Subgroups — C₁₃×#33836 #15720175

Order 3328.

664 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3285	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2219	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2217	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2211	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2209	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2185	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	D₄×Q₈×C₁₃	—	2	1	no	—
21	C₁₃×#548	—	2	1	no	—
22	C₁₃×#510	—	2	4	no	—
23	C₂×C₁₃×Q₃₂	—	2	4	no	—
24	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
35	C₁₃×#495	C₂²	1	1	yes	characteristic
36	C₁₃×#494	C₂²	1	1	yes	characteristic
37	C₁₃×#467	C₂²	1	1	yes	characteristic
38	C₁₃×#467	C₂²	1	1	yes	characteristic
39	C₁₃×#467	C₂²	1	1	yes	characteristic
40	C₁₃×#466	C₂²	1	1	yes	characteristic
41	C₁₃×#464	—	2	1	no	—
42	C₁₃×#462	—	2	1	no	—
43	C₁₃×#452	—	2	1	no	—
44	C₁₃×#451	—	2	1	no	—
45	C₁₃×#451	—	2	1	no	—
46	C₁₃×#448	—	2	1	no	—
47	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
49	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#367	C₂²	1	1	yes	characteristic
51	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
52	C₁₃×#358	C₂²	1	1	yes	characteristic
53	C₁₃×#358	C₂²	1	1	yes	characteristic
54	C₁₃×#358	C₂²	1	1	yes	characteristic
55	C₁₃×#358	C₂²	1	1	yes	characteristic
56	C₁₃×#358	C₂²	1	1	yes	characteristic
57	C₁₃×#357	C₂²	1	1	yes	characteristic
58	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
60	C₁₃×#346	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#41	—	2	1	no	—
62	C₂²×Q₈×C₁₃	—	2	1	no	—
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	—	2	1	no	—
65	C₁₃×#135	—	2	2	no	—
66	C₁₃×#135	—	4	1	no	—
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	—	2	2	no	—
69	C₂×C₁₃×Q₁₆	—	2	2	no	—
70	C₂×C₁₃×Q₁₆	—	2	1	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×Q₁₆	—	2	1	no	—
74	C₂×C₁₃×Q₁₆	—	4	1	no	—
75	C₂×C₁₃×Q₁₆	—	4	1	no	—
76	C₂×C₁₃×Q₁₆	—	4	1	no	—
77	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×SD₁₆	—	2	1	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	4	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#124	—	4	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	4	1	no	—
95	C₁₃×C₂²⋊Q₈	—	4	1	no	—
96	C₁₃×C₂²⋊Q₈	—	4	1	no	—
97	C₁₃×#121	—	2	1	no	—
98	C₁₃×#121	—	4	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×Q₈×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	4	1	no	—
102	C₄×D₄×C₁₃	—	4	1	no	—
103	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₁₃×Q₃₂	—	2	2	no	—
105	C₁₃×Q₃₂	—	2	2	no	—
106	C₁₃×Q₃₂	—	2	2	no	—
107	C₁₃×Q₃₂	—	2	2	no	—
108	C₁₃×Q₃₂	—	4	1	no	—
109	C₁₃×Q₃₂	D₄	1	4	yes	complemented
110	C₁₃×SD₃₂	—	2	2	no	—
111	C₁₃×SD₃₂	—	2	2	no	—
112	C₁₃×SD₃₂	—	4	1	no	—
113	C₁₃×M₃₂	—	2	2	no	—
114	C₂×C₁₃×C₁₆	—	2	2	no	—
115	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
119	C₁₃×#107	C₂³	1	1	yes	characteristic
120	C₁₃×#107	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
131	#33836	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₁₃×#41	—	4	2	no	—
133	C₁₃×#41	—	8	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	4	2	no	—
140	C₂×Q₈×C₁₃	—	4	2	no	—
141	C₂×Q₈×C₁₃	—	4	2	no	—
142	C₂×Q₈×C₁₃	—	4	1	no	—
143	C₂×Q₈×C₁₃	—	4	1	no	—
144	C₂×Q₈×C₁₃	—	4	1	no	—
145	C₂×Q₈×C₁₃	—	8	1	no	—
146	C₂×Q₈×C₁₃	—	8	1	no	—
147	C₂×Q₈×C₁₃	—	8	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	4	1	no	—
150	C₂×D₄×C₁₃	—	4	1	no	—
151	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	—	4	1	no	—
153	C₂²×C₄×C₁₃	—	4	1	no	—
154	C₂²×C₄×C₁₃	—	4	1	no	—
155	C₂²×C₄×C₁₃	—	4	1	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₁₃×Q₁₆	—	2	1	no	—
159	C₁₃×Q₁₆	—	2	1	no	—
160	C₁₃×Q₁₆	—	2	1	no	—
161	C₁₃×Q₁₆	—	2	1	no	—
162	C₁₃×Q₁₆	—	2	1	no	—
163	C₁₃×Q₁₆	—	2	1	no	—
164	C₁₃×Q₁₆	—	2	1	no	—
165	C₁₃×Q₁₆	—	2	1	no	—
166	C₁₃×Q₁₆	—	4	2	no	—
167	C₁₃×Q₁₆	—	4	2	no	—
168	C₁₃×Q₁₆	—	4	2	no	—
169	C₁₃×Q₁₆	—	8	1	no	—
170	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
171	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
172	C₁₃×SD₁₆	—	4	2	no	—
173	C₁₃×SD₁₆	—	8	1	no	—
174	C₁₃×D₈	—	2	1	no	—
175	C₁₃×D₈	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	4	1	no	—
187	C₁₃×C₄⋊C₄	—	4	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	—	4	1	no	—
195	C₁₃×C₂²⋊C₄	—	4	1	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
201	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
202	C₄²×C₁₃	—	4	1	no	—
203	C₄²×C₁₃	—	4	1	no	—
204	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₁₆	—	2	1	no	—
206	C₁₃×C₁₆	—	2	1	no	—
207	C₁₃×C₁₆	—	2	1	no	—
208	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
209	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂²×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
211	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3285	C₂×C₁₃	1	1	yes	characteristic
213	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2219	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2217	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2211	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2209	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2189	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2188	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2188	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2185	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2176	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2168	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	4	1	no	—
225	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
226	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
227	Q₈×C₁₃	—	2	2	no	—
228	Q₈×C₁₃	—	2	2	no	—
229	Q₈×C₁₃	—	4	1	no	—
230	Q₈×C₁₃	—	4	1	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	Q₈×C₁₃	—	4	1	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	8	2	no	—
238	Q₈×C₁₃	—	8	2	no	—
239	Q₈×C₁₃	—	8	2	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	8	2	no	—
244	D₄×C₁₃	—	8	2	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	8	2	no	—
257	C₂×C₄×C₁₃	—	8	2	no	—
258	C₂×C₄×C₁₃	—	8	2	no	—
259	C₂×C₄×C₁₃	—	8	2	no	—
260	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	1	no	—
267	C₈×C₁₃	—	2	1	no	—
268	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
270	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
274	D₄×Q₈	—	2	1	no	—
275	#548	—	2	1	no	—
276	#510	—	2	4	no	—
277	C₂×Q₃₂	—	2	4	no	—
278	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
288	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
289	#495	C₂²×C₁₃	1	1	yes	characteristic
290	#494	C₂²×C₁₃	1	1	yes	characteristic
291	#467	C₂²×C₁₃	1	1	yes	characteristic
292	#467	C₂²×C₁₃	1	1	yes	characteristic
293	#467	C₂²×C₁₃	1	1	yes	characteristic
294	#466	C₂²×C₁₃	1	1	yes	characteristic
295	#464	—	2	1	no	—
296	#462	—	2	1	no	—
297	#452	—	2	1	no	—
298	#451	—	2	1	no	—
299	#451	—	2	1	no	—
300	#448	—	2	1	no	—
301	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
303	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
304	#367	C₂²×C₁₃	1	1	yes	characteristic
305	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
306	#358	C₂²×C₁₃	1	1	yes	characteristic
307	#358	C₂²×C₁₃	1	1	yes	characteristic
308	#358	C₂²×C₁₃	1	1	yes	characteristic
309	#358	C₂²×C₁₃	1	1	yes	characteristic
310	#358	C₂²×C₁₃	1	1	yes	characteristic
311	#357	C₂²×C₁₃	1	1	yes	characteristic
312	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
314	#346	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	8	1	no	—
321	C₂²×C₁₃	—	8	1	no	—
322	C₂²×C₁₃	—	8	1	no	—
323	C₂²×C₁₃	#510	1	2	yes	complemented
324	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	8	1	no	—
332	C₄×C₁₃	—	8	1	no	—
333	C₄×C₁₃	—	8	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	—	8	1	no	—
336	C₄×C₁₃	D₄²	1	1	yes	characteristic
337	C₄×C₁₃	#576	1	1	yes	characteristic
338	C₂×#41	—	2	1	no	—
339	C₂²×Q₈	—	2	1	no	—
340	C₂²×Q₈	—	2	1	no	—
341	C₂²×Q₈	—	2	1	no	—
342	#135	—	2	2	no	—
343	#135	—	4	1	no	—
344	C₂×Q₁₆	—	2	2	no	—
345	C₂×Q₁₆	—	2	2	no	—
346	C₂×Q₁₆	—	2	2	no	—
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×Q₁₆	—	2	1	no	—
350	C₂×Q₁₆	—	2	1	no	—
351	C₂×Q₁₆	—	4	1	no	—
352	C₂×Q₁₆	—	4	1	no	—
353	C₂×Q₁₆	—	4	1	no	—
354	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	4	1	no	—
366	#124	—	2	1	no	—
367	#124	—	4	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	4	1	no	—
372	C₂²⋊Q₈	—	4	1	no	—
373	C₂²⋊Q₈	—	4	1	no	—
374	#121	—	2	1	no	—
375	#121	—	4	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×D₄	—	4	1	no	—
379	C₄×D₄	—	4	1	no	—
380	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
381	Q₃₂	—	2	2	no	—
382	Q₃₂	—	2	2	no	—
383	Q₃₂	—	2	2	no	—
384	Q₃₂	—	2	2	no	—
385	Q₃₂	—	4	1	no	—
386	Q₃₂	D₄×C₁₃	1	4	yes	complemented
387	SD₃₂	—	2	2	no	—
388	SD₃₂	—	2	2	no	—
389	SD₃₂	—	4	1	no	—
390	M₃₂	—	2	2	no	—
391	C₂×C₁₆	—	2	2	no	—
392	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
396	#107	C₂³×C₁₃	1	1	yes	characteristic
397	#107	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#102	—	2	1	no	—
405	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
406	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
407	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₁₃	—	2	2	no	—
409	C₂×C₁₃	—	4	1	no	—
410	C₂×C₁₃	—	16	1	no	—
411	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
412	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
413	C₂×C₁₃	#3417	1	1	yes	characteristic
414	#41	—	4	2	no	—
415	#41	—	8	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	—	8	1	no	—
428	C₂×Q₈	—	8	1	no	—
429	C₂×Q₈	—	8	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
434	C₂²×C₄	—	4	1	no	—
435	C₂²×C₄	—	4	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	Q₁₆	—	2	1	no	—
441	Q₁₆	—	2	1	no	—
442	Q₁₆	—	2	1	no	—
443	Q₁₆	—	2	1	no	—
444	Q₁₆	—	2	1	no	—
445	Q₁₆	—	2	1	no	—
446	Q₁₆	—	2	1	no	—
447	Q₁₆	—	2	1	no	—
448	Q₁₆	—	4	2	no	—
449	Q₁₆	—	4	2	no	—
450	Q₁₆	—	4	2	no	—
451	Q₁₆	—	8	1	no	—
452	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
453	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
454	SD₁₆	—	4	2	no	—
455	SD₁₆	—	8	1	no	—
456	D₈	—	2	1	no	—
457	D₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	1	no	—
478	C₂²⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
483	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₁₆	—	2	1	no	—
488	C₁₆	—	2	1	no	—
489	C₁₆	—	2	1	no	—
490	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
491	C₁₃	#33836	1	1	yes	characteristic, direct product factor, Sylow
492	C₂³	—	4	1	no	—
493	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
494	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
495	Q₈	—	2	2	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	8	2	no	—
506	Q₈	—	8	2	no	—
507	Q₈	—	8	2	no	—
508	D₄	—	2	2	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
529	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
530	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
531	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
537	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	C₁₃×#510	1	2	yes	complemented
547	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	D₄²×C₁₃	1	1	yes	characteristic
560	C₄	C₁₃×#576	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	16	1	no	—
564	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
565	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
566	C₂	C₁₃×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3285	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
2. C₂²×C₁₃×Q₃₂	C₂	semidirect
3. D₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#2251	C₂	semidirect
6. C₁₃×#2219	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2211	C₂	semidirect
9. C₁₃×#2209	C₂	semidirect
10. C₁₃×#2189	C₂	semidirect
11. C₁₃×#2188	C₂	semidirect
12. C₁₃×#2188	C₂	semidirect
13. C₁₃×#2185	C₂	semidirect
14. C₁₃×#2176	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
109. C₁₃×Q₃₂	D₄	semidirect
131. #33836	C₁₃	direct (N × H)
209. C₂×#510	C₂×C₁₃	semidirect
210. C₂²×Q₃₂	C₂×C₁₃	semidirect
211. D₄×Q₁₆	C₂×C₁₃	semidirect
213. #2251	C₂×C₁₃	semidirect
214. #2219	C₂×C₁₃	semidirect
215. #2217	C₂×C₁₃	semidirect
216. #2211	C₂×C₁₃	semidirect
217. #2209	C₂×C₁₃	semidirect
218. #2189	C₂×C₁₃	semidirect
219. #2188	C₂×C₁₃	semidirect
220. #2188	C₂×C₁₃	semidirect
221. #2185	C₂×C₁₃	semidirect
222. #2176	C₂×C₁₃	semidirect
223. #2168	C₂×C₁₃	semidirect
323. C₂²×C₁₃	#510	semidirect
386. Q₃₂	D₄×C₁₃	semidirect
491. C₁₃	#33836	direct (N × H)
546. C₂²	C₁₃×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#510	2
C₂²×C₁₃×Q₃₂	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#2251	2
C₁₃×#2219	2
C₁₃×#2217	2
C₁₃×#2211	2
C₁₃×#2209	2
C₁₃×#2189	2
C₁₃×#2188	2
C₁₃×#2185	2
C₁₃×#2176	2
C₁₃×#2168	2
#33836	13

Subgroups — C13×#33836 #15720175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33836 #15720175