Subgroups — C₁₃×#61319 #15747658

Order 3328.

1836 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3375	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3141	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3079	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3037	C₂	1	3	yes	maximal, complemented
10	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#137	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#137	C₂²	1	3	yes	—
13	C₁₃×#559	C₂²	1	3	yes	—
14	Q₈²×C₁₃	—	2	1	no	—
15	Q₈²×C₁₃	—	2	3	no	—
16	Q₈²×C₁₃	C₂²	1	2	yes	—
17	Q₈²×C₁₃	C₂²	1	6	yes	—
18	C₁₃×#557	C₂²	1	1	yes	characteristic
19	C₁₃×#556	C₂²	1	3	yes	—
20	C₁₃×#553	—	2	3	no	—
21	C₁₃×#550	C₂²	1	1	yes	characteristic
22	C₁₃×#548	—	2	1	no	—
23	C₁₃×#532	C₂²	1	3	yes	—
24	C₂×C₁₃×C₄⋊Q₈	—	2	3	no	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₃×#529	—	2	3	no	—
27	C₄×C₁₃×#41	—	2	1	no	—
28	C₄×C₁₃×#41	C₂²	1	3	yes	—
29	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#489	C₂²	1	12	yes	—
33	C₁₃×#487	C₂²	1	6	yes	—
34	C₁₃×#486	C₂²	1	6	yes	—
35	C₁₃×#477	C₂²	1	6	yes	—
36	C₁₃×#476	C₂²	1	6	yes	—
37	C₁₃×#475	C₂²	1	6	yes	—
38	C₁₃×#474	C₂²	1	6	yes	—
39	C₁₃×#464	C₂²	1	12	yes	—
40	C₁₃×#462	C₂²	1	6	yes	—
41	C₁₃×#460	C₂²	1	6	yes	—
42	C₁₃×#446	C₂²	1	6	yes	—
43	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
44	C₁₃×#441	C₂²	1	6	yes	—
45	C₁₃×#440	C₂²	1	6	yes	—
46	C₄×C₁₃×Q₁₆	C₂²	1	6	yes	—
47	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
48	C₁₃×#428	C₂²	1	3	yes	—
49	C₁₃×#423	C₂²	1	3	yes	—
50	C₁₃×#419	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	6	yes	—
52	C₁₃×#417	C₂²	1	3	yes	—
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	1	no	—
55	C₂×C₁₃×#41	C₂³	1	3	yes	—
56	C₂²×Q₈×C₁₃	—	2	3	no	—
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#137	—	2	12	no	—
60	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	—
61	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
64	C₁₃×C₄⋊Q₈	—	2	6	no	—
65	C₁₃×C₄⋊Q₈	—	2	6	no	—
66	C₁₃×C₄⋊Q₈	—	2	12	no	—
67	C₁₃×C₄⋊Q₈	—	2	3	no	—
68	C₁₃×C₄⋊Q₈	—	2	3	no	—
69	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
72	C₁₃×#127	C₂³	1	3	yes	—
73	C₁₃×#126	—	2	6	no	—
74	C₁₃×#125	—	2	3	no	—
75	C₁₃×#124	—	2	3	no	—
76	C₁₃×#124	C₂³	1	6	yes	—
77	C₁₃×#123	—	2	6	no	—
78	C₁₃×C₂²⋊Q₈	—	2	3	no	—
79	C₁₃×#121	—	2	3	no	—
80	C₁₃×#121	—	2	3	no	—
81	C₁₃×#121	—	2	3	no	—
82	C₄×Q₈×C₁₃	—	2	6	no	—
83	C₄×Q₈×C₁₃	—	2	2	no	—
84	C₄×Q₈×C₁₃	—	2	1	no	—
85	C₄×Q₈×C₁₃	—	2	3	no	—
86	C₄×Q₈×C₁₃	—	2	3	no	—
87	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
88	C₄×Q₈×C₁₃	D₄	1	3	yes	—
89	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
95	C₄×D₄×C₁₃	—	2	3	no	—
96	C₄×D₄×C₁₃	—	2	3	no	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	C₂³	1	3	yes	—
101	C₄×D₄×C₁₃	C₂³	1	3	yes	—
102	C₁₃×#117	—	2	3	no	—
103	C₁₃×#117	—	2	3	no	—
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
109	C₂×C₄²×C₁₃	—	2	3	no	—
110	C₂×C₄²×C₁₃	—	2	3	no	—
111	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
112	C₁₃×#107	C₂³	1	6	yes	—
113	C₁₃×#106	C₂³	1	6	yes	—
114	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₃×#103	C₂³	1	6	yes	—
117	C₁₃×#103	C₂³	1	12	yes	—
118	C₁₃×#103	C₂³	1	2	yes	—
119	C₁₃×#103	C₂³	1	2	yes	—
120	C₁₃×#102	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	12	yes	—
122	C₁₃×#97	C₂³	1	6	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#61319	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₁₃×#41	—	2	6	no	—
126	C₁₃×#41	—	2	6	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	6	no	—
131	C₂×Q₈×C₁₃	—	2	6	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	8	6	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
137	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	—	2	3	no	—
141	C₂×D₄×C₁₃	—	2	3	no	—
142	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	3	no	—
145	C₂²×C₄×C₁₃	—	2	3	no	—
146	C₂²×C₄×C₁₃	—	2	3	no	—
147	C₂²×C₄×C₁₃	—	2	3	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×Q₁₆	—	2	12	no	—
152	C₁₃×SD₁₆	—	2	12	no	—
153	C₁₃×M₁₆	—	2	6	no	—
154	C₁₃×M₁₆	—	2	2	no	—
155	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
156	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
157	C₁₃×C₄⋊C₄	—	2	6	no	—
158	C₁₃×C₄⋊C₄	—	2	6	no	—
159	C₁₃×C₄⋊C₄	—	2	6	no	—
160	C₁₃×C₄⋊C₄	—	2	6	no	—
161	C₁₃×C₄⋊C₄	—	2	3	no	—
162	C₁₃×C₄⋊C₄	—	2	3	no	—
163	C₁₃×C₄⋊C₄	—	2	3	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	3	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
172	C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₁₃×C₂²⋊C₄	—	2	6	no	—
174	C₁₃×C₂²⋊C₄	—	2	3	no	—
175	C₁₃×C₂²⋊C₄	—	2	3	no	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	3	no	—
179	C₄²×C₁₃	—	2	3	no	—
180	C₄²×C₁₃	—	2	6	no	—
181	C₄²×C₁₃	—	2	6	no	—
182	C₄²×C₁₃	C₂×D₄	1	3	yes	—
183	C₄²×C₁₃	C₂×D₄	1	3	yes	—
184	C₄²×C₁₃	C₂⁴	1	3	yes	—
185	C₄²×C₁₃	C₂⁴	1	3	yes	—
186	#3480	C₂×C₁₃	1	1	yes	characteristic
187	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#3375	C₂×C₁₃	1	6	yes	complemented
189	#3369	C₂×C₁₃	1	6	yes	complemented
190	#3363	C₂×C₁₃	1	2	yes	complemented
191	#3362	C₂×C₁₃	1	2	yes	complemented
192	#3141	C₂×C₁₃	1	3	yes	complemented
193	#3079	C₂×C₁₃	1	3	yes	complemented
194	#3037	C₂×C₁₃	1	3	yes	complemented
195	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₄×#137	C₂×C₁₃	1	3	yes	complemented
197	C₂³×C₁₃	—	2	3	no	—
198	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₁₃	—	2	4	no	—
200	Q₈×C₁₃	—	2	6	no	—
201	Q₈×C₁₃	—	2	2	no	—
202	Q₈×C₁₃	—	2	3	no	—
203	Q₈×C₁₃	—	2	3	no	—
204	Q₈×C₁₃	—	8	6	no	—
205	Q₈×C₁₃	—	8	6	no	—
206	Q₈×C₁₃	#137	1	4	yes	complemented
207	Q₈×C₁₃	C₂×#41	1	4	yes	—
208	D₄×C₁₃	—	2	3	no	—
209	D₄×C₁₃	—	2	3	no	—
210	D₄×C₁₃	—	4	6	no	—
211	D₄×C₁₃	—	4	6	no	—
212	D₄×C₁₃	—	8	3	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	6	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	3	no	—
219	C₂×C₄×C₁₃	—	2	6	no	—
220	C₂×C₄×C₁₃	—	4	3	no	—
221	C₂×C₄×C₁₃	—	4	6	no	—
222	C₂×C₄×C₁₃	—	4	6	no	—
223	C₂×C₄×C₁₃	—	4	6	no	—
224	C₂×C₄×C₁₃	—	8	3	no	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
230	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
231	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
233	C₈×C₁₃	—	2	6	no	—
234	C₈×C₁₃	—	2	2	no	—
235	C₂×#137	C₂²×C₁₃	1	3	yes	—
236	#559	C₂²×C₁₃	1	3	yes	—
237	Q₈²	—	2	1	no	—
238	Q₈²	—	2	3	no	—
239	Q₈²	C₂²×C₁₃	1	2	yes	—
240	Q₈²	C₂²×C₁₃	1	6	yes	—
241	#557	C₂²×C₁₃	1	1	yes	characteristic
242	#556	C₂²×C₁₃	1	3	yes	—
243	#553	—	2	3	no	—
244	#550	C₂²×C₁₃	1	1	yes	characteristic
245	#548	—	2	1	no	—
246	#532	C₂²×C₁₃	1	3	yes	—
247	C₂×C₄⋊Q₈	—	2	3	no	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
249	#529	—	2	3	no	—
250	C₄×#41	—	2	1	no	—
251	C₄×#41	C₂²×C₁₃	1	3	yes	—
252	C₂×C₄×Q₈	—	2	1	no	—
253	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
254	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	#489	C₂²×C₁₃	1	12	yes	—
256	#487	C₂²×C₁₃	1	6	yes	—
257	#486	C₂²×C₁₃	1	6	yes	—
258	#477	C₂²×C₁₃	1	6	yes	—
259	#476	C₂²×C₁₃	1	6	yes	—
260	#475	C₂²×C₁₃	1	6	yes	—
261	#474	C₂²×C₁₃	1	6	yes	—
262	#464	C₂²×C₁₃	1	12	yes	—
263	#462	C₂²×C₁₃	1	6	yes	—
264	#460	C₂²×C₁₃	1	6	yes	—
265	#446	C₂²×C₁₃	1	6	yes	—
266	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
267	#441	C₂²×C₁₃	1	6	yes	—
268	#440	C₂²×C₁₃	1	6	yes	—
269	C₄×Q₁₆	C₂²×C₁₃	1	6	yes	—
270	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
271	#428	C₂²×C₁₃	1	3	yes	—
272	#423	C₂²×C₁₃	1	3	yes	—
273	#419	C₂²×C₁₃	1	1	yes	characteristic
274	#417	C₂²×C₁₃	1	6	yes	—
275	#417	C₂²×C₁₃	1	3	yes	—
276	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	4	3	no	—
280	C₂²×C₁₃	—	4	3	no	—
281	C₂²×C₁₃	—	4	3	no	—
282	C₂²×C₁₃	#548	1	2	yes	—
283	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₁₃	—	2	3	no	—
285	C₄×C₁₃	—	2	3	no	—
286	C₄×C₁₃	—	2	4	no	—
287	C₄×C₁₃	—	2	3	no	—
288	C₄×C₁₃	—	4	6	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	4	3	no	—
291	C₄×C₁₃	—	4	1	no	—
292	C₄×C₁₃	#548	1	2	yes	—
293	C₄×C₁₃	C₂×#137	1	6	yes	—
294	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
295	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
296	C₂×#41	—	2	1	no	—
297	C₂×#41	C₂³×C₁₃	1	3	yes	—
298	C₂²×Q₈	—	2	3	no	—
299	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
301	#137	—	2	12	no	—
302	C₂×Q₁₆	C₂³×C₁₃	1	6	yes	—
303	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
304	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
305	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
306	C₄⋊Q₈	—	2	6	no	—
307	C₄⋊Q₈	—	2	6	no	—
308	C₄⋊Q₈	—	2	12	no	—
309	C₄⋊Q₈	—	2	3	no	—
310	C₄⋊Q₈	—	2	3	no	—
311	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
312	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
313	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
314	#127	C₂³×C₁₃	1	3	yes	—
315	#126	—	2	6	no	—
316	#125	—	2	3	no	—
317	#124	—	2	3	no	—
318	#124	C₂³×C₁₃	1	6	yes	—
319	#123	—	2	6	no	—
320	C₂²⋊Q₈	—	2	3	no	—
321	#121	—	2	3	no	—
322	#121	—	2	3	no	—
323	#121	—	2	3	no	—
324	C₄×Q₈	—	2	6	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	1	no	—
327	C₄×Q₈	—	2	3	no	—
328	C₄×Q₈	—	2	3	no	—
329	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
330	C₄×Q₈	D₄×C₁₃	1	3	yes	—
331	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
332	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
333	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
334	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
335	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
337	C₄×D₄	—	2	3	no	—
338	C₄×D₄	—	2	3	no	—
339	C₄×D₄	—	2	3	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	—	2	3	no	—
342	C₄×D₄	C₂³×C₁₃	1	3	yes	—
343	C₄×D₄	C₂³×C₁₃	1	3	yes	—
344	#117	—	2	3	no	—
345	#117	—	2	3	no	—
346	#117	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	—	2	3	no	—
348	C₂×C₄⋊C₄	—	2	3	no	—
349	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
351	C₂×C₄²	—	2	3	no	—
352	C₂×C₄²	—	2	3	no	—
353	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
354	#107	C₂³×C₁₃	1	6	yes	—
355	#106	C₂³×C₁₃	1	6	yes	—
356	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
357	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
358	#103	C₂³×C₁₃	1	6	yes	—
359	#103	C₂³×C₁₃	1	12	yes	—
360	#103	C₂³×C₁₃	1	2	yes	—
361	#103	C₂³×C₁₃	1	2	yes	—
362	#102	C₂³×C₁₃	1	6	yes	—
363	#102	C₂³×C₁₃	1	12	yes	—
364	#97	C₂³×C₁₃	1	6	yes	—
365	C₄×C₈	C₂³×C₁₃	1	6	yes	—
366	C₂×C₁₃	—	2	2	no	—
367	C₂×C₁₃	—	8	3	no	—
368	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
369	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
370	C₂×C₁₃	#3585	1	1	yes	characteristic
371	#41	—	2	6	no	—
372	#41	—	2	6	no	—
373	#41	—	4	4	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	6	no	—
377	C₂×Q₈	—	2	6	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	8	6	no	—
380	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
381	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
383	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
384	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
385	C₂×D₄	—	2	3	no	—
386	C₂×D₄	—	2	3	no	—
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	3	no	—
391	C₂²×C₄	—	2	3	no	—
392	C₂²×C₄	—	2	3	no	—
393	C₂²×C₄	—	2	3	no	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	Q₁₆	—	2	12	no	—
398	SD₁₆	—	2	12	no	—
399	M₁₆	—	2	6	no	—
400	M₁₆	—	2	2	no	—
401	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
402	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
403	C₄⋊C₄	—	2	6	no	—
404	C₄⋊C₄	—	2	6	no	—
405	C₄⋊C₄	—	2	6	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	2	3	no	—
408	C₄⋊C₄	—	2	3	no	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	3	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
413	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
414	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
415	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
416	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	6	no	—
420	C₂²⋊C₄	—	2	3	no	—
421	C₂²⋊C₄	—	2	3	no	—
422	C₂²⋊C₄	—	2	6	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	3	no	—
425	C₄²	—	2	3	no	—
426	C₄²	—	2	6	no	—
427	C₄²	—	2	6	no	—
428	C₄²	C₂×D₄×C₁₃	1	3	yes	—
429	C₄²	C₂×D₄×C₁₃	1	3	yes	—
430	C₄²	C₂⁴×C₁₃	1	3	yes	—
431	C₄²	C₂⁴×C₁₃	1	3	yes	—
432	C₁₃	#61319	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	3	no	—
434	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	Q₈	—	2	4	no	—
436	Q₈	—	2	6	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	3	no	—
439	Q₈	—	2	3	no	—
440	Q₈	—	8	6	no	—
441	Q₈	—	8	6	no	—
442	Q₈	C₁₃×#137	1	4	yes	complemented
443	Q₈	C₂×C₁₃×#41	1	4	yes	—
444	D₄	—	2	3	no	—
445	D₄	—	2	3	no	—
446	D₄	—	4	6	no	—
447	D₄	—	4	6	no	—
448	D₄	—	8	3	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	6	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	3	no	—
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	4	3	no	—
457	C₂×C₄	—	4	6	no	—
458	C₂×C₄	—	4	6	no	—
459	C₂×C₄	—	4	6	no	—
460	C₂×C₄	—	8	3	no	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
462	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
466	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
467	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
469	C₈	—	2	6	no	—
470	C₈	—	2	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	3	no	—
475	C₂²	—	4	3	no	—
476	C₂²	C₁₃×#548	1	2	yes	—
477	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
478	C₄	—	2	3	no	—
479	C₄	—	2	3	no	—
480	C₄	—	2	3	no	—
481	C₄	—	2	4	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	6	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	3	no	—
486	C₄	C₁₃×#548	1	2	yes	—
487	C₄	C₂×C₁₃×#137	1	6	yes	—
488	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
489	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
490	C₂	—	2	2	no	—
491	C₂	—	8	3	no	—
492	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
493	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
494	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈²×C₁₃	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3363	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3141	C₂	semidirect
8. C₁₃×#3079	C₂	semidirect
9. C₁₃×#3037	C₂	semidirect
10. Q₈×C₁₃×M₁₆	C₂	semidirect
11. C₄×C₁₃×#137	C₂	semidirect
124. #61319	C₁₃	direct (N × H)
136. C₂×Q₈×C₁₃	#41	semidirect
187. C₂×Q₈²	C₂×C₁₃	semidirect
188. #3375	C₂×C₁₃	semidirect
189. #3369	C₂×C₁₃	semidirect
190. #3363	C₂×C₁₃	semidirect
191. #3362	C₂×C₁₃	semidirect
192. #3141	C₂×C₁₃	semidirect
193. #3079	C₂×C₁₃	semidirect
194. #3037	C₂×C₁₃	semidirect
195. Q₈×M₁₆	C₂×C₁₃	semidirect
196. C₄×#137	C₂×C₁₃	semidirect
206. Q₈×C₁₃	#137	semidirect
382. C₂×Q₈	C₁₃×#41	semidirect
432. C₁₃	#61319	direct (N × H)
442. 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×#3480	2
C₂×Q₈²×C₁₃	2
C₁₃×#3375	2
C₁₃×#3369	2
C₁₃×#3363	2
C₁₃×#3362	2
C₁₃×#3141	2
C₁₃×#3079	2
C₁₃×#3037	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
#61319	13

Subgroups — C13×#61319 #15747658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61319 #15747658