Subgroups — C₁₃×#34308 #15720647

Order 3328.

3124 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2359	C₂	1	4	yes	maximal, complemented
7	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2344	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2322	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₁₃×#547	C₄	1	16	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#123	C₂²	1	4	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₁₃×#520	—	2	16	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	4	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	2	yes	—
43	C₁₃×#391	C₂²	1	2	yes	—
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	4	yes	—
49	C₁₃×#389	C₂²	1	2	yes	—
50	C₁₃×#389	C₂²	1	4	yes	—
51	C₁₃×#389	C₂²	1	2	yes	—
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	2	yes	—
54	C₁₃×#389	C₂²	1	2	yes	—
55	C₁₃×#388	C₂²	1	2	yes	—
56	C₁₃×#388	C₂²	1	2	yes	—
57	C₁₃×#388	C₂²	1	4	yes	—
58	C₁₃×#388	C₂²	1	4	yes	—
59	C₁₃×#387	C₂²	1	4	yes	—
60	C₁₃×#387	C₂²	1	4	yes	—
61	C₁₃×#387	C₂²	1	4	yes	—
62	C₁₃×#386	C₂²	1	4	yes	—
63	C₁₃×#386	C₂²	1	4	yes	—
64	C₁₃×#385	C₂²	1	4	yes	—
65	C₁₃×#385	C₂²	1	4	yes	—
66	C₁₃×#385	C₂²	1	4	yes	—
67	C₁₃×#384	C₂²	1	1	yes	characteristic
68	C₁₃×#381	C₂²	1	4	yes	—
69	C₁₃×#380	C₂²	1	2	yes	—
70	C₁₃×#380	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₂×C₁₃×#95	C₂²	1	4	yes	—
84	C₄³×C₁₃	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	—	2	8	no	—
86	C₂×C₁₃×#41	—	2	8	no	—
87	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
88	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
99	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
100	C₁₃×#123	C₂×C₄	1	32	yes	complemented
101	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
102	C₁₃×#121	C₂×C₄	1	16	yes	complemented
103	C₄×Q₈×C₁₃	—	2	8	no	—
104	C₄×Q₈×C₁₃	—	2	8	no	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	16	no	—
108	C₄×D₄×C₁₃	—	2	16	no	—
109	C₄×D₄×C₁₃	—	4	4	no	—
110	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
111	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
112	C₄×D₄×C₁₃	D₄	1	8	yes	complemented
113	C₁₃×#117	—	2	16	no	—
114	C₁₃×#117	—	2	8	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
118	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	—	4	4	no	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₁₃×#95	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	2	yes	—
164	C₁₃×#95	C₂³	1	2	yes	—
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	2	yes	—
168	C₁₃×#95	C₂³	1	2	yes	—
169	C₁₃×#95	C₂³	1	4	yes	—
170	C₁₃×#95	C₂³	1	4	yes	—
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	4	yes	—
173	C₁₃×#95	C₂³	1	4	yes	—
174	#34308	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
176	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
177	C₁₃×#41	—	2	64	no	—
178	C₂×Q₈×C₁₃	—	2	4	no	—
179	C₂×Q₈×C₁₃	—	2	4	no	—
180	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
181	C₂×D₄×C₁₃	—	2	8	no	—
182	C₂×D₄×C₁₃	—	2	8	no	—
183	C₂×D₄×C₁₃	—	2	2	no	—
184	C₂×D₄×C₁₃	—	2	2	no	—
185	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
186	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
187	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
188	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
189	C₂×D₄×C₁₃	#41	1	4	yes	—
190	C₂²×C₄×C₁₃	—	2	8	no	—
191	C₂²×C₄×C₁₃	—	2	8	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	8	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	8	no	—
200	C₂²×C₄×C₁₃	—	4	2	no	—
201	C₂²×C₄×C₁₃	—	4	2	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	4	4	no	—
204	C₂²×C₄×C₁₃	—	4	4	no	—
205	C₂²×C₄×C₁₃	—	4	4	no	—
206	C₂²×C₄×C₁₃	—	4	4	no	—
207	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
208	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
209	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₁₃×C₄⋊C₄	—	2	8	no	—
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	8	no	—
229	C₁₃×C₄⋊C₄	—	2	8	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	4	4	no	—
237	C₁₃×C₄⋊C₄	—	4	2	no	—
238	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
239	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
240	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
241	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
242	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
243	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
244	C₁₃×C₂²⋊C₄	—	2	8	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	4	2	no	—
250	C₁₃×C₂²⋊C₄	—	4	4	no	—
251	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
252	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
253	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
254	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
255	C₄²×C₁₃	—	2	8	no	—
256	C₄²×C₁₃	—	2	8	no	—
257	C₄²×C₁₃	—	2	4	no	—
258	C₄²×C₁₃	—	2	2	no	—
259	C₄²×C₁₃	—	2	2	no	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	2	no	—
262	C₄²×C₁₃	—	2	2	no	—
263	C₄²×C₁₃	—	4	2	no	—
264	C₄²×C₁₃	—	4	2	no	—
265	C₄²×C₁₃	—	4	1	no	—
266	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
267	C₄²×C₁₃	C₂×D₄	1	4	yes	—
268	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
269	C₂×#520	C₂×C₁₃	1	2	yes	complemented
270	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2361	C₂×C₁₃	1	2	yes	complemented
272	#2360	C₂×C₁₃	1	2	yes	complemented
273	#2359	C₂×C₁₃	1	4	yes	complemented
274	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
275	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2344	C₂×C₁₃	1	2	yes	complemented
277	#2339	C₂×C₁₃	1	2	yes	complemented
278	#2323	C₂×C₁₃	1	2	yes	complemented
279	#2322	C₂×C₁₃	1	4	yes	complemented
280	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₄×#121	C₂×C₁₃	1	2	yes	complemented
282	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#389	C₂×C₁₃	1	2	yes	complemented
284	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
296	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
297	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
298	C₂³×C₁₃	C₂×#41	1	4	yes	—
299	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
300	Q₈×C₁₃	—	2	16	no	—
301	D₄×C₁₃	—	2	32	no	—
302	D₄×C₁₃	—	2	8	no	—
303	D₄×C₁₃	C₄×D₄	1	16	yes	complemented
304	C₂×C₄×C₁₃	—	2	32	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	16	no	—
322	C₂×C₄×C₁₃	—	2	16	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	4	8	no	—
339	C₂×C₄×C₁₃	—	4	8	no	—
340	C₂×C₄×C₁₃	—	8	8	no	—
341	C₂×C₄×C₁₃	—	8	8	no	—
342	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
344	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
346	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
347	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
354	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
355	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
356	C₂²×#41	C₂²×C₁₃	1	2	yes	—
357	#547	C₄×C₁₃	1	16	yes	complemented
358	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#123	C₂²×C₁₃	1	4	yes	—
360	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
361	C₂×#121	C₂²×C₁₃	1	2	yes	—
362	#520	—	2	16	no	—
363	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
364	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
366	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
370	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#117	C₂²×C₁₃	1	2	yes	—
374	C₂×#117	C₂²×C₁₃	1	4	yes	—
375	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
376	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
377	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
378	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
380	#391	C₂²×C₁₃	1	2	yes	—
381	#391	C₂²×C₁₃	1	2	yes	—
382	#390	C₂²×C₁₃	1	1	yes	characteristic
383	#390	C₂²×C₁₃	1	1	yes	characteristic
384	#389	C₂²×C₁₃	1	2	yes	—
385	#389	C₂²×C₁₃	1	2	yes	—
386	#389	C₂²×C₁₃	1	4	yes	—
387	#389	C₂²×C₁₃	1	2	yes	—
388	#389	C₂²×C₁₃	1	1	yes	characteristic
389	#389	C₂²×C₁₃	1	2	yes	—
390	#389	C₂²×C₁₃	1	4	yes	—
391	#389	C₂²×C₁₃	1	2	yes	—
392	#389	C₂²×C₁₃	1	1	yes	characteristic
393	#388	C₂²×C₁₃	1	2	yes	—
394	#388	C₂²×C₁₃	1	4	yes	—
395	#388	C₂²×C₁₃	1	4	yes	—
396	#388	C₂²×C₁₃	1	2	yes	—
397	#387	C₂²×C₁₃	1	4	yes	—
398	#387	C₂²×C₁₃	1	4	yes	—
399	#387	C₂²×C₁₃	1	4	yes	—
400	#386	C₂²×C₁₃	1	4	yes	—
401	#386	C₂²×C₁₃	1	4	yes	—
402	#385	C₂²×C₁₃	1	4	yes	—
403	#385	C₂²×C₁₃	1	4	yes	—
404	#385	C₂²×C₁₃	1	4	yes	—
405	#384	C₂²×C₁₃	1	1	yes	characteristic
406	#381	C₂²×C₁₃	1	4	yes	—
407	#380	C₂²×C₁₃	1	2	yes	—
408	#380	C₂²×C₁₃	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
421	C₂×#95	C₂²×C₁₃	1	4	yes	—
422	C₄³	C₂²×C₁₃	1	1	yes	characteristic
423	C₂²×C₁₃	—	2	4	no	—
424	C₂²×C₁₃	—	2	4	no	—
425	C₂²×C₁₃	—	2	4	no	—
426	C₂²×C₁₃	—	2	4	no	—
427	C₂²×C₁₃	—	2	4	no	—
428	C₂²×C₁₃	—	2	4	no	—
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	2	4	no	—
431	C₂²×C₁₃	—	2	4	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	C₂×C₄×D₄	1	8	yes	—
437	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
438	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
439	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
442	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
443	C₂²×C₁₃	#585	1	1	yes	characteristic
444	C₄×C₁₃	—	2	4	no	—
445	C₄×C₁₃	—	2	8	no	—
446	C₄×C₁₃	—	2	4	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	2	4	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	2	no	—
452	C₄×C₁₃	—	4	4	no	—
453	C₄×C₁₃	—	4	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	1	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
458	C₄×C₁₃	#520	1	4	yes	complemented
459	C₂×#41	—	2	8	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
462	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
463	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
465	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
467	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
468	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
470	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
471	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
472	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
473	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
474	#123	C₂×C₄×C₁₃	1	32	yes	complemented
475	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
476	#121	C₂×C₄×C₁₃	1	16	yes	complemented
477	C₄×Q₈	—	2	8	no	—
478	C₄×Q₈	—	2	8	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	—	2	16	no	—
482	C₄×D₄	—	2	16	no	—
483	C₄×D₄	—	4	4	no	—
484	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
485	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
486	C₄×D₄	D₄×C₁₃	1	8	yes	complemented
487	#117	—	2	16	no	—
488	#117	—	2	8	no	—
489	C₂×C₄⋊C₄	—	2	16	no	—
490	C₂×C₄⋊C₄	—	2	8	no	—
491	C₂×C₄⋊C₄	—	4	4	no	—
492	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₄²	—	4	4	no	—
523	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
536	#95	C₂³×C₁₃	1	2	yes	—
537	#95	C₂³×C₁₃	1	4	yes	—
538	#95	C₂³×C₁₃	1	4	yes	—
539	#95	C₂³×C₁₃	1	4	yes	—
540	#95	C₂³×C₁₃	1	2	yes	—
541	#95	C₂³×C₁₃	1	2	yes	—
542	#95	C₂³×C₁₃	1	2	yes	—
543	#95	C₂³×C₁₃	1	4	yes	—
544	#95	C₂³×C₁₃	1	2	yes	—
545	#95	C₂³×C₁₃	1	4	yes	—
546	#95	C₂³×C₁₃	1	4	yes	—
547	#95	C₂³×C₁₃	1	2	yes	—
548	C₂×C₁₃	—	2	8	no	—
549	C₂×C₁₃	—	4	4	no	—
550	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
551	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
552	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
553	C₂×C₁₃	#3496	1	1	yes	characteristic
554	C₂×C₁₃	#3499	1	1	yes	characteristic
555	C₂×C₁₃	#3515	1	1	yes	characteristic
556	C₂×C₁₃	#3520	1	1	yes	characteristic
557	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
558	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
559	#41	—	2	64	no	—
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
568	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
569	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
570	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
571	C₂×D₄	C₁₃×#41	1	4	yes	—
572	C₂²×C₄	—	2	8	no	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
590	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
591	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
592	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
597	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	4	4	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
621	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
622	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
623	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
624	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
625	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
626	C₂²⋊C₄	—	2	8	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	—	4	2	no	—
633	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
634	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
635	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
636	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
637	C₄²	—	2	8	no	—
638	C₄²	—	2	8	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	1	no	—
648	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
649	C₄²	C₂×D₄×C₁₃	1	4	yes	—
650	C₁₃	#34308	1	1	yes	characteristic, direct product factor, Sylow
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
662	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
663	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
664	C₂³	C₂×C₁₃×#41	1	4	yes	—
665	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
666	Q₈	—	2	16	no	—
667	D₄	—	2	32	no	—
668	D₄	—	2	8	no	—
669	D₄	C₄×D₄×C₁₃	1	16	yes	complemented
670	C₂×C₄	—	2	32	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	—	8	8	no	—
708	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
709	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
711	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
712	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
713	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
716	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
718	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
719	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
720	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
721	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	C₂×C₄×D₄×C₁₃	1	8	yes	—
736	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
737	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
738	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
739	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
741	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂²	C₁₃×#585	1	1	yes	characteristic
743	C₄	—	2	2	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	8	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	1	no	—
756	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
757	C₄	C₁₃×#520	1	4	yes	complemented
758	C₂	—	2	8	no	—
759	C₂	—	4	4	no	—
760	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
761	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
762	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
763	C₂	C₁₃×#3496	1	1	yes	characteristic
764	C₂	C₁₃×#3499	1	1	yes	characteristic
765	C₂	C₁₃×#3515	1	1	yes	characteristic
766	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	C₂×C₁₃×#547	C₂
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. C₂×C₁₃×#520	C₂	semidirect
3. C₁₃×#2365	C₂	semidirect
4. C₁₃×#2361	C₂	semidirect
5. C₁₃×#2360	C₂	semidirect
6. C₁₃×#2359	C₂	semidirect
7. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
8. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
9. C₁₃×#2344	C₂	semidirect
10. C₁₃×#2339	C₂	semidirect
11. C₁₃×#2323	C₂	semidirect
12. C₁₃×#2322	C₂	semidirect
13. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₁₃×#2293	C₂	semidirect
16. C₂×C₁₃×#389	C₂	semidirect
17. C₄²×D₄×C₁₃	C₂	semidirect
19. C₁₃×#547	C₄	semidirect
87. C₂×C₁₃×#41	C₂×C₄	semidirect
99. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
100. C₁₃×#123	C₂×C₄	semidirect
101. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
102. C₁₃×#121	C₂×C₄	semidirect
110. C₄×D₄×C₁₃	C₂×C₄	semidirect
111. C₄×D₄×C₁₃	C₂×C₄	semidirect
112. C₄×D₄×C₁₃	D₄	semidirect
118. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
174. #34308	C₁₃	direct (N × H)
269. C₂×#520	C₂×C₁₃	semidirect
270. #2365	C₂×C₁₃	semidirect
271. #2361	C₂×C₁₃	semidirect
272. #2360	C₂×C₁₃	semidirect
273. #2359	C₂×C₁₃	semidirect
274. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
275. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
276. #2344	C₂×C₁₃	semidirect
277. #2339	C₂×C₁₃	semidirect
278. #2323	C₂×C₁₃	semidirect
279. #2322	C₂×C₁₃	semidirect
280. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
281. C₄×#121	C₂×C₁₃	semidirect
282. #2293	C₂×C₁₃	semidirect
283. C₂×#389	C₂×C₁₃	semidirect
284. C₄²×D₄	C₂×C₁₃	semidirect
303. D₄×C₁₃	C₄×D₄	semidirect
357. #547	C₄×C₁₃	semidirect
458. C₄×C₁₃	#520	semidirect
461. C₂×#41	C₂×C₄×C₁₃	semidirect
473. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
474. #123	C₂×C₄×C₁₃	semidirect
475. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
476. #121	C₂×C₄×C₁₃	semidirect
484. C₄×D₄	C₂×C₄×C₁₃	semidirect
485. C₄×D₄	C₂×C₄×C₁₃	semidirect
486. C₄×D₄	D₄×C₁₃	semidirect
492. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
650. C₁₃	#34308	direct (N × H)
669. D₄	C₄×D₄×C₁₃	semidirect
757. C₄	C₁₃×#520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#547	2
C₂×C₁₃×#520	2
C₁₃×#2365	2
C₁₃×#2361	2
C₁₃×#2360	2
C₁₃×#2359	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2344	2
C₁₃×#2339	2
C₁₃×#2323	2
C₁₃×#2322	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2293	2
C₂×C₁₃×#389	2
C₄²×D₄×C₁₃	2
#34308	13

Subgroups — C13×#34308 #15720647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34308 #15720647