Subgroups — C₁₃×#61157 #15747496

Order 3328.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3328	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3320	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3312	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3095	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#419	C₂	1	2	yes	maximal, complemented
18	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#555	C₂²	1	1	yes	characteristic
24	C₁₃×#554	C₂²	1	1	yes	characteristic
25	C₁₃×#553	C₂²	1	2	yes	—
26	C₁₃×#552	—	2	1	no	—
27	C₁₃×#552	C₂²	1	2	yes	—
28	C₁₃×#551	—	2	2	no	—
29	D₄×Q₈×C₁₃	—	2	1	no	—
30	D₄×Q₈×C₁₃	—	2	2	no	—
31	D₄×Q₈×C₁₃	—	2	1	no	—
32	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
34	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₁₃×#547	C₂²	1	1	yes	characteristic
36	C₁₃×#546	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₁₃×#529	—	2	2	no	—
41	C₁₃×#529	—	2	1	no	—
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₄×C₁₃×#41	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#117	C₂²	1	2	yes	—
51	C₁₃×#491	C₂²	1	4	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#487	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#485	C₂²	1	4	yes	complemented
56	C₁₃×#484	C₂²	1	4	yes	complemented
57	C₁₃×#483	C₂²	1	4	yes	complemented
58	C₁₃×#479	C₂²	1	4	yes	complemented
59	C₁₃×#477	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#470	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#467	C₂²	1	4	yes	complemented
64	C₁₃×#465	C₂²	1	4	yes	complemented
65	C₁₃×#462	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	2	yes	complemented
67	C₁₃×#461	C₂²	1	2	yes	complemented
68	C₁₃×#461	C₂²	1	2	yes	complemented
69	C₁₃×#451	C₂²	1	4	yes	complemented
70	C₁₃×#451	C₂²	1	4	yes	complemented
71	C₁₃×#448	C₂²	1	4	yes	complemented
72	C₁₃×#448	C₂²	1	4	yes	complemented
73	C₁₃×#441	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	—
78	C₁₃×#435	C₂²	1	4	yes	—
79	C₈×D₄×C₁₃	C₂²	1	2	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#423	C₂²	1	1	yes	characteristic
83	C₁₃×#419	C₂²	1	2	yes	—
84	C₁₃×#419	C₂²	1	2	yes	—
85	C₁₃×#419	C₂²	1	2	yes	—
86	C₁₃×#419	C₂²	1	2	yes	—
87	C₁₃×#419	C₂²	1	1	yes	characteristic
88	C₁₃×#419	C₂²	1	4	yes	complemented
89	C₁₃×#419	C₂²	1	4	yes	complemented
90	C₁₃×#417	C₂²	1	1	yes	characteristic
91	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	—
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	—	2	2	no	—
100	C₂²×Q₈×C₁₃	—	2	8	no	—
101	C₂²×Q₈×C₁₃	—	4	4	no	—
102	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
104	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
105	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	—	2	2	no	—
108	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
109	C₁₃×#137	—	2	4	no	—
110	C₁₃×#137	—	4	4	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×M₁₆	—	4	4	no	—
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
120	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
121	C₁₃×C₄⋊Q₈	—	2	2	no	—
122	C₁₃×C₄⋊Q₈	—	2	2	no	—
123	C₁₃×C₄⋊Q₈	—	2	4	no	—
124	C₁₃×C₄⋊Q₈	—	2	1	no	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×#126	—	2	2	no	—
131	C₁₃×#126	—	2	2	no	—
132	C₁₃×#126	—	2	2	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	1	no	—
135	C₁₃×#125	C₂³	1	2	yes	—
136	C₁₃×#124	—	2	1	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	—	2	4	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#120	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	—	2	1	no	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₃	—	2	4	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
180	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₁₃	D₄	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	C₂³	1	1	yes	characteristic
193	C₁₃×#117	C₂³	1	2	yes	—
194	C₁₃×#117	C₂³	1	2	yes	—
195	C₁₃×#117	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
207	C₂×C₄²×C₁₃	—	2	2	no	—
208	C₂×C₄²×C₁₃	—	2	1	no	—
209	C₂×C₄²×C₁₃	—	2	1	no	—
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	2	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#103	C₂³	1	2	yes	—
226	C₁₃×#103	C₂³	1	4	yes	—
227	C₁₃×#103	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₁₃	C₂³	1	2	yes	—
233	#61157	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	1	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	2	8	no	—
246	C₂×Q₈×C₁₃	—	2	8	no	—
247	C₂×Q₈×C₁₃	—	2	4	no	—
248	C₂×Q₈×C₁₃	—	2	4	no	—
249	C₂×Q₈×C₁₃	—	4	8	no	—
250	C₂×Q₈×C₁₃	—	4	4	no	—
251	C₂×Q₈×C₁₃	—	4	4	no	—
252	C₂×Q₈×C₁₃	—	4	8	no	—
253	C₂×Q₈×C₁₃	—	4	8	no	—
254	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
255	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
256	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	1	no	—
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	4	8	no	—
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₁₃×Q₁₆	—	2	4	no	—
288	C₁₃×Q₁₆	—	4	4	no	—
289	C₁₃×SD₁₆	—	2	4	no	—
290	C₁₃×SD₁₆	—	4	4	no	—
291	C₁₃×M₁₆	—	2	2	no	—
292	C₁₃×M₁₆	—	2	2	no	—
293	C₁₃×M₁₆	—	2	4	no	—
294	C₁₃×M₁₆	—	4	4	no	—
295	C₂×C₈×C₁₃	—	4	4	no	—
296	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
297	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	4	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	1	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	—	2	1	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	1	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	2	1	no	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
354	#3475	C₂×C₁₃	1	1	yes	characteristic
355	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3329	C₂×C₁₃	1	2	yes	complemented
357	#3328	C₂×C₁₃	1	2	yes	complemented
358	#3320	C₂×C₁₃	1	4	yes	complemented
359	#3312	C₂×C₁₃	1	4	yes	complemented
360	#3299	C₂×C₁₃	1	2	yes	complemented
361	#3298	C₂×C₁₃	1	2	yes	complemented
362	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3095	C₂×C₁₃	1	2	yes	complemented
364	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3056	C₂×C₁₃	1	2	yes	complemented
366	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
367	#3004	C₂×C₁₃	1	2	yes	complemented
368	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
369	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₂×#419	C₂×C₁₃	1	2	yes	complemented
371	C₂³×C₁₃	—	2	4	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	2	1	no	—
374	C₂³×C₁₃	—	4	2	no	—
375	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
378	Q₈×C₁₃	—	2	4	no	—
379	Q₈×C₁₃	—	2	2	no	—
380	Q₈×C₁₃	—	2	1	no	—
381	Q₈×C₁₃	—	2	4	no	—
382	Q₈×C₁₃	—	2	4	no	—
383	Q₈×C₁₃	—	2	1	no	—
384	Q₈×C₁₃	—	4	8	no	—
385	Q₈×C₁₃	—	4	8	no	—
386	Q₈×C₁₃	—	4	4	no	—
387	Q₈×C₁₃	—	4	2	no	—
388	Q₈×C₁₃	—	8	1	no	—
389	Q₈×C₁₃	C₂×#41	1	4	yes	—
390	D₄×C₁₃	—	2	4	no	—
391	D₄×C₁₃	—	2	2	no	—
392	D₄×C₁₃	—	2	1	no	—
393	D₄×C₁₃	—	2	1	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	8	2	no	—
397	D₄×C₁₃	#137	1	4	yes	complemented
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	2	4	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	4	1	no	—
416	C₂×C₄×C₁₃	—	4	8	no	—
417	C₂×C₄×C₁₃	—	4	8	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	4	no	—
420	C₂×C₄×C₁₃	—	4	4	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	2	no	—
423	C₂×C₄×C₁₃	—	8	1	no	—
424	C₂×C₄×C₁₃	—	8	2	no	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
433	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
435	C₈×C₁₃	—	2	2	no	—
436	C₈×C₁₃	—	2	2	no	—
437	C₈×C₁₃	—	2	4	no	—
438	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
439	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#137	C₂²×C₁₃	1	2	yes	—
441	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
442	#556	C₂²×C₁₃	1	1	yes	characteristic
443	#555	C₂²×C₁₃	1	1	yes	characteristic
444	#554	C₂²×C₁₃	1	1	yes	characteristic
445	#553	C₂²×C₁₃	1	2	yes	—
446	#552	—	2	1	no	—
447	#552	C₂²×C₁₃	1	2	yes	—
448	#551	—	2	2	no	—
449	D₄×Q₈	—	2	1	no	—
450	D₄×Q₈	—	2	2	no	—
451	D₄×Q₈	—	2	1	no	—
452	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
453	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
454	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
455	#547	C₂²×C₁₃	1	1	yes	characteristic
456	#546	—	2	1	no	—
457	#533	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	—	2	1	no	—
459	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
460	#529	—	2	2	no	—
461	#529	—	2	1	no	—
462	#525	C₂²×C₁₃	1	2	yes	—
463	C₂×C₂²⋊Q₈	—	2	2	no	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
465	C₄×#41	—	2	1	no	—
466	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×C₄×D₄	—	2	1	no	—
469	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×#117	C₂²×C₁₃	1	2	yes	—
471	#491	C₂²×C₁₃	1	4	yes	complemented
472	#487	C₂²×C₁₃	1	2	yes	complemented
473	#487	C₂²×C₁₃	1	2	yes	complemented
474	#485	C₂²×C₁₃	1	4	yes	complemented
475	#485	C₂²×C₁₃	1	4	yes	complemented
476	#484	C₂²×C₁₃	1	4	yes	complemented
477	#483	C₂²×C₁₃	1	4	yes	complemented
478	#479	C₂²×C₁₃	1	4	yes	complemented
479	#477	C₂²×C₁₃	1	2	yes	complemented
480	#475	C₂²×C₁₃	1	2	yes	complemented
481	#470	C₂²×C₁₃	1	4	yes	complemented
482	#468	C₂²×C₁₃	1	4	yes	complemented
483	#467	C₂²×C₁₃	1	4	yes	complemented
484	#465	C₂²×C₁₃	1	4	yes	complemented
485	#462	C₂²×C₁₃	1	2	yes	complemented
486	#462	C₂²×C₁₃	1	2	yes	complemented
487	#461	C₂²×C₁₃	1	2	yes	complemented
488	#461	C₂²×C₁₃	1	2	yes	complemented
489	#451	C₂²×C₁₃	1	4	yes	complemented
490	#451	C₂²×C₁₃	1	4	yes	complemented
491	#448	C₂²×C₁₃	1	4	yes	complemented
492	#448	C₂²×C₁₃	1	4	yes	complemented
493	#441	C₂²×C₁₃	1	2	yes	complemented
494	#440	C₂²×C₁₃	1	2	yes	complemented
495	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
496	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
497	#436	C₂²×C₁₃	1	2	yes	—
498	#435	C₂²×C₁₃	1	4	yes	—
499	C₈×D₄	C₂²×C₁₃	1	2	yes	—
500	#428	C₂²×C₁₃	1	2	yes	—
501	#428	C₂²×C₁₃	1	1	yes	characteristic
502	#423	C₂²×C₁₃	1	1	yes	characteristic
503	#419	C₂²×C₁₃	1	2	yes	—
504	#419	C₂²×C₁₃	1	2	yes	—
505	#419	C₂²×C₁₃	1	2	yes	—
506	#419	C₂²×C₁₃	1	2	yes	—
507	#419	C₂²×C₁₃	1	1	yes	characteristic
508	#419	C₂²×C₁₃	1	4	yes	complemented
509	#419	C₂²×C₁₃	1	4	yes	complemented
510	#417	C₂²×C₁₃	1	1	yes	characteristic
511	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
512	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
513	#407	C₂²×C₁₃	1	2	yes	—
514	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
515	C₂²×C₁₃	—	2	1	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	4	8	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	1	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	#546	1	2	yes	—
527	C₂²×C₁₃	C₂×#137	1	4	yes	—
528	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₁₃	—	2	1	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	4	no	—
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	4	no	—
539	C₄×C₁₃	—	4	1	no	—
540	C₄×C₁₃	—	4	1	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	#546	1	2	yes	—
543	C₄×C₁₃	C₂×#137	1	2	yes	—
544	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
545	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂×#41	—	2	1	no	—
547	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
548	C₂²×Q₈	—	2	2	no	—
549	C₂²×Q₈	—	2	2	no	—
550	C₂²×Q₈	—	2	2	no	—
551	C₂²×Q₈	—	2	8	no	—
552	C₂²×Q₈	—	4	4	no	—
553	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
554	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
555	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
556	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
558	C₂³×C₄	—	2	2	no	—
559	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
560	#137	—	2	4	no	—
561	#137	—	4	4	no	—
562	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
563	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
565	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×M₁₆	—	4	4	no	—
567	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
569	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
571	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
572	C₄⋊Q₈	—	2	2	no	—
573	C₄⋊Q₈	—	2	2	no	—
574	C₄⋊Q₈	—	2	4	no	—
575	C₄⋊Q₈	—	2	1	no	—
576	C₄⋊Q₈	—	2	1	no	—
577	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
578	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
579	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
580	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	#126	—	2	2	no	—
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#125	—	2	2	no	—
585	#125	—	2	1	no	—
586	#125	C₂³×C₁₃	1	2	yes	—
587	#124	—	2	1	no	—
588	#124	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
606	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	C₂³×C₁₃	1	2	yes	—
610	#121	C₂³×C₁₃	1	2	yes	—
611	#120	—	2	2	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×Q₈	—	2	1	no	—
614	C₄×Q₈	—	2	1	no	—
615	C₄×Q₈	—	2	1	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
618	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
619	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
631	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
632	C₄×D₄	D₄×C₁₃	1	2	yes	—
633	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₁₃	1	2	yes	—
637	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
638	#117	—	2	2	no	—
639	#117	—	2	2	no	—
640	#117	—	2	1	no	—
641	#117	—	2	2	no	—
642	#117	—	2	1	no	—
643	#117	C₂³×C₁₃	1	1	yes	characteristic
644	#117	C₂³×C₁₃	1	2	yes	—
645	#117	C₂³×C₁₃	1	2	yes	—
646	#117	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	2	no	—
651	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	—	2	2	no	—
656	C₂×C₂²⋊C₄	—	2	2	no	—
657	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
658	C₂×C₄²	—	2	2	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
662	#107	C₂³×C₁₃	1	2	yes	—
663	#107	C₂³×C₁₃	1	4	yes	—
664	#106	C₂³×C₁₃	1	2	yes	—
665	#106	C₂³×C₁₃	1	4	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
668	#103	C₂³×C₁₃	1	2	yes	—
669	#103	C₂³×C₁₃	1	2	yes	—
670	#103	C₂³×C₁₃	1	4	yes	—
671	#103	C₂³×C₁₃	1	4	yes	—
672	#103	C₂³×C₁₃	1	4	yes	—
673	#103	C₂³×C₁₃	1	4	yes	—
674	#103	C₂³×C₁₃	1	4	yes	—
675	#103	C₂³×C₁₃	1	4	yes	—
676	#103	C₂³×C₁₃	1	2	yes	—
677	#103	C₂³×C₁₃	1	4	yes	—
678	#103	C₂³×C₁₃	1	4	yes	—
679	#102	C₂³×C₁₃	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
681	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
682	#97	C₂³×C₁₃	1	2	yes	—
683	C₄×C₈	C₂³×C₁₃	1	2	yes	—
684	C₂×C₁₃	—	2	2	no	—
685	C₂×C₁₃	—	2	4	no	—
686	C₂×C₁₃	—	4	2	no	—
687	C₂×C₁₃	—	8	1	no	—
688	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
689	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
690	C₂×C₁₃	#3586	1	1	yes	characteristic
691	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
692	#41	—	2	2	no	—
693	#41	—	2	2	no	—
694	#41	—	4	4	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	1	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	8	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	4	8	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	—	4	4	no	—
709	C₂×Q₈	—	4	8	no	—
710	C₂×Q₈	—	4	8	no	—
711	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
712	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
713	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
714	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	4	8	no	—
736	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	Q₁₆	—	2	4	no	—
745	Q₁₆	—	4	4	no	—
746	SD₁₆	—	2	4	no	—
747	SD₁₆	—	4	4	no	—
748	M₁₆	—	2	2	no	—
749	M₁₆	—	2	2	no	—
750	M₁₆	—	2	4	no	—
751	M₁₆	—	4	4	no	—
752	C₂×C₈	—	4	4	no	—
753	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
754	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
755	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
797	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
798	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
799	C₄²	—	2	1	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	1	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
810	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₁₃	#61157	1	1	yes	characteristic, direct product factor, Sylow
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	4	2	no	—
816	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	2	4	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	1	no	—
825	Q₈	—	4	8	no	—
826	Q₈	—	4	8	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	2	no	—
829	Q₈	—	8	1	no	—
830	Q₈	C₂×C₁₃×#41	1	4	yes	—
831	D₄	—	2	4	no	—
832	D₄	—	2	2	no	—
833	D₄	—	2	1	no	—
834	D₄	—	2	1	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	8	2	no	—
838	D₄	C₁₃×#137	1	4	yes	complemented
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	8	1	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
868	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
874	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
875	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
876	C₈	—	2	2	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	4	no	—
879	C₂²	—	2	1	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	4	8	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	C₁₃×#546	1	2	yes	—
891	C₂²	C₂×C₁₃×#137	1	4	yes	—
892	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	4	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	4	no	—
905	C₄	—	4	1	no	—
906	C₄	C₁₃×#546	1	2	yes	—
907	C₄	C₂×C₁₃×#137	1	2	yes	—
908	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
909	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂	—	2	2	no	—
911	C₂	—	2	4	no	—
912	C₂	—	4	2	no	—
913	C₂	—	8	1	no	—
914	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
915	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
916	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	C₁₃×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3328	C₂	semidirect
5. C₁₃×#3320	C₂	semidirect
6. C₁₃×#3312	C₂	semidirect
7. C₁₃×#3299	C₂	semidirect
8. C₁₃×#3298	C₂	semidirect
9. C₁₃×#3139	C₂	semidirect
10. C₁₃×#3095	C₂	semidirect
11. C₁₃×#3078	C₂	semidirect
12. C₁₃×#3056	C₂	semidirect
13. C₁₃×#3039	C₂	semidirect
14. C₁₃×#3004	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₂×C₁₃×#419	C₂	semidirect
51. C₁₃×#491	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
53. C₁₃×#487	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#485	C₂²	semidirect
56. C₁₃×#484	C₂²	semidirect
57. C₁₃×#483	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#470	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#467	C₂²	semidirect
64. C₁₃×#465	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#451	C₂²	semidirect
70. C₁₃×#451	C₂²	semidirect
71. C₁₃×#448	C₂²	semidirect
72. C₁₃×#448	C₂²	semidirect
73. C₁₃×#441	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×Q₁₆	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
88. C₁₃×#419	C₂²	semidirect
89. C₁₃×#419	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
92. C₂×C₁₃×#103	C₂²	semidirect
233. #61157	C₁₃	direct (N × H)
254. C₂×Q₈×C₁₃	#41	semidirect
355. C₂×D₄×Q₈	C₂×C₁₃	semidirect
356. #3329	C₂×C₁₃	semidirect
357. #3328	C₂×C₁₃	semidirect
358. #3320	C₂×C₁₃	semidirect
359. #3312	C₂×C₁₃	semidirect
360. #3299	C₂×C₁₃	semidirect
361. #3298	C₂×C₁₃	semidirect
362. #3139	C₂×C₁₃	semidirect
363. #3095	C₂×C₁₃	semidirect
364. #3078	C₂×C₁₃	semidirect
365. #3056	C₂×C₁₃	semidirect
366. #3039	C₂×C₁₃	semidirect
367. #3004	C₂×C₁₃	semidirect
368. C₄×#137	C₂×C₁₃	semidirect
369. D₄×M₁₆	C₂×C₁₃	semidirect
370. C₂×#419	C₂×C₁₃	semidirect
397. D₄×C₁₃	#137	semidirect
471. #491	C₂²×C₁₃	semidirect
472. #487	C₂²×C₁₃	semidirect
473. #487	C₂²×C₁₃	semidirect
474. #485	C₂²×C₁₃	semidirect
475. #485	C₂²×C₁₃	semidirect
476. #484	C₂²×C₁₃	semidirect
477. #483	C₂²×C₁₃	semidirect
478. #479	C₂²×C₁₃	semidirect
479. #477	C₂²×C₁₃	semidirect
480. #475	C₂²×C₁₃	semidirect
481. #470	C₂²×C₁₃	semidirect
482. #468	C₂²×C₁₃	semidirect
483. #467	C₂²×C₁₃	semidirect
484. #465	C₂²×C₁₃	semidirect
485. #462	C₂²×C₁₃	semidirect
486. #462	C₂²×C₁₃	semidirect
487. #461	C₂²×C₁₃	semidirect
488. #461	C₂²×C₁₃	semidirect
489. #451	C₂²×C₁₃	semidirect
490. #451	C₂²×C₁₃	semidirect
491. #448	C₂²×C₁₃	semidirect
492. #448	C₂²×C₁₃	semidirect
493. #441	C₂²×C₁₃	semidirect
494. #440	C₂²×C₁₃	semidirect
495. C₄×Q₁₆	C₂²×C₁₃	semidirect
496. C₄×SD₁₆	C₂²×C₁₃	semidirect
508. #419	C₂²×C₁₃	semidirect
509. #419	C₂²×C₁₃	semidirect
511. C₂×#103	C₂²×C₁₃	semidirect
512. C₂×#103	C₂²×C₁₃	semidirect
711. C₂×Q₈	C₁₃×#41	semidirect
811. C₁₃	#61157	direct (N × H)
838. D₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3475	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3329	2
C₁₃×#3328	2
C₁₃×#3320	2
C₁₃×#3312	2
C₁₃×#3299	2
C₁₃×#3298	2
C₁₃×#3139	2
C₁₃×#3095	2
C₁₃×#3078	2
C₁₃×#3056	2
C₁₃×#3039	2
C₁₃×#3004	2
C₄×C₁₃×#137	2
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#419	2
#61157	13

Subgroups — C13×#61157 #15747496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61157 #15747496