Subgroups — C₁₃×#33516 #15719855

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#508	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2185	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2184	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2138	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂×C₁₃×#135	—	2	8	no	—
14	C₂×C₁₃×#135	—	2	1	no	—
15	C₂×C₁₃×#135	—	2	1	no	—
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	2	yes	—
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	—	2	1	no	—
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#525	—	2	1	no	—
24	C₁₃×#508	—	2	8	no	—
25	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
26	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
27	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
28	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
30	C₁₃×#467	C₂²	1	1	yes	characteristic
31	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#466	C₂²	1	1	yes	characteristic
33	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#465	—	2	1	no	—
35	C₁₃×#465	—	2	1	no	—
36	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#416	—	2	1	no	—
38	C₁₃×#358	C₂²	1	2	yes	complemented
39	C₁₃×#358	C₂²	1	2	yes	complemented
40	C₁₃×#357	C₂²	1	2	yes	complemented
41	C₁₃×#357	C₂²	1	2	yes	complemented
42	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
44	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#41	—	2	8	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂×C₁₃×#41	—	4	4	no	—
50	C₂×C₁₃×#41	—	4	1	no	—
51	C₂×C₁₃×#41	—	4	1	no	—
52	C₂²×Q₈×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	4	1	no	—
55	C₂³×C₄×C₁₃	—	4	1	no	—
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₁₃×#135	—	2	8	no	—
58	C₁₃×#135	—	2	8	no	—
59	C₁₃×#135	—	2	4	no	—
60	C₁₃×#135	—	2	4	no	—
61	C₁₃×#135	—	2	4	no	—
62	C₁₃×#135	—	2	4	no	—
63	C₁₃×#135	D₄	1	8	yes	complemented
64	C₂×C₁₃×Q₁₆	—	2	4	no	—
65	C₂×C₁₃×Q₁₆	—	2	1	no	—
66	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×SD₁₆	—	2	8	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	—	2	2	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×D₈	—	2	4	no	—
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×D₈	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₃	—	2	4	no	—
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#123	—	4	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	1	no	—
86	C₁₃×#121	—	2	1	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#120	—	4	1	no	—
89	C₄×D₄×C₁₃	—	4	1	no	—
90	C₄×D₄×C₁₃	—	4	1	no	—
91	C₁₃×#117	—	2	1	no	—
92	C₁₃×Q₃₂	—	2	4	no	—
93	C₁₃×SD₃₂	—	2	4	no	—
94	C₁₃×SD₃₂	—	2	4	no	—
95	C₁₃×D₁₆	—	2	4	no	—
96	C₂×C₁₃×C₁₆	—	2	4	no	—
97	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
99	C₁₃×#107	C₂³	1	1	yes	characteristic
100	C₁₃×#107	C₂³	1	1	yes	characteristic
101	C₁₃×#106	—	2	1	no	—
102	C₁₃×#103	—	2	1	no	—
103	C₁₃×#103	—	2	1	no	—
104	C₁₃×#102	—	2	1	no	—
105	C₁₃×#102	—	2	1	no	—
106	#33516	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	4	1	no	—
108	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
109	C₁₃×#41	—	2	8	no	—
110	C₁₃×#41	—	2	8	no	—
111	C₁₃×#41	—	4	8	no	—
112	C₁₃×#41	—	4	4	no	—
113	C₁₃×#41	—	4	8	no	—
114	C₁₃×#41	—	4	4	no	—
115	C₁₃×#41	—	4	2	no	—
116	C₁₃×#41	—	4	2	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	2	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	4	2	no	—
121	C₂×Q₈×C₁₃	—	4	1	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	—	4	8	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	4	2	no	—
129	C₂×D₄×C₁₃	—	4	1	no	—
130	C₂×D₄×C₁₃	—	4	1	no	—
131	C₂×D₄×C₁₃	—	4	1	no	—
132	C₂×D₄×C₁₃	—	4	1	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	4	8	no	—
136	C₂²×C₄×C₁₃	—	4	1	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	1	no	—
140	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×Q₁₆	—	2	4	no	—
147	C₁₃×Q₁₆	—	2	2	no	—
148	C₁₃×Q₁₆	—	2	2	no	—
149	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
150	C₁₃×SD₁₆	—	2	8	no	—
151	C₁₃×SD₁₆	—	2	8	no	—
152	C₁₃×SD₁₆	—	4	2	no	—
153	C₁₃×D₈	—	2	4	no	—
154	C₁₃×D₈	—	2	2	no	—
155	C₁₃×D₈	—	2	2	no	—
156	C₁₃×D₈	C₂×D₄	1	4	yes	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	4	1	no	—
170	C₁₃×C₄⋊C₄	—	4	1	no	—
171	C₁₃×C₂²⋊C₄	—	4	1	no	—
172	C₁₃×C₂²⋊C₄	—	4	1	no	—
173	C₁₃×C₂²⋊C₄	—	4	1	no	—
174	C₁₃×C₂²⋊C₄	—	4	1	no	—
175	C₁₃×C₂²⋊C₄	—	4	1	no	—
176	C₄²×C₁₃	—	4	1	no	—
177	C₁₃×C₁₆	—	2	2	no	—
178	C₁₃×C₁₆	—	2	2	no	—
179	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂×#508	C₂×C₁₃	1	2	yes	complemented
181	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2189	C₂×C₁₃	1	2	yes	complemented
183	#2188	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#2187	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2186	C₂×C₁₃	1	2	yes	complemented
186	#2185	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#2184	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2138	C₂×C₁₃	1	2	yes	complemented
189	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	4	1	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	2	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	8	2	no	—
197	C₂³×C₁₃	—	8	2	no	—
198	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
199	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
201	Q₈×C₁₃	—	2	4	no	—
202	Q₈×C₁₃	—	4	4	no	—
203	Q₈×C₁₃	—	4	2	no	—
204	Q₈×C₁₃	—	4	1	no	—
205	Q₈×C₁₃	—	4	1	no	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	4	8	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	4	1	no	—
213	D₄×C₁₃	—	8	2	no	—
214	D₄×C₁₃	—	8	2	no	—
215	D₄×C₁₃	—	8	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	8	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	8	2	no	—
231	C₂×C₄×C₁₃	#120	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
235	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	C₈×C₁₃	—	2	1	no	—
238	C₈×C₁₃	—	2	1	no	—
239	C₈×C₁₃	#120	1	2	yes	—
240	C₈×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂²×#41	—	2	1	no	—
242	C₂×#135	—	2	8	no	—
243	C₂×#135	—	2	1	no	—
244	C₂×#135	—	2	1	no	—
245	C₂×#135	C₂²×C₁₃	1	2	yes	—
246	C₂×#135	C₂²×C₁₃	1	2	yes	—
247	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
248	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×SD₁₆	—	2	1	no	—
250	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
252	#525	—	2	1	no	—
253	#508	—	2	8	no	—
254	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
255	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
256	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
257	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
258	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
259	#467	C₂²×C₁₃	1	1	yes	characteristic
260	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
261	#466	C₂²×C₁₃	1	1	yes	characteristic
262	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
263	#465	—	2	1	no	—
264	#465	—	2	1	no	—
265	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#416	—	2	1	no	—
267	#358	C₂²×C₁₃	1	2	yes	complemented
268	#358	C₂²×C₁₃	1	2	yes	complemented
269	#357	C₂²×C₁₃	1	2	yes	complemented
270	#357	C₂²×C₁₃	1	2	yes	complemented
271	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	4	no	—
283	C₂²×C₁₃	—	8	8	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	—	8	2	no	—
286	C₂²×C₁₃	—	8	1	no	—
287	C₂²×C₁₃	—	8	1	no	—
288	C₂²×C₁₃	—	8	1	no	—
289	C₂²×C₁₃	#447	1	2	yes	—
290	C₂²×C₁₃	#508	1	2	yes	complemented
291	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	—	8	1	no	—
297	C₄×C₁₃	—	8	1	no	—
298	C₄×C₁₃	#447	1	2	yes	—
299	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
300	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂×#41	—	2	8	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	4	4	no	—
306	C₂×#41	—	4	1	no	—
307	C₂×#41	—	4	1	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	4	1	no	—
311	C₂³×C₄	—	4	1	no	—
312	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
313	#135	—	2	8	no	—
314	#135	—	2	8	no	—
315	#135	—	2	4	no	—
316	#135	—	2	4	no	—
317	#135	—	2	4	no	—
318	#135	—	2	4	no	—
319	#135	D₄×C₁₃	1	8	yes	complemented
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	—	2	1	no	—
322	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
324	C₂×SD₁₆	—	2	8	no	—
325	C₂×SD₁₆	—	2	2	no	—
326	C₂×SD₁₆	—	2	2	no	—
327	C₂×SD₁₆	—	2	1	no	—
328	C₂×D₈	—	2	4	no	—
329	C₂×D₈	—	2	1	no	—
330	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×D₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	—	2	4	no	—
333	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	#123	—	4	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#120	—	4	1	no	—
345	C₄×D₄	—	4	1	no	—
346	C₄×D₄	—	4	1	no	—
347	#117	—	2	1	no	—
348	Q₃₂	—	2	4	no	—
349	SD₃₂	—	2	4	no	—
350	SD₃₂	—	2	4	no	—
351	D₁₆	—	2	4	no	—
352	C₂×C₁₆	—	2	4	no	—
353	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
354	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
355	#107	C₂³×C₁₃	1	1	yes	characteristic
356	#107	C₂³×C₁₃	1	1	yes	characteristic
357	#106	—	2	1	no	—
358	#103	—	2	1	no	—
359	#103	—	2	1	no	—
360	#102	—	2	1	no	—
361	#102	—	2	1	no	—
362	C₂×C₁₃	—	2	2	no	—
363	C₂×C₁₃	—	2	2	no	—
364	C₂×C₁₃	—	4	1	no	—
365	C₂×C₁₃	—	8	4	no	—
366	C₂×C₁₃	—	16	1	no	—
367	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
369	C₂×C₁₃	#3414	1	1	yes	characteristic
370	C₂⁴	—	4	1	no	—
371	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
372	#41	—	2	8	no	—
373	#41	—	2	8	no	—
374	#41	—	4	8	no	—
375	#41	—	4	8	no	—
376	#41	—	4	4	no	—
377	#41	—	4	4	no	—
378	#41	—	4	2	no	—
379	#41	—	4	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	4	2	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	—	4	1	no	—
395	C₂×D₄	—	4	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	4	8	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
404	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
405	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	Q₁₆	—	2	4	no	—
410	Q₁₆	—	2	2	no	—
411	Q₁₆	—	2	2	no	—
412	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
413	SD₁₆	—	2	8	no	—
414	SD₁₆	—	2	8	no	—
415	SD₁₆	—	4	2	no	—
416	D₈	—	2	4	no	—
417	D₈	—	2	2	no	—
418	D₈	—	2	2	no	—
419	D₈	C₂×D₄×C₁₃	1	4	yes	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
429	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	1	no	—
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	—	4	1	no	—
439	C₄²	—	4	1	no	—
440	C₁₆	—	2	2	no	—
441	C₁₆	—	2	2	no	—
442	C₁₃	#33516	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	8	2	no	—
450	C₂³	—	8	2	no	—
451	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
452	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
453	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
454	Q₈	—	2	4	no	—
455	Q₈	—	4	4	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	D₄	—	2	4	no	—
460	D₄	—	4	4	no	—
461	D₄	—	4	8	no	—
462	D₄	—	4	8	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	1	no	—
466	D₄	—	8	2	no	—
467	D₄	—	8	2	no	—
468	D₄	—	8	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	C₁₃×#120	1	2	yes	—
485	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
488	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	C₁₃×#120	1	2	yes	—
493	C₈	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	8	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	C₁₃×#447	1	2	yes	—
510	C₂²	C₁₃×#508	1	2	yes	complemented
511	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	4	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	C₁₃×#447	1	2	yes	—
519	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
520	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	2	2	no	—
523	C₂	—	4	1	no	—
524	C₂	—	8	4	no	—
525	C₂	—	16	1	no	—
526	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
527	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
528	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂×C₁₃×#508	C₂	semidirect
3. C₁₃×#3050	C₂	semidirect
4. C₁₃×#2189	C₂	semidirect
5. C₁₃×#2188	C₂	semidirect
6. C₁₃×#2187	C₂	semidirect
7. C₁₃×#2186	C₂	semidirect
8. C₁₃×#2185	C₂	semidirect
9. C₁₃×#2184	C₂	semidirect
10. C₁₃×#2138	C₂	semidirect
11. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
25. C₂×C₁₃×Q₃₂	C₂²	semidirect
26. C₂×C₁₃×SD₃₂	C₂²	semidirect
27. C₂×C₁₃×SD₃₂	C₂²	semidirect
28. C₂×C₁₃×D₁₆	C₂²	semidirect
29. C₂²×C₁₃×C₁₆	C₂²	semidirect
31. C₁₃×#467	C₂²	semidirect
33. C₁₃×#466	C₂²	semidirect
36. C₁₃×#427	C₂²	semidirect
38. C₁₃×#358	C₂²	semidirect
39. C₁₃×#358	C₂²	semidirect
40. C₁₃×#357	C₂²	semidirect
41. C₁₃×#357	C₂²	semidirect
44. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
63. C₁₃×#135	D₄	semidirect
106. #33516	C₁₃	direct (N × H)
179. C₂²×#135	C₂×C₁₃	semidirect
180. C₂×#508	C₂×C₁₃	semidirect
181. #3050	C₂×C₁₃	semidirect
182. #2189	C₂×C₁₃	semidirect
183. #2188	C₂×C₁₃	semidirect
184. #2187	C₂×C₁₃	semidirect
185. #2186	C₂×C₁₃	semidirect
186. #2185	C₂×C₁₃	semidirect
187. #2184	C₂×C₁₃	semidirect
188. #2138	C₂×C₁₃	semidirect
189. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
247. C₂×#135	C₂²×C₁₃	semidirect
254. C₂×Q₃₂	C₂²×C₁₃	semidirect
255. C₂×SD₃₂	C₂²×C₁₃	semidirect
256. C₂×SD₃₂	C₂²×C₁₃	semidirect
257. C₂×D₁₆	C₂²×C₁₃	semidirect
258. C₂²×C₁₆	C₂²×C₁₃	semidirect
260. #467	C₂²×C₁₃	semidirect
262. #466	C₂²×C₁₃	semidirect
265. #427	C₂²×C₁₃	semidirect
267. #358	C₂²×C₁₃	semidirect
268. #358	C₂²×C₁₃	semidirect
269. #357	C₂²×C₁₃	semidirect
270. #357	C₂²×C₁₃	semidirect
273. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
290. C₂²×C₁₃	#508	semidirect
319. #135	D₄×C₁₃	semidirect
442. C₁₃	#33516	direct (N × H)
510. C₂²	C₁₃×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#508	2
C₁₃×#3050	2
C₁₃×#2189	2
C₁₃×#2188	2
C₁₃×#2187	2
C₁₃×#2186	2
C₁₃×#2185	2
C₁₃×#2184	2
C₁₃×#2138	2
C₂×C₁₃×C₂²⋊C₁₆	2
#33516	13

Subgroups — C13×#33516 #15719855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33516 #15719855