Subgroups — C₁₃×#62147 #15748486

Order 3328.

1734 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3356	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3331	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3255	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3229	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3107	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3079	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₃	C₂²	1	2	yes	—
13	C₁₃×#557	—	2	1	no	—
14	C₁₃×#557	C₂²	1	1	yes	characteristic
15	C₁₃×#556	C₂²	1	3	yes	—
16	C₁₃×#554	C₂²	1	6	yes	—
17	C₁₃×#552	—	2	3	no	—
18	D₄×Q₈×C₁₃	—	2	3	no	—
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#547	C₂²	1	3	yes	—
22	C₁₃×#544	—	2	3	no	—
23	C₁₃×#533	C₂²	1	3	yes	—
24	C₁₃×#533	C₂²	1	3	yes	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₃×#529	—	2	3	no	—
27	C₁₃×#520	—	2	1	no	—
28	C₄×C₁₃×#41	C₂²	1	3	yes	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
31	C₁₃×#498	C₂²	1	6	yes	—
32	C₁₃×#487	C₂²	1	6	yes	—
33	C₁₃×#485	C₂²	1	6	yes	—
34	C₁₃×#483	C₂²	1	12	yes	—
35	C₁₃×#477	C₂²	1	6	yes	—
36	C₁₃×#476	C₂²	1	6	yes	—
37	C₁₃×#475	C₂²	1	6	yes	—
38	C₁₃×#475	C₂²	1	6	yes	—
39	C₁₃×#475	C₂²	1	3	yes	—
40	C₁₃×#474	C₂²	1	3	yes	—
41	C₁₃×#470	C₂²	1	12	yes	—
42	C₁₃×#462	C₂²	1	6	yes	—
43	C₁₃×#462	C₂²	1	3	yes	—
44	C₁₃×#461	C₂²	1	1	yes	characteristic
45	C₁₃×#452	C₂²	1	6	yes	—
46	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
47	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
49	C₁₃×#436	C₂²	1	6	yes	—
50	C₁₃×#431	C₂²	1	3	yes	—
51	C₁₃×#428	C₂²	1	6	yes	—
52	C₁₃×#423	C₂²	1	3	yes	—
53	C₁₃×#417	C₂²	1	6	yes	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	3	yes	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	—	2	3	no	—
58	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
59	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
61	C₁₃×C₄⋊Q₈	—	2	6	no	—
62	C₁₃×C₄⋊Q₈	—	2	3	no	—
63	C₁₃×C₄⋊Q₈	—	2	3	no	—
64	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
66	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₁₃×#126	—	2	6	no	—
70	C₁₃×#125	—	2	3	no	—
71	C₁₃×#125	—	2	6	no	—
72	C₁₃×#125	—	2	3	no	—
73	C₁₃×#125	—	2	3	no	—
74	C₁₃×#124	—	2	3	no	—
75	C₁₃×#123	—	2	6	no	—
76	C₁₃×C₂²⋊Q₈	—	2	3	no	—
77	C₁₃×C₂²⋊Q₈	—	2	3	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×C₂²⋊Q₈	—	2	12	no	—
80	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
81	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
82	C₁₃×#121	—	2	3	no	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	—	2	3	no	—
86	C₄×Q₈×C₁₃	—	2	3	no	—
87	C₄×Q₈×C₁₃	—	2	3	no	—
88	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₃	—	2	6	no	—
94	C₄×D₄×C₁₃	—	2	3	no	—
95	C₄×D₄×C₁₃	—	2	3	no	—
96	C₄×D₄×C₁₃	D₄	1	3	yes	—
97	C₄×D₄×C₁₃	C₂³	1	3	yes	—
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	C₂³	1	3	yes	—
100	C₁₃×#117	—	2	3	no	—
101	C₁₃×#117	—	2	3	no	—
102	C₁₃×#117	—	2	3	no	—
103	C₁₃×#117	D₄	1	3	yes	—
104	C₁₃×#117	C₂³	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×C₄²×C₁₃	—	2	3	no	—
109	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
110	C₁₃×#107	C₂³	1	6	yes	—
111	C₁₃×#106	C₂³	1	12	yes	—
112	C₁₃×#106	C₂³	1	6	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×#103	C₂³	1	12	yes	—
117	C₁₃×#103	C₂³	1	6	yes	—
118	C₁₃×#103	C₂³	1	2	yes	—
119	C₁₃×#103	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	6	yes	—
121	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
122	C₄×C₈×C₁₃	C₂³	1	6	yes	—
123	#62147	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₁₃×#41	—	2	4	no	—
125	C₁₃×#41	—	2	6	no	—
126	C₁₃×#41	—	4	3	no	—
127	C₂×Q₈×C₁₃	—	2	3	no	—
128	C₂×Q₈×C₁₃	—	2	3	no	—
129	C₂×Q₈×C₁₃	—	2	6	no	—
130	C₂×Q₈×C₁₃	—	4	4	no	—
131	C₂×Q₈×C₁₃	—	8	6	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
134	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
135	C₂×D₄×C₁₃	—	2	3	no	—
136	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
137	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	—	2	6	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	3	no	—
141	C₂²×C₄×C₁₃	—	2	3	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
145	C₁₃×Q₁₆	—	4	6	no	—
146	C₁₃×SD₁₆	—	2	4	no	—
147	C₁₃×M₁₆	—	4	6	no	—
148	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
149	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
150	C₁₃×C₄⋊C₄	—	2	3	no	—
151	C₁₃×C₄⋊C₄	—	2	6	no	—
152	C₁₃×C₄⋊C₄	—	2	3	no	—
153	C₁₃×C₄⋊C₄	—	2	6	no	—
154	C₁₃×C₄⋊C₄	—	2	6	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	3	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	1	no	—
161	C₁₃×C₄⋊C₄	—	2	6	no	—
162	C₁₃×C₄⋊C₄	—	2	6	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
168	C₁₃×C₂²⋊C₄	—	2	6	no	—
169	C₁₃×C₂²⋊C₄	—	2	6	no	—
170	C₁₃×C₂²⋊C₄	—	2	3	no	—
171	C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₁₃×C₂²⋊C₄	—	2	3	no	—
173	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
174	C₄²×C₁₃	—	2	3	no	—
175	C₄²×C₁₃	—	2	3	no	—
176	C₄²×C₁₃	—	2	3	no	—
177	C₄²×C₁₃	—	2	6	no	—
178	C₄²×C₁₃	C₂×D₄	1	3	yes	—
179	C₄²×C₁₃	C₂×D₄	1	3	yes	—
180	C₄²×C₁₃	C₂⁴	1	3	yes	—
181	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
182	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#3482	C₂×C₁₃	1	1	yes	characteristic
184	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
185	#3363	C₂×C₁₃	1	2	yes	complemented
186	#3356	C₂×C₁₃	1	6	yes	complemented
187	#3331	C₂×C₁₃	1	6	yes	complemented
188	#3255	C₂×C₁₃	1	3	yes	complemented
189	#3229	C₂×C₁₃	1	3	yes	complemented
190	#3107	C₂×C₁₃	1	3	yes	complemented
191	#3079	C₂×C₁₃	1	3	yes	complemented
192	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
195	Q₈×C₁₃	—	2	2	no	—
196	Q₈×C₁₃	—	2	3	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	3	no	—
199	Q₈×C₁₃	—	4	6	no	—
200	Q₈×C₁₃	—	4	6	no	—
201	Q₈×C₁₃	—	8	6	no	—
202	Q₈×C₁₃	#137	1	4	yes	—
203	D₄×C₁₃	—	2	6	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	4	6	no	—
206	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
207	C₂×C₄×C₁₃	—	2	6	no	—
208	C₂×C₄×C₁₃	—	2	6	no	—
209	C₂×C₄×C₁₃	—	2	3	no	—
210	C₂×C₄×C₁₃	—	2	3	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	3	no	—
214	C₂×C₄×C₁₃	—	2	3	no	—
215	C₂×C₄×C₁₃	—	2	6	no	—
216	C₂×C₄×C₁₃	—	4	6	no	—
217	C₂×C₄×C₁₃	—	4	6	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	8	6	no	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	—	2	6	no	—
228	Q₈²	C₂²×C₁₃	1	2	yes	—
229	#557	—	2	1	no	—
230	#557	C₂²×C₁₃	1	1	yes	characteristic
231	#556	C₂²×C₁₃	1	3	yes	—
232	#554	C₂²×C₁₃	1	6	yes	—
233	#552	—	2	3	no	—
234	D₄×Q₈	—	2	3	no	—
235	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	#548	—	2	1	no	—
237	#547	C₂²×C₁₃	1	3	yes	—
238	#544	—	2	3	no	—
239	#533	C₂²×C₁₃	1	3	yes	—
240	#533	C₂²×C₁₃	1	3	yes	—
241	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
242	#529	—	2	3	no	—
243	#520	—	2	1	no	—
244	C₄×#41	C₂²×C₁₃	1	3	yes	—
245	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄×Q₈	—	2	1	no	—
247	#498	C₂²×C₁₃	1	6	yes	—
248	#487	C₂²×C₁₃	1	6	yes	—
249	#485	C₂²×C₁₃	1	6	yes	—
250	#483	C₂²×C₁₃	1	12	yes	—
251	#477	C₂²×C₁₃	1	6	yes	—
252	#476	C₂²×C₁₃	1	6	yes	—
253	#475	C₂²×C₁₃	1	6	yes	—
254	#475	C₂²×C₁₃	1	6	yes	—
255	#475	C₂²×C₁₃	1	3	yes	—
256	#474	C₂²×C₁₃	1	3	yes	—
257	#470	C₂²×C₁₃	1	12	yes	—
258	#462	C₂²×C₁₃	1	6	yes	—
259	#462	C₂²×C₁₃	1	3	yes	—
260	#461	C₂²×C₁₃	1	1	yes	characteristic
261	#452	C₂²×C₁₃	1	6	yes	—
262	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
263	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
264	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
265	#436	C₂²×C₁₃	1	6	yes	—
266	#431	C₂²×C₁₃	1	3	yes	—
267	#428	C₂²×C₁₃	1	6	yes	—
268	#423	C₂²×C₁₃	1	3	yes	—
269	#417	C₂²×C₁₃	1	6	yes	—
270	C₂²×C₁₃	—	2	3	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	3	no	—
273	C₂²×C₁₃	—	2	3	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
277	C₄×C₁₃	—	2	3	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	3	no	—
280	C₄×C₁₃	—	4	3	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	3	no	—
283	C₄×C₁₃	—	4	1	no	—
284	C₄×C₁₃	—	4	6	no	—
285	C₄×C₁₃	C₂×#137	1	6	yes	—
286	C₄×C₁₃	#577	1	2	yes	—
287	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
288	C₄×C₁₃	#585	1	1	yes	characteristic
289	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
290	C₂×#41	C₂³×C₁₃	1	3	yes	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×Q₈	—	2	3	no	—
293	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
294	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
295	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
296	C₄⋊Q₈	—	2	6	no	—
297	C₄⋊Q₈	—	2	3	no	—
298	C₄⋊Q₈	—	2	3	no	—
299	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
301	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
302	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
303	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
304	#126	—	2	6	no	—
305	#125	—	2	3	no	—
306	#125	—	2	6	no	—
307	#125	—	2	3	no	—
308	#125	—	2	3	no	—
309	#124	—	2	3	no	—
310	#123	—	2	6	no	—
311	C₂²⋊Q₈	—	2	3	no	—
312	C₂²⋊Q₈	—	2	3	no	—
313	C₂²⋊Q₈	—	2	3	no	—
314	C₂²⋊Q₈	—	2	12	no	—
315	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
316	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
317	#121	—	2	3	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	3	no	—
321	C₄×Q₈	—	2	3	no	—
322	C₄×Q₈	—	2	3	no	—
323	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
324	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
325	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
326	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
327	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄×D₄	—	2	6	no	—
329	C₄×D₄	—	2	3	no	—
330	C₄×D₄	—	2	3	no	—
331	C₄×D₄	D₄×C₁₃	1	3	yes	—
332	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₄×D₄	C₂³×C₁₃	1	3	yes	—
334	C₄×D₄	C₂³×C₁₃	1	3	yes	—
335	#117	—	2	3	no	—
336	#117	—	2	3	no	—
337	#117	—	2	3	no	—
338	#117	D₄×C₁₃	1	3	yes	—
339	#117	C₂³×C₁₃	1	3	yes	—
340	C₂×C₄⋊C₄	—	2	3	no	—
341	C₂×C₄⋊C₄	—	2	3	no	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
343	C₂×C₄²	—	2	3	no	—
344	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
345	#107	C₂³×C₁₃	1	6	yes	—
346	#106	C₂³×C₁₃	1	12	yes	—
347	#106	C₂³×C₁₃	1	6	yes	—
348	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
349	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
350	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
351	#103	C₂³×C₁₃	1	12	yes	—
352	#103	C₂³×C₁₃	1	6	yes	—
353	#103	C₂³×C₁₃	1	2	yes	—
354	#103	C₂³×C₁₃	1	6	yes	—
355	#102	C₂³×C₁₃	1	6	yes	—
356	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
357	C₄×C₈	C₂³×C₁₃	1	6	yes	—
358	C₂×C₁₃	—	4	3	no	—
359	C₂×C₁₃	—	4	2	no	—
360	C₂×C₁₃	#3489	1	1	yes	characteristic
361	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
362	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
363	#41	—	2	4	no	—
364	#41	—	2	6	no	—
365	#41	—	4	3	no	—
366	C₂×Q₈	—	2	3	no	—
367	C₂×Q₈	—	2	3	no	—
368	C₂×Q₈	—	2	6	no	—
369	C₂×Q₈	—	4	4	no	—
370	C₂×Q₈	—	8	6	no	—
371	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
373	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
374	C₂×D₄	—	2	3	no	—
375	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
376	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	—	2	6	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	3	no	—
380	C₂²×C₄	—	2	3	no	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
384	Q₁₆	—	4	6	no	—
385	SD₁₆	—	2	4	no	—
386	M₁₆	—	4	6	no	—
387	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
388	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
389	C₄⋊C₄	—	2	3	no	—
390	C₄⋊C₄	—	2	6	no	—
391	C₄⋊C₄	—	2	3	no	—
392	C₄⋊C₄	—	2	6	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	3	no	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	—	2	3	no	—
398	C₄⋊C₄	—	2	3	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	6	no	—
401	C₄⋊C₄	—	2	6	no	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
404	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
405	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
406	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
407	C₂²⋊C₄	—	2	6	no	—
408	C₂²⋊C₄	—	2	6	no	—
409	C₂²⋊C₄	—	2	3	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	3	no	—
412	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
413	C₄²	—	2	3	no	—
414	C₄²	—	2	3	no	—
415	C₄²	—	2	3	no	—
416	C₄²	—	2	6	no	—
417	C₄²	C₂×D₄×C₁₃	1	3	yes	—
418	C₄²	C₂×D₄×C₁₃	1	3	yes	—
419	C₄²	C₂⁴×C₁₃	1	3	yes	—
420	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
421	C₁₃	#62147	1	1	yes	characteristic, direct product factor, Sylow
422	C₂³	—	2	1	no	—
423	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
424	Q₈	—	2	2	no	—
425	Q₈	—	2	3	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	3	no	—
428	Q₈	—	4	6	no	—
429	Q₈	—	4	6	no	—
430	Q₈	—	8	6	no	—
431	Q₈	C₁₃×#137	1	4	yes	—
432	D₄	—	2	6	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	6	no	—
435	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
436	C₂×C₄	—	2	6	no	—
437	C₂×C₄	—	2	6	no	—
438	C₂×C₄	—	2	3	no	—
439	C₂×C₄	—	2	3	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	3	no	—
443	C₂×C₄	—	2	3	no	—
444	C₂×C₄	—	2	6	no	—
445	C₂×C₄	—	4	6	no	—
446	C₂×C₄	—	4	6	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	6	no	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	6	no	—
457	C₂²	—	2	3	no	—
458	C₂²	—	2	3	no	—
459	C₂²	—	2	3	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	3	no	—
466	C₄	—	2	3	no	—
467	C₄	—	4	3	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	6	no	—
470	C₄	—	4	3	no	—
471	C₄	—	4	2	no	—
472	C₄	C₂×C₁₃×#137	1	6	yes	—
473	C₄	C₁₃×#577	1	2	yes	—
474	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
475	C₄	C₁₃×#585	1	1	yes	characteristic
476	C₂	—	4	3	no	—
477	C₂	—	4	2	no	—
478	C₂	C₁₃×#3489	1	1	yes	characteristic
479	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
480	C₂	C₂×C₁₃×#577	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
1. C₁₃×#3503	C₂	semidirect
3. Q₈×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#3363	C₂	semidirect
5. C₁₃×#3356	C₂	semidirect
6. C₁₃×#3331	C₂	semidirect
7. C₁₃×#3255	C₂	semidirect
8. C₁₃×#3229	C₂	semidirect
9. C₁₃×#3107	C₂	semidirect
10. C₁₃×#3079	C₂	semidirect
11. C₁₃×#2991	C₂	semidirect
123. #62147	C₁₃	direct (N × H)
182. #3503	C₂×C₁₃	semidirect
184. Q₈×SD₁₆	C₂×C₁₃	semidirect
185. #3363	C₂×C₁₃	semidirect
186. #3356	C₂×C₁₃	semidirect
187. #3331	C₂×C₁₃	semidirect
188. #3255	C₂×C₁₃	semidirect
189. #3229	C₂×C₁₃	semidirect
190. #3107	C₂×C₁₃	semidirect
191. #3079	C₂×C₁₃	semidirect
192. #2991	C₂×C₁₃	semidirect
421. C₁₃	#62147	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×#3503	2
C₁₃×#3482	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3363	2
C₁₃×#3356	2
C₁₃×#3331	2
C₁₃×#3255	2
C₁₃×#3229	2
C₁₃×#3107	2
C₁₃×#3079	2
C₁₃×#2991	2
#62147	13

Subgroups — C13×#62147 #15748486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62147 #15748486