	C₂²×C₁₃	C₂×#137	1	2	yes	—
266	C₂²×C₁₃	#576	1	1	yes	characteristic
267	C₂²×C₁₃	#577	1	1	yes	characteristic
268	C₄×C₁₃	—	2	4	no	—
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	4	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	8	2	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
278	C₄×C₁₃	#536	1	1	yes	characteristic
279	C₄×C₁₃	#548	1	2	yes	—
280	C₂²×Q₈	—	2	2	no	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
293	C₄⋊Q₈	—	2	16	no	—
294	C₄⋊Q₈	—	2	8	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	—	2	4	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
299	#124	—	2	2	no	—
300	#124	—	2	2	no	—
301	C₄×Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	4	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	D₄×C₁₃	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
313	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
326	C₄⋊C₈	—	2	2	no	—
327	#103	—	2	4	no	—
328	#103	—	2	2	no	—
329	#103	—	2	4	no	—
330	#102	—	2	2	no	—
331	#102	—	2	4	no	—
332	#97	—	2	2	no	—
333	#95	—	2	1	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂×C₁₃	—	16	1	no	—
337	C₂×C₁₃	#2436	1	1	yes	characteristic
338	C₂×C₁₃	#3004	1	1	yes	characteristic
339	C₂×C₁₃	#3012	1	1	yes	characteristic
340	C₂×C₁₃	#3369	1	2	yes	—
341	C₂×C₁₃	#3375	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	8	1	no	—
354	C₂×Q₈	—	8	1	no	—
355	C₂×Q₈	—	8	2	no	—
356	C₂×Q₈	—	8	2	no	—
357	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
358	C₂×Q₈	C₁₃×#41	1	4	yes	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
373	Q₁₆	—	4	4	no	—
374	SD₁₆	—	4	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
393	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	—	8	2	no	—
398	C₄²	—	2	8	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	8	1	no	—
403	C₄²	C₂×D₄×C₁₃	1	2	yes	—
404	C₄²	C₂×D₄×C₁₃	1	2	yes	—
405	C₁₃	#25942	1	1	yes	characteristic, direct product factor, Sylow
406	C₂³	—	4	1	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	Q₈	—	2	8	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	4	1	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	8	4	no	—
419	Q₈	—	8	8	no	—
420	Q₈	C₁₃×#124	1	4	yes	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	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	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	C₁₃×#120	1	2	yes	—
446	C₂×C₄	C₁₃×#120	1	2	yes	—
447	C₂×C₄	C₁₃×#137	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
451	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
461	C₂²	C₁₃×#548	1	2	yes	—
462	C₂²	C₂×C₁₃×#137	1	2	yes	—
463	C₂²	C₁₃×#576	1	1	yes	characteristic
464	C₂²	C₁₃×#577	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
475	C₄	C₁₃×#536	1	1	yes	characteristic
476	C₄	C₁₃×#548	1	2	yes	—
477	C₂	—	16	1	no	—
478	C₂	C₁₃×#2436	1	1	yes	characteristic
479	C₂	C₁₃×#3004	1	1	yes	characteristic
480	C₂	C₁₃×#3012	1	1	yes	characteristic
481	C₂	C₁₃×#3369	1	2	yes	—
482	C₂	C₁₃×#3375	1	2	yes	—

	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
1. C₂×Q₈²×C₁₃	C₂	semidirect
5. C₁₃×#2024	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1878	C₂	semidirect
11. C₁₃×#1763	C₂	semidirect
101. #25942	C₁₃	direct (N × H)
165. C₂×Q₈²	C₂×C₁₃	semidirect
169. #2024	C₂×C₁₃	semidirect
171. #1988	C₂×C₁₃	semidirect
172. #1985	C₂×C₁₃	semidirect
174. #1878	C₂×C₁₃	semidirect
175. #1763	C₂×C₁₃	semidirect
405. C₁₃	#25942	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×Q₈²×C₁₃	2
C₂×C₁₃×#489	2
C₂×C₁₃×#464	2
C₁₃×#2592	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1988	2
C₁₃×#1985	2
C₁₃×#1880	2
C₁₃×#1878	2
C₁₃×#1763	2
#25942	13

Subgroups — C13×#25942 #15712281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25942 #15712281