Subgroups — C₁₃×#61562 #15747901

Order 3328.

2370 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3298	C₂	1	8	yes	maximal, complemented
4	D₄×C₁₃×SD₁₆	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3187	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#448	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
13	D₄×Q₈×C₁₃	—	2	4	no	—
14	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
15	C₁₃×#547	C₂²	1	4	yes	—
16	C₁₃×#546	—	2	4	no	—
17	D₄²×C₁₃	C₂²	1	4	yes	—
18	C₁₃×#537	—	2	1	no	—
19	C₁₃×#534	—	2	2	no	—
20	C₁₃×#532	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	4	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₁₃	—	2	1	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#492	C₂²	1	4	yes	complemented
30	C₁₃×#487	C₂²	1	4	yes	complemented
31	C₁₃×#483	C₂²	1	8	yes	complemented
32	C₁₃×#481	C₂²	1	4	yes	complemented
33	C₁₃×#475	C₂²	1	4	yes	complemented
34	C₁₃×#465	C₂²	1	16	yes	complemented
35	C₁₃×#461	C₂²	1	8	yes	complemented
36	C₁₃×#460	C₂²	1	4	yes	complemented
37	C₁₃×#450	C₂²	1	8	yes	complemented
38	C₁₃×#448	C₂²	1	16	yes	complemented
39	C₁₃×#448	C₂²	1	4	yes	complemented
40	C₁₃×#448	C₂²	1	8	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#103	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
46	C₁₃×H(5,𝔽₂)	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	2	2	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	4	8	no	—
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	—	2	2	no	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂×C₁₃×SD₁₆	—	4	16	no	—
62	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
63	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
65	C₁₃×C₄⋊Q₈	—	2	8	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#127	C₂³	1	2	yes	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#123	—	2	8	no	—
72	C₁₃×C₂²⋊Q₈	—	2	4	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	16	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×#121	—	2	4	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#121	C₂³	1	4	yes	—
81	C₁₃×#121	C₂³	1	8	yes	—
82	C₁₃×#120	—	2	8	no	—
83	C₄×Q₈×C₁₃	—	2	2	no	—
84	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₄×D₄×C₁₃	—	2	8	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	D₄	1	4	yes	—
88	C₄×D₄×C₁₃	C₂³	1	4	yes	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#106	C₂³	1	8	yes	—
103	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#103	C₂³	1	16	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
109	C₄×C₈×C₁₃	C₂³	1	4	yes	—
110	#61562	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
113	C₁₃×#41	—	4	16	no	—
114	C₁₃×#41	—	4	8	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	16	no	—
121	C₂×Q₈×C₁₃	—	4	8	no	—
122	C₂×Q₈×C₁₃	—	4	4	no	—
123	C₂×Q₈×C₁₃	—	4	8	no	—
124	C₂×Q₈×C₁₃	—	4	16	no	—
125	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
126	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	4	8	no	—
133	C₂×D₄×C₁₃	—	4	16	no	—
134	C₂×D₄×C₁₃	—	4	16	no	—
135	C₂×D₄×C₁₃	SD₁₆	1	8	yes	complemented
136	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
137	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	8	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	—	4	8	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₁₃×SD₁₆	—	2	16	no	—
153	C₁₃×SD₁₆	—	4	16	no	—
154	C₂×C₈×C₁₃	—	4	8	no	—
155	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
171	C₄²×C₁₃	—	2	4	no	—
172	C₄²×C₁₃	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃	C₂⁴	1	2	yes	—
174	#3496	C₂×C₁₃	1	1	yes	characteristic
175	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3298	C₂×C₁₃	1	8	yes	complemented
177	D₄×SD₁₆	C₂×C₁₃	1	8	yes	complemented
178	#3206	C₂×C₁₃	1	2	yes	complemented
179	#3187	C₂×C₁₃	1	4	yes	complemented
180	#3103	C₂×C₁₃	1	2	yes	complemented
181	C₂×#448	C₂×C₁₃	1	4	yes	complemented
182	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	8	no	—
187	C₂³×C₁₃	—	8	4	no	—
188	C₂³×C₁₃	—	8	4	no	—
189	C₂³×C₁₃	C₂×SD₁₆	1	8	yes	complemented
190	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	2	2	no	—
194	Q₈×C₁₃	—	2	8	no	—
195	Q₈×C₁₃	—	4	16	no	—
196	Q₈×C₁₃	—	4	4	no	—
197	Q₈×C₁₃	—	4	4	no	—
198	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
199	D₄×C₁₃	—	2	8	no	—
200	D₄×C₁₃	—	4	16	no	—
201	D₄×C₁₃	—	4	8	no	—
202	D₄×C₁₃	—	4	4	no	—
203	D₄×C₁₃	—	8	2	no	—
204	D₄×C₁₃	—	8	4	no	—
205	D₄×C₁₃	C₂×SD₁₆	1	16	yes	complemented
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	16	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	8	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	complemented
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
227	C₈×C₁₃	—	2	8	no	—
228	C₂×H(5,𝔽₂)	—	2	1	no	—
229	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
230	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
231	D₄×Q₈	—	2	4	no	—
232	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
233	#547	C₂²×C₁₃	1	4	yes	—
234	#546	—	2	4	no	—
235	D₄²	C₂²×C₁₃	1	4	yes	—
236	#537	—	2	1	no	—
237	#534	—	2	2	no	—
238	#532	C₂²×C₁₃	1	2	yes	—
239	C₂×C₄⋊Q₈	—	2	1	no	—
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	C₂×C₂²⋊Q₈	—	2	2	no	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
243	C₂×#121	C₂²×C₁₃	1	4	yes	—
244	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
245	C₂×C₄×D₄	—	2	1	no	—
246	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
247	#492	C₂²×C₁₃	1	4	yes	complemented
248	#487	C₂²×C₁₃	1	4	yes	complemented
249	#483	C₂²×C₁₃	1	8	yes	complemented
250	#481	C₂²×C₁₃	1	4	yes	complemented
251	#475	C₂²×C₁₃	1	4	yes	complemented
252	#465	C₂²×C₁₃	1	16	yes	complemented
253	#461	C₂²×C₁₃	1	8	yes	complemented
254	#460	C₂²×C₁₃	1	4	yes	complemented
255	#450	C₂²×C₁₃	1	8	yes	complemented
256	#448	C₂²×C₁₃	1	4	yes	complemented
257	#448	C₂²×C₁₃	1	8	yes	complemented
258	#448	C₂²×C₁₃	1	16	yes	complemented
259	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
260	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
261	#431	C₂²×C₁₃	1	2	yes	complemented
262	C₂×#103	C₂²×C₁₃	1	8	yes	complemented
263	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	complemented
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	4	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	4	no	—
268	C₂²×C₁₃	—	4	8	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	16	8	no	—
273	C₂²×C₁₃	C₂²×SD₁₆	1	8	yes	—
274	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
275	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	2	4	no	—
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	4	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	—
284	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
285	H(5,𝔽₂)	—	4	8	no	—
286	C₂×#41	—	2	4	no	—
287	C₂×#41	—	2	2	no	—
288	C₂²×Q₈	—	2	2	no	—
289	C₂²×Q₈	—	2	4	no	—
290	C₂²×Q₈	—	4	8	no	—
291	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
293	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	—	2	4	no	—
296	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	C₂×SD₁₆	—	4	16	no	—
301	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
302	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
304	C₄⋊Q₈	—	2	8	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
307	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
308	#127	C₂³×C₁₃	1	2	yes	—
309	#124	—	2	2	no	—
310	#123	—	2	8	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	16	no	—
314	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
315	#121	—	2	4	no	—
316	#121	—	2	4	no	—
317	#121	—	2	2	no	—
318	#121	—	2	4	no	—
319	#121	C₂³×C₁₃	1	4	yes	—
320	#121	C₂³×C₁₃	1	8	yes	—
321	#120	—	2	8	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
324	C₄×D₄	—	2	8	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	D₄×C₁₃	1	4	yes	—
327	C₄×D₄	C₂³×C₁₃	1	4	yes	—
328	C₄×D₄	C₂³×C₁₃	1	4	yes	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	#106	C₂³×C₁₃	1	8	yes	—
342	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
343	#103	C₂³×C₁₃	1	8	yes	—
344	#103	C₂³×C₁₃	1	16	yes	—
345	#102	C₂³×C₁₃	1	8	yes	—
346	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
347	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
348	C₄×C₈	C₂³×C₁₃	1	4	yes	—
349	C₂×C₁₃	—	2	2	no	—
350	C₂×C₁₃	—	2	8	no	—
351	C₂×C₁₃	—	8	4	no	—
352	C₂×C₁₃	#3484	1	1	yes	characteristic
353	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
354	C₂×C₁₃	#3586	1	1	yes	characteristic
355	C₂⁴	—	2	4	no	—
356	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
357	#41	—	4	16	no	—
358	#41	—	4	8	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	8	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	16	no	—
365	C₂×Q₈	—	4	8	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×Q₈	—	4	8	no	—
368	C₂×Q₈	—	4	16	no	—
369	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
370	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	—	4	16	no	—
378	C₂×D₄	—	4	16	no	—
379	C₂×D₄	C₁₃×SD₁₆	1	8	yes	complemented
380	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
381	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	—	4	8	no	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
396	SD₁₆	—	2	16	no	—
397	SD₁₆	—	4	16	no	—
398	C₂×C₈	—	4	8	no	—
399	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
408	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
409	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
415	C₄²	—	2	4	no	—
416	C₄²	C₂×D₄×C₁₃	1	2	yes	—
417	C₄²	C₂⁴×C₁₃	1	2	yes	—
418	C₁₃	#61562	1	1	yes	characteristic, direct product factor, Sylow
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	8	4	no	—
424	C₂³	—	8	4	no	—
425	C₂³	C₂×C₁₃×SD₁₆	1	8	yes	complemented
426	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
427	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	Q₈	—	2	4	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	2	8	no	—
431	Q₈	—	4	16	no	—
432	Q₈	—	4	4	no	—
433	Q₈	—	4	4	no	—
434	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
435	D₄	—	2	8	no	—
436	D₄	—	4	16	no	—
437	D₄	—	4	8	no	—
438	D₄	—	4	4	no	—
439	D₄	—	8	4	no	—
440	D₄	—	8	2	no	—
441	D₄	C₂×C₁₃×SD₁₆	1	16	yes	complemented
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	16	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	complemented
458	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
462	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
463	C₈	—	2	8	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	16	8	no	—
473	C₂²	C₂²×C₁₃×SD₁₆	1	8	yes	—
474	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
475	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	4	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	4	no	—
483	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	—
484	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	2	8	no	—
487	C₂	—	8	4	no	—
488	C₂	C₁₃×#3484	1	1	yes	characteristic
489	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
490	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×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3298	C₂	semidirect
4. D₄×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#3206	C₂	semidirect
6. C₁₃×#3187	C₂	semidirect
7. C₁₃×#3103	C₂	semidirect
8. C₂×C₁₃×#448	C₂	semidirect
9. C₁₃×#2972	C₂	semidirect
11. C₂³×Q₈×C₁₃	C₂²	semidirect
12. C₂²×C₁₃×SD₁₆	C₂²	semidirect
14. D₄×Q₈×C₁₃	C₂²	semidirect
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#492	C₂²	semidirect
30. C₁₃×#487	C₂²	semidirect
31. C₁₃×#483	C₂²	semidirect
32. C₁₃×#481	C₂²	semidirect
33. C₁₃×#475	C₂²	semidirect
34. C₁₃×#465	C₂²	semidirect
35. C₁₃×#461	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
37. C₁₃×#450	C₂²	semidirect
38. C₁₃×#448	C₂²	semidirect
39. C₁₃×#448	C₂²	semidirect
40. C₁₃×#448	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₈×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#431	C₂²	semidirect
44. C₂×C₁₃×#103	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
110. #61562	C₁₃	direct (N × H)
135. C₂×D₄×C₁₃	SD₁₆	semidirect
175. C₂×D₄×Q₈	C₂×C₁₃	semidirect
176. #3298	C₂×C₁₃	semidirect
177. D₄×SD₁₆	C₂×C₁₃	semidirect
178. #3206	C₂×C₁₃	semidirect
179. #3187	C₂×C₁₃	semidirect
180. #3103	C₂×C₁₃	semidirect
181. C₂×#448	C₂×C₁₃	semidirect
182. #2972	C₂×C₁₃	semidirect
189. C₂³×C₁₃	C₂×SD₁₆	semidirect
198. Q₈×C₁₃	H(5,𝔽₂)	semidirect
205. D₄×C₁₃	C₂×SD₁₆	semidirect
221. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
229. C₂³×Q₈	C₂²×C₁₃	semidirect
230. C₂²×SD₁₆	C₂²×C₁₃	semidirect
232. D₄×Q₈	C₂²×C₁₃	semidirect
240. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
242. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
244. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
247. #492	C₂²×C₁₃	semidirect
248. #487	C₂²×C₁₃	semidirect
249. #483	C₂²×C₁₃	semidirect
250. #481	C₂²×C₁₃	semidirect
251. #475	C₂²×C₁₃	semidirect
252. #465	C₂²×C₁₃	semidirect
253. #461	C₂²×C₁₃	semidirect
254. #460	C₂²×C₁₃	semidirect
255. #450	C₂²×C₁₃	semidirect
256. #448	C₂²×C₁₃	semidirect
257. #448	C₂²×C₁₃	semidirect
258. #448	C₂²×C₁₃	semidirect
259. C₄×SD₁₆	C₂²×C₁₃	semidirect
260. C₈×D₄	C₂²×C₁₃	semidirect
261. #431	C₂²×C₁₃	semidirect
262. C₂×#103	C₂²×C₁₃	semidirect
263. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
379. C₂×D₄	C₁₃×SD₁₆	semidirect
418. C₁₃	#61562	direct (N × H)
425. C₂³	C₂×C₁₃×SD₁₆	semidirect
434. Q₈	C₁₃×H(5,𝔽₂)	semidirect
441. D₄	C₂×C₁₃×SD₁₆	semidirect
457. 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×#3496	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3298	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3206	2
C₁₃×#3187	2
C₁₃×#3103	2
C₂×C₁₃×#448	2
C₁₃×#2972	2
#61562	13

Subgroups — C13×#61562 #15747901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61562 #15747901