Subgroups — C₂×C₁₃×#2334 #15720416

Order 3328.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#126	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2334	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#126	C₄	1	16	yes	complemented
19	C₂×C₁₃×#126	C₂²	1	8	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	8	yes	complemented
43	C₁₃×#389	C₂²	1	8	yes	complemented
44	C₁₃×#388	C₂²	1	8	yes	—
45	C₁₃×#388	C₂²	1	8	yes	—
46	C₁₃×#388	C₂²	1	8	yes	—
47	C₁₃×#387	C₂²	1	8	yes	complemented
48	C₁₃×#387	C₂²	1	8	yes	complemented
49	C₁₃×#387	C₂²	1	8	yes	complemented
50	C₁₃×#385	C₂²	1	8	yes	—
51	C₁₃×#385	C₂²	1	8	yes	—
52	C₁₃×#382	C₂²	1	8	yes	complemented
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
55	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
56	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
68	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	—	2	4	no	—
70	C₂³×C₄×C₁₃	—	4	2	no	—
71	C₂³×C₄×C₁₃	—	4	2	no	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
87	C₁₃×#126	C₂×C₄	1	64	yes	complemented
88	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
93	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
95	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
96	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
97	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	8	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	—	2	4	no	—
121	C₂×C₄²×C₁₃	—	4	2	no	—
122	C₂×C₄²×C₁₃	—	4	2	no	—
123	C₂×C₄²×C₁₃	—	4	2	no	—
124	C₂×C₄²×C₁₃	—	4	2	no	—
125	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
126	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	4	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₂×#2334	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	2	no	—
146	C₂⁴×C₁₃	—	2	2	no	—
147	C₂⁴×C₁₃	—	2	2	no	—
148	C₂⁴×C₁₃	—	2	2	no	—
149	C₂⁴×C₁₃	—	2	2	no	—
150	C₂⁴×C₁₃	—	2	2	no	—
151	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	2	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	2	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	8	no	—
189	C₂²×C₄×C₁₃	—	4	4	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	—	4	16	no	—
192	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₁₃	#41	1	4	yes	—
199	C₂²×C₄×C₁₃	#41	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₁₃×C₄⋊C₄	—	2	8	no	—
215	C₁₃×C₄⋊C₄	—	2	8	no	—
216	C₁₃×C₄⋊C₄	—	2	8	no	—
217	C₁₃×C₄⋊C₄	—	4	4	no	—
218	C₁₃×C₄⋊C₄	—	4	4	no	—
219	C₁₃×C₄⋊C₄	—	4	4	no	—
220	C₁₃×C₄⋊C₄	—	4	4	no	—
221	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
222	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
223	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
224	C₁₃×C₂²⋊C₄	—	2	8	no	—
225	C₁₃×C₂²⋊C₄	—	4	4	no	—
226	C₁₃×C₂²⋊C₄	—	4	4	no	—
227	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
228	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
229	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
230	C₄²×C₁₃	—	2	8	no	—
231	C₄²×C₁₃	—	4	4	no	—
232	C₄²×C₁₃	—	4	4	no	—
233	C₄²×C₁₃	—	4	4	no	—
234	C₄²×C₁₃	—	4	4	no	—
235	C₄²×C₁₃	C₂²×C₄	1	16	yes	complemented
236	C₂²×#126	C₂×C₁₃	1	1	yes	characteristic
237	#2334	C₂×C₁₃	1	16	yes	direct product factor
238	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
239	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#388	C₂×C₁₃	1	1	yes	characteristic
241	C₂×#388	C₂×C₁₃	1	1	yes	characteristic
242	C₂×#388	C₂×C₁₃	1	1	yes	characteristic
243	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
244	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂×#387	C₂×C₁₃	1	1	yes	characteristic, complemented
246	C₂×#385	C₂×C₁₃	1	1	yes	characteristic
247	C₂×#385	C₂×C₁₃	1	1	yes	characteristic
248	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
251	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
252	C₂³×C₁₃	—	2	8	no	—
253	C₂³×C₁₃	—	2	8	no	—
254	C₂³×C₁₃	—	2	8	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	4	4	no	—
262	C₂³×C₁₃	—	4	4	no	—
263	C₂³×C₁₃	—	4	4	no	—
264	C₂³×C₁₃	—	4	4	no	—
265	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
266	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
267	C₂³×C₁₃	C₂×#41	1	2	yes	—
268	C₂³×C₁₃	C₂×#41	1	2	yes	—
269	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
270	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
271	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
272	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
273	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
274	C₂×C₄×C₁₃	—	2	8	no	—
275	C₂×C₄×C₁₃	—	2	8	no	—
276	C₂×C₄×C₁₃	—	2	8	no	—
277	C₂×C₄×C₁₃	—	2	8	no	—
278	C₂×C₄×C₁₃	—	2	8	no	—
279	C₂×C₄×C₁₃	—	2	8	no	—
280	C₂×C₄×C₁₃	—	2	8	no	—
281	C₂×C₄×C₁₃	—	2	8	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	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	2	no	—
291	C₂×C₄×C₁₃	—	2	2	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	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	2	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	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	4	16	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	—	4	4	no	—
319	C₂×C₄×C₁₃	—	4	4	no	—
320	C₂×C₄×C₁₃	—	4	4	no	—
321	C₂×C₄×C₁₃	—	4	4	no	—
322	C₂×C₄×C₁₃	—	4	4	no	—
323	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
324	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
325	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
326	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
327	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
328	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
329	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
330	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
331	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#126	C₄×C₁₃	1	16	yes	complemented
333	C₂×#126	C₂²×C₁₃	1	8	yes	—
334	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
340	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
341	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
350	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
352	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
354	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
355	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
356	#389	C₂²×C₁₃	1	8	yes	complemented
357	#389	C₂²×C₁₃	1	8	yes	complemented
358	#388	C₂²×C₁₃	1	8	yes	—
359	#388	C₂²×C₁₃	1	8	yes	—
360	#388	C₂²×C₁₃	1	8	yes	—
361	#387	C₂²×C₁₃	1	8	yes	complemented
362	#387	C₂²×C₁₃	1	8	yes	complemented
363	#387	C₂²×C₁₃	1	8	yes	complemented
364	#385	C₂²×C₁₃	1	8	yes	—
365	#385	C₂²×C₁₃	1	8	yes	—
366	#382	C₂²×C₁₃	1	8	yes	complemented
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
369	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
370	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
382	C₂²×C₁₃	—	2	4	no	—
383	C₂²×C₁₃	—	2	4	no	—
384	C₂²×C₁₃	—	2	4	no	—
385	C₂²×C₁₃	—	4	16	no	—
386	C₂²×C₁₃	—	4	2	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	C₄×#41	1	4	yes	—
391	C₂²×C₁₃	#520	1	4	yes	—
392	C₂²×C₁₃	#520	1	4	yes	—
393	C₂²×C₁₃	#538	1	4	yes	—
394	C₂²×C₁₃	#539	1	4	yes	—
395	C₂²×C₁₃	#541	1	4	yes	—
396	C₂²×C₁₃	#542	1	4	yes	—
397	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
398	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
400	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
403	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
404	C₄×C₁₃	—	2	4	no	—
405	C₄×C₁₃	—	2	4	no	—
406	C₄×C₁₃	—	2	4	no	—
407	C₄×C₁₃	—	2	4	no	—
408	C₄×C₁₃	—	2	4	no	—
409	C₄×C₁₃	—	2	4	no	—
410	C₄×C₁₃	—	2	4	no	—
411	C₄×C₁₃	—	2	4	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	2	no	—
414	C₄×C₁₃	—	4	2	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
419	C₂³×C₄	—	2	4	no	—
420	C₂³×C₄	—	4	2	no	—
421	C₂³×C₄	—	4	2	no	—
422	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
437	#126	C₂×C₄×C₁₃	1	64	yes	complemented
438	C₂×C₄⋊C₄	—	2	4	no	—
439	C₂×C₄⋊C₄	—	2	4	no	—
440	C₂×C₄⋊C₄	—	2	4	no	—
441	C₂×C₄⋊C₄	—	4	2	no	—
442	C₂×C₄⋊C₄	—	4	2	no	—
443	C₂×C₄⋊C₄	—	4	2	no	—
444	C₂×C₄⋊C₄	—	4	2	no	—
445	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
446	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
447	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₂²⋊C₄	—	2	4	no	—
459	C₂×C₂²⋊C₄	—	4	2	no	—
460	C₂×C₂²⋊C₄	—	4	2	no	—
461	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
462	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
463	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
470	C₂×C₄²	—	2	4	no	—
471	C₂×C₄²	—	4	2	no	—
472	C₂×C₄²	—	4	2	no	—
473	C₂×C₄²	—	4	2	no	—
474	C₂×C₄²	—	4	2	no	—
475	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
476	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
477	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
478	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
479	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
480	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
481	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	4	yes	—
485	#95	C₂³×C₁₃	1	4	yes	—
486	#95	C₂³×C₁₃	1	4	yes	—
487	#95	C₂³×C₁₃	1	4	yes	—
488	#95	C₂³×C₁₃	1	4	yes	—
489	#95	C₂³×C₁₃	1	4	yes	—
490	#95	C₂³×C₁₃	1	4	yes	—
491	#95	C₂³×C₁₃	1	4	yes	—
492	#95	C₂³×C₁₃	1	4	yes	—
493	#95	C₂³×C₁₃	1	4	yes	—
494	C₂×C₁₃	—	4	4	no	—
495	C₂×C₁₃	#2334	1	8	yes	direct product factor
496	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
497	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
498	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
499	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
500	C₂×C₁₃	C₂×#539	1	1	yes	characteristic
501	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
502	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
503	C₂⁴	—	2	2	no	—
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	2	2	no	—
508	C₂⁴	—	2	2	no	—
509	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
510	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
511	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	16	no	—
550	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
551	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
552	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
553	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
554	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
556	C₂²×C₄	C₁₃×#41	1	4	yes	—
557	C₂²×C₄	C₁₃×#41	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
562	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	8	no	—
574	C₄⋊C₄	—	2	8	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
580	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
581	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
588	C₄²	—	2	8	no	—
589	C₄²	—	4	4	no	—
590	C₄²	—	4	4	no	—
591	C₄²	—	4	4	no	—
592	C₄²	—	4	4	no	—
593	C₄²	C₂²×C₄×C₁₃	1	16	yes	complemented
594	C₁₃	C₂×#2334	1	1	yes	characteristic, direct product factor, Sylow
595	C₂³	—	2	8	no	—
596	C₂³	—	2	8	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	4	no	—
608	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
609	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
610	C₂³	C₂×C₁₃×#41	1	2	yes	—
611	C₂³	C₂×C₁₃×#41	1	2	yes	—
612	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
613	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
614	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
615	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
616	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	8	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	8	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	16	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
667	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
670	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
671	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
672	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
673	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
674	C₂²	—	2	4	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	4	16	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	C₄×C₁₃×#41	1	4	yes	—
683	C₂²	C₁₃×#520	1	4	yes	—
684	C₂²	C₁₃×#520	1	4	yes	—
685	C₂²	C₁₃×#538	1	4	yes	—
686	C₂²	C₁₃×#539	1	4	yes	—
687	C₂²	C₁₃×#541	1	4	yes	—
688	C₂²	C₁₃×#542	1	4	yes	—
689	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
690	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
691	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
692	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
695	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
696	C₄	—	2	4	no	—
697	C₄	—	2	4	no	—
698	C₄	—	2	4	no	—
699	C₄	—	2	4	no	—
700	C₄	—	2	4	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	4	no	—
703	C₄	—	2	4	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₂	—	4	4	no	—
711	C₂	C₁₃×#2334	1	8	yes	direct product factor
712	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
713	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
714	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
715	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
716	C₂	C₂×C₁₃×#539	1	1	yes	characteristic
717	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
718	C₂	C₂×C₁₃×#542	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2334	C₂	direct (N × H)
3. C₂×C₁₃×#389	C₂	semidirect
4. C₂×C₁₃×#389	C₂	semidirect
8. C₂×C₁₃×#387	C₂	semidirect
9. C₂×C₁₃×#387	C₂	semidirect
10. C₂×C₁₃×#387	C₂	semidirect
13. C₂×C₁₃×#382	C₂	semidirect
14. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
18. C₂×C₁₃×#126	C₄	semidirect
42. C₁₃×#389	C₂²	semidirect
43. C₁₃×#389	C₂²	semidirect
47. C₁₃×#387	C₂²	semidirect
48. C₁₃×#387	C₂²	semidirect
49. C₁₃×#387	C₂²	semidirect
52. C₁₃×#382	C₂²	semidirect
53. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
54. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
87. C₁₃×#126	C₂×C₄	semidirect
95. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
96. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
97. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
125. C₂×C₄²×C₁₃	C₂×C₄	semidirect
144. C₂×#2334	C₁₃	direct (N × H)
221. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
222. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
223. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
235. C₄²×C₁₃	C₂²×C₄	semidirect
237. #2334	C₂×C₁₃	direct (N × H)
238. C₂×#389	C₂×C₁₃	semidirect
239. C₂×#389	C₂×C₁₃	semidirect
243. C₂×#387	C₂×C₁₃	semidirect
244. C₂×#387	C₂×C₁₃	semidirect
245. C₂×#387	C₂×C₁₃	semidirect
248. C₂×#382	C₂×C₁₃	semidirect
249. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
250. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
332. C₂×#126	C₄×C₁₃	semidirect
356. #389	C₂²×C₁₃	semidirect
357. #389	C₂²×C₁₃	semidirect
361. #387	C₂²×C₁₃	semidirect
362. #387	C₂²×C₁₃	semidirect
363. #387	C₂²×C₁₃	semidirect
366. #382	C₂²×C₁₃	semidirect
367. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
368. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
437. #126	C₂×C₄×C₁₃	semidirect
445. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
446. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
447. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
475. C₂×C₄²	C₂×C₄×C₁₃	semidirect
495. C₂×C₁₃	#2334	direct (N × H)
579. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
580. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
581. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
593. C₄²	C₂²×C₄×C₁₃	semidirect
594. C₁₃	C₂×#2334	direct (N × H)
711. C₂	C₁₃×#2334	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#126	2
C₁₃×#2334	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₁₃×#387	2
C₂×C₁₃×#385	2
C₂×C₁₃×#382	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2334	13

Subgroups — C2×C13×#2334 #15720416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2334 #15720416