Subgroups — C₂×C₁₃×#3390 #15747703

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	2	yes	maximal
2	C₁₃×#3390	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#501	C₂	1	2	yes	maximal
4	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#479	C₂	1	2	yes	maximal
6	C₂×C₁₃×#479	C₂	1	2	yes	maximal
7	C₂×C₁₃×#477	C₂	1	2	yes	maximal
8	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#441	C₂	1	2	yes	maximal
10	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×#557	—	2	8	no	—
13	C₁₃×#557	C₂²	1	16	yes	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#125	—	2	2	no	—
17	C₂×C₁₃×#125	—	2	2	no	—
18	C₂×C₁₃×#125	C₂²	1	2	yes	—
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#501	C₂²	1	16	yes	—
26	C₁₃×#499	C₂²	1	8	yes	—
27	C₁₃×#479	C₂²	1	16	yes	—
28	C₁₃×#479	C₂²	1	16	yes	—
29	C₁₃×#477	C₂²	1	16	yes	—
30	C₁₃×#446	C₂²	1	8	yes	—
31	C₁₃×#441	C₂²	1	16	yes	—
32	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	C₂²	1	2	yes	—
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	C₂²	1	2	yes	—
38	C₂×C₁₃×#106	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	C₂²	1	2	yes	—
42	C₂×C₁₃×#103	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂×C₁₃×Q₁₆	Q₈	1	8	yes	complemented
50	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	16	no	—
55	C₁₃×C₄⋊Q₈	—	2	4	no	—
56	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
57	C₁₃×#125	—	2	16	no	—
58	C₁₃×#125	—	2	16	no	—
59	C₁₃×#125	—	2	4	no	—
60	C₁₃×#125	—	2	4	no	—
61	C₁₃×#125	C₂³	1	8	yes	—
62	C₁₃×#125	C₂³	1	8	yes	—
63	C₄×Q₈×C₁₃	—	2	16	no	—
64	C₄×Q₈×C₁₃	—	2	4	no	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×Q₈×C₁₃	D₄	1	4	yes	—
68	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
69	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
70	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
71	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃	—	2	2	no	—
86	C₂×C₄²×C₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	2	no	—
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₁₃×#107	C₂³	1	4	yes	—
91	C₁₃×#107	C₂³	1	4	yes	—
92	C₁₃×#107	C₂³	1	8	yes	—
93	C₁₃×#107	C₂³	1	4	yes	—
94	C₁₃×#106	C₂³	1	8	yes	—
95	C₁₃×#106	C₂³	1	8	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
98	C₁₃×#103	C₂³	1	8	yes	—
99	C₁₃×#103	C₂³	1	8	yes	—
100	C₁₃×#103	C₂³	1	8	yes	—
101	C₁₃×#97	C₂³	1	8	yes	—
102	C₄×C₈×C₁₃	C₂³	1	4	yes	—
103	C₂×#3390	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	4	2	no	—
108	C₂×Q₈×C₁₃	—	4	8	no	—
109	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
110	C₂×Q₈×C₁₃	C₂×Q₈	1	8	yes	—
111	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×Q₁₆	C₂×Q₈	1	16	yes	complemented
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
125	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
126	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
127	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
141	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
142	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
144	C₄²×C₁₃	—	2	8	no	—
145	C₄²×C₁₃	—	2	8	no	—
146	C₄²×C₁₃	—	2	8	no	—
147	C₄²×C₁₃	C₂×D₄	1	2	yes	—
148	C₄²×C₁₃	C₂×D₄	1	4	yes	—
149	C₄²×C₁₃	C₂⁴	1	2	yes	—
150	C₄²×C₁₃	C₂⁴	1	4	yes	—
151	C₂×#557	C₂×C₁₃	1	2	yes	—
152	#3390	C₂×C₁₃	1	16	yes	direct product factor
153	C₂×#501	C₂×C₁₃	1	2	yes	—
154	C₂×#499	C₂×C₁₃	1	1	yes	characteristic
155	C₂×#479	C₂×C₁₃	1	2	yes	—
156	C₂×#479	C₂×C₁₃	1	2	yes	—
157	C₂×#477	C₂×C₁₃	1	2	yes	—
158	C₂×#446	C₂×C₁₃	1	1	yes	characteristic
159	C₂×#441	C₂×C₁₃	1	2	yes	—
160	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	8	no	—
163	Q₈×C₁₃	—	2	4	no	—
164	Q₈×C₁₃	—	4	4	no	—
165	Q₈×C₁₃	—	4	16	no	—
166	Q₈×C₁₃	C₂²×Q₈	1	8	yes	—
167	C₂×C₄×C₁₃	—	2	8	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
185	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
186	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	—	2	4	no	—
189	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
190	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
191	#557	—	2	8	no	—
192	#557	C₂²×C₁₃	1	16	yes	—
193	C₂×C₄⋊Q₈	—	2	2	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
195	C₂×#125	—	2	2	no	—
196	C₂×#125	—	2	2	no	—
197	C₂×#125	C₂²×C₁₃	1	2	yes	—
198	C₂×#125	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×Q₈	—	2	2	no	—
200	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
204	#501	C₂²×C₁₃	1	16	yes	—
205	#499	C₂²×C₁₃	1	8	yes	—
206	#479	C₂²×C₁₃	1	16	yes	—
207	#479	C₂²×C₁₃	1	16	yes	—
208	#477	C₂²×C₁₃	1	16	yes	—
209	#446	C₂²×C₁₃	1	8	yes	—
210	#441	C₂²×C₁₃	1	16	yes	—
211	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	—
212	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#107	C₂²×C₁₃	1	2	yes	—
214	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#106	C₂²×C₁₃	1	2	yes	—
217	C₂×#106	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#103	C₂²×C₁₃	1	2	yes	—
222	C₂×#103	C₂²×C₁₃	1	2	yes	—
223	C₂×#97	C₂²×C₁₃	1	2	yes	—
224	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
226	C₂²×C₁₃	#575	1	2	yes	—
227	C₂²×C₁₃	#578	1	2	yes	—
228	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
229	C₄×C₁₃	—	2	8	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	—	4	4	no	—
235	C₄×C₁₃	—	4	4	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	D₄×Q₈	1	2	yes	—
238	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
239	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
242	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
243	C₂×Q₁₆	Q₈×C₁₃	1	8	yes	complemented
244	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
245	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
248	C₄⋊Q₈	—	2	16	no	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
251	#125	—	2	16	no	—
252	#125	—	2	16	no	—
253	#125	—	2	4	no	—
254	#125	—	2	4	no	—
255	#125	C₂³×C₁₃	1	8	yes	—
256	#125	C₂³×C₁₃	1	8	yes	—
257	C₄×Q₈	—	2	16	no	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×Q₈	—	2	4	no	—
261	C₄×Q₈	D₄×C₁₃	1	4	yes	—
262	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
263	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
264	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
265	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
275	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
284	#107	C₂³×C₁₃	1	4	yes	—
285	#107	C₂³×C₁₃	1	4	yes	—
286	#107	C₂³×C₁₃	1	8	yes	—
287	#107	C₂³×C₁₃	1	4	yes	—
288	#106	C₂³×C₁₃	1	8	yes	—
289	#106	C₂³×C₁₃	1	8	yes	—
290	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
291	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
292	#103	C₂³×C₁₃	1	8	yes	—
293	#103	C₂³×C₁₃	1	8	yes	—
294	#103	C₂³×C₁₃	1	8	yes	—
295	#97	C₂³×C₁₃	1	8	yes	—
296	C₄×C₈	C₂³×C₁₃	1	4	yes	—
297	C₂×C₁₃	#3390	1	4	yes	direct product factor
298	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
299	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	8	no	—
306	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
307	C₂×Q₈	C₂×Q₈×C₁₃	1	8	yes	—
308	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
318	Q₁₆	C₂×Q₈×C₁₃	1	16	yes	complemented
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
322	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
323	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
324	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
337	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
338	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
339	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
340	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
341	C₄²	—	2	8	no	—
342	C₄²	—	2	8	no	—
343	C₄²	—	2	8	no	—
344	C₄²	C₂×D₄×C₁₃	1	2	yes	—
345	C₄²	C₂×D₄×C₁₃	1	4	yes	—
346	C₄²	C₂⁴×C₁₃	1	2	yes	—
347	C₄²	C₂⁴×C₁₃	1	4	yes	—
348	C₁₃	C₂×#3390	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
350	Q₈	—	2	8	no	—
351	Q₈	—	2	4	no	—
352	Q₈	—	4	4	no	—
353	Q₈	—	4	16	no	—
354	Q₈	C₂²×Q₈×C₁₃	1	8	yes	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
369	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
371	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
373	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
374	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	4	no	—
377	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
378	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
379	C₂²	C₁₃×#575	1	2	yes	—
380	C₂²	C₁₃×#578	1	2	yes	—
381	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	4	no	—
386	C₄	—	2	8	no	—
387	C₄	—	4	4	no	—
388	C₄	—	4	4	no	—
389	C₄	—	4	4	no	—
390	C₄	D₄×Q₈×C₁₃	1	2	yes	—
391	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
392	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂	C₁₃×#3390	1	4	yes	direct product factor
394	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
395	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
396	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×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
2. C₁₃×#3390	C₂	direct (N × H)
49. C₂×C₁₃×Q₁₆	Q₈	semidirect
103. C₂×#3390	C₁₃	direct (N × H)
121. C₁₃×Q₁₆	C₂×Q₈	semidirect
152. #3390	C₂×C₁₃	direct (N × H)
243. C₂×Q₁₆	Q₈×C₁₃	semidirect
297. C₂×C₁₃	#3390	direct (N × H)
318. Q₁₆	C₂×Q₈×C₁₃	semidirect
348. C₁₃	C₂×#3390	direct (N × H)
393. C₂	C₁₃×#3390	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×#557	2
C₁₃×#3390	2
C₂×C₁₃×#501	2
C₂×C₁₃×#499	2
C₂×C₁₃×#479	2
C₂×C₁₃×#477	2
C₂×C₁₃×#446	2
C₂×C₁₃×#441	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×#3390	13

Subgroups — C2×C13×#3390 #15747703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3390 #15747703