Subgroups — C₁₃×#61470 #15747809

Order 3328.

1812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3356	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3331	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3328	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3276	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3185	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3116	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3113	C₂	1	3	yes	maximal, complemented
14	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#137	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₃×#137	C₂²	1	3	yes	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#557	C₂²	1	1	yes	characteristic
21	C₁₃×#556	C₂²	1	3	yes	—
22	C₁₃×#554	—	2	3	no	—
23	C₁₃×#554	C₂²	1	3	yes	—
24	C₁₃×#552	—	2	3	no	—
25	D₄×Q₈×C₁₃	C₂²	1	3	yes	—
26	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#548	—	2	1	no	—
28	C₁₃×#547	C₂²	1	3	yes	—
29	C₁₃×#533	—	2	3	no	—
30	C₁₃×#533	C₂²	1	3	yes	—
31	C₁₃×#533	C₂²	1	3	yes	—
32	C₁₃×#529	—	2	3	no	—
33	C₄×C₁₃×#41	—	2	1	no	—
34	C₄×C₁₃×#41	C₂²	1	3	yes	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
37	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
38	C₁₃×#498	C₂²	1	3	yes	—
39	C₁₃×#494	C₂²	1	3	yes	—
40	C₁₃×#487	C₂²	1	3	yes	—
41	C₁₃×#487	C₂²	1	3	yes	—
42	C₁₃×#485	C₂²	1	6	yes	—
43	C₁₃×#483	C₂²	1	6	yes	—
44	C₁₃×#477	C₂²	1	3	yes	—
45	C₁₃×#476	C₂²	1	3	yes	—
46	C₁₃×#475	C₂²	1	3	yes	—
47	C₁₃×#475	C₂²	1	3	yes	—
48	C₁₃×#470	C₂²	1	6	yes	—
49	C₁₃×#470	C₂²	1	6	yes	—
50	C₁₃×#462	C₂²	1	3	yes	—
51	C₁₃×#462	C₂²	1	3	yes	—
52	C₁₃×#462	C₂²	1	3	yes	—
53	C₁₃×#461	C₂²	1	3	yes	—
54	C₁₃×#452	C₂²	1	6	yes	—
55	C₁₃×#451	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₁₃×#441	C₂²	1	3	yes	—
59	C₁₃×#441	C₂²	1	6	yes	—
60	C₁₃×#441	C₂²	1	3	yes	—
61	C₁₃×#440	C₂²	1	3	yes	—
62	C₁₃×#440	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
64	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
65	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
66	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
67	C₁₃×#436	C₂²	1	3	yes	—
68	C₁₃×#436	C₂²	1	3	yes	—
69	C₁₃×#432	C₂²	1	3	yes	—
70	C₁₃×#428	C₂²	1	3	yes	—
71	C₁₃×#419	C₂²	1	3	yes	—
72	C₁₃×#417	C₂²	1	3	yes	—
73	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
74	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂³	1	3	yes	—
76	C₂²×Q₈×C₁₃	—	2	1	no	—
77	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
78	C₁₃×#137	—	2	12	no	—
79	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
80	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
81	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
85	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
86	C₁₃×C₄⋊Q₈	—	2	3	no	—
87	C₁₃×C₄⋊Q₈	—	2	3	no	—
88	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₃×#126	—	2	6	no	—
93	C₁₃×#125	—	2	3	no	—
94	C₁₃×#125	—	2	3	no	—
95	C₁₃×#125	—	2	3	no	—
96	C₁₃×#125	—	2	3	no	—
97	C₁₃×#125	—	2	3	no	—
98	C₁₃×#124	—	2	3	no	—
99	C₁₃×#123	—	2	6	no	—
100	C₁₃×C₂²⋊Q₈	—	2	3	no	—
101	C₁₃×C₂²⋊Q₈	—	2	3	no	—
102	C₁₃×C₂²⋊Q₈	—	2	3	no	—
103	C₁₃×C₂²⋊Q₈	—	2	6	no	—
104	C₁₃×C₂²⋊Q₈	—	2	6	no	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
107	C₁₃×#121	—	2	3	no	—
108	C₄×Q₈×C₁₃	—	2	1	no	—
109	C₄×Q₈×C₁₃	—	2	1	no	—
110	C₄×Q₈×C₁₃	—	2	1	no	—
111	C₄×Q₈×C₁₃	—	2	3	no	—
112	C₄×Q₈×C₁₃	—	2	3	no	—
113	C₄×Q₈×C₁₃	—	2	3	no	—
114	C₄×Q₈×C₁₃	—	2	3	no	—
115	C₄×Q₈×C₁₃	—	2	3	no	—
116	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
118	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
120	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₁₃	—	2	3	no	—
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	D₄	1	3	yes	—
129	C₄×D₄×C₁₃	C₂³	1	3	yes	—
130	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₄×D₄×C₁₃	C₂³	1	3	yes	—
132	C₁₃×#117	—	2	3	no	—
133	C₁₃×#117	—	2	3	no	—
134	C₁₃×#117	—	2	3	no	—
135	C₁₃×#117	D₄	1	3	yes	—
136	C₁₃×#117	C₂³	1	3	yes	—
137	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
138	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
140	C₂×C₄²×C₁₃	—	2	3	no	—
141	C₂×C₄²×C₁₃	—	2	3	no	—
142	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
143	C₁₃×#107	C₂³	1	1	yes	characteristic
144	C₁₃×#107	C₂³	1	3	yes	—
145	C₁₃×#106	C₂³	1	3	yes	—
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×#106	C₂³	1	6	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×#103	C₂³	1	3	yes	—
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	1	yes	characteristic
153	C₁₃×#103	C₂³	1	3	yes	—
154	C₁₃×#103	C₂³	1	3	yes	—
155	C₁₃×#103	C₂³	1	3	yes	—
156	C₁₃×#103	C₂³	1	6	yes	—
157	C₁₃×#103	C₂³	1	6	yes	—
158	C₁₃×#102	C₂³	1	1	yes	characteristic
159	C₁₃×#102	C₂³	1	3	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
161	C₁₃×#97	C₂³	1	1	yes	characteristic
162	C₁₃×#97	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	#61470	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	2	6	no	—
168	C₁₃×#41	—	4	3	no	—
169	C₂×Q₈×C₁₃	—	2	3	no	—
170	C₂×Q₈×C₁₃	—	2	3	no	—
171	C₂×Q₈×C₁₃	—	2	3	no	—
172	C₂×Q₈×C₁₃	—	2	6	no	—
173	C₂×Q₈×C₁₃	—	4	3	no	—
174	C₂×Q₈×C₁₃	—	4	4	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×D₄×C₁₃	—	2	3	no	—
180	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	—	2	3	no	—
183	C₂²×C₄×C₁₃	—	2	3	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	3	no	—
186	C₂²×C₄×C₁₃	—	2	3	no	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
190	C₁₃×Q₁₆	—	2	6	no	—
191	C₁₃×Q₁₆	—	2	6	no	—
192	C₁₃×Q₁₆	—	4	6	no	—
193	C₁₃×SD₁₆	—	2	6	no	—
194	C₁₃×SD₁₆	#41	1	4	yes	complemented
195	C₁₃×M₁₆	—	2	6	no	—
196	C₁₃×M₁₆	—	4	3	no	—
197	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
199	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
200	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	3	no	—
203	C₁₃×C₄⋊C₄	—	2	6	no	—
204	C₁₃×C₄⋊C₄	—	2	3	no	—
205	C₁₃×C₄⋊C₄	—	2	3	no	—
206	C₁₃×C₄⋊C₄	—	2	3	no	—
207	C₁₃×C₄⋊C₄	—	2	3	no	—
208	C₁₃×C₄⋊C₄	—	2	3	no	—
209	C₁₃×C₄⋊C₄	—	2	3	no	—
210	C₁₃×C₄⋊C₄	—	2	3	no	—
211	C₁₃×C₄⋊C₄	—	2	3	no	—
212	C₁₃×C₄⋊C₄	—	2	3	no	—
213	C₁₃×C₄⋊C₄	—	2	3	no	—
214	C₁₃×C₄⋊C₄	—	2	3	no	—
215	C₁₃×C₄⋊C₄	—	2	6	no	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
218	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
219	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₄	—	2	6	no	—
223	C₁₃×C₂²⋊C₄	—	2	6	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	1	no	—
226	C₁₃×C₂²⋊C₄	—	2	3	no	—
227	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	2	3	no	—
230	C₄²×C₁₃	—	2	3	no	—
231	C₄²×C₁₃	—	2	3	no	—
232	C₄²×C₁₃	—	2	3	no	—
233	C₄²×C₁₃	—	2	3	no	—
234	C₄²×C₁₃	—	2	3	no	—
235	C₄²×C₁₃	C₂×D₄	1	3	yes	—
236	C₄²×C₁₃	C₂×D₄	1	3	yes	—
237	C₄²×C₁₃	C₂⁴	1	3	yes	—
238	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
239	#3482	C₂×C₁₃	1	1	yes	characteristic
240	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
242	Q₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3356	C₂×C₁₃	1	3	yes	complemented
246	#3331	C₂×C₁₃	1	3	yes	complemented
247	#3328	C₂×C₁₃	1	3	yes	complemented
248	#3276	C₂×C₁₃	1	3	yes	complemented
249	#3185	C₂×C₁₃	1	3	yes	complemented
250	#3116	C₂×C₁₃	1	3	yes	complemented
251	#3113	C₂×C₁₃	1	3	yes	complemented
252	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₄×#137	C₂×C₁₃	1	3	yes	complemented
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	2	3	no	—
258	Q₈×C₁₃	—	2	3	no	—
259	Q₈×C₁₃	—	2	3	no	—
260	Q₈×C₁₃	—	2	3	no	—
261	Q₈×C₁₃	—	4	6	no	—
262	Q₈×C₁₃	—	4	6	no	—
263	Q₈×C₁₃	—	8	3	no	—
264	Q₈×C₁₃	#137	1	4	yes	complemented
265	Q₈×C₁₃	C₂×#41	1	2	yes	—
266	D₄×C₁₃	—	2	6	no	—
267	D₄×C₁₃	—	2	1	no	—
268	D₄×C₁₃	—	4	6	no	—
269	D₄×C₁₃	C₂×#41	1	2	yes	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	6	no	—
272	C₂×C₄×C₁₃	—	2	3	no	—
273	C₂×C₄×C₁₃	—	2	3	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	3	no	—
277	C₂×C₄×C₁₃	—	2	3	no	—
278	C₂×C₄×C₁₃	—	2	3	no	—
279	C₂×C₄×C₁₃	—	2	3	no	—
280	C₂×C₄×C₁₃	—	4	3	no	—
281	C₂×C₄×C₁₃	—	4	6	no	—
282	C₂×C₄×C₁₃	—	4	6	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	6	no	—
285	C₂×C₄×C₁₃	—	8	3	no	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
291	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
292	C₈×C₁₃	—	2	3	no	—
293	C₈×C₁₃	—	2	1	no	—
294	C₈×C₁₃	—	2	3	no	—
295	C₈×C₁₃	C₂×#41	1	2	yes	—
296	C₂×#137	C₂²×C₁₃	1	3	yes	—
297	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
298	#557	—	2	1	no	—
299	#557	C₂²×C₁₃	1	1	yes	characteristic
300	#557	C₂²×C₁₃	1	1	yes	characteristic
301	#556	C₂²×C₁₃	1	3	yes	—
302	#554	—	2	3	no	—
303	#554	C₂²×C₁₃	1	3	yes	—
304	#552	—	2	3	no	—
305	D₄×Q₈	C₂²×C₁₃	1	3	yes	—
306	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	#548	—	2	1	no	—
308	#547	C₂²×C₁₃	1	3	yes	—
309	#533	—	2	3	no	—
310	#533	C₂²×C₁₃	1	3	yes	—
311	#533	C₂²×C₁₃	1	3	yes	—
312	#529	—	2	3	no	—
313	C₄×#41	—	2	1	no	—
314	C₄×#41	C₂²×C₁₃	1	3	yes	—
315	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄×Q₈	—	2	1	no	—
317	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
318	#498	C₂²×C₁₃	1	3	yes	—
319	#494	C₂²×C₁₃	1	3	yes	—
320	#487	C₂²×C₁₃	1	3	yes	—
321	#487	C₂²×C₁₃	1	3	yes	—
322	#485	C₂²×C₁₃	1	6	yes	—
323	#483	C₂²×C₁₃	1	6	yes	—
324	#477	C₂²×C₁₃	1	3	yes	—
325	#476	C₂²×C₁₃	1	3	yes	—
326	#475	C₂²×C₁₃	1	3	yes	—
327	#475	C₂²×C₁₃	1	3	yes	—
328	#470	C₂²×C₁₃	1	6	yes	—
329	#470	C₂²×C₁₃	1	6	yes	—
330	#462	C₂²×C₁₃	1	3	yes	—
331	#462	C₂²×C₁₃	1	3	yes	—
332	#462	C₂²×C₁₃	1	3	yes	—
333	#461	C₂²×C₁₃	1	3	yes	—
334	#452	C₂²×C₁₃	1	6	yes	—
335	#451	C₂²×C₁₃	1	6	yes	—
336	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
338	#441	C₂²×C₁₃	1	3	yes	—
339	#441	C₂²×C₁₃	1	6	yes	—
340	#441	C₂²×C₁₃	1	3	yes	—
341	#440	C₂²×C₁₃	1	3	yes	—
342	#440	C₂²×C₁₃	1	1	yes	characteristic
343	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
344	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
345	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
346	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
347	#436	C₂²×C₁₃	1	3	yes	—
348	#436	C₂²×C₁₃	1	3	yes	—
349	#432	C₂²×C₁₃	1	3	yes	—
350	#428	C₂²×C₁₃	1	3	yes	—
351	#419	C₂²×C₁₃	1	3	yes	—
352	#417	C₂²×C₁₃	1	3	yes	—
353	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
354	C₂²×C₁₃	—	2	3	no	—
355	C₂²×C₁₃	—	2	3	no	—
356	C₂²×C₁₃	—	2	2	no	—
357	C₂²×C₁₃	—	2	3	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₁₃	—	2	1	no	—
362	C₄×C₁₃	—	2	3	no	—
363	C₄×C₁₃	—	2	3	no	—
364	C₄×C₁₃	—	2	2	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	3	no	—
369	C₄×C₁₃	—	4	3	no	—
370	C₄×C₁₃	—	4	3	no	—
371	C₄×C₁₃	—	4	3	no	—
372	C₄×C₁₃	C₂×#137	1	6	yes	—
373	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
374	C₄×C₁₃	#585	1	1	yes	characteristic
375	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
376	C₂×#41	C₂³×C₁₃	1	3	yes	—
377	C₂²×Q₈	—	2	1	no	—
378	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
379	#137	—	2	12	no	—
380	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
381	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
382	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
383	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
384	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
386	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
387	C₄⋊Q₈	—	2	3	no	—
388	C₄⋊Q₈	—	2	3	no	—
389	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
390	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
391	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
392	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
393	#126	—	2	6	no	—
394	#125	—	2	3	no	—
395	#125	—	2	3	no	—
396	#125	—	2	3	no	—
397	#125	—	2	3	no	—
398	#125	—	2	3	no	—
399	#124	—	2	3	no	—
400	#123	—	2	6	no	—
401	C₂²⋊Q₈	—	2	3	no	—
402	C₂²⋊Q₈	—	2	3	no	—
403	C₂²⋊Q₈	—	2	3	no	—
404	C₂²⋊Q₈	—	2	6	no	—
405	C₂²⋊Q₈	—	2	6	no	—
406	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
407	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
408	#121	—	2	3	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	3	no	—
413	C₄×Q₈	—	2	3	no	—
414	C₄×Q₈	—	2	3	no	—
415	C₄×Q₈	—	2	3	no	—
416	C₄×Q₈	—	2	3	no	—
417	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
418	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
420	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
421	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
422	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
425	C₄×D₄	—	2	3	no	—
426	C₄×D₄	—	2	3	no	—
427	C₄×D₄	—	2	3	no	—
428	C₄×D₄	—	2	3	no	—
429	C₄×D₄	D₄×C₁₃	1	3	yes	—
430	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₄×D₄	C₂³×C₁₃	1	3	yes	—
432	C₄×D₄	C₂³×C₁₃	1	3	yes	—
433	#117	—	2	3	no	—
434	#117	—	2	3	no	—
435	#117	—	2	3	no	—
436	#117	D₄×C₁₃	1	3	yes	—
437	#117	C₂³×C₁₃	1	3	yes	—
438	C₂×C₄⋊C₄	—	2	3	no	—
439	C₂×C₄⋊C₄	—	2	3	no	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
441	C₂×C₄²	—	2	3	no	—
442	C₂×C₄²	—	2	3	no	—
443	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
444	#107	C₂³×C₁₃	1	1	yes	characteristic
445	#107	C₂³×C₁₃	1	3	yes	—
446	#106	C₂³×C₁₃	1	3	yes	—
447	#106	C₂³×C₁₃	1	3	yes	—
448	#106	C₂³×C₁₃	1	6	yes	—
449	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
450	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
451	#103	C₂³×C₁₃	1	3	yes	—
452	#103	C₂³×C₁₃	1	3	yes	—
453	#103	C₂³×C₁₃	1	1	yes	characteristic
454	#103	C₂³×C₁₃	1	3	yes	—
455	#103	C₂³×C₁₃	1	3	yes	—
456	#103	C₂³×C₁₃	1	3	yes	—
457	#103	C₂³×C₁₃	1	6	yes	—
458	#103	C₂³×C₁₃	1	6	yes	—
459	#102	C₂³×C₁₃	1	1	yes	characteristic
460	#102	C₂³×C₁₃	1	3	yes	—
461	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
462	#97	C₂³×C₁₃	1	1	yes	characteristic
463	#97	C₂³×C₁₃	1	3	yes	—
464	C₄×C₈	C₂³×C₁₃	1	3	yes	—
465	C₄×C₈	C₂³×C₁₃	1	3	yes	—
466	C₂×C₁₃	—	4	3	no	—
467	C₂×C₁₃	—	4	2	no	—
468	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
469	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
470	C₂×C₁₃	#3586	1	1	yes	characteristic
471	#41	—	2	4	no	—
472	#41	—	2	6	no	—
473	#41	—	4	3	no	—
474	C₂×Q₈	—	2	3	no	—
475	C₂×Q₈	—	2	3	no	—
476	C₂×Q₈	—	2	3	no	—
477	C₂×Q₈	—	2	6	no	—
478	C₂×Q₈	—	4	3	no	—
479	C₂×Q₈	—	4	4	no	—
480	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
482	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
483	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
484	C₂×D₄	—	2	3	no	—
485	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
486	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	—	2	3	no	—
488	C₂²×C₄	—	2	3	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	3	no	—
491	C₂²×C₄	—	2	3	no	—
492	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
495	Q₁₆	—	2	6	no	—
496	Q₁₆	—	2	6	no	—
497	Q₁₆	—	4	6	no	—
498	SD₁₆	—	2	6	no	—
499	SD₁₆	C₁₃×#41	1	4	yes	complemented
500	M₁₆	—	2	6	no	—
501	M₁₆	—	4	3	no	—
502	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
504	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
505	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	—	2	6	no	—
509	C₄⋊C₄	—	2	3	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	3	no	—
514	C₄⋊C₄	—	2	3	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	3	no	—
520	C₄⋊C₄	—	2	6	no	—
521	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
522	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
523	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
525	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
526	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₂²⋊C₄	—	2	6	no	—
528	C₂²⋊C₄	—	2	6	no	—
529	C₂²⋊C₄	—	2	3	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	3	no	—
535	C₄²	—	2	3	no	—
536	C₄²	—	2	3	no	—
537	C₄²	—	2	3	no	—
538	C₄²	—	2	3	no	—
539	C₄²	—	2	3	no	—
540	C₄²	C₂×D₄×C₁₃	1	3	yes	—
541	C₄²	C₂×D₄×C₁₃	1	3	yes	—
542	C₄²	C₂⁴×C₁₃	1	3	yes	—
543	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
544	C₁₃	#61470	1	1	yes	characteristic, direct product factor, Sylow
545	C₂³	—	2	1	no	—
546	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
547	Q₈	—	2	1	no	—
548	Q₈	—	2	3	no	—
549	Q₈	—	2	3	no	—
550	Q₈	—	2	3	no	—
551	Q₈	—	2	3	no	—
552	Q₈	—	4	6	no	—
553	Q₈	—	4	6	no	—
554	Q₈	—	8	3	no	—
555	Q₈	C₁₃×#137	1	4	yes	complemented
556	Q₈	C₂×C₁₃×#41	1	2	yes	—
557	D₄	—	2	6	no	—
558	D₄	—	2	1	no	—
559	D₄	—	4	6	no	—
560	D₄	C₂×C₁₃×#41	1	2	yes	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	6	no	—
563	C₂×C₄	—	2	3	no	—
564	C₂×C₄	—	2	3	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	3	no	—
568	C₂×C₄	—	2	3	no	—
569	C₂×C₄	—	2	3	no	—
570	C₂×C₄	—	2	3	no	—
571	C₂×C₄	—	4	3	no	—
572	C₂×C₄	—	4	6	no	—
573	C₂×C₄	—	4	6	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	6	no	—
576	C₂×C₄	—	8	3	no	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
582	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
583	C₈	—	2	3	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	3	no	—
586	C₈	C₂×C₁₃×#41	1	2	yes	—
587	C₂²	—	2	3	no	—
588	C₂²	—	2	3	no	—
589	C₂²	—	2	3	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	3	no	—
597	C₄	—	2	3	no	—
598	C₄	—	2	2	no	—
599	C₄	—	4	3	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	3	no	—
603	C₄	—	4	3	no	—
604	C₄	—	4	3	no	—
605	C₄	C₂×C₁₃×#137	1	6	yes	—
606	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
607	C₄	C₁₃×#585	1	1	yes	characteristic
608	C₂	—	4	3	no	—
609	C₂	—	4	2	no	—
610	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
611	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
612	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3395	C₂	semidirect
4. Q₈×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#3363	C₂	semidirect
6. C₁₃×#3359	C₂	semidirect
7. C₁₃×#3356	C₂	semidirect
8. C₁₃×#3331	C₂	semidirect
9. C₁₃×#3328	C₂	semidirect
10. C₁₃×#3276	C₂	semidirect
11. C₁₃×#3185	C₂	semidirect
12. C₁₃×#3116	C₂	semidirect
13. C₁₃×#3113	C₂	semidirect
14. C₁₃×#2971	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
165. #61470	C₁₃	direct (N × H)
194. C₁₃×SD₁₆	#41	semidirect
240. Q₈×#41	C₂×C₁₃	semidirect
241. #3395	C₂×C₁₃	semidirect
242. Q₈×SD₁₆	C₂×C₁₃	semidirect
243. #3363	C₂×C₁₃	semidirect
244. #3359	C₂×C₁₃	semidirect
245. #3356	C₂×C₁₃	semidirect
246. #3331	C₂×C₁₃	semidirect
247. #3328	C₂×C₁₃	semidirect
248. #3276	C₂×C₁₃	semidirect
249. #3185	C₂×C₁₃	semidirect
250. #3116	C₂×C₁₃	semidirect
251. #3113	C₂×C₁₃	semidirect
252. #2971	C₂×C₁₃	semidirect
253. C₄×#137	C₂×C₁₃	semidirect
264. Q₈×C₁₃	#137	semidirect
499. SD₁₆	C₁₃×#41	semidirect
544. C₁₃	#61470	direct (N × H)
555. Q₈	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3482	2
Q₈×C₁₃×#41	2
C₁₃×#3395	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3363	2
C₁₃×#3359	2
C₁₃×#3356	2
C₁₃×#3331	2
C₁₃×#3328	2
C₁₃×#3276	2
C₁₃×#3185	2
C₁₃×#3116	2
C₁₃×#3113	2
C₁₃×#2971	2
C₄×C₁₃×#137	2
#61470	13

Subgroups — C13×#61470 #15747809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61470 #15747809