Subgroups — C₁₃×#34334 #15720673

Order 3328.

2500 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2369	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2368	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2349	C₂	1	2	yes	maximal
8	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	Q₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2331	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2329	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2275	C₂	1	2	yes	maximal
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
19	D₄×Q₈×C₁₃	C₄	1	16	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×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	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	4	yes	—
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#391	C₂²	1	4	yes	—
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	4	yes	—
42	C₁₃×#391	C₂²	1	4	yes	—
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	4	yes	—
48	C₁₃×#389	C₂²	1	2	yes	—
49	C₁₃×#389	C₂²	1	2	yes	—
50	C₁₃×#387	C₂²	1	2	yes	—
51	C₁₃×#387	C₂²	1	2	yes	—
52	C₁₃×#387	C₂²	1	4	yes	—
53	C₁₃×#387	C₂²	1	4	yes	—
54	C₁₃×#387	C₂²	1	4	yes	—
55	C₁₃×#387	C₂²	1	4	yes	—
56	C₁₃×#385	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#385	C₂²	1	4	yes	—
59	C₁₃×#384	C₂²	1	1	yes	characteristic
60	C₁₃×#382	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	2	yes	—
62	C₁₃×#380	C₂²	1	4	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₁₃×#376	C₂²	1	2	yes	—
81	C₂×C₁₃×#95	C₂²	1	4	yes	—
82	C₂×C₁₃×#95	C₂²	1	4	yes	—
83	C₄³×C₁₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	—	4	4	no	—
85	C₂²×Q₈×C₁₃	—	4	4	no	—
86	C₂²×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
96	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
98	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
99	C₁₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
100	C₄×Q₈×C₁₃	—	4	4	no	—
101	C₄×Q₈×C₁₃	—	4	4	no	—
102	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	—	2	8	no	—
105	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
106	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	—
107	C₄×D₄×C₁₃	Q₈	1	8	yes	complemented
108	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	—	4	4	no	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	2	yes	—
153	C₁₃×#95	C₂³	1	2	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	2	yes	—
162	C₁₃×#95	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	2	yes	—
166	#34334	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
168	C₂×Q₈×C₁₃	—	2	4	no	—
169	C₂×Q₈×C₁₃	—	2	4	no	—
170	C₂×Q₈×C₁₃	—	2	2	no	—
171	C₂×Q₈×C₁₃	—	2	2	no	—
172	C₂×Q₈×C₁₃	—	4	4	no	—
173	C₂×Q₈×C₁₃	—	4	4	no	—
174	C₂×Q₈×C₁₃	—	4	32	no	—
175	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
176	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
177	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	—
178	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
179	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
180	C₂×D₄×C₁₃	#41	1	4	yes	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	8	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	4	4	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	—	4	4	no	—
192	C₂²×C₄×C₁₃	—	4	4	no	—
193	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
194	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
195	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	complemented
196	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	4	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₁₃×C₄⋊C₄	—	2	4	no	—
218	C₁₃×C₄⋊C₄	—	4	4	no	—
219	C₁₃×C₄⋊C₄	—	4	2	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₄⋊C₄	—	4	4	no	—
222	C₁₃×C₄⋊C₄	—	4	4	no	—
223	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
224	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
225	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
226	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
227	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
228	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
229	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	complemented
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	8	no	—
232	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
233	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
234	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	complemented
235	C₄²×C₁₃	—	2	2	no	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	2	no	—
238	C₄²×C₁₃	—	2	4	no	—
239	C₄²×C₁₃	—	2	2	no	—
240	C₄²×C₁₃	—	2	2	no	—
241	C₄²×C₁₃	—	4	2	no	—
242	C₄²×C₁₃	—	4	2	no	—
243	C₄²×C₁₃	—	4	4	no	—
244	C₄²×C₁₃	—	4	1	no	—
245	C₄²×C₁₃	—	4	4	no	—
246	C₄²×C₁₃	—	4	4	no	—
247	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
248	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
249	C₄²×C₁₃	C₂×Q₈	1	4	yes	complemented
250	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
251	#2369	C₂×C₁₃	1	2	yes	complemented
252	#2368	C₂×C₁₃	1	4	yes	complemented
253	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2360	C₂×C₁₃	1	2	yes	complemented
255	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#2349	C₂×C₁₃	1	2	yes	—
257	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
258	Q₈×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
259	#2331	C₂×C₁₃	1	2	yes	complemented
260	#2329	C₂×C₁₃	1	4	yes	complemented
261	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
263	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
264	C₂×#391	C₂×C₁₃	1	2	yes	complemented
265	#2275	C₂×C₁₃	1	2	yes	—
266	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	—	2	2	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
272	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
273	C₂³×C₁₃	C₂×#41	1	4	yes	—
274	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
275	Q₈×C₁₃	—	2	8	no	—
276	Q₈×C₁₃	—	2	16	no	—
277	Q₈×C₁₃	—	4	16	no	—
278	D₄×C₁₃	C₄×Q₈	1	16	yes	complemented
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	16	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	4	16	no	—
314	C₂×C₄×C₁₃	—	4	8	no	—
315	C₂×C₄×C₁₃	—	4	8	no	—
316	C₂×C₄×C₁₃	—	8	8	no	—
317	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
318	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
319	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
320	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
321	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
322	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
323	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
324	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
325	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
326	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
327	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
328	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
329	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
331	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
332	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
333	D₄×Q₈	C₄×C₁₃	1	16	yes	complemented
334	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
336	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
337	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
338	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
339	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
340	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
345	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
347	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
348	#391	C₂²×C₁₃	1	2	yes	—
349	#391	C₂²×C₁₃	1	4	yes	—
350	#391	C₂²×C₁₃	1	4	yes	—
351	#391	C₂²×C₁₃	1	4	yes	—
352	#391	C₂²×C₁₃	1	1	yes	characteristic
353	#391	C₂²×C₁₃	1	2	yes	—
354	#391	C₂²×C₁₃	1	2	yes	—
355	#391	C₂²×C₁₃	1	4	yes	—
356	#391	C₂²×C₁₃	1	1	yes	characteristic
357	#389	C₂²×C₁₃	1	2	yes	—
358	#389	C₂²×C₁₃	1	2	yes	—
359	#389	C₂²×C₁₃	1	4	yes	—
360	#389	C₂²×C₁₃	1	2	yes	—
361	#389	C₂²×C₁₃	1	2	yes	—
362	#389	C₂²×C₁₃	1	1	yes	characteristic
363	#389	C₂²×C₁₃	1	1	yes	characteristic
364	#387	C₂²×C₁₃	1	2	yes	—
365	#387	C₂²×C₁₃	1	4	yes	—
366	#387	C₂²×C₁₃	1	4	yes	—
367	#387	C₂²×C₁₃	1	4	yes	—
368	#387	C₂²×C₁₃	1	4	yes	—
369	#387	C₂²×C₁₃	1	2	yes	—
370	#385	C₂²×C₁₃	1	4	yes	—
371	#385	C₂²×C₁₃	1	4	yes	—
372	#385	C₂²×C₁₃	1	4	yes	—
373	#384	C₂²×C₁₃	1	1	yes	characteristic
374	#382	C₂²×C₁₃	1	2	yes	—
375	#380	C₂²×C₁₃	1	4	yes	—
376	#380	C₂²×C₁₃	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
381	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
382	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
383	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
384	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
385	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
386	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
387	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
389	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
390	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
391	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
392	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
393	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
394	#376	C₂²×C₁₃	1	2	yes	—
395	C₂×#95	C₂²×C₁₃	1	4	yes	—
396	C₂×#95	C₂²×C₁₃	1	4	yes	—
397	C₄³	C₂²×C₁₃	1	1	yes	characteristic
398	C₂²×C₁₃	—	2	4	no	—
399	C₂²×C₁₃	—	2	4	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	2	4	no	—
402	C₂²×C₁₃	—	2	4	no	—
403	C₂²×C₁₃	—	2	4	no	—
404	C₂²×C₁₃	C₂×C₄×Q₈	1	8	yes	—
405	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
406	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
407	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
408	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂²×C₁₃	#585	1	1	yes	characteristic
412	C₄×C₁₃	—	2	4	no	—
413	C₄×C₁₃	—	2	4	no	—
414	C₄×C₁₃	—	2	8	no	—
415	C₄×C₁₃	—	2	2	no	—
416	C₄×C₁₃	—	2	4	no	—
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	2	4	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	4	1	no	—
422	C₄×C₁₃	—	4	4	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	C₂×C₄×Q₈	1	4	yes	—
427	C₄×C₁₃	#518	1	4	yes	—
428	C₂²×Q₈	—	4	4	no	—
429	C₂²×Q₈	—	4	4	no	—
430	C₂²×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
431	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
432	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
434	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
436	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
437	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
438	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
439	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
440	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
441	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
442	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
443	C₂²⋊Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
444	C₄×Q₈	—	4	4	no	—
445	C₄×Q₈	—	4	4	no	—
446	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
447	C₄×D₄	—	2	4	no	—
448	C₄×D₄	—	2	8	no	—
449	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
450	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	—
451	C₄×D₄	Q₈×C₁₃	1	8	yes	complemented
452	C₂×C₄⋊C₄	—	4	4	no	—
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₄²	—	4	4	no	—
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
481	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
484	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
485	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
487	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
492	#95	C₂³×C₁₃	1	2	yes	—
493	#95	C₂³×C₁₃	1	2	yes	—
494	#95	C₂³×C₁₃	1	4	yes	—
495	#95	C₂³×C₁₃	1	4	yes	—
496	#95	C₂³×C₁₃	1	4	yes	—
497	#95	C₂³×C₁₃	1	4	yes	—
498	#95	C₂³×C₁₃	1	4	yes	—
499	#95	C₂³×C₁₃	1	4	yes	—
500	#95	C₂³×C₁₃	1	2	yes	—
501	#95	C₂³×C₁₃	1	2	yes	—
502	#95	C₂³×C₁₃	1	2	yes	—
503	#95	C₂³×C₁₃	1	2	yes	—
504	#95	C₂³×C₁₃	1	2	yes	—
505	#95	C₂³×C₁₃	1	2	yes	—
506	#95	C₂³×C₁₃	1	2	yes	—
507	#95	C₂³×C₁₃	1	4	yes	—
508	#95	C₂³×C₁₃	1	4	yes	—
509	#95	C₂³×C₁₃	1	2	yes	—
510	C₂×C₁₃	—	2	8	no	—
511	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
512	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
513	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂×C₁₃	#3501	1	1	yes	characteristic
515	C₂×C₁₃	#3503	1	1	yes	characteristic
516	C₂×C₁₃	#3514	1	1	yes	characteristic
517	C₂×C₁₃	#3520	1	1	yes	characteristic
518	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	4	4	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	32	no	—
526	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
527	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
528	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	—
529	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
530	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
531	C₂×D₄	C₁₃×#41	1	4	yes	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
545	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
546	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	complemented
547	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	4	4	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	2	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
576	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
577	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
578	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
579	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
580	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	complemented
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
585	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	complemented
586	C₄²	—	2	2	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	4	2	no	—
593	C₄²	—	4	2	no	—
594	C₄²	—	4	4	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	4	no	—
597	C₄²	—	4	1	no	—
598	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
599	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
600	C₄²	C₂×Q₈×C₁₃	1	4	yes	complemented
601	C₁₃	#34334	1	1	yes	characteristic, direct product factor, Sylow
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
607	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
608	C₂³	C₂×C₁₃×#41	1	4	yes	—
609	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
610	Q₈	—	2	8	no	—
611	Q₈	—	2	16	no	—
612	Q₈	—	4	16	no	—
613	D₄	C₄×Q₈×C₁₃	1	16	yes	complemented
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	16	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	16	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	8	8	no	—
652	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
657	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
659	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
660	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
661	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
662	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
663	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
664	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
665	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
666	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	C₂×C₄×Q₈×C₁₃	1	8	yes	—
674	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
675	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
676	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
677	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂²	C₁₃×#585	1	1	yes	characteristic
681	C₄	—	2	2	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	8	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	4	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	C₂×C₄×Q₈×C₁₃	1	4	yes	—
696	C₄	C₁₃×#518	1	4	yes	—
697	C₂	—	2	8	no	—
698	C₂	C₂²×C₄×Q₈×C₁₃	1	1	yes	characteristic
699	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
700	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
701	C₂	C₁₃×#3501	1	1	yes	characteristic
702	C₂	C₁₃×#3503	1	1	yes	characteristic
703	C₂	C₁₃×#3514	1	1	yes	characteristic
704	C₂	C₁₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2369	C₂	semidirect
3. C₁₃×#2368	C₂	semidirect
4. C₁₃×#2365	C₂	semidirect
5. C₁₃×#2360	C₂	semidirect
6. C₁₃×#2355	C₂	semidirect
9. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
10. C₁₃×#2331	C₂	semidirect
11. C₁₃×#2329	C₂	semidirect
12. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₁₃×#2295	C₂	semidirect
15. C₂×C₁₃×#391	C₂	semidirect
19. D₄×Q₈×C₁₃	C₄	semidirect
86. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
96. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
97. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
98. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
102. C₄×Q₈×C₁₃	C₂×C₄	semidirect
107. C₄×D₄×C₁₃	Q₈	semidirect
166. #34334	C₁₃	direct (N × H)
195. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
229. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
234. C₁₃×C₂²⋊C₄	C₂×Q₈	semidirect
249. C₄²×C₁₃	C₂×Q₈	semidirect
251. #2369	C₂×C₁₃	semidirect
252. #2368	C₂×C₁₃	semidirect
253. #2365	C₂×C₁₃	semidirect
254. #2360	C₂×C₁₃	semidirect
255. #2355	C₂×C₁₃	semidirect
258. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
259. #2331	C₂×C₁₃	semidirect
260. #2329	C₂×C₁₃	semidirect
261. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
262. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
263. #2295	C₂×C₁₃	semidirect
264. C₂×#391	C₂×C₁₃	semidirect
278. D₄×C₁₃	C₄×Q₈	semidirect
333. D₄×Q₈	C₄×C₁₃	semidirect
430. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
440. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
441. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
442. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
443. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
446. C₄×Q₈	C₂×C₄×C₁₃	semidirect
451. C₄×D₄	Q₈×C₁₃	semidirect
546. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
580. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
585. C₂²⋊C₄	C₂×Q₈×C₁₃	semidirect
600. C₄²	C₂×Q₈×C₁₃	semidirect
601. C₁₃	#34334	direct (N × H)
613. D₄	C₄×Q₈×C₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×Q₈×C₁₃	2
C₁₃×#2369	2
C₁₃×#2368	2
C₁₃×#2365	2
C₁₃×#2360	2
C₁₃×#2355	2
C₁₃×#2349	2
D₄×C₁₃×C₄⋊C₄	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2331	2
C₁₃×#2329	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₂×C₁₃×#391	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34334	13

Subgroups — C13×#34334 #15720673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34334 #15720673