Subgroups — C₁₃×#36635 #15722974

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2864	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2863	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2857	C₂	1	2	yes	maximal
6	C₁₃×#2855	C₂	1	4	yes	maximal
7	C₁₃×#2851	C₂	1	2	yes	maximal
8	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal
11	C₁₃×#2295	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2283	C₂	1	2	yes	maximal
13	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#125	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#391	C₂²	1	4	yes	—
24	C₁₃×#391	C₂²	1	4	yes	—
25	C₁₃×#391	C₂²	1	4	yes	—
26	C₁₃×#391	C₂²	1	4	yes	—
27	C₁₃×#389	C₂²	1	4	yes	—
28	C₁₃×#389	C₂²	1	4	yes	—
29	C₁₃×#389	C₂²	1	4	yes	—
30	C₁₃×#389	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#389	C₂²	1	4	yes	—
33	C₁₃×#387	C₂²	1	8	yes	—
34	C₁₃×#387	C₂²	1	8	yes	—
35	C₁₃×#387	C₂²	1	8	yes	—
36	C₁₃×#387	C₂²	1	8	yes	—
37	C₁₃×#385	C₂²	1	8	yes	—
38	C₁₃×#384	C₂²	1	2	yes	—
39	C₁₃×#383	C₂²	1	4	yes	—
40	C₁₃×#382	C₂²	1	2	yes	—
41	C₁₃×#382	C₂²	1	2	yes	—
42	C₁₃×#382	C₂²	1	2	yes	—
43	C₁₃×#381	C₂²	1	4	yes	—
44	C₁₃×#380	C₂²	1	4	yes	—
45	C₁₃×#380	C₂²	1	4	yes	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
50	C₁₃×#376	C₂²	1	4	yes	—
51	C₄³×C₁₃	C₂²	1	2	yes	—
52	C₄³×C₁₃	C₂²	1	1	yes	characteristic
53	C₄³×C₁₃	C₂²	1	1	yes	characteristic
54	C₄³×C₁₃	C₂²	1	1	yes	characteristic
55	C₄³×C₁₃	C₂²	1	2	yes	—
56	C₄³×C₁₃	C₂²	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	—	2	8	no	—
64	C₁₃×#125	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	16	no	—
66	C₄×Q₈×C₁₃	—	2	16	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₄²×C₁₃	—	2	8	no	—
77	C₂×C₄²×C₁₃	—	2	8	no	—
78	C₂×C₄²×C₁₃	—	2	4	no	—
79	C₂×C₄²×C₁₃	—	2	4	no	—
80	C₂×C₄²×C₁₃	Q₈	1	8	yes	complemented
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	C₁₃×#95	C₂³	1	8	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	#36635	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂×Q₈×C₁₃	—	2	8	no	—
112	C₂×Q₈×C₁₃	—	2	8	no	—
113	C₂×Q₈×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₁₃	#41	1	8	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×C₄⋊C₄	—	2	8	no	—
140	C₁₃×C₄⋊C₄	—	2	16	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	16	no	—
143	C₁₃×C₄⋊C₄	—	2	16	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₂²⋊C₄	—	2	16	no	—
148	C₄²×C₁₃	—	2	4	no	—
149	C₄²×C₁₃	—	2	4	no	—
150	C₄²×C₁₃	—	2	4	no	—
151	C₄²×C₁₃	—	2	4	no	—
152	C₄²×C₁₃	—	2	4	no	—
153	C₄²×C₁₃	—	2	4	no	—
154	C₄²×C₁₃	—	2	4	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	—	2	4	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	16	no	—
160	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
161	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
162	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
163	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
164	C₄²×C₁₃	#41	1	8	yes	—
165	C₄²×C₁₃	#41	1	4	yes	—
166	C₄²×C₁₃	#41	1	4	yes	—
167	#2864	C₂×C₁₃	1	2	yes	complemented
168	#2863	C₂×C₁₃	1	4	yes	complemented
169	#2862	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2857	C₂×C₁₃	1	2	yes	—
172	#2855	C₂×C₁₃	1	4	yes	—
173	#2851	C₂×C₁₃	1	2	yes	—
174	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
175	C₄×#125	C₂×C₁₃	1	2	yes	complemented
176	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	—
177	#2295	C₂×C₁₃	1	4	yes	complemented
178	#2283	C₂×C₁₃	1	2	yes	—
179	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
184	C₂³×C₁₃	C₂×#41	1	4	yes	—
185	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
186	Q₈×C₁₃	—	4	16	no	—
187	C₂×C₄×C₁₃	—	2	16	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	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	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	16	no	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	2	8	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	8	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
213	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
215	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
216	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
217	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
218	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
219	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
220	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
221	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
222	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
225	C₂×#125	C₂²×C₁₃	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
227	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
228	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
229	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
232	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
233	#391	C₂²×C₁₃	1	4	yes	—
234	#391	C₂²×C₁₃	1	4	yes	—
235	#391	C₂²×C₁₃	1	4	yes	—
236	#391	C₂²×C₁₃	1	4	yes	—
237	#389	C₂²×C₁₃	1	4	yes	—
238	#389	C₂²×C₁₃	1	4	yes	—
239	#389	C₂²×C₁₃	1	4	yes	—
240	#389	C₂²×C₁₃	1	4	yes	—
241	#389	C₂²×C₁₃	1	4	yes	—
242	#389	C₂²×C₁₃	1	4	yes	—
243	#387	C₂²×C₁₃	1	8	yes	—
244	#387	C₂²×C₁₃	1	8	yes	—
245	#387	C₂²×C₁₃	1	8	yes	—
246	#387	C₂²×C₁₃	1	8	yes	—
247	#385	C₂²×C₁₃	1	8	yes	—
248	#384	C₂²×C₁₃	1	2	yes	—
249	#383	C₂²×C₁₃	1	4	yes	—
250	#382	C₂²×C₁₃	1	2	yes	—
251	#382	C₂²×C₁₃	1	2	yes	—
252	#382	C₂²×C₁₃	1	2	yes	—
253	#381	C₂²×C₁₃	1	4	yes	—
254	#380	C₂²×C₁₃	1	4	yes	—
255	#380	C₂²×C₁₃	1	4	yes	—
256	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
257	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
258	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
260	#376	C₂²×C₁₃	1	4	yes	—
261	C₄³	C₂²×C₁₃	1	1	yes	characteristic
262	C₄³	C₂²×C₁₃	1	1	yes	characteristic
263	C₄³	C₂²×C₁₃	1	1	yes	characteristic
264	C₄³	C₂²×C₁₃	1	2	yes	—
265	C₄³	C₂²×C₁₃	1	1	yes	characteristic
266	C₄³	C₂²×C₁₃	1	2	yes	—
267	C₂²×C₁₃	—	2	4	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	#533	1	4	yes	—
272	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
273	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
274	C₂²×C₁₃	C₂²×#41	1	2	yes	—
275	C₂²×C₁₃	C₂²×#41	1	2	yes	—
276	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
277	C₄×C₁₃	—	2	4	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	4	no	—
283	C₄×C₁₃	—	2	4	no	—
284	C₄×C₁₃	—	4	8	no	—
285	C₄×C₁₃	—	4	8	no	—
286	C₄×C₁₃	#529	1	8	yes	—
287	C₄×C₁₃	#533	1	4	yes	—
288	C₄×C₁₃	#533	1	4	yes	—
289	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
290	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
295	C₄⋊Q₈	—	2	8	no	—
296	#125	—	2	8	no	—
297	C₂²⋊Q₈	—	2	16	no	—
298	C₄×Q₈	—	2	16	no	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
308	C₂×C₄²	—	2	8	no	—
309	C₂×C₄²	—	2	8	no	—
310	C₂×C₄²	—	2	4	no	—
311	C₂×C₄²	—	2	4	no	—
312	C₂×C₄²	Q₈×C₁₃	1	8	yes	complemented
313	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
314	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
317	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
319	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
322	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
324	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	#95	C₂³×C₁₃	1	8	yes	—
333	#95	C₂³×C₁₃	1	4	yes	—
334	#95	C₂³×C₁₃	1	4	yes	—
335	#95	C₂³×C₁₃	1	4	yes	—
336	#95	C₂³×C₁₃	1	4	yes	—
337	#95	C₂³×C₁₃	1	8	yes	—
338	#95	C₂³×C₁₃	1	8	yes	—
339	#95	C₂³×C₁₃	1	8	yes	—
340	#95	C₂³×C₁₃	1	8	yes	—
341	C₂×C₁₃	—	2	4	no	—
342	C₂×C₁₃	C₂×#529	1	2	yes	—
343	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
344	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
346	C₂×C₁₃	#3444	1	2	yes	—
347	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	2	8	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
361	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
362	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
363	C₂²×C₄	C₁₃×#41	1	8	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
371	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	16	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	16	no	—
380	C₄⋊C₄	—	2	16	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	16	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	4	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	16	no	—
397	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
398	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
399	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
400	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
401	C₄²	C₁₃×#41	1	8	yes	—
402	C₄²	C₁₃×#41	1	4	yes	—
403	C₄²	C₁₃×#41	1	4	yes	—
404	C₁₃	#36635	1	1	yes	characteristic, direct product factor, Sylow
405	C₂³	—	2	1	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
409	C₂³	C₂×C₁₃×#41	1	4	yes	—
410	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
411	Q₈	—	4	16	no	—
412	C₂×C₄	—	2	16	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	16	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
435	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
436	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
437	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
438	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
439	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
440	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
441	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
442	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
443	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
444	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
445	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
446	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
447	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
448	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	C₁₃×#533	1	4	yes	—
454	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
455	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
456	C₂²	C₂²×C₁₃×#41	1	2	yes	—
457	C₂²	C₂²×C₁₃×#41	1	2	yes	—
458	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	4	no	—
466	C₄	—	4	8	no	—
467	C₄	—	4	8	no	—
468	C₄	C₁₃×#529	1	8	yes	—
469	C₄	C₁₃×#533	1	4	yes	—
470	C₄	C₁₃×#533	1	4	yes	—
471	C₂	—	2	4	no	—
472	C₂	C₂×C₁₃×#529	1	2	yes	—
473	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
474	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
475	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
476	C₂	C₁₃×#3444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2864	C₂	semidirect
2. C₁₃×#2863	C₂	semidirect
3. C₁₃×#2862	C₂	semidirect
4. C₁₃×#2859	C₂	semidirect
8. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
9. C₄×C₁₃×#125	C₂	semidirect
11. C₁₃×#2295	C₂	semidirect
80. C₂×C₄²×C₁₃	Q₈	semidirect
109. #36635	C₁₃	direct (N × H)
167. #2864	C₂×C₁₃	semidirect
168. #2863	C₂×C₁₃	semidirect
169. #2862	C₂×C₁₃	semidirect
170. #2859	C₂×C₁₃	semidirect
174. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
175. C₄×#125	C₂×C₁₃	semidirect
177. #2295	C₂×C₁₃	semidirect
312. C₂×C₄²	Q₈×C₁₃	semidirect
404. C₁₃	#36635	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×#2864	2
C₁₃×#2863	2
C₁₃×#2862	2
C₁₃×#2859	2
C₁₃×#2857	2
C₁₃×#2855	2
C₁₃×#2851	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₁₃×#2283	2
C₂×C₄³×C₁₃	2
#36635	13

Subgroups — C13×#36635 #15722974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36635 #15722974