Subgroups — C₂×C₁₃×#3225 #15747135

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#433	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×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
27	C₁₃×#542	—	2	4	no	—
28	C₁₃×#542	C₂²	1	8	yes	complemented
29	C₁₃×#536	—	2	4	no	—
30	C₁₃×#536	C₂²	1	8	yes	complemented
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#126	—	2	1	no	—
35	C₂×C₁₃×#124	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#123	—	2	1	no	—
40	C₂×C₁₃×#123	—	2	1	no	—
41	C₂×C₁₃×#123	—	2	1	no	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
50	C₁₃×#497	C₂²	1	8	yes	complemented
51	C₁₃×#495	C₂²	1	8	yes	complemented
52	C₁₃×#489	C₂²	1	8	yes	complemented
53	C₁₃×#487	C₂²	1	8	yes	complemented
54	C₁₃×#464	C₂²	1	8	yes	complemented
55	C₁₃×#463	C₂²	1	8	yes	complemented
56	C₁₃×#462	C₂²	1	8	yes	complemented
57	C₁₃×#461	C₂²	1	8	yes	complemented
58	C₁₃×#452	C₂²	1	8	yes	complemented
59	C₁₃×#451	C₂²	1	8	yes	complemented
60	C₁₃×#449	C₂²	1	8	yes	—
61	C₁₃×#448	C₂²	1	8	yes	complemented
62	C₁₃×#433	C₂²	1	8	yes	complemented
63	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₈	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#97	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	—	4	2	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	1	no	—
84	C₂²×Q₈×C₁₃	—	4	2	no	—
85	C₂²×Q₈×C₁₃	—	4	2	no	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×Q₁₆	—	4	2	no	—
100	C₂×C₁₃×Q₁₆	—	4	2	no	—
101	C₂×C₁₃×Q₁₆	—	4	2	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	—	4	2	no	—
106	C₂×C₁₃×SD₁₆	—	4	2	no	—
107	C₂×C₁₃×SD₁₆	—	4	2	no	—
108	C₂×C₁₃×SD₁₆	—	4	2	no	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×D₈	—	4	2	no	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	—	2	2	no	—
120	C₁₃×C₄⋊Q₈	—	2	2	no	—
121	C₁₃×C₄⋊Q₈	—	2	2	no	—
122	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#126	—	2	8	no	—
126	C₁₃×#124	—	2	8	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	C₂³	1	4	yes	—
131	C₁₃×#124	C₂³	1	4	yes	—
132	C₁₃×#124	C₂³	1	4	yes	—
133	C₁₃×#123	—	2	8	no	—
134	C₁₃×#123	—	2	8	no	—
135	C₁₃×#123	—	2	8	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	8	no	—
138	C₁₃×C₂²⋊Q₈	—	2	8	no	—
139	C₁₃×C₂²⋊Q₈	—	2	8	no	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	C₂³	1	4	yes	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	C₂³	1	4	yes	—
147	C₁₃×#117	D₄	1	4	yes	—
148	C₁₃×#117	C₂³	1	4	yes	—
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
175	C₁₃×C₄⋊C₈	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×#103	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#102	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	4	yes	—
184	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₁₃×#97	C₂³	1	4	yes	—
187	C₄×C₈×C₁₃	C₂³	1	4	yes	—
188	C₂×#3225	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂⁴×C₁₃	—	2	1	no	—
190	C₂⁴×C₁₃	—	2	1	no	—
191	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₁₃×#41	—	4	4	no	—
193	C₁₃×#41	—	4	4	no	—
194	C₁₃×#41	—	4	8	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	4	no	—
197	C₂×Q₈×C₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	1	no	—
200	C₂×Q₈×C₁₃	—	2	4	no	—
201	C₂×Q₈×C₁₃	—	2	2	no	—
202	C₂×Q₈×C₁₃	—	2	2	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	2	2	no	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	2	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	4	4	no	—
210	C₂×Q₈×C₁₃	—	4	4	no	—
211	C₂×Q₈×C₁₃	—	4	4	no	—
212	C₂×Q₈×C₁₃	—	4	8	no	—
213	C₂×Q₈×C₁₃	—	8	2	no	—
214	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	2	no	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	4	4	no	—
227	C₂×D₄×C₁₃	—	8	2	no	—
228	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	4	4	no	—
242	C₂²×C₄×C₁₃	—	4	4	no	—
243	C₂²×C₄×C₁₃	—	8	2	no	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₁₃×Q₁₆	—	4	4	no	—
253	C₁₃×Q₁₆	—	4	4	no	—
254	C₁₃×Q₁₆	—	4	4	no	—
255	C₁₃×SD₁₆	—	4	4	no	—
256	C₁₃×SD₁₆	—	4	4	no	—
257	C₁₃×SD₁₆	—	4	4	no	—
258	C₁₃×SD₁₆	—	4	4	no	—
259	C₁₃×D₈	—	4	4	no	—
260	C₂×C₈×C₁₃	—	2	2	no	—
261	C₂×C₈×C₁₃	—	2	2	no	—
262	C₂×C₈×C₁₃	—	2	2	no	—
263	C₂×C₈×C₁₃	—	2	2	no	—
264	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₄²×C₁₃	—	2	4	no	—
293	C₄²×C₁₃	C₂×D₄	1	2	yes	—
294	C₄²×C₁₃	C₂×D₄	1	2	yes	—
295	C₄²×C₁₃	C₂⁴	1	2	yes	—
296	C₄²×C₁₃	C₂⁴	1	2	yes	—
297	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#3225	C₂×C₁₃	1	16	yes	direct product factor
300	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#449	C₂×C₁₃	1	1	yes	characteristic
310	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	4	2	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	4	2	no	—
321	C₂³×C₁₃	—	4	2	no	—
322	C₂³×C₁₃	—	4	2	no	—
323	C₂³×C₁₃	—	4	2	no	—
324	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
325	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	2	2	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	2	2	no	—
334	Q₈×C₁₃	—	4	8	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	4	2	no	—
337	Q₈×C₁₃	—	4	2	no	—
338	Q₈×C₁₃	—	4	2	no	—
339	Q₈×C₁₃	—	8	4	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	4	8	no	—
345	D₄×C₁₃	—	4	2	no	—
346	D₄×C₁₃	—	4	2	no	—
347	D₄×C₁₃	—	8	4	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	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	4	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	4	8	no	—
363	C₂×C₄×C₁₃	—	4	8	no	—
364	C₂×C₄×C₁₃	—	4	2	no	—
365	C₂×C₄×C₁₃	—	4	2	no	—
366	C₂×C₄×C₁₃	—	4	2	no	—
367	C₂×C₄×C₁₃	—	4	2	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	8	4	no	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
378	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
380	C₈×C₁₃	—	2	2	no	—
381	C₈×C₁₃	—	2	2	no	—
382	C₈×C₁₃	—	2	2	no	—
383	C₈×C₁₃	—	2	2	no	—
384	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
385	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
389	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
394	#542	—	2	4	no	—
395	#542	C₂²×C₁₃	1	8	yes	complemented
396	#536	—	2	4	no	—
397	#536	C₂²×C₁₃	1	8	yes	complemented
398	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#126	—	2	1	no	—
402	C₂×#124	—	2	1	no	—
403	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#123	—	2	1	no	—
407	C₂×#123	—	2	1	no	—
408	C₂×#123	—	2	1	no	—
409	C₂×C₂²⋊Q₈	—	2	1	no	—
410	C₂×C₂²⋊Q₈	—	2	1	no	—
411	C₂×C₂²⋊Q₈	—	2	1	no	—
412	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
417	#497	C₂²×C₁₃	1	8	yes	complemented
418	#495	C₂²×C₁₃	1	8	yes	complemented
419	#489	C₂²×C₁₃	1	8	yes	complemented
420	#487	C₂²×C₁₃	1	8	yes	complemented
421	#464	C₂²×C₁₃	1	8	yes	complemented
422	#463	C₂²×C₁₃	1	8	yes	complemented
423	#462	C₂²×C₁₃	1	8	yes	complemented
424	#461	C₂²×C₁₃	1	8	yes	complemented
425	#452	C₂²×C₁₃	1	8	yes	complemented
426	#451	C₂²×C₁₃	1	8	yes	complemented
427	#449	C₂²×C₁₃	1	8	yes	—
428	#448	C₂²×C₁₃	1	8	yes	complemented
429	#433	C₂²×C₁₃	1	8	yes	complemented
430	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	4	4	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	8	4	no	—
455	C₂²×C₁₃	—	8	4	no	—
456	C₂²×C₁₃	#535	1	2	yes	—
457	C₂²×C₁₃	#577	1	2	yes	—
458	C₂²×C₁₃	#578	1	2	yes	—
459	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
460	C₄×C₁₃	—	2	2	no	—
461	C₄×C₁₃	—	2	2	no	—
462	C₄×C₁₃	—	2	2	no	—
463	C₄×C₁₃	—	2	2	no	—
464	C₄×C₁₃	—	2	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	2	no	—
471	C₄×C₁₃	#535	1	2	yes	—
472	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	4	2	no	—
476	C₂×#41	—	4	2	no	—
477	C₂×#41	C₂³×C₁₃	1	4	yes	—
478	C₂²×Q₈	—	2	1	no	—
479	C₂²×Q₈	—	2	2	no	—
480	C₂²×Q₈	—	2	1	no	—
481	C₂²×Q₈	—	4	2	no	—
482	C₂²×Q₈	—	4	2	no	—
483	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
491	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×Q₁₆	—	4	2	no	—
497	C₂×Q₁₆	—	4	2	no	—
498	C₂×Q₁₆	—	4	2	no	—
499	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
500	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
501	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
502	C₂×SD₁₆	—	4	2	no	—
503	C₂×SD₁₆	—	4	2	no	—
504	C₂×SD₁₆	—	4	2	no	—
505	C₂×SD₁₆	—	4	2	no	—
506	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
509	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×D₈	—	4	2	no	—
511	C₂×D₈	C₂³×C₁₃	1	4	yes	—
512	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	2	2	no	—
519	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
521	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
522	#126	—	2	8	no	—
523	#124	—	2	8	no	—
524	#124	—	2	2	no	—
525	#124	—	2	2	no	—
526	#124	—	2	2	no	—
527	#124	C₂³×C₁₃	1	4	yes	—
528	#124	C₂³×C₁₃	1	4	yes	—
529	#124	C₂³×C₁₃	1	4	yes	—
530	#123	—	2	8	no	—
531	#123	—	2	8	no	—
532	#123	—	2	8	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	8	no	—
535	C₂²⋊Q₈	—	2	8	no	—
536	C₂²⋊Q₈	—	2	8	no	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
538	#121	—	2	2	no	—
539	#121	C₂³×C₁₃	1	4	yes	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	C₂³×C₁₃	1	4	yes	—
544	#117	D₄×C₁₃	1	4	yes	—
545	#117	C₂³×C₁₃	1	4	yes	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
572	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
573	#103	C₂³×C₁₃	1	4	yes	—
574	#103	C₂³×C₁₃	1	4	yes	—
575	#103	C₂³×C₁₃	1	4	yes	—
576	#103	C₂³×C₁₃	1	4	yes	—
577	#103	C₂³×C₁₃	1	4	yes	—
578	#103	C₂³×C₁₃	1	4	yes	—
579	#102	C₂³×C₁₃	1	4	yes	—
580	#102	C₂³×C₁₃	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
583	#97	C₂³×C₁₃	1	4	yes	—
584	C₄×C₈	C₂³×C₁₃	1	4	yes	—
585	C₂×C₁₃	—	4	2	no	—
586	C₂×C₁₃	—	8	2	no	—
587	C₂×C₁₃	—	8	2	no	—
588	C₂×C₁₃	#3225	1	4	yes	direct product factor
589	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
590	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
591	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
592	C₂⁴	—	2	1	no	—
593	C₂⁴	—	2	1	no	—
594	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	#41	—	4	8	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	4	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	4	4	no	—
613	C₂×Q₈	—	4	4	no	—
614	C₂×Q₈	—	4	4	no	—
615	C₂×Q₈	—	4	8	no	—
616	C₂×Q₈	—	8	2	no	—
617	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
618	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	8	2	no	—
631	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	8	2	no	—
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	Q₁₆	—	4	4	no	—
656	Q₁₆	—	4	4	no	—
657	Q₁₆	—	4	4	no	—
658	SD₁₆	—	4	4	no	—
659	SD₁₆	—	4	4	no	—
660	SD₁₆	—	4	4	no	—
661	SD₁₆	—	4	4	no	—
662	D₈	—	4	4	no	—
663	C₂×C₈	—	2	2	no	—
664	C₂×C₈	—	2	2	no	—
665	C₂×C₈	—	2	2	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
668	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
669	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
670	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
681	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
682	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
694	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
695	C₄²	—	2	4	no	—
696	C₄²	C₂×D₄×C₁₃	1	2	yes	—
697	C₄²	C₂×D₄×C₁₃	1	2	yes	—
698	C₄²	C₂⁴×C₁₃	1	2	yes	—
699	C₄²	C₂⁴×C₁₃	1	2	yes	—
700	C₁₃	C₂×#3225	1	1	yes	characteristic, direct product factor, Sylow
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
713	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	8	no	—
723	Q₈	—	4	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	Q₈	—	4	2	no	—
727	Q₈	—	8	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	2	no	—
735	D₄	—	8	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
764	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
765	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
766	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
767	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	8	4	no	—
783	C₂²	—	8	4	no	—
784	C₂²	C₁₃×#535	1	2	yes	—
785	C₂²	C₁₃×#577	1	2	yes	—
786	C₂²	C₁₃×#578	1	2	yes	—
787	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	C₁₃×#535	1	2	yes	—
800	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
801	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	2	no	—
805	C₂	C₁₃×#3225	1	4	yes	direct product factor
806	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
807	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
808	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×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#542	C₂	semidirect
2. C₂×C₁₃×#536	C₂	semidirect
3. C₁₃×#3225	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#495	C₂	semidirect
6. C₂×C₁₃×#489	C₂	semidirect
7. C₂×C₁₃×#487	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#462	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#461	C₂	semidirect
12. C₂×C₁₃×#452	C₂	semidirect
14. C₂×C₁₃×#451	C₂	semidirect
15. C₂×C₁₃×#448	C₂	semidirect
16. C₂×C₁₃×#433	C₂	semidirect
28. C₁₃×#542	C₂²	semidirect
30. C₁₃×#536	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
51. C₁₃×#495	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
53. C₁₃×#487	C₂²	semidirect
54. C₁₃×#464	C₂²	semidirect
55. C₁₃×#463	C₂²	semidirect
56. C₁₃×#462	C₂²	semidirect
57. C₁₃×#461	C₂²	semidirect
58. C₁₃×#452	C₂²	semidirect
59. C₁₃×#451	C₂²	semidirect
61. C₁₃×#448	C₂²	semidirect
62. C₁₃×#433	C₂²	semidirect
188. C₂×#3225	C₁₃	direct (N × H)
297. C₂×#542	C₂×C₁₃	semidirect
298. C₂×#536	C₂×C₁₃	semidirect
299. #3225	C₂×C₁₃	direct (N × H)
300. C₂×#497	C₂×C₁₃	semidirect
301. C₂×#495	C₂×C₁₃	semidirect
302. C₂×#489	C₂×C₁₃	semidirect
303. C₂×#487	C₂×C₁₃	semidirect
304. C₂×#464	C₂×C₁₃	semidirect
305. C₂×#462	C₂×C₁₃	semidirect
306. C₂×#463	C₂×C₁₃	semidirect
307. C₂×#461	C₂×C₁₃	semidirect
308. C₂×#452	C₂×C₁₃	semidirect
310. C₂×#451	C₂×C₁₃	semidirect
311. C₂×#448	C₂×C₁₃	semidirect
312. C₂×#433	C₂×C₁₃	semidirect
395. #542	C₂²×C₁₃	semidirect
397. #536	C₂²×C₁₃	semidirect
417. #497	C₂²×C₁₃	semidirect
418. #495	C₂²×C₁₃	semidirect
419. #489	C₂²×C₁₃	semidirect
420. #487	C₂²×C₁₃	semidirect
421. #464	C₂²×C₁₃	semidirect
422. #463	C₂²×C₁₃	semidirect
423. #462	C₂²×C₁₃	semidirect
424. #461	C₂²×C₁₃	semidirect
425. #452	C₂²×C₁₃	semidirect
426. #451	C₂²×C₁₃	semidirect
428. #448	C₂²×C₁₃	semidirect
429. #433	C₂²×C₁₃	semidirect
588. C₂×C₁₃	#3225	direct (N × H)
700. C₁₃	C₂×#3225	direct (N × H)
805. C₂	C₁₃×#3225	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×#542	2
C₂×C₁₃×#536	2
C₁₃×#3225	2
C₂×C₁₃×#497	2
C₂×C₁₃×#495	2
C₂×C₁₃×#489	2
C₂×C₁₃×#487	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₂×C₁₃×#433	2
C₂×#3225	13

Subgroups — C2×C13×#3225 #15747135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3225 #15747135