Subgroups — C₁₃×#61948 #15748287

Order 3328.

2114 conjugacy classes of subgroups.

The subgroup lattice has 524 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	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3298	C₂	1	6	yes	maximal, complemented
6	D₄×C₁₃×SD₁₆	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3246	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3206	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3101	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#461	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	6	yes	—
14	Q₈²×C₁₃	—	2	1	no	—
15	C₁₃×#557	C₂²	1	2	yes	complemented
16	C₁₃×#554	—	2	3	no	—
17	C₁₃×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	C₂²	1	6	yes	complemented
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#547	C₂²	1	3	yes	—
22	C₁₃×#546	—	2	3	no	—
23	D₄²×C₁₃	C₂²	1	3	yes	—
24	C₁₃×#544	—	2	3	no	—
25	C₁₃×#533	C₂²	1	3	yes	complemented
26	C₁₃×#532	C₂²	1	3	yes	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
28	C₁₃×#525	—	2	3	no	—
29	C₁₃×#520	—	2	1	no	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
32	C₁₃×#492	C₂²	1	6	yes	complemented
33	C₁₃×#487	C₂²	1	6	yes	complemented
34	C₁₃×#483	C₂²	1	6	yes	complemented
35	C₁₃×#476	C₂²	1	1	yes	characteristic
36	C₁₃×#476	C₂²	1	3	yes	complemented
37	C₁₃×#475	C₂²	1	6	yes	complemented
38	C₁₃×#465	C₂²	1	12	yes	complemented
39	C₁₃×#461	C₂²	1	6	yes	—
40	C₁₃×#461	C₂²	1	3	yes	—
41	C₁₃×#461	C₂²	1	6	yes	complemented
42	C₁₃×#461	C₂²	1	6	yes	complemented
43	C₁₃×#461	C₂²	1	3	yes	complemented
44	C₁₃×#460	C₂²	1	6	yes	complemented
45	C₁₃×#450	C₂²	1	6	yes	—
46	C₁₃×#448	C₂²	1	12	yes	complemented
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
49	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
50	C₈×D₄×C₁₃	C₂²	1	6	yes	complemented
51	C₁₃×#431	C₂²	1	3	yes	complemented
52	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	complemented
53	C₂×C₁₃×#103	C₂²	1	6	yes	complemented
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	—	2	3	no	—
56	C₂×C₁₃×#41	—	2	3	no	—
57	C₂×C₁₃×#41	—	4	8	no	—
58	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
61	C₂²×D₄×C₁₃	—	2	3	no	—
62	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃	—	2	3	no	—
64	C₂×C₁₃×SD₁₆	—	4	12	no	—
65	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
66	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
67	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
69	C₁₃×C₄⋊Q₈	—	2	6	no	—
70	C₁₃×C₄⋊Q₈	—	2	3	no	—
71	C₁₃×C₄⋊Q₈	—	2	3	no	—
72	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₃×#127	C₂³	1	3	yes	—
77	C₁₃×#125	—	2	6	no	—
78	C₁₃×#125	—	2	3	no	—
79	C₁₃×#124	—	2	3	no	—
80	C₁₃×#123	—	2	6	no	—
81	C₁₃×C₂²⋊Q₈	—	2	3	no	—
82	C₁₃×C₂²⋊Q₈	—	2	3	no	—
83	C₁₃×C₂²⋊Q₈	—	2	3	no	—
84	C₁₃×C₂²⋊Q₈	—	2	12	no	—
85	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
86	C₁₃×#121	—	2	3	no	—
87	C₁₃×#121	—	2	3	no	—
88	C₁₃×#121	—	2	3	no	—
89	C₁₃×#121	C₂³	1	6	yes	—
90	C₁₃×#120	—	2	6	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	3	no	—
93	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	6	no	—
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	3	yes	—
102	C₄×D₄×C₁₃	C₂³	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂³	1	3	yes	—
105	C₄×D₄×C₁₃	C₂³	1	3	yes	—
106	C₁₃×#117	—	2	3	no	—
107	C₁₃×#117	D₄	1	3	yes	—
108	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
112	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
113	C₁₃×#106	C₂³	1	6	yes	—
114	C₁₃×#106	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	C₂³	1	6	yes	—
119	C₁₃×#103	C₂³	1	12	yes	—
120	C₁₃×#103	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	2	yes	—
122	C₁₃×#102	C₂³	1	6	yes	—
123	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
124	C₄×C₈×C₁₃	C₂³	1	6	yes	—
125	#61948	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	3	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	12	no	—
129	C₁₃×#41	—	4	12	no	—
130	C₁₃×#41	SD₁₆	1	8	yes	complemented
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	3	no	—
133	C₂×Q₈×C₁₃	—	2	6	no	—
134	C₂×Q₈×C₁₃	—	4	6	no	—
135	C₂×Q₈×C₁₃	—	4	6	no	—
136	C₂×Q₈×C₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
139	C₂×D₄×C₁₃	—	2	6	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	3	no	—
142	C₂×D₄×C₁₃	—	2	3	no	—
143	C₂×D₄×C₁₃	—	2	3	no	—
144	C₂×D₄×C₁₃	—	4	3	no	—
145	C₂×D₄×C₁₃	—	4	12	no	—
146	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	—	2	3	no	—
150	C₂²×C₄×C₁₃	—	2	6	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	3	no	—
153	C₂²×C₄×C₁₃	—	2	3	no	—
154	C₂²×C₄×C₁₃	—	2	3	no	—
155	C₂²×C₄×C₁₃	—	4	12	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
159	C₁₃×SD₁₆	—	2	12	no	—
160	C₁₃×SD₁₆	—	4	12	no	—
161	C₁₃×SD₁₆	—	4	6	no	—
162	C₂×C₈×C₁₃	—	4	6	no	—
163	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
164	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
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	—	2	6	no	—
169	C₁₃×C₄⋊C₄	—	2	3	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	3	no	—
172	C₁₃×C₄⋊C₄	—	2	6	no	—
173	C₁₃×C₄⋊C₄	—	2	6	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
179	C₁₃×C₂²⋊C₄	—	2	6	no	—
180	C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	3	no	—
182	C₁₃×C₂²⋊C₄	—	2	3	no	—
183	C₁₃×C₂²⋊C₄	—	2	3	no	—
184	C₁₃×C₂²⋊C₄	—	2	6	no	—
185	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
186	C₄²×C₁₃	—	2	6	no	—
187	C₄²×C₁₃	C₂×D₄	1	3	yes	—
188	C₄²×C₁₃	C₂×D₄	1	3	yes	—
189	C₄²×C₁₃	C₂⁴	1	3	yes	—
190	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
191	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
192	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
193	#3392	C₂×C₁₃	1	2	yes	complemented
194	#3359	C₂×C₁₃	1	2	yes	complemented
195	#3298	C₂×C₁₃	1	6	yes	complemented
196	D₄×SD₁₆	C₂×C₁₃	1	6	yes	complemented
197	#3246	C₂×C₁₃	1	3	yes	complemented
198	#3206	C₂×C₁₃	1	3	yes	complemented
199	#3101	C₂×C₁₃	1	3	yes	complemented
200	C₂×#461	C₂×C₁₃	1	3	yes	complemented
201	#2988	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	—	2	3	no	—
204	C₂³×C₁₃	—	4	6	no	—
205	C₂³×C₁₃	—	4	6	no	—
206	C₂³×C₁₃	—	8	3	no	—
207	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
208	Q₈×C₁₃	—	2	6	no	—
209	Q₈×C₁₃	—	2	6	no	—
210	Q₈×C₁₃	—	4	2	no	—
211	Q₈×C₁₃	—	4	6	no	—
212	Q₈×C₁₃	—	8	6	no	—
213	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	complemented
214	D₄×C₁₃	—	2	3	no	—
215	D₄×C₁₃	—	2	1	no	—
216	D₄×C₁₃	—	2	3	no	—
217	D₄×C₁₃	—	4	6	no	—
218	D₄×C₁₃	—	4	12	no	—
219	D₄×C₁₃	—	4	6	no	—
220	D₄×C₁₃	—	8	3	no	—
221	D₄×C₁₃	C₂×SD₁₆	1	12	yes	complemented
222	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
223	C₂×C₄×C₁₃	—	2	3	no	—
224	C₂×C₄×C₁₃	—	2	3	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	6	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	3	no	—
229	C₂×C₄×C₁₃	—	4	3	no	—
230	C₂×C₄×C₁₃	—	4	6	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	6	no	—
233	C₂×C₄×C₁₃	—	4	6	no	—
234	C₂×C₄×C₁₃	—	4	6	no	—
235	C₂×C₄×C₁₃	—	8	6	no	—
236	C₂×C₄×C₁₃	C₂×SD₁₆	1	12	yes	complemented
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
243	C₈×C₁₃	—	2	6	no	—
244	C₈×C₁₃	—	2	2	no	—
245	C₂²×#41	—	2	1	no	—
246	C₂²×SD₁₆	C₂²×C₁₃	1	6	yes	—
247	Q₈²	—	2	1	no	—
248	#557	C₂²×C₁₃	1	2	yes	complemented
249	#554	—	2	3	no	—
250	#550	C₂²×C₁₃	1	1	yes	characteristic
251	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
252	D₄×Q₈	C₂²×C₁₃	1	6	yes	complemented
253	#548	—	2	1	no	—
254	#547	C₂²×C₁₃	1	3	yes	—
255	#546	—	2	3	no	—
256	D₄²	C₂²×C₁₃	1	3	yes	—
257	#544	—	2	3	no	—
258	#533	C₂²×C₁₃	1	3	yes	complemented
259	#532	C₂²×C₁₃	1	3	yes	—
260	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
261	#525	—	2	3	no	—
262	#520	—	2	1	no	—
263	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
265	#492	C₂²×C₁₃	1	6	yes	complemented
266	#487	C₂²×C₁₃	1	6	yes	complemented
267	#483	C₂²×C₁₃	1	6	yes	complemented
268	#476	C₂²×C₁₃	1	1	yes	characteristic
269	#476	C₂²×C₁₃	1	3	yes	complemented
270	#475	C₂²×C₁₃	1	6	yes	complemented
271	#465	C₂²×C₁₃	1	12	yes	complemented
272	#461	C₂²×C₁₃	1	3	yes	—
273	#461	C₂²×C₁₃	1	6	yes	—
274	#461	C₂²×C₁₃	1	3	yes	complemented
275	#461	C₂²×C₁₃	1	6	yes	complemented
276	#461	C₂²×C₁₃	1	6	yes	complemented
277	#460	C₂²×C₁₃	1	6	yes	complemented
278	#450	C₂²×C₁₃	1	6	yes	—
279	#448	C₂²×C₁₃	1	12	yes	complemented
280	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
281	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
282	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
283	C₈×D₄	C₂²×C₁₃	1	6	yes	complemented
284	#431	C₂²×C₁₃	1	3	yes	complemented
285	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	complemented
286	C₂×#103	C₂²×C₁₃	1	6	yes	complemented
287	C₂²×C₁₃	—	2	3	no	—
288	C₂²×C₁₃	—	2	3	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	3	no	—
293	C₂²×C₁₃	—	4	3	no	—
294	C₂²×C₁₃	—	4	3	no	—
295	C₂²×C₁₃	—	8	12	no	—
296	C₂²×C₁₃	C₂²×SD₁₆	1	6	yes	—
297	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	3	no	—
300	C₄×C₁₃	—	2	3	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	6	no	—
303	C₄×C₁₃	—	4	1	no	—
304	C₄×C₁₃	—	4	3	no	—
305	C₄×C₁₃	C₂²×SD₁₆	1	2	yes	—
306	C₄×C₁₃	C₂²×SD₁₆	1	6	yes	—
307	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	C₄×C₁₃	#585	1	1	yes	characteristic
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	2	3	no	—
311	C₂×#41	—	2	3	no	—
312	C₂×#41	—	4	8	no	—
313	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
316	C₂²×D₄	—	2	3	no	—
317	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
318	C₂³×C₄	—	2	3	no	—
319	C₂×SD₁₆	—	4	12	no	—
320	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
321	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
322	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
323	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
324	C₄⋊Q₈	—	2	6	no	—
325	C₄⋊Q₈	—	2	3	no	—
326	C₄⋊Q₈	—	2	3	no	—
327	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
328	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
329	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
330	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	#127	C₂³×C₁₃	1	3	yes	—
332	#125	—	2	6	no	—
333	#125	—	2	3	no	—
334	#124	—	2	3	no	—
335	#123	—	2	6	no	—
336	C₂²⋊Q₈	—	2	3	no	—
337	C₂²⋊Q₈	—	2	3	no	—
338	C₂²⋊Q₈	—	2	3	no	—
339	C₂²⋊Q₈	—	2	12	no	—
340	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
341	#121	—	2	3	no	—
342	#121	—	2	3	no	—
343	#121	—	2	3	no	—
344	#121	C₂³×C₁₃	1	6	yes	—
345	#120	—	2	6	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	3	no	—
348	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
349	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
350	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₄×D₄	—	2	6	no	—
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	—	2	3	no	—
355	C₄×D₄	D₄×C₁₃	1	3	yes	—
356	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₄×D₄	C₂³×C₁₃	1	3	yes	—
358	C₄×D₄	C₂³×C₁₃	1	3	yes	—
359	C₄×D₄	C₂³×C₁₃	1	3	yes	—
360	C₄×D₄	C₂³×C₁₃	1	3	yes	—
361	#117	—	2	3	no	—
362	#117	D₄×C₁₃	1	3	yes	—
363	C₂×C₄⋊C₄	—	2	3	no	—
364	C₂×C₄⋊C₄	—	2	3	no	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
366	C₂×C₂²⋊C₄	—	2	3	no	—
367	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
368	#106	C₂³×C₁₃	1	6	yes	—
369	#106	C₂³×C₁₃	1	2	yes	—
370	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
371	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
372	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
373	#103	C₂³×C₁₃	1	6	yes	—
374	#103	C₂³×C₁₃	1	12	yes	—
375	#103	C₂³×C₁₃	1	6	yes	—
376	#102	C₂³×C₁₃	1	2	yes	—
377	#102	C₂³×C₁₃	1	6	yes	—
378	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
379	C₄×C₈	C₂³×C₁₃	1	6	yes	—
380	C₂×C₁₃	—	2	6	no	—
381	C₂×C₁₃	—	4	2	no	—
382	C₂×C₁₃	—	8	3	no	—
383	C₂×C₁₃	#3488	1	1	yes	characteristic
384	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
385	C₂×C₁₃	#3586	1	1	yes	characteristic
386	C₂⁴	—	2	3	no	—
387	#41	—	4	4	no	—
388	#41	—	4	12	no	—
389	#41	—	4	12	no	—
390	#41	C₁₃×SD₁₆	1	8	yes	complemented
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	3	no	—
393	C₂×Q₈	—	2	6	no	—
394	C₂×Q₈	—	4	6	no	—
395	C₂×Q₈	—	4	6	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
399	C₂×D₄	—	2	6	no	—
400	C₂×D₄	—	2	6	no	—
401	C₂×D₄	—	2	3	no	—
402	C₂×D₄	—	2	3	no	—
403	C₂×D₄	—	2	3	no	—
404	C₂×D₄	—	4	3	no	—
405	C₂×D₄	—	4	12	no	—
406	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
407	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
408	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	—	2	3	no	—
410	C₂²×C₄	—	2	6	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	3	no	—
413	C₂²×C₄	—	2	3	no	—
414	C₂²×C₄	—	2	3	no	—
415	C₂²×C₄	—	4	12	no	—
416	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
417	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
419	SD₁₆	—	2	12	no	—
420	SD₁₆	—	4	12	no	—
421	SD₁₆	—	4	6	no	—
422	C₂×C₈	—	4	6	no	—
423	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
424	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
425	C₄⋊C₄	—	2	3	no	—
426	C₄⋊C₄	—	2	3	no	—
427	C₄⋊C₄	—	2	6	no	—
428	C₄⋊C₄	—	2	6	no	—
429	C₄⋊C₄	—	2	3	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	3	no	—
432	C₄⋊C₄	—	2	6	no	—
433	C₄⋊C₄	—	2	6	no	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
436	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
437	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
439	C₂²⋊C₄	—	2	6	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	3	no	—
442	C₂²⋊C₄	—	2	3	no	—
443	C₂²⋊C₄	—	2	3	no	—
444	C₂²⋊C₄	—	2	6	no	—
445	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
446	C₄²	—	2	6	no	—
447	C₄²	C₂×D₄×C₁₃	1	3	yes	—
448	C₄²	C₂×D₄×C₁₃	1	3	yes	—
449	C₄²	C₂⁴×C₁₃	1	3	yes	—
450	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₁₃	#61948	1	1	yes	characteristic, direct product factor, Sylow
452	C₂³	—	2	1	no	—
453	C₂³	—	2	3	no	—
454	C₂³	—	4	6	no	—
455	C₂³	—	4	6	no	—
456	C₂³	—	8	3	no	—
457	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
458	Q₈	—	2	6	no	—
459	Q₈	—	2	6	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	6	no	—
462	Q₈	—	8	6	no	—
463	Q₈	C₂×C₁₃×SD₁₆	1	4	yes	complemented
464	D₄	—	2	3	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	3	no	—
467	D₄	—	4	6	no	—
468	D₄	—	4	12	no	—
469	D₄	—	4	6	no	—
470	D₄	—	8	3	no	—
471	D₄	C₂×C₁₃×SD₁₆	1	12	yes	complemented
472	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	2	3	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	3	no	—
479	C₂×C₄	—	4	3	no	—
480	C₂×C₄	—	4	6	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	6	no	—
483	C₂×C₄	—	4	6	no	—
484	C₂×C₄	—	4	6	no	—
485	C₂×C₄	—	8	6	no	—
486	C₂×C₄	C₂×C₁₃×SD₁₆	1	12	yes	complemented
487	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
490	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
493	C₈	—	2	6	no	—
494	C₈	—	2	2	no	—
495	C₂²	—	2	3	no	—
496	C₂²	—	2	3	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	3	no	—
501	C₂²	—	4	3	no	—
502	C₂²	—	4	3	no	—
503	C₂²	—	8	12	no	—
504	C₂²	C₂²×C₁₃×SD₁₆	1	6	yes	—
505	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	3	no	—
508	C₄	—	2	3	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	3	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	6	no	—
513	C₄	C₂²×C₁₃×SD₁₆	1	2	yes	—
514	C₄	C₂²×C₁₃×SD₁₆	1	6	yes	—
515	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
516	C₄	C₁₃×#585	1	1	yes	characteristic
517	C₂	—	2	6	no	—
518	C₂	—	4	2	no	—
519	C₂	—	8	3	no	—
520	C₂	C₁₃×#3488	1	1	yes	characteristic
521	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
522	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	D₄×C₁₃×#41	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. C₁₃×#3392	C₂	semidirect
4. C₁₃×#3359	C₂	semidirect
5. C₁₃×#3298	C₂	semidirect
6. D₄×C₁₃×SD₁₆	C₂	semidirect
7. C₁₃×#3246	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3101	C₂	semidirect
10. C₂×C₁₃×#461	C₂	semidirect
11. C₁₃×#2988	C₂	semidirect
15. C₁₃×#557	C₂²	semidirect
19. D₄×Q₈×C₁₃	C₂²	semidirect
25. C₁₃×#533	C₂²	semidirect
27. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₁₃×#492	C₂²	semidirect
33. C₁₃×#487	C₂²	semidirect
34. C₁₃×#483	C₂²	semidirect
36. C₁₃×#476	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
38. C₁₃×#465	C₂²	semidirect
41. C₁₃×#461	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
43. C₁₃×#461	C₂²	semidirect
44. C₁₃×#460	C₂²	semidirect
46. C₁₃×#448	C₂²	semidirect
47. C₈×Q₈×C₁₃	C₂²	semidirect
49. C₄×C₁₃×SD₁₆	C₂²	semidirect
50. C₈×D₄×C₁₃	C₂²	semidirect
51. C₁₃×#431	C₂²	semidirect
52. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
53. C₂×C₁₃×#103	C₂²	semidirect
125. #61948	C₁₃	direct (N × H)
130. C₁₃×#41	SD₁₆	semidirect
191. #3503	C₂×C₁₃	semidirect
193. #3392	C₂×C₁₃	semidirect
194. #3359	C₂×C₁₃	semidirect
195. #3298	C₂×C₁₃	semidirect
196. D₄×SD₁₆	C₂×C₁₃	semidirect
197. #3246	C₂×C₁₃	semidirect
198. #3206	C₂×C₁₃	semidirect
199. #3101	C₂×C₁₃	semidirect
200. C₂×#461	C₂×C₁₃	semidirect
201. #2988	C₂×C₁₃	semidirect
213. Q₈×C₁₃	C₂×SD₁₆	semidirect
221. D₄×C₁₃	C₂×SD₁₆	semidirect
236. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
248. #557	C₂²×C₁₃	semidirect
252. D₄×Q₈	C₂²×C₁₃	semidirect
258. #533	C₂²×C₁₃	semidirect
260. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
265. #492	C₂²×C₁₃	semidirect
266. #487	C₂²×C₁₃	semidirect
267. #483	C₂²×C₁₃	semidirect
269. #476	C₂²×C₁₃	semidirect
270. #475	C₂²×C₁₃	semidirect
271. #465	C₂²×C₁₃	semidirect
274. #461	C₂²×C₁₃	semidirect
275. #461	C₂²×C₁₃	semidirect
276. #461	C₂²×C₁₃	semidirect
277. #460	C₂²×C₁₃	semidirect
279. #448	C₂²×C₁₃	semidirect
280. C₈×Q₈	C₂²×C₁₃	semidirect
282. C₄×SD₁₆	C₂²×C₁₃	semidirect
283. C₈×D₄	C₂²×C₁₃	semidirect
284. #431	C₂²×C₁₃	semidirect
285. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
286. C₂×#103	C₂²×C₁₃	semidirect
390. #41	C₁₃×SD₁₆	semidirect
451. C₁₃	#61948	direct (N × H)
463. Q₈	C₂×C₁₃×SD₁₆	semidirect
471. D₄	C₂×C₁₃×SD₁₆	semidirect
486. C₂×C₄	C₂×C₁₃×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3503	2
D₄×C₁₃×#41	2
C₁₃×#3392	2
C₁₃×#3359	2
C₁₃×#3298	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3246	2
C₁₃×#3206	2
C₁₃×#3101	2
C₂×C₁₃×#461	2
C₁₃×#2988	2
#61948	13

Subgroups — C13×#61948 #15748287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61948 #15748287