Subgroups — C₁₃×#61369 #15747708

Order 3328.

1750 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	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3383	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3166	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3080	C₂	1	2	yes	maximal
12	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
15	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
17	C₄×C₁₃×#137	C₂	1	2	yes	maximal
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#557	—	2	1	no	—
21	C₁₃×#557	—	2	2	no	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	1	yes	characteristic
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	4	yes	—
27	C₁₃×#557	C₂²	1	2	yes	—
28	C₁₃×#554	—	2	1	no	—
29	C₁₃×#554	—	2	2	no	—
30	C₁₃×#554	C₂²	1	1	yes	characteristic
31	C₁₃×#554	C₂²	1	2	yes	—
32	D₄×Q₈×C₁₃	—	2	1	no	—
33	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#533	—	2	2	no	—
35	C₁₃×#533	—	2	1	no	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	2	yes	—
38	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#125	—	2	2	no	—
41	C₂×C₁₃×#125	C₂²	1	2	yes	—
42	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×#41	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#501	C₂²	1	4	yes	—
50	C₁₃×#501	C₂²	1	4	yes	—
51	C₁₃×#501	C₂²	1	4	yes	—
52	C₁₃×#500	C₂²	1	2	yes	—
53	C₁₃×#499	C₂²	1	4	yes	—
54	C₁₃×#499	C₂²	1	4	yes	—
55	C₁₃×#498	C₂²	1	2	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#479	C₂²	1	4	yes	—
59	C₁₃×#479	C₂²	1	4	yes	—
60	C₁₃×#479	C₂²	1	4	yes	—
61	C₁₃×#478	C₂²	1	4	yes	—
62	C₁₃×#478	C₂²	1	4	yes	—
63	C₁₃×#477	C₂²	1	2	yes	—
64	C₁₃×#477	C₂²	1	4	yes	—
65	C₁₃×#477	C₂²	1	2	yes	—
66	C₁₃×#476	C₂²	1	2	yes	—
67	C₁₃×#475	C₂²	1	2	yes	—
68	C₁₃×#475	C₂²	1	4	yes	—
69	C₁₃×#475	C₂²	1	2	yes	—
70	C₁₃×#474	C₂²	1	2	yes	—
71	C₁₃×#446	C₂²	1	2	yes	—
72	C₁₃×#446	C₂²	1	4	yes	—
73	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
74	C₁₃×#441	C₂²	1	4	yes	—
75	C₁₃×#441	C₂²	1	2	yes	—
76	C₁₃×#440	C₂²	1	4	yes	—
77	C₁₃×#440	C₂²	1	2	yes	—
78	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
82	C₁₃×#428	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	2	yes	—
85	C₁₃×#428	C₂²	1	2	yes	—
86	C₁₃×#428	C₂²	1	1	yes	characteristic
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	—
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#419	C₂²	1	1	yes	characteristic
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#137	Q₈	1	8	yes	complemented
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	4	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	—	2	2	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×#125	—	2	4	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	C₂³	1	4	yes	—
131	C₁₃×#125	C₂³	1	4	yes	—
132	C₁₃×#125	C₂³	1	2	yes	—
133	C₁₃×#125	C₂³	1	2	yes	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	4	no	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	D₄	1	2	yes	—
162	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	—	2	1	no	—
184	C₁₃×#117	C₂³	1	1	yes	characteristic
185	C₁₃×#117	C₂³	1	2	yes	—
186	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	—	2	2	no	—
198	C₂×C₄²×C₁₃	—	2	1	no	—
199	C₂×C₄²×C₁₃	—	2	2	no	—
200	C₂×C₄²×C₁₃	—	2	1	no	—
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#107	C₂³	1	4	yes	—
207	C₁₃×#107	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	4	yes	—
212	C₁₃×#106	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	2	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	C₄×C₈×C₁₃	C₂³	1	4	yes	—
229	#61369	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₃×#41	—	2	2	no	—
231	C₁₃×#41	C₂×Q₈	1	4	yes	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	4	2	no	—
241	C₂×Q₈×C₁₃	—	4	4	no	—
242	C₂×Q₈×C₁₃	—	4	4	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	complemented
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×Q₁₆	C₂×Q₈	1	8	yes	complemented
265	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
266	C₁₃×M₁₆	—	2	2	no	—
267	C₁₃×M₁₆	—	2	4	no	—
268	C₁₃×M₁₆	C₂×Q₈	1	4	yes	complemented
269	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
271	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	—	2	1	no	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	1	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	1	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	C₂×D₄	1	2	yes	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic
336	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3390	C₂×C₁₃	1	4	yes	complemented
338	#3388	C₂×C₁₃	1	4	yes	complemented
339	#3387	C₂×C₁₃	1	2	yes	complemented
340	#3386	C₂×C₁₃	1	2	yes	complemented
341	#3383	C₂×C₁₃	1	2	yes	complemented
342	#3381	C₂×C₁₃	1	2	yes	complemented
343	#3166	C₂×C₁₃	1	2	yes	complemented
344	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3080	C₂×C₁₃	1	2	yes	—
346	#3079	C₂×C₁₃	1	1	yes	characteristic
347	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3078	C₂×C₁₃	1	2	yes	complemented
349	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
351	C₄×#137	C₂×C₁₃	1	2	yes	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₁₃	—	2	4	no	—
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	2	2	no	—
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	1	no	—
359	Q₈×C₁₃	—	4	2	no	—
360	Q₈×C₁₃	—	4	4	no	—
361	Q₈×C₁₃	—	4	4	no	—
362	Q₈×C₁₃	—	4	2	no	—
363	Q₈×C₁₃	—	4	4	no	—
364	Q₈×C₁₃	—	8	2	no	—
365	Q₈×C₁₃	—	8	1	no	—
366	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
367	Q₈×C₁₃	C₂²×Q₈	1	2	yes	—
368	D₄×C₁₃	—	2	4	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	C₂²×Q₈	1	2	yes	—
371	C₂×C₄×C₁₃	—	2	4	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	4	no	—
382	C₂×C₄×C₁₃	—	4	2	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	4	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	4	4	no	—
388	C₂×C₄×C₁₃	—	4	2	no	—
389	C₂×C₄×C₁₃	—	8	2	no	—
390	C₂×C₄×C₁₃	—	8	1	no	—
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
401	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
402	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	2	4	no	—
405	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
406	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
407	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
408	#557	—	2	1	no	—
409	#557	—	2	2	no	—
410	#557	—	2	1	no	—
411	#557	C₂²×C₁₃	1	2	yes	—
412	#557	C₂²×C₁₃	1	1	yes	characteristic
413	#557	C₂²×C₁₃	1	2	yes	—
414	#557	C₂²×C₁₃	1	4	yes	—
415	#557	C₂²×C₁₃	1	2	yes	—
416	#554	—	2	1	no	—
417	#554	—	2	2	no	—
418	#554	C₂²×C₁₃	1	1	yes	characteristic
419	#554	C₂²×C₁₃	1	2	yes	—
420	D₄×Q₈	—	2	1	no	—
421	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
422	#533	—	2	2	no	—
423	#533	—	2	1	no	—
424	#533	C₂²×C₁₃	1	1	yes	characteristic
425	#533	C₂²×C₁₃	1	2	yes	—
426	C₂×C₄⋊Q₈	—	2	1	no	—
427	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#125	—	2	2	no	—
429	C₂×#125	C₂²×C₁₃	1	2	yes	—
430	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
431	C₄×#41	C₂²×C₁₃	1	2	yes	—
432	C₂×C₄×Q₈	—	2	1	no	—
433	C₂×C₄×Q₈	—	2	1	no	—
434	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
435	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
437	#501	C₂²×C₁₃	1	4	yes	—
438	#501	C₂²×C₁₃	1	4	yes	—
439	#501	C₂²×C₁₃	1	4	yes	—
440	#500	C₂²×C₁₃	1	2	yes	—
441	#499	C₂²×C₁₃	1	4	yes	—
442	#499	C₂²×C₁₃	1	4	yes	—
443	#498	C₂²×C₁₃	1	2	yes	—
444	#479	C₂²×C₁₃	1	4	yes	—
445	#479	C₂²×C₁₃	1	4	yes	—
446	#479	C₂²×C₁₃	1	4	yes	—
447	#479	C₂²×C₁₃	1	4	yes	—
448	#479	C₂²×C₁₃	1	4	yes	—
449	#478	C₂²×C₁₃	1	4	yes	—
450	#478	C₂²×C₁₃	1	4	yes	—
451	#477	C₂²×C₁₃	1	2	yes	—
452	#477	C₂²×C₁₃	1	4	yes	—
453	#477	C₂²×C₁₃	1	2	yes	—
454	#476	C₂²×C₁₃	1	2	yes	—
455	#475	C₂²×C₁₃	1	2	yes	—
456	#475	C₂²×C₁₃	1	4	yes	—
457	#475	C₂²×C₁₃	1	2	yes	—
458	#474	C₂²×C₁₃	1	2	yes	—
459	#446	C₂²×C₁₃	1	2	yes	—
460	#446	C₂²×C₁₃	1	4	yes	—
461	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
462	#441	C₂²×C₁₃	1	4	yes	—
463	#441	C₂²×C₁₃	1	2	yes	—
464	#440	C₂²×C₁₃	1	4	yes	—
465	#440	C₂²×C₁₃	1	2	yes	—
466	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
467	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
468	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
469	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
470	#428	C₂²×C₁₃	1	2	yes	—
471	#428	C₂²×C₁₃	1	2	yes	—
472	#428	C₂²×C₁₃	1	2	yes	—
473	#428	C₂²×C₁₃	1	2	yes	—
474	#428	C₂²×C₁₃	1	1	yes	characteristic
475	#423	C₂²×C₁₃	1	1	yes	characteristic
476	#423	C₂²×C₁₃	1	2	yes	—
477	#419	C₂²×C₁₃	1	2	yes	—
478	#419	C₂²×C₁₃	1	1	yes	characteristic
479	#417	C₂²×C₁₃	1	2	yes	—
480	#417	C₂²×C₁₃	1	1	yes	characteristic
481	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
482	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	1	no	—
485	C₂²×C₁₃	—	2	2	no	—
486	C₂²×C₁₃	—	4	1	no	—
487	C₂²×C₁₃	—	4	1	no	—
488	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
489	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	—	2	1	no	—
492	C₄×C₁₃	—	2	2	no	—
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	2	4	no	—
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	2	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	4	2	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	1	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	1	no	—
504	C₄×C₁₃	—	4	4	no	—
505	C₄×C₁₃	D₄×Q₈	1	2	yes	—
506	C₄×C₁₃	#575	1	2	yes	—
507	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
508	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
509	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×Q₈	—	2	1	no	—
511	C₂²×Q₈	—	2	1	no	—
512	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
514	#137	Q₈×C₁₃	1	8	yes	complemented
515	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
516	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
517	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
519	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
520	C₄⋊Q₈	—	2	2	no	—
521	C₄⋊Q₈	—	2	2	no	—
522	C₄⋊Q₈	—	2	4	no	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	#125	—	2	4	no	—
536	#125	—	2	4	no	—
537	#125	—	2	4	no	—
538	#125	—	2	4	no	—
539	#125	—	2	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₁₃	1	4	yes	—
545	#125	C₂³×C₁₃	1	4	yes	—
546	#125	C₂³×C₁₃	1	2	yes	—
547	#125	C₂³×C₁₃	1	2	yes	—
548	#125	C₂³×C₁₃	1	2	yes	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	4	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
575	C₄×Q₈	D₄×C₁₃	1	2	yes	—
576	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
577	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
578	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
579	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
580	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
581	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
585	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×D₄	C₂³×C₁₃	1	2	yes	—
594	C₄×D₄	C₂³×C₁₃	1	2	yes	—
595	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
596	#117	—	2	2	no	—
597	#117	—	2	1	no	—
598	#117	C₂³×C₁₃	1	1	yes	characteristic
599	#117	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	—	2	2	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	2	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	—	2	2	no	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	—	2	2	no	—
614	C₂×C₄²	—	2	1	no	—
615	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
617	#107	C₂³×C₁₃	1	2	yes	—
618	#107	C₂³×C₁₃	1	4	yes	—
619	#107	C₂³×C₁₃	1	4	yes	—
620	#107	C₂³×C₁₃	1	4	yes	—
621	#107	C₂³×C₁₃	1	4	yes	—
622	#106	C₂³×C₁₃	1	4	yes	—
623	#106	C₂³×C₁₃	1	2	yes	—
624	#106	C₂³×C₁₃	1	4	yes	—
625	#106	C₂³×C₁₃	1	4	yes	—
626	#106	C₂³×C₁₃	1	4	yes	—
627	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
628	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
630	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
631	#103	C₂³×C₁₃	1	4	yes	—
632	#103	C₂³×C₁₃	1	2	yes	—
633	#103	C₂³×C₁₃	1	4	yes	—
634	#103	C₂³×C₁₃	1	2	yes	—
635	#103	C₂³×C₁₃	1	2	yes	—
636	#103	C₂³×C₁₃	1	4	yes	—
637	#102	C₂³×C₁₃	1	4	yes	—
638	#102	C₂³×C₁₃	1	2	yes	—
639	#97	C₂³×C₁₃	1	2	yes	—
640	#97	C₂³×C₁₃	1	4	yes	—
641	C₄×C₈	C₂³×C₁₃	1	2	yes	—
642	C₄×C₈	C₂³×C₁₃	1	4	yes	—
643	C₂×C₁₃	—	2	2	no	—
644	C₂×C₁₃	—	4	2	no	—
645	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
646	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
647	C₂×C₁₃	#3586	1	1	yes	characteristic
648	#41	—	2	2	no	—
649	#41	C₂×Q₈×C₁₃	1	4	yes	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	4	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
664	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	complemented
665	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	Q₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
683	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
684	M₁₆	—	2	2	no	—
685	M₁₆	—	2	4	no	—
686	M₁₆	C₂×Q₈×C₁₃	1	4	yes	complemented
687	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
688	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
689	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	1	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	4	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	C₂×D₄×C₁₃	1	2	yes	—
746	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₁₃	1	2	yes	—
748	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄²	C₂⁴×C₁₃	1	2	yes	—
750	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄²	C₂⁴×C₁₃	1	2	yes	—
752	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₁₃	#61369	1	1	yes	characteristic, direct product factor, Sylow
754	C₂³	—	2	1	no	—
755	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	4	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	2	no	—
765	Q₈	—	4	4	no	—
766	Q₈	—	8	2	no	—
767	Q₈	—	8	1	no	—
768	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
769	Q₈	C₂²×Q₈×C₁₃	1	2	yes	—
770	D₄	—	2	4	no	—
771	D₄	—	2	1	no	—
772	D₄	C₂²×Q₈×C₁₃	1	2	yes	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	2	no	—
792	C₂×C₄	—	8	1	no	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
803	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
804	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
805	C₈	—	2	2	no	—
806	C₈	—	2	4	no	—
807	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
814	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
815	C₄	—	2	1	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	4	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	D₄×Q₈×C₁₃	1	2	yes	—
831	C₄	C₁₃×#575	1	2	yes	—
832	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
833	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
834	C₂	—	2	2	no	—
835	C₂	—	4	2	no	—
836	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
837	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
838	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3388	C₂	semidirect
5. C₁₃×#3387	C₂	semidirect
6. C₁₃×#3386	C₂	semidirect
7. C₁₃×#3383	C₂	semidirect
8. C₁₃×#3381	C₂	semidirect
9. C₁₃×#3166	C₂	semidirect
10. C₁₃×#3165	C₂	semidirect
13. C₁₃×#3078	C₂	semidirect
14. C₁₃×#3078	C₂	semidirect
15. Q₈×C₁₃×M₁₆	C₂	semidirect
100. C₁₃×#137	Q₈	semidirect
229. #61369	C₁₃	direct (N × H)
246. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
264. C₁₃×Q₁₆	C₂×Q₈	semidirect
265. C₁₃×SD₁₆	C₂×Q₈	semidirect
268. C₁₃×M₁₆	C₂×Q₈	semidirect
336. C₂×#557	C₂×C₁₃	semidirect
337. #3390	C₂×C₁₃	semidirect
338. #3388	C₂×C₁₃	semidirect
339. #3387	C₂×C₁₃	semidirect
340. #3386	C₂×C₁₃	semidirect
341. #3383	C₂×C₁₃	semidirect
342. #3381	C₂×C₁₃	semidirect
343. #3166	C₂×C₁₃	semidirect
344. #3165	C₂×C₁₃	semidirect
347. #3078	C₂×C₁₃	semidirect
348. #3078	C₂×C₁₃	semidirect
349. Q₈×M₁₆	C₂×C₁₃	semidirect
514. #137	Q₈×C₁₃	semidirect
664. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
682. Q₁₆	C₂×Q₈×C₁₃	semidirect
683. SD₁₆	C₂×Q₈×C₁₃	semidirect
686. M₁₆	C₂×Q₈×C₁₃	semidirect
753. C₁₃	#61369	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×#41	2
C₂×C₁₃×#557	2
C₁₃×#3390	2
C₁₃×#3388	2
C₁₃×#3387	2
C₁₃×#3386	2
C₁₃×#3383	2
C₁₃×#3381	2
C₁₃×#3166	2
C₁₃×#3165	2
C₁₃×#3080	2
C₁₃×#3079	2
C₁₃×#3078	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×#137	2
#61369	13

Subgroups — C13×#61369 #15747708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61369 #15747708