Subgroups — C₁₃×#33834 #15720173

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2220	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2211	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2186	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2186	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2175	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	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#550	—	2	1	no	—
21	C₁₃×#546	—	2	1	no	—
22	C₁₃×#509	—	2	4	no	—
23	C₁₃×#508	—	2	4	no	—
24	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#495	C₂²	1	1	yes	characteristic
36	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#467	C₂²	1	1	yes	characteristic
38	C₁₃×#466	C₂²	1	1	yes	characteristic
39	C₁₃×#466	C₂²	1	1	yes	characteristic
40	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#463	—	2	1	no	—
42	C₁₃×#460	—	2	1	no	—
43	C₁₃×#450	—	2	1	no	—
44	C₁₃×#449	—	2	1	no	—
45	C₁₃×#449	—	2	1	no	—
46	C₁₃×#449	—	2	1	no	—
47	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
49	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#358	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#357	C₂²	1	1	yes	characteristic
55	C₁₃×#357	C₂²	1	1	yes	characteristic
56	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#357	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#346	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#41	—	2	1	no	—
62	C₂×C₁₃×#41	—	2	1	no	—
63	C₂×C₁₃×#41	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	1	no	—
65	C₁₃×#135	—	2	2	no	—
66	C₁₃×#135	—	2	2	no	—
67	C₁₃×#135	—	2	2	no	—
68	C₁₃×#135	—	4	1	no	—
69	C₁₃×#135	—	4	1	no	—
70	C₁₃×#135	—	4	1	no	—
71	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	2	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	1	no	—
80	C₂×C₁₃×D₈	—	4	1	no	—
81	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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×#127	—	2	1	no	—
88	C₁₃×#127	—	4	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	4	1	no	—
96	C₁₃×#121	—	4	1	no	—
97	C₁₃×#121	—	4	1	no	—
98	C₁₃×#120	—	4	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	4	1	no	—
102	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×Q₃₂	—	2	2	no	—
105	C₁₃×SD₃₂	—	2	2	no	—
106	C₁₃×SD₃₂	—	2	2	no	—
107	C₁₃×SD₃₂	—	4	1	no	—
108	C₁₃×SD₃₂	D₄	1	4	yes	complemented
109	C₁₃×D₁₆	—	2	2	no	—
110	C₁₃×D₁₆	—	2	2	no	—
111	C₁₃×D₁₆	—	2	2	no	—
112	C₁₃×D₁₆	—	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×#102	—	2	1	no	—
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	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	#33834	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	4	1	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₁₃×#41	—	8	1	no	—
137	C₁₃×#41	—	8	1	no	—
138	C₁₃×#41	—	8	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	—	4	1	no	—
147	C₂×D₄×C₁₃	—	4	1	no	—
148	C₂×D₄×C₁₃	—	4	1	no	—
149	C₂×D₄×C₁₃	—	4	1	no	—
150	C₂×D₄×C₁₃	—	4	1	no	—
151	C₂×D₄×C₁₃	—	4	1	no	—
152	C₂×D₄×C₁₃	—	4	1	no	—
153	C₂×D₄×C₁₃	—	4	1	no	—
154	C₂×D₄×C₁₃	—	4	1	no	—
155	C₂×D₄×C₁₃	—	8	1	no	—
156	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	—	4	1	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₂²×C₄×C₁₃	—	4	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	2	1	no	—
164	C₁₃×Q₁₆	—	2	1	no	—
165	C₁₃×Q₁₆	—	2	1	no	—
166	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
167	C₁₃×SD₁₆	—	4	2	no	—
168	C₁₃×SD₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×D₈	—	2	1	no	—
172	C₁₃×D₈	—	2	1	no	—
173	C₁₃×D₈	—	2	1	no	—
174	C₁₃×D₈	—	2	1	no	—
175	C₁₃×D₈	—	2	1	no	—
176	C₁₃×D₈	—	2	1	no	—
177	C₁₃×D₈	—	2	1	no	—
178	C₁₃×D₈	—	4	2	no	—
179	C₁₃×D₈	—	8	1	no	—
180	C₁₃×D₈	C₂×D₄	1	2	yes	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	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	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
202	C₁₃×C₂²⋊C₄	D₈	1	1	yes	characteristic
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×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#3287	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3280	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2250	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2220	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2215	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2211	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2189	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2186	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2186	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2184	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2175	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	—	4	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	8	2	no	—
229	C₂³×C₁₃	—	8	2	no	—
230	C₂³×C₁₃	—	16	1	no	—
231	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
232	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	8	2	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	8	2	no	—
249	D₄×C₁₃	—	8	2	no	—
250	D₄×C₁₃	—	8	2	no	—
251	D₄×C₁₃	—	16	1	no	—
252	D₄×C₁₃	—	16	1	no	—
253	D₄×C₁₃	—	16	1	no	—
254	D₄×C₁₃	—	16	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	8	2	no	—
264	C₂×C₄×C₁₃	—	8	2	no	—
265	C₂×C₄×C₁₃	—	8	2	no	—
266	C₂×C₄×C₁₃	—	16	1	no	—
267	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
281	#550	—	2	1	no	—
282	#546	—	2	1	no	—
283	#509	—	2	4	no	—
284	#508	—	2	4	no	—
285	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
289	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
290	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
295	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
296	#495	C₂²×C₁₃	1	1	yes	characteristic
297	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	#467	C₂²×C₁₃	1	1	yes	characteristic
299	#466	C₂²×C₁₃	1	1	yes	characteristic
300	#466	C₂²×C₁₃	1	1	yes	characteristic
301	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
302	#463	—	2	1	no	—
303	#460	—	2	1	no	—
304	#450	—	2	1	no	—
305	#449	—	2	1	no	—
306	#449	—	2	1	no	—
307	#449	—	2	1	no	—
308	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
311	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	#358	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	#357	C₂²×C₁₃	1	1	yes	characteristic
316	#357	C₂²×C₁₃	1	1	yes	characteristic
317	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	#357	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
320	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	#346	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	8	1	no	—
330	C₂²×C₁₃	—	8	1	no	—
331	C₂²×C₁₃	—	8	1	no	—
332	C₂²×C₁₃	—	8	1	no	—
333	C₂²×C₁₃	—	8	1	no	—
334	C₂²×C₁₃	—	8	1	no	—
335	C₂²×C₁₃	—	8	1	no	—
336	C₂²×C₁₃	—	8	1	no	—
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	16	4	no	—
341	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	D₄²	1	1	yes	characteristic
351	C₄×C₁₃	#576	1	1	yes	characteristic
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	#135	—	2	2	no	—
357	#135	—	2	2	no	—
358	#135	—	2	2	no	—
359	#135	—	4	1	no	—
360	#135	—	4	1	no	—
361	#135	—	4	1	no	—
362	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×D₈	—	2	2	no	—
369	C₂×D₈	—	2	1	no	—
370	C₂×D₈	—	2	1	no	—
371	C₂×D₈	—	4	1	no	—
372	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
378	#127	—	2	1	no	—
379	#127	—	4	1	no	—
380	#124	—	2	1	no	—
381	#123	—	4	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	4	1	no	—
387	#121	—	4	1	no	—
388	#121	—	4	1	no	—
389	#120	—	4	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	4	1	no	—
393	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	4	1	no	—
395	Q₃₂	—	2	2	no	—
396	SD₃₂	—	2	2	no	—
397	SD₃₂	—	2	2	no	—
398	SD₃₂	—	4	1	no	—
399	SD₃₂	D₄×C₁₃	1	4	yes	complemented
400	D₁₆	—	2	2	no	—
401	D₁₆	—	2	2	no	—
402	D₁₆	—	2	2	no	—
403	D₁₆	—	4	1	no	—
404	M₃₂	—	2	2	no	—
405	C₂×C₁₆	—	2	2	no	—
406	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
410	#107	C₂³×C₁₃	1	1	yes	characteristic
411	#107	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
420	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₁₃	—	4	1	no	—
423	C₂×C₁₃	—	4	1	no	—
424	C₂×C₁₃	—	8	2	no	—
425	C₂×C₁₃	—	16	1	no	—
426	C₂×C₁₃	—	16	1	no	—
427	C₂×C₁₃	—	16	1	no	—
428	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
429	C₂×C₁₃	#3414	1	1	yes	characteristic
430	C₂×C₁₃	#3415	1	1	yes	characteristic
431	C₂⁴	—	4	1	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	#41	—	4	2	no	—
435	#41	—	8	1	no	—
436	#41	—	8	1	no	—
437	#41	—	8	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	8	1	no	—
455	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	Q₁₆	—	2	1	no	—
463	Q₁₆	—	2	1	no	—
464	Q₁₆	—	2	1	no	—
465	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
466	SD₁₆	—	4	2	no	—
467	SD₁₆	—	4	2	no	—
468	SD₁₆	—	4	2	no	—
469	SD₁₆	—	8	1	no	—
470	D₈	—	2	1	no	—
471	D₈	—	2	1	no	—
472	D₈	—	2	1	no	—
473	D₈	—	2	1	no	—
474	D₈	—	2	1	no	—
475	D₈	—	2	1	no	—
476	D₈	—	2	1	no	—
477	D₈	—	4	2	no	—
478	D₈	—	8	1	no	—
479	D₈	C₂×D₄×C₁₃	1	2	yes	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
501	C₂²⋊C₄	C₁₃×D₈	1	1	yes	characteristic
502	C₄²	—	4	1	no	—
503	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₁₆	—	2	1	no	—
505	C₁₆	—	2	1	no	—
506	C₁₆	—	2	1	no	—
507	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
508	C₁₃	#33834	1	1	yes	characteristic, direct product factor, Sylow
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	8	2	no	—
514	C₂³	—	8	2	no	—
515	C₂³	—	16	1	no	—
516	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
517	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	8	2	no	—
532	D₄	—	8	2	no	—
533	D₄	—	8	2	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	2	no	—
536	D₄	—	16	1	no	—
537	D₄	—	16	1	no	—
538	D₄	—	16	1	no	—
539	D₄	—	16	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	16	1	no	—
552	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
553	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
554	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
555	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
561	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	16	4	no	—
581	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	D₄²×C₁₃	1	1	yes	characteristic
591	C₄	C₁₃×#576	1	1	yes	characteristic
592	C₂	—	4	1	no	—
593	C₂	—	4	1	no	—
594	C₂	—	8	2	no	—
595	C₂	—	16	1	no	—
596	C₂	—	16	1	no	—
597	C₂	—	16	1	no	—
598	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
599	C₂	C₁₃×#3414	1	1	yes	characteristic
600	C₂	C₁₃×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
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×#509	C₂	semidirect
2. C₂×C₁₃×#508	C₂	semidirect
3. C₁₃×#3287	C₂	semidirect
4. C₁₃×#3280	C₂	semidirect
5. C₁₃×#2250	C₂	semidirect
6. C₁₃×#2220	C₂	semidirect
7. C₁₃×#2215	C₂	semidirect
8. C₁₃×#2211	C₂	semidirect
9. C₁₃×#2206	C₂	semidirect
10. C₁₃×#2189	C₂	semidirect
11. C₁₃×#2186	C₂	semidirect
12. C₁₃×#2186	C₂	semidirect
13. C₁₃×#2184	C₂	semidirect
14. C₁₃×#2175	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
24. C₂×C₁₃×Q₃₂	C₂²	semidirect
27. C₂×C₁₃×SD₃₂	C₂²	semidirect
28. C₂×C₁₃×SD₃₂	C₂²	semidirect
34. C₂²×C₁₃×C₁₆	C₂²	semidirect
36. C₁₃×#493	C₂²	semidirect
40. C₁₃×#466	C₂²	semidirect
47. C₄×C₁₃×Q₁₆	C₂²	semidirect
50. C₁₃×#366	C₂²	semidirect
51. C₁₃×C₄⋊C₁₆	C₂²	semidirect
52. C₁₃×#358	C₂²	semidirect
53. C₁₃×#358	C₂²	semidirect
56. C₁₃×#357	C₂²	semidirect
57. C₁₃×#357	C₂²	semidirect
59. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
60. C₁₃×#346	C₂²	semidirect
108. C₁₃×SD₃₂	D₄	semidirect
131. #33834	C₁₃	direct (N × H)
209. C₂×#509	C₂×C₁₃	semidirect
210. C₂×#508	C₂×C₁₃	semidirect
211. #3287	C₂×C₁₃	semidirect
212. #3280	C₂×C₁₃	semidirect
213. #2250	C₂×C₁₃	semidirect
214. #2220	C₂×C₁₃	semidirect
215. #2215	C₂×C₁₃	semidirect
216. #2211	C₂×C₁₃	semidirect
217. #2206	C₂×C₁₃	semidirect
218. #2189	C₂×C₁₃	semidirect
219. #2186	C₂×C₁₃	semidirect
220. #2186	C₂×C₁₃	semidirect
221. #2184	C₂×C₁₃	semidirect
222. #2175	C₂×C₁₃	semidirect
223. #2168	C₂×C₁₃	semidirect
279. C₂×#135	C₂²×C₁₃	semidirect
285. C₂×Q₃₂	C₂²×C₁₃	semidirect
288. C₂×SD₃₂	C₂²×C₁₃	semidirect
289. C₂×SD₃₂	C₂²×C₁₃	semidirect
295. C₂²×C₁₆	C₂²×C₁₃	semidirect
297. #493	C₂²×C₁₃	semidirect
301. #466	C₂²×C₁₃	semidirect
308. C₄×Q₁₆	C₂²×C₁₃	semidirect
311. #366	C₂²×C₁₃	semidirect
312. C₄⋊C₁₆	C₂²×C₁₃	semidirect
313. #358	C₂²×C₁₃	semidirect
314. #358	C₂²×C₁₃	semidirect
317. #357	C₂²×C₁₃	semidirect
318. #357	C₂²×C₁₃	semidirect
320. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
321. #346	C₂²×C₁₃	semidirect
399. SD₃₂	D₄×C₁₃	semidirect
508. C₁₃	#33834	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#509	2
C₂×C₁₃×#508	2
C₁₃×#3287	2
C₁₃×#3280	2
C₁₃×#2250	2
C₁₃×#2220	2
C₁₃×#2215	2
C₁₃×#2211	2
C₁₃×#2206	2
C₁₃×#2189	2
C₁₃×#2186	2
C₁₃×#2184	2
C₁₃×#2175	2
C₁₃×#2168	2
#33834	13

Subgroups — C13×#33834 #15720173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33834 #15720173