Subgroups — C₁₃×#23618 #15709957

Order 3328.

1318 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2067	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2065	C₂	1	4	yes	maximal, complemented
9	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#428	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
21	C₁₃×#423	—	2	4	no	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	complemented
23	C₁₃×#418	—	2	4	no	—
24	C₁₃×#418	—	2	4	no	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	4	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₁₃×#390	—	2	1	no	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#390	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	2	yes	complemented
32	C₁₃×#389	C₂²	1	2	yes	complemented
33	C₁₃×#385	—	2	2	no	—
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
36	C₁₃×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	D₄	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×#117	—	2	2	no	—
58	C₁₃×#117	—	2	2	no	—
59	C₁₃×#117	—	2	2	no	—
60	C₁₃×#117	D₄	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₁₃×#107	—	2	4	no	—
83	C₁₃×#106	—	2	4	no	—
84	C₁₃×C₄⋊C₈	—	2	8	no	—
85	C₁₃×#102	—	2	8	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₁₃×#102	—	2	4	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	#23618	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂⁴×C₁₃	—	4	4	no	—
94	C₂⁴×C₁₃	—	4	4	no	—
95	C₂⁴×C₁₃	—	4	2	no	—
96	C₂⁴×C₁₃	—	4	2	no	—
97	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₁₃	—	2	8	no	—
99	C₂×D₄×C₁₃	—	2	8	no	—
100	C₂×D₄×C₁₃	—	2	4	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	4	2	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₁₃	#41	1	2	yes	—
127	C₂²×C₄×C₁₃	#41	1	2	yes	—
128	C₂²×C₄×C₁₃	#41	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₁₃×M₁₆	—	2	8	no	—
131	C₁₃×M₁₆	—	4	4	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	4	4	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	4	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₁₃×C₂²⋊C₄	—	4	8	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	4	8	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	4	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	4	2	no	—
159	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
162	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
163	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
165	#2067	C₂×C₁₃	1	4	yes	complemented
166	#2065	C₂×C₁₃	1	4	yes	complemented
167	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	4	16	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	4	no	—
175	C₂³×C₁₃	—	4	4	no	—
176	C₂³×C₁₃	—	4	8	no	—
177	C₂³×C₁₃	—	8	4	no	—
178	C₂³×C₁₃	—	8	4	no	—
179	C₂³×C₁₃	—	8	8	no	—
180	C₂³×C₁₃	#121	1	2	yes	—
181	C₂³×C₁₃	#121	1	2	yes	—
182	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	D₄×C₁₃	—	2	4	no	—
185	D₄×C₁₃	—	2	4	no	—
186	D₄×C₁₃	—	4	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	4	8	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	8	4	no	—
205	C₂×C₄×C₁₃	#121	1	4	yes	—
206	C₂×C₄×C₁₃	#121	1	2	yes	—
207	C₂×C₄×C₁₃	#121	1	2	yes	—
208	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
209	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
211	C₂×C₄×C₁₃	#126	1	4	yes	—
212	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₈×C₁₃	—	2	4	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	—	2	2	no	—
228	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
229	#428	—	2	4	no	—
230	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
231	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
232	#423	—	2	4	no	—
233	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
234	#418	—	2	4	no	—
235	#418	—	2	4	no	—
236	C₂×#102	C₂²×C₁₃	1	2	yes	—
237	C₂×#102	C₂²×C₁₃	1	4	yes	—
238	C₂×#102	C₂²×C₁₃	1	2	yes	—
239	#390	—	2	1	no	—
240	#390	—	2	1	no	—
241	#390	C₂²×C₁₃	1	4	yes	—
242	#389	C₂²×C₁₃	1	2	yes	complemented
243	#389	C₂²×C₁₃	1	2	yes	complemented
244	#385	—	2	2	no	—
245	C₄×C₄⋊C₄	—	2	1	no	—
246	C₄×C₄⋊C₄	—	2	1	no	—
247	#340	C₂²×C₁₃	1	4	yes	complemented
248	C₂²×C₁₃	—	2	4	no	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	4	8	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	8	16	no	—
255	C₂²×C₁₃	—	8	2	no	—
256	C₂²×C₁₃	—	8	2	no	—
257	C₂²×C₁₃	—	8	4	no	—
258	C₂²×C₁₃	#396	1	4	yes	—
259	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
260	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
261	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
263	C₂²×C₁₃	#575	1	2	yes	—
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	—	8	2	no	—
270	C₄×C₁₃	#396	1	4	yes	—
271	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
272	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
273	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
274	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
275	C₂⁵	—	2	1	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
283	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	D₄×C₁₃	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
293	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	D₄×C₁₃	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	4	8	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
320	#107	—	2	4	no	—
321	#106	—	2	4	no	—
322	C₄⋊C₈	—	2	8	no	—
323	#102	—	2	8	no	—
324	#102	—	2	4	no	—
325	#102	—	2	4	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂×C₁₃	—	2	4	no	—
329	C₂×C₁₃	—	8	4	no	—
330	C₂×C₁₃	C₂×#396	1	1	yes	characteristic
331	C₂×C₁₃	#3038	1	1	yes	characteristic
332	C₂×C₁₃	#3040	1	1	yes	characteristic
333	C₂×C₁₃	#3055	1	2	yes	—
334	C₂×C₁₃	#3077	1	2	yes	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	2	no	—
337	C₂⁴	—	4	4	no	—
338	C₂⁴	—	4	4	no	—
339	C₂⁴	—	4	2	no	—
340	C₂⁴	—	4	2	no	—
341	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
370	C₂²×C₄	C₁₃×#41	1	2	yes	—
371	C₂²×C₄	C₁₃×#41	1	2	yes	—
372	C₂²×C₄	C₁₃×#41	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
374	M₁₆	—	2	8	no	—
375	M₁₆	—	4	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
392	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	8	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	8	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	4	2	no	—
403	C₁₃	#23618	1	1	yes	characteristic, direct product factor, Sylow
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	4	16	no	—
408	C₂³	—	4	8	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	4	no	—
413	C₂³	—	8	4	no	—
414	C₂³	—	8	4	no	—
415	C₂³	—	8	8	no	—
416	C₂³	C₁₃×#121	1	2	yes	—
417	C₂³	C₁₃×#121	1	2	yes	—
418	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
419	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	8	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	C₁₃×#121	1	2	yes	—
442	C₂×C₄	C₁₃×#121	1	2	yes	—
443	C₂×C₄	C₁₃×#121	1	4	yes	—
444	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
445	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
446	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
447	C₂×C₄	C₁₃×#126	1	4	yes	—
448	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
453	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	8	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	16	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	4	no	—
467	C₂²	C₁₃×#396	1	4	yes	—
468	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
469	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
470	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
471	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
472	C₂²	C₁₃×#575	1	2	yes	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	C₁₃×#396	1	4	yes	—
480	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
481	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
482	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
483	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
484	C₂	—	2	4	no	—
485	C₂	—	8	4	no	—
486	C₂	C₂×C₁₃×#396	1	1	yes	characteristic
487	C₂	C₁₃×#3038	1	1	yes	characteristic
488	C₂	C₁₃×#3040	1	1	yes	characteristic
489	C₂	C₁₃×#3055	1	2	yes	—
490	C₂	C₁₃×#3077	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#428	C₂	semidirect
2. C₂×C₁₃×#423	C₂	semidirect
5. C₁₃×#2296	C₂	semidirect
7. C₁₃×#2067	C₂	semidirect
8. C₁₃×#2065	C₂	semidirect
9. C₁₃×#1736	C₂	semidirect
19. C₂×C₁₃×#107	C₂²	semidirect
20. C₂×C₁₃×#106	C₂²	semidirect
22. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
31. C₁₃×#389	C₂²	semidirect
32. C₁₃×#389	C₂²	semidirect
36. C₁₃×#340	C₂²	semidirect
90. #23618	C₁₃	direct (N × H)
159. C₂×#428	C₂×C₁₃	semidirect
160. C₂×#423	C₂×C₁₃	semidirect
163. #2296	C₂×C₁₃	semidirect
165. #2067	C₂×C₁₃	semidirect
166. #2065	C₂×C₁₃	semidirect
167. #1736	C₂×C₁₃	semidirect
230. C₂×#107	C₂²×C₁₃	semidirect
231. C₂×#106	C₂²×C₁₃	semidirect
233. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
242. #389	C₂²×C₁₃	semidirect
243. #389	C₂²×C₁₃	semidirect
247. #340	C₂²×C₁₃	semidirect
403. C₁₃	#23618	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×#428	2
C₂×C₁₃×#423	2
C₂×C₁₃×#418	2
C₁₃×#2296	2
C₂×C₁₃×#390	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#1736	2
#23618	13

Subgroups — C13×#23618 #15709957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23618 #15709957