Subgroups — C₁₃×#62005 #15748344

Order 3328.

1836 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3333	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3331	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3278	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3276	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3252	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3210	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3108	C₂	1	3	yes	maximal, complemented
14	C₁₃×#3037	C₂	1	3	yes	maximal, complemented
15	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	6	yes	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#557	C₂²	1	1	yes	characteristic
21	C₁₃×#554	—	2	3	no	—
22	C₁₃×#554	C₂²	1	3	yes	—
23	C₁₃×#553	—	2	3	no	—
24	C₁₃×#550	—	2	1	no	—
25	C₁₃×#550	C₂²	1	3	yes	—
26	C₁₃×#550	C₂²	1	1	yes	characteristic
27	D₄×Q₈×C₁₃	C₂²	1	3	yes	—
28	C₁₃×#547	C₂²	1	3	yes	—
29	C₁₃×#540	—	2	3	no	—
30	C₁₃×#533	—	2	3	no	—
31	C₁₃×#533	C₂²	1	3	yes	—
32	C₁₃×#532	C₂²	1	3	yes	—
33	C₁₃×#529	C₂²	1	3	yes	—
34	C₁₃×#520	—	2	1	no	—
35	C₄×C₁₃×#41	—	2	1	no	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
38	C₁₃×#494	C₂²	1	3	yes	—
39	C₁₃×#492	C₂²	1	3	yes	—
40	C₁₃×#487	C₂²	1	3	yes	—
41	C₁₃×#486	C₂²	1	3	yes	—
42	C₁₃×#483	C₂²	1	3	yes	—
43	C₁₃×#480	C₂²	1	3	yes	—
44	C₁₃×#479	C₂²	1	1	yes	characteristic
45	C₁₃×#479	C₂²	1	3	yes	—
46	C₁₃×#477	C₂²	1	3	yes	—
47	C₁₃×#476	C₂²	1	3	yes	—
48	C₁₃×#470	C₂²	1	6	yes	—
49	C₁₃×#468	C₂²	1	6	yes	—
50	C₁₃×#464	C₂²	1	3	yes	—
51	C₁₃×#464	C₂²	1	6	yes	—
52	C₁₃×#464	C₂²	1	3	yes	—
53	C₁₃×#462	C₂²	1	3	yes	—
54	C₁₃×#462	C₂²	1	3	yes	—
55	C₁₃×#462	C₂²	1	3	yes	—
56	C₁₃×#461	C₂²	1	3	yes	—
57	C₁₃×#460	C₂²	1	3	yes	—
58	C₁₃×#460	C₂²	1	3	yes	—
59	C₁₃×#452	C₂²	1	6	yes	—
60	C₁₃×#452	C₂²	1	6	yes	—
61	C₁₃×#451	C₂²	1	3	yes	—
62	C₁₃×#448	C₂²	1	3	yes	—
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
66	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
67	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
68	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
69	C₁₃×#436	C₂²	1	3	yes	—
70	C₁₃×#436	C₂²	1	3	yes	—
71	C₁₃×#431	C₂²	1	3	yes	—
72	C₁₃×#423	C₂²	1	3	yes	—
73	C₁₃×#417	C₂²	1	6	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
76	C₂×C₁₃×#41	C₂³	1	6	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
78	C₁₃×#137	—	4	12	no	—
79	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
80	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
81	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
85	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
86	C₁₃×C₄⋊Q₈	—	2	3	no	—
87	C₁₃×C₄⋊Q₈	—	2	3	no	—
88	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×#127	—	2	3	no	—
92	C₁₃×#127	C₂³	1	3	yes	—
93	C₁₃×#126	—	2	3	no	—
94	C₁₃×#125	—	2	3	no	—
95	C₁₃×#125	—	2	3	no	—
96	C₁₃×#125	—	2	3	no	—
97	C₁₃×#125	—	2	3	no	—
98	C₁₃×#125	C₂³	1	1	yes	characteristic
99	C₁₃×#124	C₂³	1	3	yes	—
100	C₁₃×#123	—	2	3	no	—
101	C₁₃×#123	—	2	6	no	—
102	C₁₃×C₂²⋊Q₈	—	2	3	no	—
103	C₁₃×C₂²⋊Q₈	—	2	6	no	—
104	C₁₃×C₂²⋊Q₈	—	2	6	no	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
106	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
107	C₁₃×#121	—	2	3	no	—
108	C₁₃×#121	—	2	3	no	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	—	2	6	no	—
112	C₁₃×#121	C₂³	1	3	yes	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	—	2	1	no	—
115	C₄×Q₈×C₁₃	—	2	1	no	—
116	C₄×Q₈×C₁₃	—	2	3	no	—
117	C₄×Q₈×C₁₃	—	2	3	no	—
118	C₄×Q₈×C₁₃	—	2	3	no	—
119	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
125	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	—	2	3	no	—
129	C₄×D₄×C₁₃	—	2	3	no	—
130	C₄×D₄×C₁₃	—	2	3	no	—
131	C₄×D₄×C₁₃	—	2	3	no	—
132	C₄×D₄×C₁₃	D₄	1	3	yes	—
133	C₄×D₄×C₁₃	C₂³	1	3	yes	—
134	C₄×D₄×C₁₃	C₂³	1	3	yes	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	—	2	3	no	—
137	C₁₃×#117	D₄	1	3	yes	—
138	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
139	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
141	C₂×C₄²×C₁₃	—	2	3	no	—
142	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
143	C₁₃×#107	C₂³	1	1	yes	characteristic
144	C₁₃×#107	C₂³	1	3	yes	—
145	C₁₃×#106	C₂³	1	1	yes	characteristic
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	6	yes	—
153	C₁₃×#103	C₂³	1	1	yes	characteristic
154	C₁₃×#103	C₂³	1	3	yes	—
155	C₁₃×#103	C₂³	1	1	yes	characteristic
156	C₁₃×#103	C₂³	1	3	yes	—
157	C₁₃×#103	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	6	yes	—
160	C₁₃×#102	C₂³	1	3	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	#62005	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	4	6	no	—
168	C₁₃×#41	—	4	6	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	2	3	no	—
171	C₂×Q₈×C₁₃	—	2	3	no	—
172	C₂×Q₈×C₁₃	—	2	6	no	—
173	C₂×Q₈×C₁₃	—	4	3	no	—
174	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₃	—	2	3	no	—
179	C₂×D₄×C₁₃	—	2	6	no	—
180	C₂×D₄×C₁₃	—	2	3	no	—
181	C₂×D₄×C₁₃	—	2	3	no	—
182	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
184	C₂²×C₄×C₁₃	—	2	3	no	—
185	C₂²×C₄×C₁₃	—	2	3	no	—
186	C₂²×C₄×C₁₃	—	2	3	no	—
187	C₂²×C₄×C₁₃	—	2	6	no	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
191	C₁₃×Q₁₆	—	2	6	no	—
192	C₁₃×Q₁₆	—	4	3	no	—
193	C₁₃×Q₁₆	—	4	6	no	—
194	C₁₃×SD₁₆	—	2	6	no	—
195	C₁₃×SD₁₆	—	4	3	no	—
196	C₁₃×SD₁₆	—	4	6	no	—
197	C₁₃×M₁₆	—	4	6	no	—
198	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
201	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	3	no	—
204	C₁₃×C₄⋊C₄	—	2	3	no	—
205	C₁₃×C₄⋊C₄	—	2	3	no	—
206	C₁₃×C₄⋊C₄	—	2	3	no	—
207	C₁₃×C₄⋊C₄	—	2	3	no	—
208	C₁₃×C₄⋊C₄	—	2	3	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	3	no	—
211	C₁₃×C₄⋊C₄	—	2	3	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	3	no	—
214	C₁₃×C₄⋊C₄	—	2	3	no	—
215	C₁₃×C₄⋊C₄	—	2	6	no	—
216	C₁₃×C₄⋊C₄	—	2	3	no	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
222	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
223	C₁₃×C₂²⋊C₄	—	2	6	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	3	no	—
226	C₁₃×C₂²⋊C₄	—	2	3	no	—
227	C₁₃×C₂²⋊C₄	—	2	3	no	—
228	C₁₃×C₂²⋊C₄	—	2	3	no	—
229	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	3	no	—
232	C₄²×C₁₃	—	2	3	no	—
233	C₄²×C₁₃	—	2	3	no	—
234	C₄²×C₁₃	—	2	3	no	—
235	C₄²×C₁₃	C₂×D₄	1	3	yes	—
236	C₄²×C₁₃	C₂×D₄	1	3	yes	—
237	C₄²×C₁₃	C₂⁴	1	3	yes	—
238	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
239	#3517	C₂×C₁₃	1	1	yes	characteristic
240	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3333	C₂×C₁₃	1	3	yes	complemented
246	#3331	C₂×C₁₃	1	3	yes	complemented
247	#3278	C₂×C₁₃	1	3	yes	complemented
248	#3276	C₂×C₁₃	1	3	yes	complemented
249	#3252	C₂×C₁₃	1	3	yes	complemented
250	#3210	C₂×C₁₃	1	3	yes	complemented
251	#3108	C₂×C₁₃	1	3	yes	complemented
252	#3037	C₂×C₁₃	1	3	yes	complemented
253	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂³×C₁₃	—	2	3	no	—
255	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
256	Q₈×C₁₃	—	2	1	no	—
257	Q₈×C₁₃	—	2	3	no	—
258	Q₈×C₁₃	—	2	3	no	—
259	Q₈×C₁₃	—	2	3	no	—
260	Q₈×C₁₃	—	2	3	no	—
261	Q₈×C₁₃	—	4	6	no	—
262	Q₈×C₁₃	—	8	3	no	—
263	Q₈×C₁₃	#137	1	4	yes	complemented
264	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
265	D₄×C₁₃	—	2	6	no	—
266	D₄×C₁₃	—	2	3	no	—
267	D₄×C₁₃	—	2	3	no	—
268	D₄×C₁₃	—	4	6	no	—
269	D₄×C₁₃	—	8	3	no	—
270	D₄×C₁₃	—	8	3	no	—
271	D₄×C₁₃	—	8	6	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	6	no	—
274	C₂×C₄×C₁₃	—	2	3	no	—
275	C₂×C₄×C₁₃	—	2	3	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	3	no	—
279	C₂×C₄×C₁₃	—	2	3	no	—
280	C₂×C₄×C₁₃	—	2	3	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	4	3	no	—
283	C₂×C₄×C₁₃	—	4	6	no	—
284	C₂×C₄×C₁₃	—	4	6	no	—
285	C₂×C₄×C₁₃	—	8	6	no	—
286	C₂×C₄×C₁₃	—	8	3	no	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
291	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₁₃	—	2	3	no	—
294	C₈×C₁₃	—	2	3	no	—
295	C₈×C₁₃	—	2	1	no	—
296	C₈×C₁₃	—	2	1	no	—
297	C₂×#137	C₂²×C₁₃	1	6	yes	—
298	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
299	#557	—	2	1	no	—
300	#557	C₂²×C₁₃	1	1	yes	characteristic
301	#557	C₂²×C₁₃	1	1	yes	characteristic
302	#554	—	2	3	no	—
303	#554	C₂²×C₁₃	1	3	yes	—
304	#553	—	2	3	no	—
305	#550	—	2	1	no	—
306	#550	C₂²×C₁₃	1	3	yes	—
307	#550	C₂²×C₁₃	1	1	yes	characteristic
308	D₄×Q₈	C₂²×C₁₃	1	3	yes	—
309	#547	C₂²×C₁₃	1	3	yes	—
310	#540	—	2	3	no	—
311	#533	—	2	3	no	—
312	#533	C₂²×C₁₃	1	3	yes	—
313	#532	C₂²×C₁₃	1	3	yes	—
314	#529	C₂²×C₁₃	1	3	yes	—
315	#520	—	2	1	no	—
316	C₄×#41	—	2	1	no	—
317	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
319	#494	C₂²×C₁₃	1	3	yes	—
320	#492	C₂²×C₁₃	1	3	yes	—
321	#487	C₂²×C₁₃	1	3	yes	—
322	#486	C₂²×C₁₃	1	3	yes	—
323	#483	C₂²×C₁₃	1	3	yes	—
324	#480	C₂²×C₁₃	1	3	yes	—
325	#479	C₂²×C₁₃	1	1	yes	characteristic
326	#479	C₂²×C₁₃	1	3	yes	—
327	#477	C₂²×C₁₃	1	3	yes	—
328	#476	C₂²×C₁₃	1	3	yes	—
329	#470	C₂²×C₁₃	1	6	yes	—
330	#468	C₂²×C₁₃	1	6	yes	—
331	#464	C₂²×C₁₃	1	3	yes	—
332	#464	C₂²×C₁₃	1	3	yes	—
333	#464	C₂²×C₁₃	1	6	yes	—
334	#462	C₂²×C₁₃	1	3	yes	—
335	#462	C₂²×C₁₃	1	3	yes	—
336	#462	C₂²×C₁₃	1	3	yes	—
337	#461	C₂²×C₁₃	1	3	yes	—
338	#460	C₂²×C₁₃	1	3	yes	—
339	#460	C₂²×C₁₃	1	3	yes	—
340	#452	C₂²×C₁₃	1	6	yes	—
341	#452	C₂²×C₁₃	1	6	yes	—
342	#451	C₂²×C₁₃	1	3	yes	—
343	#448	C₂²×C₁₃	1	3	yes	—
344	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
345	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
346	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
347	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
348	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
349	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
350	#436	C₂²×C₁₃	1	3	yes	—
351	#436	C₂²×C₁₃	1	3	yes	—
352	#431	C₂²×C₁₃	1	3	yes	—
353	#423	C₂²×C₁₃	1	3	yes	—
354	#417	C₂²×C₁₃	1	6	yes	—
355	C₂²×C₁₃	—	2	3	no	—
356	C₂²×C₁₃	—	2	3	no	—
357	C₂²×C₁₃	—	2	3	no	—
358	C₂²×C₁₃	—	4	3	no	—
359	C₂²×C₁₃	—	4	3	no	—
360	C₂²×C₁₃	—	4	3	no	—
361	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	3	no	—
364	C₄×C₁₃	—	2	3	no	—
365	C₄×C₁₃	—	2	2	no	—
366	C₄×C₁₃	—	2	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	3	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	3	no	—
371	C₄×C₁₃	—	4	3	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	C₂×#137	1	6	yes	—
374	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₄×C₁₃	#585	1	1	yes	characteristic
376	C₂×#41	—	2	1	no	—
377	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
378	C₂×#41	C₂³×C₁₃	1	6	yes	—
379	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
380	#137	—	4	12	no	—
381	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
382	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
383	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
384	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
385	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
386	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
387	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
388	C₄⋊Q₈	—	2	3	no	—
389	C₄⋊Q₈	—	2	3	no	—
390	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
391	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
392	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
393	#127	—	2	3	no	—
394	#127	C₂³×C₁₃	1	3	yes	—
395	#126	—	2	3	no	—
396	#125	—	2	3	no	—
397	#125	—	2	3	no	—
398	#125	—	2	3	no	—
399	#125	—	2	3	no	—
400	#125	C₂³×C₁₃	1	1	yes	characteristic
401	#124	C₂³×C₁₃	1	3	yes	—
402	#123	—	2	3	no	—
403	#123	—	2	6	no	—
404	C₂²⋊Q₈	—	2	3	no	—
405	C₂²⋊Q₈	—	2	6	no	—
406	C₂²⋊Q₈	—	2	6	no	—
407	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
408	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
409	#121	—	2	3	no	—
410	#121	—	2	3	no	—
411	#121	—	2	3	no	—
412	#121	—	2	3	no	—
413	#121	—	2	6	no	—
414	#121	C₂³×C₁₃	1	3	yes	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	—	2	3	no	—
419	C₄×Q₈	—	2	3	no	—
420	C₄×Q₈	—	2	3	no	—
421	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
422	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
427	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×D₄	—	2	3	no	—
429	C₄×D₄	—	2	3	no	—
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	D₄×C₁₃	1	3	yes	—
435	C₄×D₄	C₂³×C₁₃	1	3	yes	—
436	C₄×D₄	C₂³×C₁₃	1	3	yes	—
437	#117	—	2	3	no	—
438	#117	—	2	3	no	—
439	#117	D₄×C₁₃	1	3	yes	—
440	C₂×C₄⋊C₄	—	2	3	no	—
441	C₂×C₄⋊C₄	—	2	3	no	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
443	C₂×C₄²	—	2	3	no	—
444	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
445	#107	C₂³×C₁₃	1	1	yes	characteristic
446	#107	C₂³×C₁₃	1	3	yes	—
447	#106	C₂³×C₁₃	1	1	yes	characteristic
448	#106	C₂³×C₁₃	1	3	yes	—
449	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
450	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
451	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
452	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
453	#103	C₂³×C₁₃	1	3	yes	—
454	#103	C₂³×C₁₃	1	6	yes	—
455	#103	C₂³×C₁₃	1	1	yes	characteristic
456	#103	C₂³×C₁₃	1	3	yes	—
457	#103	C₂³×C₁₃	1	1	yes	characteristic
458	#103	C₂³×C₁₃	1	3	yes	—
459	#103	C₂³×C₁₃	1	3	yes	—
460	#102	C₂³×C₁₃	1	3	yes	—
461	#102	C₂³×C₁₃	1	6	yes	—
462	#102	C₂³×C₁₃	1	3	yes	—
463	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
464	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
465	C₄×C₈	C₂³×C₁₃	1	3	yes	—
466	C₄×C₈	C₂³×C₁₃	1	3	yes	—
467	C₂×C₁₃	—	4	3	no	—
468	C₂×C₁₃	—	8	3	no	—
469	C₂×C₁₃	#3488	1	1	yes	characteristic
470	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
471	C₂×C₁₃	#3584	1	1	yes	characteristic
472	#41	—	2	4	no	—
473	#41	—	4	6	no	—
474	#41	—	4	6	no	—
475	#41	—	4	4	no	—
476	C₂×Q₈	—	2	3	no	—
477	C₂×Q₈	—	2	3	no	—
478	C₂×Q₈	—	2	6	no	—
479	C₂×Q₈	—	4	3	no	—
480	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
482	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
483	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
484	C₂×D₄	—	2	3	no	—
485	C₂×D₄	—	2	6	no	—
486	C₂×D₄	—	2	3	no	—
487	C₂×D₄	—	2	3	no	—
488	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
489	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
490	C₂²×C₄	—	2	3	no	—
491	C₂²×C₄	—	2	3	no	—
492	C₂²×C₄	—	2	3	no	—
493	C₂²×C₄	—	2	6	no	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
495	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
497	Q₁₆	—	2	6	no	—
498	Q₁₆	—	4	6	no	—
499	Q₁₆	—	4	3	no	—
500	SD₁₆	—	2	6	no	—
501	SD₁₆	—	4	6	no	—
502	SD₁₆	—	4	3	no	—
503	M₁₆	—	4	6	no	—
504	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
505	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
507	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	3	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	3	no	—
514	C₄⋊C₄	—	2	3	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	3	no	—
520	C₄⋊C₄	—	2	3	no	—
521	C₄⋊C₄	—	2	6	no	—
522	C₄⋊C₄	—	2	3	no	—
523	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
524	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
525	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
527	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₂²⋊C₄	—	2	6	no	—
530	C₂²⋊C₄	—	2	3	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₂²⋊C₄	—	2	3	no	—
534	C₂²⋊C₄	—	2	3	no	—
535	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	3	no	—
538	C₄²	—	2	3	no	—
539	C₄²	—	2	3	no	—
540	C₄²	—	2	3	no	—
541	C₄²	C₂×D₄×C₁₃	1	3	yes	—
542	C₄²	C₂×D₄×C₁₃	1	3	yes	—
543	C₄²	C₂⁴×C₁₃	1	3	yes	—
544	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
545	C₁₃	#62005	1	1	yes	characteristic, direct product factor, Sylow
546	C₂³	—	2	3	no	—
547	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
548	Q₈	—	2	1	no	—
549	Q₈	—	2	3	no	—
550	Q₈	—	2	3	no	—
551	Q₈	—	2	3	no	—
552	Q₈	—	2	3	no	—
553	Q₈	—	4	6	no	—
554	Q₈	—	8	3	no	—
555	Q₈	C₁₃×#137	1	4	yes	complemented
556	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
557	D₄	—	2	6	no	—
558	D₄	—	2	3	no	—
559	D₄	—	2	3	no	—
560	D₄	—	4	6	no	—
561	D₄	—	8	3	no	—
562	D₄	—	8	3	no	—
563	D₄	—	8	6	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	6	no	—
566	C₂×C₄	—	2	3	no	—
567	C₂×C₄	—	2	3	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	3	no	—
571	C₂×C₄	—	2	3	no	—
572	C₂×C₄	—	2	3	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	4	3	no	—
575	C₂×C₄	—	4	6	no	—
576	C₂×C₄	—	4	6	no	—
577	C₂×C₄	—	8	6	no	—
578	C₂×C₄	—	8	3	no	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
582	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
583	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
584	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
585	C₈	—	2	3	no	—
586	C₈	—	2	3	no	—
587	C₈	—	2	1	no	—
588	C₈	—	2	1	no	—
589	C₂²	—	2	3	no	—
590	C₂²	—	2	3	no	—
591	C₂²	—	2	3	no	—
592	C₂²	—	4	3	no	—
593	C₂²	—	4	3	no	—
594	C₂²	—	4	3	no	—
595	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	3	no	—
599	C₄	—	2	3	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	3	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	3	no	—
606	C₄	—	4	3	no	—
607	C₄	C₂×C₁₃×#137	1	6	yes	—
608	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
609	C₄	C₁₃×#585	1	1	yes	characteristic
610	C₂	—	4	3	no	—
611	C₂	—	8	3	no	—
612	C₂	C₁₃×#3488	1	1	yes	characteristic
613	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
614	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3517	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3395	C₂	semidirect
4. C₁₃×#3392	C₂	semidirect
5. C₁₃×#3363	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3333	C₂	semidirect
8. C₁₃×#3331	C₂	semidirect
9. C₁₃×#3278	C₂	semidirect
10. C₁₃×#3276	C₂	semidirect
11. C₁₃×#3252	C₂	semidirect
12. C₁₃×#3210	C₂	semidirect
13. C₁₃×#3108	C₂	semidirect
14. C₁₃×#3037	C₂	semidirect
15. C₁₃×#2991	C₂	semidirect
165. #62005	C₁₃	direct (N × H)
240. Q₈×#41	C₂×C₁₃	semidirect
241. #3395	C₂×C₁₃	semidirect
242. #3392	C₂×C₁₃	semidirect
243. #3363	C₂×C₁₃	semidirect
244. #3362	C₂×C₁₃	semidirect
245. #3333	C₂×C₁₃	semidirect
246. #3331	C₂×C₁₃	semidirect
247. #3278	C₂×C₁₃	semidirect
248. #3276	C₂×C₁₃	semidirect
249. #3252	C₂×C₁₃	semidirect
250. #3210	C₂×C₁₃	semidirect
251. #3108	C₂×C₁₃	semidirect
252. #3037	C₂×C₁₃	semidirect
253. #2991	C₂×C₁₃	semidirect
263. Q₈×C₁₃	#137	semidirect
545. C₁₃	#62005	direct (N × H)
555. Q₈	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3517	2
Q₈×C₁₃×#41	2
C₁₃×#3395	2
C₁₃×#3392	2
C₁₃×#3363	2
C₁₃×#3362	2
C₁₃×#3333	2
C₁₃×#3331	2
C₁₃×#3278	2
C₁₃×#3276	2
C₁₃×#3252	2
C₁₃×#3210	2
C₁₃×#3108	2
C₁₃×#3037	2
C₁₃×#2991	2
#62005	13

Subgroups — C13×#62005 #15748344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62005 #15748344