Subgroups — C₁₃×#24345 #15710684

Order 3328.

1020 conjugacy classes of subgroups.

The subgroup lattice has 466 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
2	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2058	C₂	1	2	yes	maximal
6	C₁₃×#2024	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1878	C₂	1	2	yes	maximal
10	C₁₃×#1865	C₂	1	2	yes	maximal
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	Q₈²×C₁₃	—	2	4	no	—
14	Q₈²×C₁₃	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#475	—	2	4	no	—
25	C₁₃×#441	—	2	4	no	—
26	C₂×C₁₃×#106	C₂²	1	2	yes	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#400	—	2	1	no	—
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#387	—	2	2	no	—
39	C₁₃×#382	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	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	Q₈	1	4	yes	complemented
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	—	2	16	no	—
57	C₁₃×C₄⋊Q₈	—	2	8	no	—
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
62	C₄×Q₈×C₁₃	—	2	8	no	—
63	C₄×Q₈×C₁₃	—	2	4	no	—
64	C₄×Q₈×C₁₃	—	2	4	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	D₄	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#106	—	2	2	no	—
89	C₁₃×#106	—	2	4	no	—
90	C₁₃×C₄⋊C₈	—	2	2	no	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	#24345	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂×Q₈×C₁₃	—	2	8	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	4	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	8	2	no	—
115	C₂×Q₈×C₁₃	—	8	4	no	—
116	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
118	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
119	C₂×Q₈×C₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×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	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×Q₁₆	—	2	8	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
156	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃	—	2	8	no	—
158	C₄²×C₁₃	—	2	4	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	4	2	no	—
162	C₄²×C₁₃	C₂×D₄	1	2	yes	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic
165	C₂×#475	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#441	C₂×C₁₃	1	1	yes	characteristic
167	#2581	C₂×C₁₃	1	1	yes	characteristic
168	#2058	C₂×C₁₃	1	2	yes	—
169	#2024	C₂×C₁₃	1	2	yes	—
170	#1993	C₂×C₁₃	1	1	yes	characteristic
171	#1985	C₂×C₁₃	1	1	yes	characteristic
172	#1878	C₂×C₁₃	1	2	yes	—
173	#1865	C₂×C₁₃	1	2	yes	—
174	#1805	C₂×C₁₃	1	1	yes	characteristic
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	8	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	2	2	no	—
180	Q₈×C₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	4	1	no	—
183	Q₈×C₁₃	—	4	1	no	—
184	Q₈×C₁₃	—	8	4	no	—
185	Q₈×C₁₃	—	8	8	no	—
186	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	#120	1	2	yes	—
209	C₂×C₄×C₁₃	#120	1	2	yes	—
210	C₂×C₄×C₁₃	#137	1	4	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
216	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
217	C₈×C₁₃	—	2	2	no	—
218	C₈×C₁₃	—	4	1	no	—
219	C₈×C₁₃	—	4	2	no	—
220	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
221	Q₈²	—	2	4	no	—
222	Q₈²	—	2	4	no	—
223	C₂×C₄⋊Q₈	—	2	2	no	—
224	C₂×C₄⋊Q₈	—	2	1	no	—
225	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄×Q₈	—	2	1	no	—
228	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
232	#475	—	2	4	no	—
233	#441	—	2	4	no	—
234	C₂×#106	C₂²×C₁₃	1	2	yes	—
235	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#103	C₂²×C₁₃	1	2	yes	—
238	C₂×#103	C₂²×C₁₃	1	2	yes	—
239	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
242	#400	—	2	1	no	—
243	#395	—	2	1	no	—
244	#391	C₂²×C₁₃	1	2	yes	—
245	#389	C₂²×C₁₃	1	2	yes	—
246	#387	—	2	2	no	—
247	#382	C₂²×C₁₃	1	1	yes	characteristic
248	#340	C₂²×C₁₃	1	2	yes	—
249	#340	C₂²×C₁₃	1	2	yes	—
250	#340	C₂²×C₁₃	1	2	yes	—
251	#336	C₂²×C₁₃	1	2	yes	—
252	#336	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₁₃	#548	1	1	yes	characteristic
255	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
256	C₂²×C₁₃	C₂×#137	1	2	yes	—
257	C₂²×C₁₃	#577	1	2	yes	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	4	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	8	2	no	—
267	C₄×C₁₃	—	8	1	no	—
268	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
269	C₄×C₁₃	#536	1	1	yes	characteristic
270	C₄×C₁₃	#548	1	1	yes	characteristic
271	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
275	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	Q₈×C₁₃	1	4	yes	complemented
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	16	no	—
284	C₄⋊Q₈	—	2	8	no	—
285	C₄⋊Q₈	—	2	4	no	—
286	C₄⋊Q₈	—	2	4	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
289	C₄×Q₈	—	2	8	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	D₄×C₁₃	1	4	yes	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
305	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	#106	—	2	2	no	—
316	#106	—	2	4	no	—
317	C₄⋊C₈	—	2	2	no	—
318	#103	—	2	2	no	—
319	#103	—	2	4	no	—
320	#103	—	2	2	no	—
321	#103	—	2	4	no	—
322	#97	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂×C₁₃	#2409	1	1	yes	characteristic
329	C₂×C₁₃	#3004	1	1	yes	characteristic
330	C₂×C₁₃	#3009	1	1	yes	characteristic
331	C₂×C₁₃	#3369	1	2	yes	—
332	C₂×C₁₃	#3387	1	2	yes	—
333	C₂×Q₈	—	2	8	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	8	2	no	—
346	C₂×Q₈	—	8	4	no	—
347	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
348	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
349	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
350	C₂×Q₈	C₁₃×#41	1	2	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
362	Q₁₆	—	2	8	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
387	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₄²	—	2	8	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	2	no	—
393	C₄²	C₂×D₄×C₁₃	1	2	yes	—
394	C₄²	C₂×D₄×C₁₃	1	2	yes	—
395	C₁₃	#24345	1	1	yes	characteristic, direct product factor, Sylow
396	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
397	Q₈	—	2	8	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	8	4	no	—
406	Q₈	—	8	8	no	—
407	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	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	C₁₃×#120	1	2	yes	—
430	C₂×C₄	C₁₃×#120	1	2	yes	—
431	C₂×C₄	C₁₃×#137	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
436	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
442	C₂²	C₁₃×#548	1	1	yes	characteristic
443	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
444	C₂²	C₂×C₁₃×#137	1	2	yes	—
445	C₂²	C₁₃×#577	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
457	C₄	C₁₃×#536	1	1	yes	characteristic
458	C₄	C₁₃×#548	1	1	yes	characteristic
459	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
460	C₂	C₁₃×#2409	1	1	yes	characteristic
461	C₂	C₁₃×#3004	1	1	yes	characteristic
462	C₂	C₁₃×#3009	1	1	yes	characteristic
463	C₂	C₁₃×#3369	1	2	yes	—
464	C₂	C₁₃×#3387	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
52. C₂×C₁₃×Q₁₆	Q₈	semidirect
101. #24345	C₁₃	direct (N × H)
279. C₂×Q₁₆	Q₈×C₁₃	semidirect
395. C₁₃	#24345	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×#475	2
C₂×C₁₃×#441	2
C₁₃×#2581	2
C₁₃×#2058	2
C₁₃×#2024	2
C₁₃×#1993	2
C₁₃×#1985	2
C₁₃×#1878	2
C₁₃×#1865	2
C₁₃×#1805	2
#24345	13

Subgroups — C13×#24345 #15710684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24345 #15710684