Subgroups — C₂×C₁₃×#3322 #15747481

Order 3328.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3322	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₁₃×D₈	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×#418	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#553	—	2	4	no	—
25	C₁₃×#553	C₂²	1	8	yes	complemented
26	C₁₃×#546	—	2	4	no	—
27	C₁₃×#546	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#126	—	2	1	no	—
29	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#123	—	2	1	no	—
32	C₂×C₁₃×#123	—	2	1	no	—
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#121	—	2	1	no	—
35	C₂×C₁₃×#121	—	2	1	no	—
36	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#120	—	2	1	no	—
40	C₂×C₄×D₄×C₁₃	—	2	1	no	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
47	C₁₃×#488	C₂²	1	8	yes	complemented
48	C₁₃×#485	C₂²	1	8	yes	complemented
49	C₁₃×#480	C₂²	1	8	yes	complemented
50	C₁₃×#478	C₂²	1	8	yes	complemented
51	C₁₃×#469	C₂²	1	8	yes	complemented
52	C₁₃×#468	C₂²	1	8	yes	complemented
53	C₁₃×#463	C₂²	1	8	yes	complemented
54	C₁₃×#449	C₂²	1	8	yes	complemented
55	C₁₃×#447	C₂²	1	8	yes	complemented
56	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
57	C₁₃×#436	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#418	C₂²	1	8	yes	complemented
63	C₁₃×#417	C₂²	1	8	yes	complemented
64	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#102	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, complemented
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₃	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	4	no	—
80	C₂×C₁₃×#41	—	4	2	no	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	—	2	4	no	—
84	C₂²×D₄×C₁₃	—	2	1	no	—
85	C₂²×D₄×C₁₃	—	2	1	no	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	1	no	—
89	C₂²×D₄×C₁₃	—	2	2	no	—
90	C₂²×D₄×C₁₃	—	4	2	no	—
91	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₂³×C₄×C₁₃	—	2	1	no	—
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×SD₁₆	—	4	2	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
104	C₂×C₁₃×D₈	—	2	4	no	—
105	C₂×C₁₃×D₈	—	4	2	no	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂×C₁₃×D₈	C₂³	1	4	yes	—
108	C₂×C₁₃×M₁₆	—	4	2	no	—
109	C₂×C₁₃×M₁₆	—	4	2	no	—
110	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
112	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×#126	—	2	8	no	—
117	C₁₃×#125	—	2	2	no	—
118	C₁₃×#125	C₂³	1	4	yes	complemented
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	C₂³	1	4	yes	—
121	C₁₃×#123	—	2	8	no	—
122	C₁₃×#123	—	2	8	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#121	—	2	8	no	—
126	C₁₃×#121	—	2	2	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	8	no	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₁₃×#121	C₂³	1	4	yes	—
132	C₁₃×#121	C₂³	1	4	yes	complemented
133	C₁₃×#120	—	2	8	no	—
134	C₄×D₄×C₁₃	—	2	8	no	—
135	C₄×D₄×C₁₃	—	2	2	no	—
136	C₄×D₄×C₁₃	—	2	2	no	—
137	C₄×D₄×C₁₃	D₄	1	4	yes	—
138	C₄×D₄×C₁₃	C₂³	1	4	yes	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	—
140	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	C₂³	1	4	yes	—
143	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	2	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	D₄	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	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	4	yes	complemented
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	4	yes	complemented
169	C₁₃×#107	C₂³	1	4	yes	complemented
170	C₁₃×#106	C₂³	1	4	yes	complemented
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
172	C₁₃×#103	C₂³	1	4	yes	complemented
173	C₁₃×#103	C₂³	1	4	yes	complemented
174	C₁₃×#103	C₂³	1	4	yes	complemented
175	C₁₃×#102	C₂³	1	4	yes	—
176	C₁₃×#102	C₂³	1	4	yes	—
177	C₁₃×#102	C₂³	1	4	yes	—
178	C₁₃×#102	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	complemented
182	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
184	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
185	C₂×#3322	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂⁴×C₁₃	—	2	1	no	—
187	C₂⁴×C₁₃	—	2	1	no	—
188	C₂⁴×C₁₃	—	2	1	no	—
189	C₂⁴×C₁₃	—	2	4	no	—
190	C₂⁴×C₁₃	—	4	4	no	—
191	C₂⁴×C₁₃	—	4	4	no	—
192	C₂⁴×C₁₃	—	8	2	no	—
193	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₁₃×#41	—	2	8	no	—
196	C₁₃×#41	—	4	4	no	—
197	C₁₃×#41	—	4	8	no	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	2	no	—
200	C₂×Q₈×C₁₃	—	2	2	no	—
201	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
202	C₂×D₄×C₁₃	—	2	8	no	—
203	C₂×D₄×C₁₃	—	2	4	no	—
204	C₂×D₄×C₁₃	—	2	4	no	—
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	2	no	—
216	C₂×D₄×C₁₃	—	4	4	no	—
217	C₂×D₄×C₁₃	—	4	8	no	—
218	C₂×D₄×C₁₃	—	4	2	no	—
219	C₂×D₄×C₁₃	—	4	4	no	—
220	C₂×D₄×C₁₃	—	4	4	no	—
221	C₂×D₄×C₁₃	—	4	4	no	—
222	C₂×D₄×C₁₃	—	8	2	no	—
223	C₂×D₄×C₁₃	—	8	2	no	—
224	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
225	C₂×D₄×C₁₃	#41	1	4	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	4	4	no	—
243	C₂²×C₄×C₁₃	—	8	2	no	—
244	C₂²×C₄×C₁₃	—	8	2	no	—
245	C₂²×C₄×C₁₃	—	8	2	no	—
246	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₁₃×SD₁₆	—	4	4	no	—
256	C₁₃×D₈	—	2	8	no	—
257	C₁₃×D₈	—	4	4	no	—
258	C₁₃×M₁₆	—	4	4	no	—
259	C₁₃×M₁₆	—	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	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	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	C₂⁴	1	2	yes	—
295	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#3322	C₂×C₁₃	1	16	yes	direct product factor
298	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂×#468	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂×#418	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	4	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	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	4	8	no	—
322	C₂³×C₁₃	—	4	8	no	—
323	C₂³×C₁₃	—	4	2	no	—
324	C₂³×C₁₃	—	4	2	no	—
325	C₂³×C₁₃	—	4	2	no	—
326	C₂³×C₁₃	—	4	2	no	—
327	C₂³×C₁₃	—	4	2	no	—
328	C₂³×C₁₃	—	4	2	no	—
329	C₂³×C₁₃	—	4	2	no	—
330	C₂³×C₁₃	—	4	2	no	—
331	C₂³×C₁₃	—	8	4	no	—
332	C₂³×C₁₃	—	8	16	no	—
333	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
334	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
335	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₁₃	—	2	2	no	—
337	Q₈×C₁₃	—	2	2	no	—
338	Q₈×C₁₃	—	4	2	no	—
339	D₄×C₁₃	—	2	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	—	2	2	no	—
345	D₄×C₁₃	—	4	4	no	—
346	D₄×C₁₃	—	4	8	no	—
347	D₄×C₁₃	—	4	8	no	—
348	D₄×C₁₃	—	4	8	no	—
349	D₄×C₁₃	—	4	2	no	—
350	D₄×C₁₃	—	4	2	no	—
351	D₄×C₁₃	—	8	4	no	—
352	D₄×C₁₃	—	8	4	no	—
353	D₄×C₁₃	C₂×#41	1	4	yes	—
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	4	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	4	8	no	—
370	C₂×C₄×C₁₃	—	4	2	no	—
371	C₂×C₄×C₁₃	—	4	2	no	—
372	C₂×C₄×C₁₃	—	4	2	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	2	no	—
375	C₂×C₄×C₁₃	—	8	4	no	—
376	C₂×C₄×C₁₃	—	8	4	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
384	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₁₃	—	2	2	no	—
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	2	2	no	—
389	C₈×C₁₃	—	2	2	no	—
390	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
391	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	#553	—	2	4	no	—
398	#553	C₂²×C₁₃	1	8	yes	complemented
399	#546	—	2	4	no	—
400	#546	C₂²×C₁₃	1	8	yes	complemented
401	C₂×#126	—	2	1	no	—
402	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#123	—	2	1	no	—
405	C₂×#123	—	2	1	no	—
406	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#121	—	2	1	no	—
408	C₂×#121	—	2	1	no	—
409	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₂×#120	—	2	1	no	—
413	C₂×C₄×D₄	—	2	1	no	—
414	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	C₂²×C₂²⋊C₄	—	2	1	no	—
420	#488	C₂²×C₁₃	1	8	yes	complemented
421	#485	C₂²×C₁₃	1	8	yes	complemented
422	#480	C₂²×C₁₃	1	8	yes	complemented
423	#478	C₂²×C₁₃	1	8	yes	complemented
424	#469	C₂²×C₁₃	1	8	yes	complemented
425	#468	C₂²×C₁₃	1	8	yes	complemented
426	#463	C₂²×C₁₃	1	8	yes	complemented
427	#449	C₂²×C₁₃	1	8	yes	complemented
428	#447	C₂²×C₁₃	1	8	yes	complemented
429	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
430	#436	C₂²×C₁₃	1	8	yes	complemented
431	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#418	C₂²×C₁₃	1	8	yes	complemented
436	#417	C₂²×C₁₃	1	8	yes	complemented
437	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	C₂²×C₁₃	—	2	2	no	—
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	4	no	—
453	C₂²×C₁₃	—	2	2	no	—
454	C₂²×C₁₃	—	2	2	no	—
455	C₂²×C₁₃	—	2	2	no	—
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	4	4	no	—
458	C₂²×C₁₃	—	4	4	no	—
459	C₂²×C₁₃	—	4	8	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	8	16	no	—
469	C₂²×C₁₃	—	8	4	no	—
470	C₂²×C₁₃	—	8	4	no	—
471	C₂²×C₁₃	#546	1	2	yes	—
472	C₂²×C₁₃	#575	1	2	yes	—
473	C₂²×C₁₃	#576	1	2	yes	—
474	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
475	C₄×C₁₃	—	2	2	no	—
476	C₄×C₁₃	—	2	2	no	—
477	C₄×C₁₃	—	2	2	no	—
478	C₄×C₁₃	—	2	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	4	2	no	—
484	C₄×C₁₃	#546	1	2	yes	—
485	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
486	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	4	no	—
490	C₂×#41	—	4	2	no	—
491	C₂×#41	C₂³×C₁₃	1	4	yes	—
492	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×D₄	—	2	4	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	4	2	no	—
501	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
505	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×SD₁₆	—	4	2	no	—
513	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
514	C₂×D₈	—	2	4	no	—
515	C₂×D₈	—	4	2	no	—
516	C₂×D₈	C₂³×C₁₃	1	4	yes	—
517	C₂×D₈	C₂³×C₁₃	1	4	yes	—
518	C₂×M₁₆	—	4	2	no	—
519	C₂×M₁₆	—	4	2	no	—
520	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
521	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
522	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
526	#126	—	2	8	no	—
527	#125	—	2	2	no	—
528	#125	C₂³×C₁₃	1	4	yes	complemented
529	#124	—	2	2	no	—
530	#124	C₂³×C₁₃	1	4	yes	—
531	#123	—	2	8	no	—
532	#123	—	2	8	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
535	#121	—	2	8	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	8	no	—
540	#121	C₂³×C₁₃	1	4	yes	—
541	#121	C₂³×C₁₃	1	4	yes	—
542	#121	C₂³×C₁₃	1	4	yes	complemented
543	#120	—	2	8	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	D₄×C₁₃	1	4	yes	—
548	C₄×D₄	C₂³×C₁₃	1	4	yes	—
549	C₄×D₄	C₂³×C₁₃	1	4	yes	—
550	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
551	#117	—	2	2	no	—
552	#117	C₂³×C₁₃	1	4	yes	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	8	no	—
574	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
576	C₂×C₄²	—	2	1	no	—
577	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
578	#107	C₂³×C₁₃	1	4	yes	complemented
579	#107	C₂³×C₁₃	1	4	yes	complemented
580	#106	C₂³×C₁₃	1	4	yes	complemented
581	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
582	#103	C₂³×C₁₃	1	4	yes	complemented
583	#103	C₂³×C₁₃	1	4	yes	complemented
584	#103	C₂³×C₁₃	1	4	yes	complemented
585	#102	C₂³×C₁₃	1	4	yes	—
586	#102	C₂³×C₁₃	1	4	yes	—
587	#102	C₂³×C₁₃	1	4	yes	—
588	#102	C₂³×C₁₃	1	4	yes	—
589	#102	C₂³×C₁₃	1	4	yes	—
590	#102	C₂³×C₁₃	1	4	yes	—
591	#102	C₂³×C₁₃	1	4	yes	complemented
592	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
593	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
594	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
595	C₂×C₁₃	—	4	2	no	—
596	C₂×C₁₃	—	4	2	no	—
597	C₂×C₁₃	—	4	4	no	—
598	C₂×C₁₃	—	8	2	no	—
599	C₂×C₁₃	—	8	2	no	—
600	C₂×C₁₃	#3322	1	4	yes	direct product factor
601	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
602	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
603	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	4	4	no	—
609	C₂⁴	—	4	4	no	—
610	C₂⁴	—	8	2	no	—
611	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
613	#41	—	2	8	no	—
614	#41	—	4	4	no	—
615	#41	—	4	8	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
620	C₂×D₄	—	2	8	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	8	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	8	2	no	—
641	C₂×D₄	—	8	2	no	—
642	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
643	C₂×D₄	C₁₃×#41	1	4	yes	—
644	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
646	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	4	4	no	—
661	C₂²×C₄	—	8	2	no	—
662	C₂²×C₄	—	8	2	no	—
663	C₂²×C₄	—	8	2	no	—
664	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	SD₁₆	—	4	4	no	—
674	D₈	—	2	8	no	—
675	D₈	—	4	4	no	—
676	M₁₆	—	4	4	no	—
677	M₁₆	—	4	4	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	2	2	no	—
682	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
683	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
684	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
695	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
709	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
710	C₄²	—	2	4	no	—
711	C₄²	C₂×D₄×C₁₃	1	2	yes	—
712	C₄²	C₂⁴×C₁₃	1	2	yes	—
713	C₁₃	C₂×#3322	1	1	yes	characteristic, direct product factor, Sylow
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	4	8	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	—	4	2	no	—
731	C₂³	—	4	2	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	8	4	no	—
735	C₂³	—	8	16	no	—
736	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
737	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
738	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	4	2	no	—
742	D₄	—	2	4	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	8	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	8	4	no	—
755	D₄	—	8	4	no	—
756	D₄	C₂×C₁₃×#41	1	4	yes	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
783	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
786	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
787	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
788	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
789	C₈	—	2	2	no	—
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	4	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	4	no	—
802	C₂²	—	4	8	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	16	no	—
812	C₂²	—	8	4	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₁₃×#546	1	2	yes	—
815	C₂²	C₁₃×#575	1	2	yes	—
816	C₂²	C₁₃×#576	1	2	yes	—
817	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	C₁₃×#546	1	2	yes	—
828	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
829	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂	—	4	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	4	4	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	2	no	—
835	C₂	C₁₃×#3322	1	4	yes	direct product factor
836	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
837	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
838	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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×#553	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3322	C₂	direct (N × H)
4. C₂×C₁₃×#488	C₂	semidirect
5. C₂×C₁₃×#485	C₂	semidirect
6. C₂×C₁₃×#480	C₂	semidirect
7. C₂×C₁₃×#478	C₂	semidirect
8. C₂×C₁₃×#469	C₂	semidirect
9. C₂×C₁₃×#468	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#449	C₂	semidirect
12. C₂×C₁₃×#447	C₂	semidirect
13. C₂×C₄×C₁₃×D₈	C₂	semidirect
14. C₂×C₁₃×#436	C₂	semidirect
15. C₂×C₁₃×#417	C₂	semidirect
16. C₂×C₁₃×#418	C₂	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₂²×C₁₃×M₁₆	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
27. C₁₃×#546	C₂²	semidirect
29. C₂×C₁₃×#125	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₁₃×#488	C₂²	semidirect
48. C₁₃×#485	C₂²	semidirect
49. C₁₃×#480	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#469	C₂²	semidirect
52. C₁₃×#468	C₂²	semidirect
53. C₁₃×#463	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
55. C₁₃×#447	C₂²	semidirect
56. C₄×C₁₃×D₈	C₂²	semidirect
57. C₁₃×#436	C₂²	semidirect
58. C₂×C₁₃×#107	C₂²	semidirect
59. C₂×C₁₃×#107	C₂²	semidirect
60. C₂×C₁₃×#106	C₂²	semidirect
61. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
62. C₁₃×#418	C₂²	semidirect
63. C₁₃×#417	C₂²	semidirect
64. C₂×C₁₃×#103	C₂²	semidirect
65. C₂×C₁₃×#103	C₂²	semidirect
66. C₂×C₁₃×#103	C₂²	semidirect
73. C₂×C₁₃×#102	C₂²	semidirect
75. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₄×C₈×C₁₃	C₂²	semidirect
103. C₂×C₁₃×SD₁₆	C₂³	semidirect
111. C₂×C₁₃×M₁₆	C₂³	semidirect
118. C₁₃×#125	C₂³	semidirect
132. C₁₃×#121	C₂³	semidirect
140. C₄×D₄×C₁₃	C₂³	semidirect
153. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
168. C₁₃×#107	C₂³	semidirect
169. C₁₃×#107	C₂³	semidirect
170. C₁₃×#106	C₂³	semidirect
171. C₁₃×C₄⋊C₈	C₂³	semidirect
172. C₁₃×#103	C₂³	semidirect
173. C₁₃×#103	C₂³	semidirect
174. C₁₃×#103	C₂³	semidirect
181. C₁₃×#102	C₂³	semidirect
183. C₁₃×C₂²⋊C₈	C₂³	semidirect
184. C₄×C₈×C₁₃	C₂³	semidirect
185. C₂×#3322	C₁₃	direct (N × H)
295. C₂×#553	C₂×C₁₃	semidirect
296. C₂×#546	C₂×C₁₃	semidirect
297. #3322	C₂×C₁₃	direct (N × H)
298. C₂×#488	C₂×C₁₃	semidirect
299. C₂×#485	C₂×C₁₃	semidirect
300. C₂×#480	C₂×C₁₃	semidirect
301. C₂×#478	C₂×C₁₃	semidirect
302. C₂×#469	C₂×C₁₃	semidirect
303. C₂×#468	C₂×C₁₃	semidirect
304. C₂×#463	C₂×C₁₃	semidirect
305. C₂×#449	C₂×C₁₃	semidirect
306. C₂×#447	C₂×C₁₃	semidirect
307. C₂×C₄×D₈	C₂×C₁₃	semidirect
308. C₂×#436	C₂×C₁₃	semidirect
309. C₂×#417	C₂×C₁₃	semidirect
310. C₂×#418	C₂×C₁₃	semidirect
392. C₂²×SD₁₆	C₂²×C₁₃	semidirect
396. C₂²×M₁₆	C₂²×C₁₃	semidirect
398. #553	C₂²×C₁₃	semidirect
400. #546	C₂²×C₁₃	semidirect
402. C₂×#125	C₂²×C₁₃	semidirect
411. C₂×#121	C₂²×C₁₃	semidirect
416. C₂×C₄×D₄	C₂²×C₁₃	semidirect
418. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
420. #488	C₂²×C₁₃	semidirect
421. #485	C₂²×C₁₃	semidirect
422. #480	C₂²×C₁₃	semidirect
423. #478	C₂²×C₁₃	semidirect
424. #469	C₂²×C₁₃	semidirect
425. #468	C₂²×C₁₃	semidirect
426. #463	C₂²×C₁₃	semidirect
427. #449	C₂²×C₁₃	semidirect
428. #447	C₂²×C₁₃	semidirect
429. C₄×D₈	C₂²×C₁₃	semidirect
430. #436	C₂²×C₁₃	semidirect
431. C₂×#107	C₂²×C₁₃	semidirect
432. C₂×#107	C₂²×C₁₃	semidirect
433. C₂×#106	C₂²×C₁₃	semidirect
434. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
435. #418	C₂²×C₁₃	semidirect
436. #417	C₂²×C₁₃	semidirect
437. C₂×#103	C₂²×C₁₃	semidirect
438. C₂×#103	C₂²×C₁₃	semidirect
439. C₂×#103	C₂²×C₁₃	semidirect
446. C₂×#102	C₂²×C₁₃	semidirect
448. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
449. C₂×C₄×C₈	C₂²×C₁₃	semidirect
513. C₂×SD₁₆	C₂³×C₁₃	semidirect
521. C₂×M₁₆	C₂³×C₁₃	semidirect
528. #125	C₂³×C₁₃	semidirect
542. #121	C₂³×C₁₃	semidirect
550. C₄×D₄	C₂³×C₁₃	semidirect
563. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
578. #107	C₂³×C₁₃	semidirect
579. #107	C₂³×C₁₃	semidirect
580. #106	C₂³×C₁₃	semidirect
581. C₄⋊C₈	C₂³×C₁₃	semidirect
582. #103	C₂³×C₁₃	semidirect
583. #103	C₂³×C₁₃	semidirect
584. #103	C₂³×C₁₃	semidirect
591. #102	C₂³×C₁₃	semidirect
593. C₂²⋊C₈	C₂³×C₁₃	semidirect
594. C₄×C₈	C₂³×C₁₃	semidirect
600. C₂×C₁₃	#3322	direct (N × H)
713. C₁₃	C₂×#3322	direct (N × H)
835. C₂	C₁₃×#3322	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×#553	2
C₂×C₁₃×#546	2
C₁₃×#3322	2
C₂×C₁₃×#488	2
C₂×C₁₃×#485	2
C₂×C₁₃×#480	2
C₂×C₁₃×#478	2
C₂×C₁₃×#469	2
C₂×C₁₃×#468	2
C₂×C₁₃×#463	2
C₂×C₁₃×#449	2
C₂×C₁₃×#447	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#436	2
C₂×C₁₃×#417	2
C₂×C₁₃×#418	2
C₂×#3322	13

Subgroups — C2×C13×#3322 #15747481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3322 #15747481