Subgroups — C₂×C₁₃×#3327 #15747486

Order 3328.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3327	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₁₃×#552	—	2	4	no	—
25	C₁₃×#552	C₂²	1	8	yes	complemented
26	C₁₃×#548	—	2	4	no	—
27	C₁₃×#548	C₂²	1	8	yes	—
28	C₂×C₁₃×#126	—	2	1	no	—
29	C₂×C₁₃×#125	—	2	1	no	—
30	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#124	—	2	1	no	—
32	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#123	—	2	1	no	—
34	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	—	2	1	no	—
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#117	—	2	1	no	—
45	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#488	C₂²	1	8	yes	complemented
48	C₁₃×#484	C₂²	1	8	yes	complemented
49	C₁₃×#482	C₂²	1	8	yes	complemented
50	C₁₃×#479	C₂²	1	8	yes	complemented
51	C₁₃×#470	C₂²	1	8	yes	complemented
52	C₁₃×#468	C₂²	1	8	yes	complemented
53	C₁₃×#464	C₂²	1	8	yes	complemented
54	C₁₃×#452	C₂²	1	8	yes	complemented
55	C₁₃×#451	C₂²	1	8	yes	complemented
56	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
57	C₁₃×#436	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₃×#419	C₂²	1	8	yes	complemented
63	C₁₃×#417	C₂²	1	8	yes	complemented
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#41	—	2	2	no	—
78	C₂×C₁₃×#41	—	2	4	no	—
79	C₂×C₁₃×#41	—	4	2	no	—
80	C₂×C₁₃×#41	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃	—	2	1	no	—
82	C₂²×Q₈×C₁₃	—	2	2	no	—
83	C₂²×Q₈×C₁₃	—	2	4	no	—
84	C₂²×Q₈×C₁₃	—	4	2	no	—
85	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	—	2	1	no	—
94	C₂³×C₄×C₁₃	—	2	1	no	—
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×Q₁₆	—	2	4	no	—
99	C₂×C₁₃×Q₁₆	—	4	2	no	—
100	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×SD₁₆	—	4	2	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×M₁₆	—	4	2	no	—
105	C₂×C₁₃×M₁₆	—	4	2	no	—
106	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#126	—	2	8	no	—
113	C₁₃×#125	—	2	8	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	C₂³	1	4	yes	—
116	C₁₃×#124	—	2	8	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	C₂³	1	4	yes	—
119	C₁₃×#123	—	2	8	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	8	no	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₁₃×#121	—	2	8	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	C₂³	1	4	yes	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×D₄×C₁₃	—	2	8	no	—
135	C₄×D₄×C₁₃	D₄	1	4	yes	—
136	C₄×D₄×C₁₃	C₂³	1	4	yes	—
137	C₁₃×#117	—	2	2	no	—
138	C₁₃×#117	—	2	8	no	—
139	C₁₃×#117	C₂³	1	4	yes	—
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
163	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	—	2	1	no	—
165	C₂×C₄²×C₁₃	—	2	1	no	—
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	4	yes	—
169	C₁₃×#107	C₂³	1	4	yes	—
170	C₁₃×#106	C₂³	1	4	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×#103	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₄×C₈×C₁₃	C₂³	1	4	yes	—
185	C₂×#3327	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂⁴×C₁₃	—	2	1	no	—
187	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₁₃×#41	—	2	8	no	—
190	C₁₃×#41	—	4	4	no	—
191	C₁₃×#41	—	4	8	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	4	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	2	no	—
197	C₂×Q₈×C₁₃	—	2	8	no	—
198	C₂×Q₈×C₁₃	—	2	2	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	2	no	—
201	C₂×Q₈×C₁₃	—	2	2	no	—
202	C₂×Q₈×C₁₃	—	4	4	no	—
203	C₂×Q₈×C₁₃	—	4	4	no	—
204	C₂×Q₈×C₁₃	—	4	8	no	—
205	C₂×Q₈×C₁₃	#41	1	4	yes	—
206	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	4	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
218	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	4	4	no	—
234	C₂²×C₄×C₁₃	—	4	4	no	—
235	C₂²×C₄×C₁₃	—	4	4	no	—
236	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×Q₁₆	—	2	8	no	—
246	C₁₃×Q₁₆	—	4	4	no	—
247	C₁₃×SD₁₆	—	4	4	no	—
248	C₁₃×M₁₆	—	4	4	no	—
249	C₁₃×M₁₆	—	4	4	no	—
250	C₂×C₈×C₁₃	—	2	2	no	—
251	C₂×C₈×C₁₃	—	2	2	no	—
252	C₂×C₈×C₁₃	—	2	2	no	—
253	C₂×C₈×C₁₃	—	2	2	no	—
254	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
272	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
273	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
283	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	4	no	—
287	C₄²×C₁₃	C₂×D₄	1	2	yes	—
288	C₄²×C₁₃	C₂⁴	1	2	yes	—
289	C₂×#552	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#548	C₂×C₁₃	1	1	yes	characteristic
291	#3327	C₂×C₁₃	1	16	yes	direct product factor
292	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
293	C₂×#484	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#419	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	4	2	no	—
313	C₂³×C₁₃	—	4	2	no	—
314	C₂³×C₁₃	—	4	2	no	—
315	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
316	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
317	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₁₃	—	2	4	no	—
319	Q₈×C₁₃	—	2	2	no	—
320	Q₈×C₁₃	—	2	2	no	—
321	Q₈×C₁₃	—	2	2	no	—
322	Q₈×C₁₃	—	2	2	no	—
323	Q₈×C₁₃	—	2	2	no	—
324	Q₈×C₁₃	—	4	8	no	—
325	Q₈×C₁₃	—	4	2	no	—
326	Q₈×C₁₃	—	4	2	no	—
327	Q₈×C₁₃	C₂×#41	1	4	yes	—
328	D₄×C₁₃	—	2	2	no	—
329	D₄×C₁₃	—	2	2	no	—
330	D₄×C₁₃	—	4	4	no	—
331	D₄×C₁₃	—	4	8	no	—
332	D₄×C₁₃	—	4	8	no	—
333	D₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	4	8	no	—
353	C₂×C₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	—	4	8	no	—
355	C₂×C₄×C₁₃	—	4	2	no	—
356	C₂×C₄×C₁₃	—	4	2	no	—
357	C₂×C₄×C₁₃	—	4	2	no	—
358	C₂×C₄×C₁₃	—	4	2	no	—
359	C₂×C₄×C₁₃	—	4	2	no	—
360	C₂×C₄×C₁₃	—	4	2	no	—
361	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
369	C₈×C₁₃	—	2	2	no	—
370	C₈×C₁₃	—	2	2	no	—
371	C₈×C₁₃	—	2	2	no	—
372	C₈×C₁₃	—	2	2	no	—
373	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
374	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
380	#552	—	2	4	no	—
381	#552	C₂²×C₁₃	1	8	yes	complemented
382	#548	—	2	4	no	—
383	#548	C₂²×C₁₃	1	8	yes	—
384	C₂×#126	—	2	1	no	—
385	C₂×#125	—	2	1	no	—
386	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#124	—	2	1	no	—
388	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#123	—	2	1	no	—
390	C₂×C₂²⋊Q₈	—	2	1	no	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#121	—	2	1	no	—
395	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×D₄	—	2	1	no	—
399	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#117	—	2	1	no	—
401	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	#488	C₂²×C₁₃	1	8	yes	complemented
404	#484	C₂²×C₁₃	1	8	yes	complemented
405	#482	C₂²×C₁₃	1	8	yes	complemented
406	#479	C₂²×C₁₃	1	8	yes	complemented
407	#470	C₂²×C₁₃	1	8	yes	complemented
408	#468	C₂²×C₁₃	1	8	yes	complemented
409	#464	C₂²×C₁₃	1	8	yes	complemented
410	#452	C₂²×C₁₃	1	8	yes	complemented
411	#451	C₂²×C₁₃	1	8	yes	complemented
412	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
413	#436	C₂²×C₁₃	1	8	yes	complemented
414	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
418	#419	C₂²×C₁₃	1	8	yes	complemented
419	#417	C₂²×C₁₃	1	8	yes	complemented
420	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
433	C₂²×C₁₃	—	2	2	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	2	2	no	—
437	C₂²×C₁₃	—	2	2	no	—
438	C₂²×C₁₃	—	2	2	no	—
439	C₂²×C₁₃	—	4	4	no	—
440	C₂²×C₁₃	—	4	4	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	8	4	no	—
445	C₂²×C₁₃	#546	1	2	yes	—
446	C₂²×C₁₃	#575	1	2	yes	—
447	C₂²×C₁₃	#578	1	2	yes	—
448	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	4	no	—
452	C₄×C₁₃	—	2	2	no	—
453	C₄×C₁₃	—	2	2	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	#546	1	2	yes	—
461	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
462	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	4	no	—
465	C₂×#41	—	4	2	no	—
466	C₂×#41	C₂³×C₁₃	1	4	yes	—
467	C₂²×Q₈	—	2	1	no	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	—	2	4	no	—
470	C₂²×Q₈	—	4	2	no	—
471	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
474	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×Q₁₆	—	2	4	no	—
485	C₂×Q₁₆	—	4	2	no	—
486	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
487	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
488	C₂×SD₁₆	—	4	2	no	—
489	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
490	C₂×M₁₆	—	4	2	no	—
491	C₂×M₁₆	—	4	2	no	—
492	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
494	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
498	#126	—	2	8	no	—
499	#125	—	2	8	no	—
500	#125	—	2	2	no	—
501	#125	C₂³×C₁₃	1	4	yes	—
502	#124	—	2	8	no	—
503	#124	—	2	2	no	—
504	#124	C₂³×C₁₃	1	4	yes	—
505	#123	—	2	8	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	8	no	—
510	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
511	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
512	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
513	#121	—	2	8	no	—
514	#121	—	2	2	no	—
515	#121	C₂³×C₁₃	1	4	yes	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
519	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
520	C₄×D₄	—	2	8	no	—
521	C₄×D₄	D₄×C₁₃	1	4	yes	—
522	C₄×D₄	C₂³×C₁₃	1	4	yes	—
523	#117	—	2	2	no	—
524	#117	—	2	8	no	—
525	#117	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	2	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₄²	—	2	1	no	—
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	—	2	1	no	—
553	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
554	#107	C₂³×C₁₃	1	4	yes	—
555	#107	C₂³×C₁₃	1	4	yes	—
556	#106	C₂³×C₁₃	1	4	yes	—
557	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
558	#103	C₂³×C₁₃	1	4	yes	—
559	#103	C₂³×C₁₃	1	4	yes	—
560	#103	C₂³×C₁₃	1	4	yes	—
561	#103	C₂³×C₁₃	1	4	yes	—
562	#103	C₂³×C₁₃	1	4	yes	—
563	#103	C₂³×C₁₃	1	4	yes	—
564	#103	C₂³×C₁₃	1	4	yes	—
565	#102	C₂³×C₁₃	1	4	yes	—
566	#102	C₂³×C₁₃	1	4	yes	—
567	#102	C₂³×C₁₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
570	C₄×C₈	C₂³×C₁₃	1	4	yes	—
571	C₂×C₁₃	—	4	2	no	—
572	C₂×C₁₃	—	4	2	no	—
573	C₂×C₁₃	—	8	2	no	—
574	C₂×C₁₃	#3327	1	4	yes	direct product factor
575	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
576	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
577	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
578	C₂⁴	—	2	1	no	—
579	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
581	#41	—	2	8	no	—
582	#41	—	4	4	no	—
583	#41	—	4	8	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	4	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	—	2	8	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	2	2	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	—	2	2	no	—
594	C₂×Q₈	—	4	4	no	—
595	C₂×Q₈	—	4	4	no	—
596	C₂×Q₈	—	4	8	no	—
597	C₂×Q₈	C₁₃×#41	1	4	yes	—
598	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
599	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
600	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
610	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
637	Q₁₆	—	2	8	no	—
638	Q₁₆	—	4	4	no	—
639	SD₁₆	—	4	4	no	—
640	M₁₆	—	4	4	no	—
641	M₁₆	—	4	4	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
647	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
648	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
649	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
663	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
675	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	C₂×D₄×C₁₃	1	2	yes	—
680	C₄²	C₂⁴×C₁₃	1	2	yes	—
681	C₁₃	C₂×#3327	1	1	yes	characteristic, direct product factor, Sylow
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
693	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
694	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	2	2	no	—
701	Q₈	—	4	8	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	C₂×C₁₃×#41	1	4	yes	—
705	D₄	—	2	2	no	—
706	D₄	—	2	2	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	4	8	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
743	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
744	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
745	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	8	4	no	—
762	C₂²	C₁₃×#546	1	2	yes	—
763	C₂²	C₁₃×#575	1	2	yes	—
764	C₂²	C₁₃×#578	1	2	yes	—
765	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	4	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₁₃×#546	1	2	yes	—
778	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
779	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
780	C₂	—	4	2	no	—
781	C₂	—	4	2	no	—
782	C₂	—	8	2	no	—
783	C₂	C₁₃×#3327	1	4	yes	direct product factor
784	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
785	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
786	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#552	C₂	semidirect
3. C₁₃×#3327	C₂	direct (N × H)
4. C₂×C₁₃×#488	C₂	semidirect
5. C₂×C₁₃×#484	C₂	semidirect
6. C₂×C₁₃×#482	C₂	semidirect
7. C₂×C₁₃×#479	C₂	semidirect
8. C₂×C₁₃×#470	C₂	semidirect
9. C₂×C₁₃×#468	C₂	semidirect
10. C₂×C₁₃×#464	C₂	semidirect
11. C₂×C₁₃×#452	C₂	semidirect
12. C₂×C₁₃×#451	C₂	semidirect
13. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
14. C₂×C₁₃×#436	C₂	semidirect
15. C₂×C₁₃×#417	C₂	semidirect
16. C₂×C₁₃×#419	C₂	semidirect
25. C₁₃×#552	C₂²	semidirect
47. C₁₃×#488	C₂²	semidirect
48. C₁₃×#484	C₂²	semidirect
49. C₁₃×#482	C₂²	semidirect
50. C₁₃×#479	C₂²	semidirect
51. C₁₃×#470	C₂²	semidirect
52. C₁₃×#468	C₂²	semidirect
53. C₁₃×#464	C₂²	semidirect
54. C₁₃×#452	C₂²	semidirect
55. C₁₃×#451	C₂²	semidirect
56. C₄×C₁₃×Q₁₆	C₂²	semidirect
57. C₁₃×#436	C₂²	semidirect
62. C₁₃×#419	C₂²	semidirect
63. C₁₃×#417	C₂²	semidirect
185. C₂×#3327	C₁₃	direct (N × H)
289. C₂×#552	C₂×C₁₃	semidirect
291. #3327	C₂×C₁₃	direct (N × H)
292. C₂×#488	C₂×C₁₃	semidirect
293. C₂×#484	C₂×C₁₃	semidirect
294. C₂×#482	C₂×C₁₃	semidirect
295. C₂×#479	C₂×C₁₃	semidirect
296. C₂×#470	C₂×C₁₃	semidirect
297. C₂×#468	C₂×C₁₃	semidirect
298. C₂×#464	C₂×C₁₃	semidirect
299. C₂×#452	C₂×C₁₃	semidirect
300. C₂×#451	C₂×C₁₃	semidirect
301. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
302. C₂×#436	C₂×C₁₃	semidirect
303. C₂×#417	C₂×C₁₃	semidirect
304. C₂×#419	C₂×C₁₃	semidirect
381. #552	C₂²×C₁₃	semidirect
403. #488	C₂²×C₁₃	semidirect
404. #484	C₂²×C₁₃	semidirect
405. #482	C₂²×C₁₃	semidirect
406. #479	C₂²×C₁₃	semidirect
407. #470	C₂²×C₁₃	semidirect
408. #468	C₂²×C₁₃	semidirect
409. #464	C₂²×C₁₃	semidirect
410. #452	C₂²×C₁₃	semidirect
411. #451	C₂²×C₁₃	semidirect
412. C₄×Q₁₆	C₂²×C₁₃	semidirect
413. #436	C₂²×C₁₃	semidirect
418. #419	C₂²×C₁₃	semidirect
419. #417	C₂²×C₁₃	semidirect
574. C₂×C₁₃	#3327	direct (N × H)
681. C₁₃	C₂×#3327	direct (N × H)
783. C₂	C₁₃×#3327	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×#552	2
C₂×C₁₃×#548	2
C₁₃×#3327	2
C₂×C₁₃×#488	2
C₂×C₁₃×#484	2
C₂×C₁₃×#482	2
C₂×C₁₃×#479	2
C₂×C₁₃×#470	2
C₂×C₁₃×#468	2
C₂×C₁₃×#464	2
C₂×C₁₃×#452	2
C₂×C₁₃×#451	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₁₃×#436	2
C₂×C₁₃×#417	2
C₂×C₁₃×#419	2
C₂×#3327	13

Subgroups — C2×C13×#3327 #15747486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3327 #15747486