Subgroups — C₁₃×#62099 #15748438

Order 3328.

1948 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3335	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3298	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3246	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3229	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3103	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#475	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
13	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#557	—	2	1	no	—
15	C₁₃×#557	C₂²	1	1	yes	characteristic
16	C₁₃×#554	—	2	3	no	—
17	C₁₃×#554	C₂²	1	3	yes	—
18	D₄×Q₈×C₁₃	—	2	1	no	—
19	D₄×Q₈×C₁₃	C₂²	1	3	yes	—
20	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#547	—	2	3	no	—
22	C₁₃×#547	C₂²	1	6	yes	—
23	C₁₃×#536	—	2	3	no	—
24	C₁₃×#533	—	2	3	no	—
25	C₁₃×#533	C₂²	1	3	yes	—
26	C₁₃×#532	C₂²	1	3	yes	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
28	C₄×C₁₃×#41	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
31	C₁₃×#498	C₂²	1	6	yes	—
32	C₁₃×#487	C₂²	1	6	yes	—
33	C₁₃×#483	C₂²	1	12	yes	—
34	C₁₃×#481	C₂²	1	6	yes	—
35	C₁₃×#476	C₂²	1	6	yes	—
36	C₁₃×#475	C₂²	1	6	yes	—
37	C₁₃×#475	C₂²	1	3	yes	—
38	C₁₃×#475	C₂²	1	6	yes	—
39	C₁₃×#475	C₂²	1	6	yes	—
40	C₁₃×#475	C₂²	1	3	yes	—
41	C₁₃×#465	C₂²	1	12	yes	—
42	C₁₃×#461	C₂²	1	6	yes	—
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#460	C₂²	1	3	yes	—
45	C₁₃×#448	C₂²	1	6	yes	—
46	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
47	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
49	C₈×D₄×C₁₃	C₂²	1	6	yes	—
50	C₁₃×#431	C₂²	1	3	yes	—
51	C₂×C₁₃×#106	C₂²	1	6	yes	—
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
53	C₂×C₁₃×#103	C₂²	1	6	yes	—
54	C₁₃×2₋¹⁺⁴	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	6	no	—
56	C₂×C₁₃×#41	—	2	3	no	—
57	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	—	2	2	no	—
59	C₂²×Q₈×C₁₃	—	2	3	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
64	C₁₃×C₄⋊Q₈	—	2	3	no	—
65	C₁₃×C₄⋊Q₈	—	2	3	no	—
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	—	2	3	no	—
68	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
72	C₁₃×#127	C₂³	1	1	yes	characteristic
73	C₁₃×#125	—	2	3	no	—
74	C₁₃×#125	—	2	3	no	—
75	C₁₃×#125	—	2	3	no	—
76	C₁₃×#124	—	2	3	no	—
77	C₁₃×#123	—	2	12	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×C₂²⋊Q₈	—	2	6	no	—
80	C₁₃×C₂²⋊Q₈	—	2	6	no	—
81	C₁₃×C₂²⋊Q₈	—	2	6	no	—
82	C₁₃×C₂²⋊Q₈	—	2	6	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
84	C₁₃×#121	—	2	3	no	—
85	C₁₃×#121	C₂³	1	6	yes	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	—	2	3	no	—
90	C₄×Q₈×C₁₃	—	2	3	no	—
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	D₄	1	3	yes	—
101	C₄×D₄×C₁₃	C₂³	1	6	yes	—
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₁₃×#117	—	2	3	no	—
104	C₁₃×#117	D₄	1	3	yes	—
105	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
109	C₂×C₄²×C₁₃	—	2	3	no	—
110	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
111	C₁₃×#106	C₂³	1	6	yes	—
112	C₁₃×#106	C₂³	1	12	yes	—
113	C₁₃×#106	C₂³	1	6	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×#103	C₂³	1	6	yes	—
118	C₁₃×#103	C₂³	1	12	yes	—
119	C₁₃×#103	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	2	yes	—
121	C₁₃×#102	C₂³	1	6	yes	—
122	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62099	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₁₃×#41	—	4	24	no	—
126	C₁₃×#41	—	4	12	no	—
127	C₁₃×#41	SD₁₆	1	8	yes	complemented
128	C₂×Q₈×C₁₃	—	2	3	no	—
129	C₂×Q₈×C₁₃	—	2	6	no	—
130	C₂×Q₈×C₁₃	—	2	3	no	—
131	C₂×Q₈×C₁₃	—	2	3	no	—
132	C₂×Q₈×C₁₃	—	2	6	no	—
133	C₂×Q₈×C₁₃	—	4	3	no	—
134	C₂×Q₈×C₁₃	—	4	8	no	—
135	C₂×Q₈×C₁₃	—	4	12	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	3	no	—
145	C₂²×C₄×C₁₃	—	2	6	no	—
146	C₂²×C₄×C₁₃	—	2	3	no	—
147	C₂²×C₄×C₁₃	—	2	6	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
151	C₁₃×SD₁₆	—	2	4	no	—
152	C₁₃×SD₁₆	—	4	6	no	—
153	C₂×C₈×C₁₃	—	4	6	no	—
154	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
155	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	3	no	—
158	C₁₃×C₄⋊C₄	—	2	3	no	—
159	C₁₃×C₄⋊C₄	—	2	3	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	6	no	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	6	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	3	no	—
166	C₁₃×C₄⋊C₄	—	2	3	no	—
167	C₁₃×C₄⋊C₄	—	2	6	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
173	C₁₃×C₂²⋊C₄	—	2	6	no	—
174	C₁₃×C₂²⋊C₄	—	2	6	no	—
175	C₁₃×C₂²⋊C₄	—	2	6	no	—
176	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	3	no	—
179	C₄²×C₁₃	—	2	3	no	—
180	C₄²×C₁₃	—	2	3	no	—
181	C₄²×C₁₃	C₂×D₄	1	3	yes	—
182	C₄²×C₁₃	C₂×D₄	1	3	yes	—
183	C₄²×C₁₃	C₂⁴	1	3	yes	—
184	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
185	#3499	C₂×C₁₃	1	1	yes	characteristic
186	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
187	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
188	#3359	C₂×C₁₃	1	2	yes	complemented
189	#3335	C₂×C₁₃	1	6	yes	complemented
190	#3298	C₂×C₁₃	1	6	yes	complemented
191	#3246	C₂×C₁₃	1	3	yes	complemented
192	#3229	C₂×C₁₃	1	3	yes	complemented
193	#3103	C₂×C₁₃	1	3	yes	complemented
194	C₂×#475	C₂×C₁₃	1	3	yes	complemented
195	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
198	Q₈×C₁₃	—	2	1	no	—
199	Q₈×C₁₃	—	2	3	no	—
200	Q₈×C₁₃	—	2	3	no	—
201	Q₈×C₁₃	—	4	6	no	—
202	Q₈×C₁₃	—	4	12	no	—
203	Q₈×C₁₃	—	4	6	no	—
204	Q₈×C₁₃	—	8	3	no	—
205	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	—
206	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	complemented
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	4	12	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	C₂×SD₁₆	1	12	yes	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	3	no	—
215	C₂×C₄×C₁₃	—	2	3	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	3	no	—
218	C₂×C₄×C₁₃	—	2	3	no	—
219	C₂×C₄×C₁₃	—	2	6	no	—
220	C₂×C₄×C₁₃	—	4	3	no	—
221	C₂×C₄×C₁₃	—	4	6	no	—
222	C₂×C₄×C₁₃	—	4	12	no	—
223	C₂×C₄×C₁₃	—	4	12	no	—
224	C₂×C₄×C₁₃	—	8	3	no	—
225	C₂×C₄×C₁₃	C₂×SD₁₆	1	12	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
232	C₈×C₁₃	—	2	2	no	—
233	C₈×C₁₃	—	2	6	no	—
234	C₂×2₋¹⁺⁴	—	2	1	no	—
235	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
236	#557	—	2	1	no	—
237	#557	C₂²×C₁₃	1	1	yes	characteristic
238	#554	—	2	3	no	—
239	#554	C₂²×C₁₃	1	3	yes	—
240	D₄×Q₈	—	2	1	no	—
241	D₄×Q₈	C₂²×C₁₃	1	3	yes	—
242	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
243	#547	—	2	3	no	—
244	#547	C₂²×C₁₃	1	6	yes	—
245	#536	—	2	3	no	—
246	#533	—	2	3	no	—
247	#533	C₂²×C₁₃	1	3	yes	—
248	#532	C₂²×C₁₃	1	3	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
250	C₄×#41	—	2	1	no	—
251	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
253	#498	C₂²×C₁₃	1	6	yes	—
254	#487	C₂²×C₁₃	1	6	yes	—
255	#483	C₂²×C₁₃	1	12	yes	—
256	#481	C₂²×C₁₃	1	6	yes	—
257	#476	C₂²×C₁₃	1	6	yes	—
258	#475	C₂²×C₁₃	1	3	yes	—
259	#475	C₂²×C₁₃	1	6	yes	—
260	#475	C₂²×C₁₃	1	6	yes	—
261	#475	C₂²×C₁₃	1	6	yes	—
262	#475	C₂²×C₁₃	1	3	yes	—
263	#465	C₂²×C₁₃	1	12	yes	—
264	#461	C₂²×C₁₃	1	6	yes	—
265	#460	C₂²×C₁₃	1	1	yes	characteristic
266	#460	C₂²×C₁₃	1	3	yes	—
267	#448	C₂²×C₁₃	1	6	yes	—
268	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
269	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
270	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
271	C₈×D₄	C₂²×C₁₃	1	6	yes	—
272	#431	C₂²×C₁₃	1	3	yes	—
273	C₂×#106	C₂²×C₁₃	1	6	yes	—
274	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
275	C₂×#103	C₂²×C₁₃	1	6	yes	—
276	C₂²×C₁₃	—	2	3	no	—
277	C₂²×C₁₃	—	2	3	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	C₂²×SD₁₆	1	6	yes	—
282	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	3	no	—
285	C₄×C₁₃	—	2	3	no	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	—	4	3	no	—
289	C₄×C₁₃	—	4	3	no	—
290	C₄×C₁₃	—	4	6	no	—
291	C₄×C₁₃	C₂²×SD₁₆	1	6	yes	—
292	C₄×C₁₃	C₂²×SD₁₆	1	2	yes	—
293	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
294	C₄×C₁₃	#585	1	1	yes	characteristic
295	2₋¹⁺⁴	—	4	8	no	—
296	C₂×#41	—	2	6	no	—
297	C₂×#41	—	2	3	no	—
298	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
299	C₂²×Q₈	—	2	2	no	—
300	C₂²×Q₈	—	2	3	no	—
301	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
302	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
303	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
304	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
305	C₄⋊Q₈	—	2	3	no	—
306	C₄⋊Q₈	—	2	3	no	—
307	C₄⋊Q₈	—	2	3	no	—
308	C₄⋊Q₈	—	2	3	no	—
309	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
310	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
311	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
312	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
313	#127	C₂³×C₁₃	1	1	yes	characteristic
314	#125	—	2	3	no	—
315	#125	—	2	3	no	—
316	#125	—	2	3	no	—
317	#124	—	2	3	no	—
318	#123	—	2	12	no	—
319	C₂²⋊Q₈	—	2	3	no	—
320	C₂²⋊Q₈	—	2	6	no	—
321	C₂²⋊Q₈	—	2	6	no	—
322	C₂²⋊Q₈	—	2	6	no	—
323	C₂²⋊Q₈	—	2	6	no	—
324	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
325	#121	—	2	3	no	—
326	#121	C₂³×C₁₃	1	6	yes	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	3	no	—
330	C₄×Q₈	—	2	3	no	—
331	C₄×Q₈	—	2	3	no	—
332	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
335	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
336	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
337	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₄×D₄	—	2	3	no	—
339	C₄×D₄	—	2	3	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	D₄×C₁₃	1	3	yes	—
342	C₄×D₄	C₂³×C₁₃	1	6	yes	—
343	C₄×D₄	C₂³×C₁₃	1	3	yes	—
344	#117	—	2	3	no	—
345	#117	D₄×C₁₃	1	3	yes	—
346	C₂×C₄⋊C₄	—	2	3	no	—
347	C₂×C₄⋊C₄	—	2	3	no	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
350	C₂×C₄²	—	2	3	no	—
351	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
352	#106	C₂³×C₁₃	1	6	yes	—
353	#106	C₂³×C₁₃	1	12	yes	—
354	#106	C₂³×C₁₃	1	6	yes	—
355	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
356	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
357	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
358	#103	C₂³×C₁₃	1	6	yes	—
359	#103	C₂³×C₁₃	1	12	yes	—
360	#103	C₂³×C₁₃	1	6	yes	—
361	#102	C₂³×C₁₃	1	2	yes	—
362	#102	C₂³×C₁₃	1	6	yes	—
363	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
364	C₄×C₈	C₂³×C₁₃	1	6	yes	—
365	C₂×C₁₃	—	2	6	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	#3489	1	1	yes	characteristic
368	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
369	C₂×C₁₃	#3586	1	1	yes	characteristic
370	#41	—	4	24	no	—
371	#41	—	4	12	no	—
372	#41	C₁₃×SD₁₆	1	8	yes	complemented
373	C₂×Q₈	—	2	3	no	—
374	C₂×Q₈	—	2	6	no	—
375	C₂×Q₈	—	2	3	no	—
376	C₂×Q₈	—	2	3	no	—
377	C₂×Q₈	—	2	6	no	—
378	C₂×Q₈	—	4	3	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	—	4	12	no	—
381	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
383	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
384	C₂×D₄	—	2	6	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
388	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
389	C₂²×C₄	—	2	3	no	—
390	C₂²×C₄	—	2	6	no	—
391	C₂²×C₄	—	2	3	no	—
392	C₂²×C₄	—	2	6	no	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
396	SD₁₆	—	2	4	no	—
397	SD₁₆	—	4	6	no	—
398	C₂×C₈	—	4	6	no	—
399	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
400	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	3	no	—
403	C₄⋊C₄	—	2	3	no	—
404	C₄⋊C₄	—	2	3	no	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	2	3	no	—
408	C₄⋊C₄	—	2	6	no	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	3	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	—	2	6	no	—
413	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
414	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
415	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
417	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
418	C₂²⋊C₄	—	2	6	no	—
419	C₂²⋊C₄	—	2	6	no	—
420	C₂²⋊C₄	—	2	6	no	—
421	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	3	no	—
424	C₄²	—	2	3	no	—
425	C₄²	—	2	3	no	—
426	C₄²	C₂×D₄×C₁₃	1	3	yes	—
427	C₄²	C₂×D₄×C₁₃	1	3	yes	—
428	C₄²	C₂⁴×C₁₃	1	3	yes	—
429	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₁₃	#62099	1	1	yes	characteristic, direct product factor, Sylow
431	C₂³	—	2	2	no	—
432	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
433	Q₈	—	2	1	no	—
434	Q₈	—	2	3	no	—
435	Q₈	—	2	3	no	—
436	Q₈	—	4	6	no	—
437	Q₈	—	4	12	no	—
438	Q₈	—	4	6	no	—
439	Q₈	—	8	3	no	—
440	Q₈	C₂×C₁₃×SD₁₆	1	4	yes	—
441	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	complemented
442	D₄	—	2	2	no	—
443	D₄	—	2	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	12	no	—
446	D₄	—	4	2	no	—
447	D₄	C₂×C₁₃×SD₁₆	1	12	yes	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	3	no	—
450	C₂×C₄	—	2	3	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	6	no	—
455	C₂×C₄	—	4	3	no	—
456	C₂×C₄	—	4	6	no	—
457	C₂×C₄	—	4	12	no	—
458	C₂×C₄	—	4	12	no	—
459	C₂×C₄	—	8	3	no	—
460	C₂×C₄	C₂×C₁₃×SD₁₆	1	12	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
466	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	6	no	—
469	C₂²	—	2	3	no	—
470	C₂²	—	2	3	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	C₂²×C₁₃×SD₁₆	1	6	yes	—
475	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	3	no	—
478	C₄	—	2	3	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	6	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	3	no	—
483	C₄	—	4	3	no	—
484	C₄	C₂²×C₁₃×SD₁₆	1	6	yes	—
485	C₄	C₂²×C₁₃×SD₁₆	1	2	yes	—
486	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
487	C₄	C₁₃×#585	1	1	yes	characteristic
488	C₂	—	2	6	no	—
489	C₂	—	8	2	no	—
490	C₂	C₁₃×#3489	1	1	yes	characteristic
491	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
492	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×#3499	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. Q₈×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#3359	C₂	semidirect
5. C₁₃×#3335	C₂	semidirect
6. C₁₃×#3298	C₂	semidirect
7. C₁₃×#3246	C₂	semidirect
8. C₁₃×#3229	C₂	semidirect
9. C₁₃×#3103	C₂	semidirect
10. C₂×C₁₃×#475	C₂	semidirect
11. C₁₃×#2988	C₂	semidirect
124. #62099	C₁₃	direct (N × H)
127. C₁₃×#41	SD₁₆	semidirect
186. Q₈×#41	C₂×C₁₃	semidirect
187. Q₈×SD₁₆	C₂×C₁₃	semidirect
188. #3359	C₂×C₁₃	semidirect
189. #3335	C₂×C₁₃	semidirect
190. #3298	C₂×C₁₃	semidirect
191. #3246	C₂×C₁₃	semidirect
192. #3229	C₂×C₁₃	semidirect
193. #3103	C₂×C₁₃	semidirect
194. C₂×#475	C₂×C₁₃	semidirect
195. #2988	C₂×C₁₃	semidirect
206. Q₈×C₁₃	2₋¹⁺⁴	semidirect
372. #41	C₁₃×SD₁₆	semidirect
430. C₁₃	#62099	direct (N × H)
441. Q₈	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3499	2
Q₈×C₁₃×#41	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3359	2
C₁₃×#3335	2
C₁₃×#3298	2
C₁₃×#3246	2
C₁₃×#3229	2
C₁₃×#3103	2
C₂×C₁₃×#475	2
C₁₃×#2988	2
#62099	13

Subgroups — C13×#62099 #15748438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62099 #15748438