Subgroups — C₁₃×#24172 #15710511

Order 3328.

1058 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2040	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2007	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1882	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1860	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	C₂²	1	2	yes	—
14	C₁₃×#556	—	2	1	no	—
15	C₁₃×#555	—	2	1	no	—
16	C₁₃×#554	—	2	1	no	—
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#548	—	2	2	no	—
19	C₁₃×#547	—	2	1	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#537	C₂²	1	2	yes	—
22	C₁₃×#533	—	2	1	no	—
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×#520	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#464	—	2	2	no	—
30	C₁₃×#462	—	2	1	no	—
31	C₁₃×#460	—	2	1	no	—
32	C₁₃×#441	—	2	1	no	—
33	C₁₃×#440	—	2	1	no	—
34	C₄×C₁₃×Q₁₆	—	2	1	no	—
35	C₄×C₁₃×SD₁₆	—	2	1	no	—
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	2	yes	—
39	C₂×C₁₃×#104	C₂²	1	2	yes	—
40	C₂×C₁₃×#104	C₂²	1	2	yes	—
41	C₁₃×#419	C₂²	1	1	yes	characteristic
42	C₁₃×#417	C₂²	1	2	yes	—
43	C₁₃×#417	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
45	C₁₃×#400	—	2	2	no	—
46	C₁₃×#391	—	2	2	no	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#382	C₂²	1	2	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₁₃×#343	C₂²	1	2	yes	—
51	C₁₃×#343	C₂²	1	2	yes	—
52	C₁₃×#339	C₂²	1	2	yes	—
53	C₂×C₁₃×#41	—	2	2	no	—
54	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#137	—	2	2	no	—
59	C₁₃×#137	—	2	4	no	—
60	C₁₃×#137	—	2	2	no	—
61	C₁₃×#137	—	4	2	no	—
62	C₂×C₁₃×Q₁₆	—	2	1	no	—
63	C₂×C₁₃×Q₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	2	1	no	—
65	C₂×C₁₃×SD₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	—	2	1	no	—
70	C₁₃×C₄⋊Q₈	—	2	1	no	—
71	C₁₃×C₄⋊Q₈	—	2	1	no	—
72	C₁₃×C₄⋊Q₈	—	2	1	no	—
73	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
74	C₁₃×#127	D₄	1	1	yes	characteristic
75	C₁₃×#126	—	2	4	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#124	—	2	2	no	—
78	C₁₃×#124	—	2	4	no	—
79	C₁₃×#124	D₄	1	2	yes	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	2	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	—	2	1	no	—
106	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
107	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
108	C₁₃×#117	—	2	2	no	—
109	C₁₃×#117	—	2	2	no	—
110	C₁₃×#117	—	2	1	no	—
111	C₁₃×#117	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	—	2	1	no	—
119	C₂×C₄²×C₁₃	—	2	1	no	—
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#107	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×#104	—	2	4	no	—
127	C₁₃×#104	—	4	2	no	—
128	C₁₃×#104	—	4	2	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#97	—	2	1	no	—
136	C₄×C₈×C₁₃	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	4	no	—
139	C₁₃×#95	—	2	4	no	—
140	#24172	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	2	2	no	—
142	C₁₃×#41	—	2	2	no	—
143	C₁₃×#41	—	2	1	no	—
144	C₁₃×#41	—	2	1	no	—
145	C₁₃×#41	—	2	1	no	—
146	C₁₃×#41	—	2	2	no	—
147	C₁₃×#41	—	2	2	no	—
148	C₁₃×#41	—	2	1	no	—
149	C₁₃×#41	—	8	4	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	4	4	no	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
159	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×Q₁₆	—	2	4	no	—
181	C₁₃×Q₁₆	—	4	4	no	—
182	C₁₃×SD₁₆	—	2	4	no	—
183	C₁₃×SD₁₆	—	4	4	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	2	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	2	no	—
188	C₁₃×M₁₆	—	2	1	no	—
189	C₁₃×M₁₆	#41	1	2	yes	complemented
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	1	no	—
207	C₁₃×C₄⋊C₄	—	4	1	no	—
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	1	no	—
214	C₁₃×C₂²⋊C₄	—	2	1	no	—
215	C₁₃×C₂²⋊C₄	—	2	1	no	—
216	C₁₃×C₂²⋊C₄	—	2	2	no	—
217	C₁₃×C₂²⋊C₄	—	2	2	no	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	—	2	1	no	—
220	C₄²×C₁₃	—	2	1	no	—
221	C₄²×C₁₃	—	2	1	no	—
222	C₄²×C₁₃	—	2	2	no	—
223	C₄²×C₁₃	—	2	2	no	—
224	C₄²×C₁₃	—	4	1	no	—
225	C₄²×C₁₃	—	4	1	no	—
226	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
230	#3511	C₂×C₁₃	1	1	yes	characteristic
231	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2040	C₂×C₁₃	1	2	yes	complemented
235	#2007	C₂×C₁₃	1	2	yes	complemented
236	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1882	C₂×C₁₃	1	2	yes	complemented
239	#1860	C₂×C₁₃	1	2	yes	complemented
240	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	2	2	no	—
245	Q₈×C₁₃	—	2	1	no	—
246	Q₈×C₁₃	—	2	1	no	—
247	Q₈×C₁₃	—	2	2	no	—
248	Q₈×C₁₃	—	2	2	no	—
249	Q₈×C₁₃	—	2	2	no	—
250	Q₈×C₁₃	—	4	1	no	—
251	Q₈×C₁₃	—	4	1	no	—
252	Q₈×C₁₃	—	4	4	no	—
253	Q₈×C₁₃	—	8	2	no	—
254	D₄×C₁₃	—	2	1	no	—
255	D₄×C₁₃	—	2	1	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	4	2	no	—
259	D₄×C₁₃	—	4	2	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	2	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	2	no	—
264	D₄×C₁₃	—	8	4	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	2	no	—
287	C₂×C₄×C₁₃	—	8	4	no	—
288	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
289	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
290	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
291	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₃	—	2	2	no	—
299	C₈×C₁₃	—	4	1	no	—
300	C₈×C₁₃	—	4	2	no	—
301	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#137	C₂²×C₁₃	1	2	yes	—
303	#556	—	2	1	no	—
304	#555	—	2	1	no	—
305	#554	—	2	1	no	—
306	#553	—	2	2	no	—
307	#548	—	2	2	no	—
308	#547	—	2	1	no	—
309	#542	—	2	2	no	—
310	#537	C₂²×C₁₃	1	2	yes	—
311	#533	—	2	1	no	—
312	#532	—	2	1	no	—
313	#532	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
315	#520	C₂²×C₁₃	1	2	yes	—
316	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
318	#464	—	2	2	no	—
319	#462	—	2	1	no	—
320	#460	—	2	1	no	—
321	#441	—	2	1	no	—
322	#440	—	2	1	no	—
323	C₄×Q₁₆	—	2	1	no	—
324	C₄×SD₁₆	—	2	1	no	—
325	#428	C₂²×C₁₃	1	1	yes	characteristic
326	#423	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#104	C₂²×C₁₃	1	2	yes	—
328	C₂×#104	C₂²×C₁₃	1	2	yes	—
329	C₂×#104	C₂²×C₁₃	1	2	yes	—
330	#419	C₂²×C₁₃	1	1	yes	characteristic
331	#417	C₂²×C₁₃	1	2	yes	—
332	#417	C₂²×C₁₃	1	1	yes	characteristic
333	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
334	#400	—	2	2	no	—
335	#391	—	2	2	no	—
336	#391	C₂²×C₁₃	1	2	yes	—
337	#382	C₂²×C₁₃	1	2	yes	—
338	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
339	#343	C₂²×C₁₃	1	2	yes	—
340	#343	C₂²×C₁₃	1	2	yes	—
341	#339	C₂²×C₁₃	1	2	yes	—
342	C₂²×C₁₃	—	2	1	no	—
343	C₂²×C₁₃	—	2	1	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	2	no	—
350	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
351	C₂²×C₁₃	#548	1	1	yes	characteristic
352	C₂²×C₁₃	#550	1	1	yes	characteristic
353	C₄×C₁₃	—	2	1	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	4	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	8	2	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	#455	1	2	yes	—
365	C₄×C₁₃	#525	1	1	yes	characteristic
366	C₄×C₁₃	#537	1	1	yes	characteristic
367	C₄×C₁₃	#546	1	1	yes	characteristic
368	C₄×C₁₃	#547	1	1	yes	characteristic
369	C₂×#41	—	2	2	no	—
370	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×#41	C₂³×C₁₃	1	2	yes	—
372	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
373	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	#137	—	2	2	no	—
375	#137	—	2	4	no	—
376	#137	—	2	2	no	—
377	#137	—	4	2	no	—
378	C₂×Q₁₆	—	2	1	no	—
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	1	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
383	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
385	C₄⋊Q₈	—	2	1	no	—
386	C₄⋊Q₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
390	#127	D₄×C₁₃	1	1	yes	characteristic
391	#126	—	2	4	no	—
392	#125	—	2	2	no	—
393	#124	—	2	2	no	—
394	#124	—	2	4	no	—
395	#124	D₄×C₁₃	1	2	yes	—
396	#123	—	2	4	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	—	2	4	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	#121	—	2	2	no	—
402	#121	—	2	2	no	—
403	#121	—	2	2	no	—
404	#121	—	2	1	no	—
405	#121	—	2	1	no	—
406	#121	—	2	4	no	—
407	C₄×Q₈	—	2	2	no	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
414	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	4	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	—	2	1	no	—
422	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
423	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
424	#117	—	2	2	no	—
425	#117	—	2	2	no	—
426	#117	—	2	1	no	—
427	#117	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
437	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
438	#107	—	2	1	no	—
439	#106	—	2	1	no	—
440	C₄⋊C₈	—	2	1	no	—
441	C₄⋊C₈	—	2	1	no	—
442	#104	—	2	4	no	—
443	#104	—	4	2	no	—
444	#104	—	4	2	no	—
445	#103	—	2	1	no	—
446	#103	—	2	2	no	—
447	#103	—	2	1	no	—
448	#103	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	2	no	—
451	#97	—	2	1	no	—
452	C₄×C₈	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	4	no	—
455	#95	—	2	4	no	—
456	C₂×C₁₃	—	2	1	no	—
457	C₂×C₁₃	—	2	1	no	—
458	C₂×C₁₃	—	8	1	no	—
459	C₂×C₁₃	—	8	2	no	—
460	C₂×C₁₃	#2407	1	1	yes	characteristic
461	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
462	C₂×C₁₃	#3020	1	1	yes	characteristic
463	#41	—	2	2	no	—
464	#41	—	2	2	no	—
465	#41	—	2	1	no	—
466	#41	—	2	1	no	—
467	#41	—	2	1	no	—
468	#41	—	2	2	no	—
469	#41	—	2	2	no	—
470	#41	—	2	1	no	—
471	#41	—	8	4	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	4	4	no	—
480	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
481	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
489	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
502	Q₁₆	—	2	4	no	—
503	Q₁₆	—	4	4	no	—
504	SD₁₆	—	2	4	no	—
505	SD₁₆	—	4	4	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	2	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	C₁₃×#41	1	2	yes	complemented
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	2	no	—
515	C₄⋊C₄	—	2	4	no	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	4	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	4	1	no	—
547	C₄²	—	4	1	no	—
548	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₁₃	#24172	1	1	yes	characteristic, direct product factor, Sylow
553	C₂³	—	2	1	no	—
554	C₂³	—	2	2	no	—
555	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	2	1	no	—
558	Q₈	—	2	1	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	4	4	no	—
563	Q₈	—	4	1	no	—
564	Q₈	—	4	1	no	—
565	Q₈	—	8	2	no	—
566	D₄	—	2	1	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	2	no	—
570	D₄	—	4	2	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	2	no	—
576	D₄	—	8	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	8	4	no	—
600	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
601	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
602	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
603	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
607	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
608	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
610	C₈	—	2	2	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
622	C₂²	C₁₃×#548	1	1	yes	characteristic
623	C₂²	C₁₃×#550	1	1	yes	characteristic
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	4	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	8	2	no	—
634	C₄	—	8	1	no	—
635	C₄	C₁₃×#455	1	2	yes	—
636	C₄	C₁₃×#525	1	1	yes	characteristic
637	C₄	C₁₃×#537	1	1	yes	characteristic
638	C₄	C₁₃×#546	1	1	yes	characteristic
639	C₄	C₁₃×#547	1	1	yes	characteristic
640	C₂	—	2	1	no	—
641	C₂	—	2	1	no	—
642	C₂	—	8	1	no	—
643	C₂	—	8	2	no	—
644	C₂	C₁₃×#2407	1	1	yes	characteristic
645	C₂	C₂×C₁₃×#455	1	1	yes	characteristic
646	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3511	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3037	C₂	semidirect
3. C₄×C₁₃×#137	C₂	semidirect
4. C₁₃×#2568	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2007	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1980	C₂	semidirect
9. C₁₃×#1882	C₂	semidirect
10. C₁₃×#1860	C₂	semidirect
11. C₁₃×#1806	C₂	semidirect
140. #24172	C₁₃	direct (N × H)
160. C₂×Q₈×C₁₃	#41	semidirect
189. C₁₃×M₁₆	#41	semidirect
231. #3037	C₂×C₁₃	semidirect
232. C₄×#137	C₂×C₁₃	semidirect
233. #2568	C₂×C₁₃	semidirect
234. #2040	C₂×C₁₃	semidirect
235. #2007	C₂×C₁₃	semidirect
236. #1997	C₂×C₁₃	semidirect
237. #1980	C₂×C₁₃	semidirect
238. #1882	C₂×C₁₃	semidirect
239. #1860	C₂×C₁₃	semidirect
240. #1806	C₂×C₁₃	semidirect
482. C₂×Q₈	C₁₃×#41	semidirect
511. M₁₆	C₁₃×#41	semidirect
552. C₁₃	#24172	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3037	2
C₄×C₁₃×#137	2
C₁₃×#2568	2
C₁₃×#2040	2
C₁₃×#2007	2
C₁₃×#1997	2
C₁₃×#1980	2
C₁₃×#1882	2
C₁₃×#1860	2
C₁₃×#1806	2
#24172	13

Subgroups — C13×#24172 #15710511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24172 #15710511