Subgroups — C₂×C₁₃×#3385 #15747698

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 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, complemented
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3385	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#474	C₂	1	2	yes	maximal
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#440	C₂	1	2	yes	maximal
12	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
14	Q₈²×C₁₃	—	2	4	no	—
15	Q₈²×C₁₃	C₂²	1	8	yes	complemented
16	C₁₃×#554	—	2	4	no	—
17	C₁₃×#554	C₂²	1	8	yes	—
18	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₁₃×#501	C₂²	1	16	yes	complemented
34	C₁₃×#500	C₂²	1	8	yes	complemented
35	C₁₃×#479	C₂²	1	16	yes	complemented
36	C₁₃×#477	C₂²	1	8	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	—
38	C₁₃×#474	C₂²	1	16	yes	—
39	C₁₃×#446	C₂²	1	8	yes	complemented
40	C₁₃×#440	C₂²	1	16	yes	—
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
42	C₂×C₁₃×#107	C₂²	1	2	yes	—
43	C₂×C₁₃×#107	C₂²	1	2	yes	—
44	C₂×C₁₃×#107	C₂²	1	2	yes	—
45	C₂×C₁₃×#106	C₂²	1	2	yes	—
46	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	—	2	2	no	—
58	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	Q₈	1	8	yes	complemented
64	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	—	2	8	no	—
69	C₁₃×C₄⋊Q₈	—	2	16	no	—
70	C₁₃×C₄⋊Q₈	—	2	2	no	—
71	C₁₃×C₄⋊Q₈	—	2	4	no	—
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
74	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	C₂³	1	8	yes	—
78	C₁₃×C₂²⋊Q₈	—	2	8	no	—
79	C₁₃×C₂²⋊Q₈	—	2	16	no	—
80	C₄×Q₈×C₁₃	—	2	8	no	—
81	C₄×Q₈×C₁₃	—	2	4	no	—
82	C₄×Q₈×C₁₃	—	2	2	no	—
83	C₄×Q₈×C₁₃	D₄	1	4	yes	—
84	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
85	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
86	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	8	yes	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
99	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₄²×C₁₃	—	2	2	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₁₃×#107	C₂³	1	8	yes	—
112	C₁₃×#107	C₂³	1	8	yes	—
113	C₁₃×#107	C₂³	1	8	yes	—
114	C₁₃×#106	C₂³	1	4	yes	—
115	C₁₃×#106	C₂³	1	8	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
118	C₁₃×#103	C₂³	1	4	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	4	yes	—
121	C₁₃×#102	C₂³	1	8	yes	—
122	C₁₃×#97	C₂³	1	8	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	C₂×#3385	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	8	4	no	—
133	C₂×Q₈×C₁₃	—	8	2	no	—
134	C₂×Q₈×C₁₃	—	8	2	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
136	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
137	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
141	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	8	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	8	4	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₁₃×SD₁₆	C₂×Q₈	1	16	yes	complemented
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	4	no	—
159	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
160	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
162	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₄²×C₁₃	—	2	8	no	—
183	C₄²×C₁₃	—	2	4	no	—
184	C₄²×C₁₃	C₂×D₄	1	4	yes	—
185	C₄²×C₁₃	C₂×D₄	1	2	yes	—
186	C₄²×C₁₃	C₂⁴	1	2	yes	—
187	C₄²×C₁₃	C₂⁴	1	4	yes	—
188	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
190	#3385	C₂×C₁₃	1	16	yes	direct product factor
191	C₂×#501	C₂×C₁₃	1	2	yes	complemented
192	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×#479	C₂×C₁₃	1	2	yes	complemented
194	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
196	C₂×#474	C₂×C₁₃	1	2	yes	—
197	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#440	C₂×C₁₃	1	2	yes	—
199	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
200	C₂³×C₁₃	—	2	4	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	4	2	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₃	—	2	4	no	—
206	Q₈×C₁₃	—	2	8	no	—
207	Q₈×C₁₃	—	2	2	no	—
208	Q₈×C₁₃	—	8	8	no	—
209	Q₈×C₁₃	—	8	4	no	—
210	Q₈×C₁₃	—	8	4	no	—
211	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
212	D₄×C₁₃	—	2	4	no	—
213	D₄×C₁₃	—	2	2	no	—
214	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	8	no	—
229	C₂×C₄×C₁₃	—	8	8	no	—
230	C₂×C₄×C₁₃	#137	1	4	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
237	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	2	4	no	—
241	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
242	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
243	Q₈²	—	2	4	no	—
244	Q₈²	C₂²×C₁₃	1	8	yes	complemented
245	#554	—	2	4	no	—
246	#554	C₂²×C₁₃	1	8	yes	—
247	C₂×C₄⋊Q₈	—	2	1	no	—
248	C₂×C₄⋊Q₈	—	2	2	no	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
252	C₂×#125	C₂²×C₁₃	1	2	yes	—
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	C₂×C₂²⋊Q₈	—	2	2	no	—
255	C₂×C₄×Q₈	—	2	1	no	—
256	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
258	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₄⋊C₄	—	2	1	no	—
262	#501	C₂²×C₁₃	1	16	yes	complemented
263	#500	C₂²×C₁₃	1	8	yes	complemented
264	#479	C₂²×C₁₃	1	16	yes	complemented
265	#477	C₂²×C₁₃	1	8	yes	complemented
266	#476	C₂²×C₁₃	1	8	yes	—
267	#474	C₂²×C₁₃	1	16	yes	—
268	#446	C₂²×C₁₃	1	8	yes	complemented
269	#440	C₂²×C₁₃	1	16	yes	—
270	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
271	C₂×#107	C₂²×C₁₃	1	2	yes	—
272	C₂×#107	C₂²×C₁₃	1	2	yes	—
273	C₂×#107	C₂²×C₁₃	1	2	yes	—
274	C₂×#106	C₂²×C₁₃	1	2	yes	—
275	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
278	C₂×#103	C₂²×C₁₃	1	2	yes	—
279	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#102	C₂²×C₁₃	1	2	yes	—
282	C₂×#97	C₂²×C₁₃	1	2	yes	—
283	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	4	8	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
289	C₂²×C₁₃	C₂×#137	1	2	yes	—
290	C₂²×C₁₃	#576	1	2	yes	—
291	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₃	—	2	4	no	—
293	C₄×C₁₃	—	2	4	no	—
294	C₄×C₁₃	—	2	4	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	4	no	—
300	C₄×C₁₃	D₄×Q₈	1	2	yes	—
301	C₄×C₁₃	C₂×#137	1	4	yes	—
302	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
303	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
308	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	2	no	—
312	C₂×SD₁₆	Q₈×C₁₃	1	8	yes	complemented
313	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
314	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	8	no	—
318	C₄⋊Q₈	—	2	16	no	—
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	—	2	4	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
323	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
324	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
325	#125	—	2	4	no	—
326	#125	C₂³×C₁₃	1	8	yes	—
327	C₂²⋊Q₈	—	2	8	no	—
328	C₂²⋊Q₈	—	2	16	no	—
329	C₄×Q₈	—	2	8	no	—
330	C₄×Q₈	—	2	4	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	D₄×C₁₃	1	4	yes	—
333	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
334	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
335	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	C₂³×C₁₃	1	4	yes	—
339	C₄×D₄	C₂³×C₁₃	1	8	yes	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	8	no	—
348	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
360	#107	C₂³×C₁₃	1	8	yes	—
361	#107	C₂³×C₁₃	1	8	yes	—
362	#107	C₂³×C₁₃	1	8	yes	—
363	#106	C₂³×C₁₃	1	4	yes	—
364	#106	C₂³×C₁₃	1	8	yes	—
365	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
366	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
367	#103	C₂³×C₁₃	1	4	yes	—
368	#103	C₂³×C₁₃	1	8	yes	—
369	#102	C₂³×C₁₃	1	4	yes	—
370	#102	C₂³×C₁₃	1	8	yes	—
371	#97	C₂³×C₁₃	1	8	yes	—
372	C₄×C₈	C₂³×C₁₃	1	4	yes	—
373	C₂×C₁₃	—	4	4	no	—
374	C₂×C₁₃	#3385	1	4	yes	direct product factor
375	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
376	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
377	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
378	C₂⁴	—	2	1	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	8	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	8	4	no	—
386	C₂×Q₈	—	8	2	no	—
387	C₂×Q₈	—	8	2	no	—
388	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
389	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
390	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
394	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	8	4	no	—
404	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	SD₁₆	C₂×Q₈×C₁₃	1	16	yes	complemented
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	4	no	—
412	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
413	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
414	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
415	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
429	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
430	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
431	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
432	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₄²	—	2	8	no	—
436	C₄²	—	2	4	no	—
437	C₄²	C₂×D₄×C₁₃	1	4	yes	—
438	C₄²	C₂×D₄×C₁₃	1	2	yes	—
439	C₄²	C₂⁴×C₁₃	1	2	yes	—
440	C₄²	C₂⁴×C₁₃	1	4	yes	—
441	C₁₃	C₂×#3385	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	Q₈	—	2	4	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	2	2	no	—
450	Q₈	—	8	8	no	—
451	Q₈	—	8	4	no	—
452	Q₈	—	8	4	no	—
453	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
454	D₄	—	2	4	no	—
455	D₄	—	2	2	no	—
456	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	8	8	no	—
472	C₂×C₄	C₁₃×#137	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
478	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
479	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
480	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	2	4	no	—
483	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
484	C₂²	—	2	4	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	8	no	—
488	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
489	C₂²	C₂×C₁₃×#137	1	2	yes	—
490	C₂²	C₁₃×#576	1	2	yes	—
491	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	4	no	—
500	C₄	D₄×Q₈×C₁₃	1	2	yes	—
501	C₄	C₂×C₁₃×#137	1	4	yes	—
502	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
503	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
504	C₂	—	4	4	no	—
505	C₂	C₁₃×#3385	1	4	yes	direct product factor
506	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
507	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
508	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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
1. C₂×Q₈²×C₁₃	C₂	semidirect
3. C₁₃×#3385	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#500	C₂	semidirect
6. C₂×C₁₃×#479	C₂	semidirect
7. C₂×C₁₃×#477	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
15. Q₈²×C₁₃	C₂²	semidirect
33. C₁₃×#501	C₂²	semidirect
34. C₁₃×#500	C₂²	semidirect
35. C₁₃×#479	C₂²	semidirect
36. C₁₃×#477	C₂²	semidirect
39. C₁₃×#446	C₂²	semidirect
63. C₂×C₁₃×SD₁₆	Q₈	semidirect
124. C₂×#3385	C₁₃	direct (N × H)
156. C₁₃×SD₁₆	C₂×Q₈	semidirect
188. C₂×Q₈²	C₂×C₁₃	semidirect
190. #3385	C₂×C₁₃	direct (N × H)
191. C₂×#501	C₂×C₁₃	semidirect
192. C₂×#500	C₂×C₁₃	semidirect
193. C₂×#479	C₂×C₁₃	semidirect
194. C₂×#477	C₂×C₁₃	semidirect
197. C₂×#446	C₂×C₁₃	semidirect
244. Q₈²	C₂²×C₁₃	semidirect
262. #501	C₂²×C₁₃	semidirect
263. #500	C₂²×C₁₃	semidirect
264. #479	C₂²×C₁₃	semidirect
265. #477	C₂²×C₁₃	semidirect
268. #446	C₂²×C₁₃	semidirect
312. C₂×SD₁₆	Q₈×C₁₃	semidirect
374. C₂×C₁₃	#3385	direct (N × H)
409. SD₁₆	C₂×Q₈×C₁₃	semidirect
441. C₁₃	C₂×#3385	direct (N × H)
505. C₂	C₁₃×#3385	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×#554	2
C₁₃×#3385	2
C₂×C₁₃×#501	2
C₂×C₁₃×#500	2
C₂×C₁₃×#479	2
C₂×C₁₃×#477	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₂×C₁₃×#446	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3385	13

Subgroups — C2×C13×#3385 #15747698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3385 #15747698