Subgroups — C₁₃×#25847 #15712186

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2584	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2058	C₂	1	2	yes	maximal
6	C₁₃×#2057	C₂	1	2	yes	maximal
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1865	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₁₃	—	2	4	no	—
13	Q₈²×C₁₃	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#501	—	2	4	no	—
24	C₁₃×#479	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	2	yes	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#398	—	2	1	no	—
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#389	C₂²	1	2	yes	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	2	16	no	—
53	C₁₃×C₄⋊Q₈	—	2	8	no	—
54	C₁₃×C₄⋊Q₈	—	2	4	no	—
55	C₁₃×C₄⋊Q₈	—	2	4	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
58	C₁₃×#125	—	2	2	no	—
59	C₁₃×#125	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	8	no	—
61	C₄×Q₈×C₁₃	—	2	4	no	—
62	C₄×Q₈×C₁₃	—	2	4	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	D₄	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	1	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#107	—	2	2	no	—
88	C₁₃×#107	—	2	4	no	—
89	C₁₃×#106	—	2	2	no	—
90	C₁₃×#106	—	2	4	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	Q₈	1	8	yes	complemented
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	#25847	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	2	4	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	8	1	no	—
107	C₂×Q₈×C₁₃	—	8	1	no	—
108	C₂×Q₈×C₁₃	—	8	2	no	—
109	C₂×Q₈×C₁₃	—	8	2	no	—
110	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	4	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	4	no	—
146	C₁₃×C₄⋊C₄	—	8	2	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
150	C₄²×C₁₃	—	2	8	no	—
151	C₄²×C₁₃	—	2	4	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	8	1	no	—
155	C₄²×C₁₃	C₂×D₄	1	2	yes	—
156	C₄²×C₁₃	C₂×D₄	1	2	yes	—
157	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic
158	C₂×#501	C₂×C₁₃	1	1	yes	characteristic
159	C₂×#479	C₂×C₁₃	1	1	yes	characteristic
160	#2584	C₂×C₁₃	1	1	yes	characteristic
161	#2058	C₂×C₁₃	1	2	yes	—
162	#2057	C₂×C₁₃	1	2	yes	—
163	#1988	C₂×C₁₃	1	1	yes	characteristic
164	#1985	C₂×C₁₃	1	1	yes	characteristic
165	#1865	C₂×C₁₃	1	2	yes	—
166	#1863	C₂×C₁₃	1	2	yes	—
167	#1763	C₂×C₁₃	1	1	yes	characteristic
168	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	2	8	no	—
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	—	8	4	no	—
173	Q₈×C₁₃	—	8	8	no	—
174	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	#120	1	2	yes	—
200	C₂×C₄×C₁₃	#120	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	4	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
205	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
206	C₈×C₁₃	—	2	4	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	Q₈²	—	2	4	no	—
210	Q₈²	—	2	4	no	—
211	C₂×C₄⋊Q₈	—	2	2	no	—
212	C₂×C₄⋊Q₈	—	2	1	no	—
213	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×Q₈	—	2	1	no	—
217	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	#501	—	2	4	no	—
221	#479	—	2	4	no	—
222	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#107	C₂²×C₁₃	1	2	yes	—
224	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#106	C₂²×C₁₃	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#103	C₂²×C₁₃	1	2	yes	—
230	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
231	#398	—	2	1	no	—
232	#395	—	2	1	no	—
233	#389	—	2	2	no	—
234	#389	C₂²×C₁₃	1	2	yes	—
235	#389	C₂²×C₁₃	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	#340	C₂²×C₁₃	1	2	yes	—
238	#340	C₂²×C₁₃	1	2	yes	—
239	#340	C₂²×C₁₃	1	2	yes	—
240	#336	C₂²×C₁₃	1	2	yes	—
241	#336	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
243	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
244	C₂²×C₁₃	C₂×#137	1	2	yes	—
245	C₂²×C₁₃	#576	1	1	yes	characteristic
246	C₂²×C₁₃	#577	1	1	yes	characteristic
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	4	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	4	4	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	1	no	—
257	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
258	C₄×C₁₃	#536	1	1	yes	characteristic
259	C₄×C₁₃	D₄×Q₈	1	2	yes	—
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
267	C₄⋊Q₈	—	2	16	no	—
268	C₄⋊Q₈	—	2	8	no	—
269	C₄⋊Q₈	—	2	4	no	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
273	#125	—	2	2	no	—
274	#125	—	2	2	no	—
275	C₄×Q₈	—	2	8	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	D₄×C₁₃	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
301	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#107	—	2	4	no	—
304	#106	—	2	2	no	—
305	#106	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	Q₈×C₁₃	1	8	yes	complemented
310	#97	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂×C₁₃	#2434	1	1	yes	characteristic
315	C₂×C₁₃	#3004	1	1	yes	characteristic
316	C₂×C₁₃	#3012	1	1	yes	characteristic
317	C₂×C₁₃	#3385	1	2	yes	—
318	C₂×C₁₃	#3387	1	2	yes	—
319	C₂×Q₈	—	2	8	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	8	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	—	8	2	no	—
328	C₂×Q₈	—	8	2	no	—
329	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	8	2	no	—
366	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
367	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
369	C₄²	—	2	8	no	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	8	1	no	—
374	C₄²	C₂×D₄×C₁₃	1	2	yes	—
375	C₄²	C₂×D₄×C₁₃	1	2	yes	—
376	C₁₃	#25847	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	Q₈	—	2	8	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	4	no	—
381	Q₈	—	8	4	no	—
382	Q₈	—	8	8	no	—
383	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	C₁₃×#120	1	2	yes	—
409	C₂×C₄	C₁₃×#120	1	2	yes	—
410	C₂×C₄	C₁₃×#137	1	4	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
414	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
415	C₈	—	2	4	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
419	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
420	C₂²	C₂×C₁₃×#137	1	2	yes	—
421	C₂²	C₁₃×#576	1	1	yes	characteristic
422	C₂²	C₁₃×#577	1	1	yes	characteristic
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	4	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
434	C₄	C₁₃×#536	1	1	yes	characteristic
435	C₄	D₄×Q₈×C₁₃	1	2	yes	—
436	C₂	C₁₃×#2434	1	1	yes	characteristic
437	C₂	C₁₃×#3004	1	1	yes	characteristic
438	C₂	C₁₃×#3012	1	1	yes	characteristic
439	C₂	C₁₃×#3385	1	2	yes	—
440	C₂	C₁₃×#3387	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
94. C₁₃×#103	Q₈	semidirect
99. #25847	C₁₃	direct (N × H)
309. #103	Q₈×C₁₃	semidirect
376. C₁₃	#25847	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×Q₈²×C₁₃	2
C₂×C₁₃×#501	2
C₂×C₁₃×#479	2
C₁₃×#2584	2
C₁₃×#2058	2
C₁₃×#2057	2
C₁₃×#1988	2
C₁₃×#1985	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1763	2
#25847	13

Subgroups — C13×#25847 #15712186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25847 #15712186