Subgroups — C₁₃×#61602 #15747941

Order 3328.

2084 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3328	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3312	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3270	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3195	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#451	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
21	C₁₃×#556	C₂²	1	1	yes	characteristic
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#552	C₂²	1	2	yes	—
24	C₁₃×#551	—	2	2	no	—
25	D₄×Q₈×C₁₃	—	2	1	no	—
26	D₄×Q₈×C₁₃	—	2	2	no	—
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#547	C₂²	1	1	yes	characteristic
34	C₁₃×#547	C₂²	1	1	yes	characteristic
35	C₁₃×#546	—	2	1	no	—
36	C₁₃×#542	—	2	1	no	—
37	C₁₃×#539	—	2	2	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#529	C₂²	1	1	yes	characteristic
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	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₁₃×#520	—	2	1	no	—
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	C₁₃×#497	C₂²	1	2	yes	complemented
51	C₁₃×#494	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	2	yes	complemented
53	C₁₃×#487	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#483	C₂²	1	1	yes	characteristic
56	C₁₃×#483	C₂²	1	2	yes	—
57	C₁₃×#483	C₂²	1	4	yes	complemented
58	C₁₃×#480	C₂²	1	1	yes	characteristic
59	C₁₃×#479	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#470	C₂²	1	4	yes	complemented
62	C₁₃×#470	C₂²	1	4	yes	complemented
63	C₁₃×#467	C₂²	1	4	yes	complemented
64	C₁₃×#465	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#462	C₂²	1	2	yes	complemented
69	C₁₃×#461	C₂²	1	2	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#451	C₂²	1	1	yes	characteristic
72	C₁₃×#451	C₂²	1	2	yes	—
73	C₁₃×#451	C₂²	1	2	yes	—
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#451	C₂²	1	2	yes	—
76	C₁₃×#451	C₂²	1	4	yes	complemented
77	C₁₃×#451	C₂²	1	4	yes	complemented
78	C₁₃×#451	C₂²	1	4	yes	complemented
79	C₁₃×#451	C₂²	1	4	yes	complemented
80	C₁₃×#448	C₂²	1	1	yes	characteristic
81	C₁₃×#448	C₂²	1	2	yes	—
82	C₁₃×#448	C₂²	1	4	yes	complemented
83	C₁₃×#441	C₂²	1	4	yes	complemented
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₁₃×#436	C₂²	1	2	yes	—
87	C₁₃×#435	C₂²	1	4	yes	—
88	C₈×D₄×C₁₃	C₂²	1	2	yes	—
89	C₁₃×#432	C₂²	1	1	yes	characteristic
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#419	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	—
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
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	—	4	8	no	—
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
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	—	4	8	no	—
110	C₂×C₁₃×Q₁₆	—	4	8	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
120	C₁₃×C₄⋊Q₈	—	2	2	no	—
121	C₁₃×C₄⋊Q₈	—	2	4	no	—
122	C₁₃×C₄⋊Q₈	—	2	2	no	—
123	C₁₃×C₄⋊Q₈	—	2	1	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	1	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	1	no	—
135	C₁₃×#125	C₂³	1	1	yes	characteristic
136	C₁₃×#124	—	2	1	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	C₂³	1	1	yes	characteristic
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	1	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	4	no	—
152	C₁₃×C₂²⋊Q₈	—	2	4	no	—
153	C₁₃×C₂²⋊Q₈	—	2	4	no	—
154	C₁₃×C₂²⋊Q₈	—	2	4	no	—
155	C₁₃×C₂²⋊Q₈	—	2	2	no	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
163	C₁₃×#121	—	2	2	no	—
164	C₁₃×#121	—	2	1	no	—
165	C₁₃×#121	C₂³	1	1	yes	characteristic
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#120	—	2	2	no	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	1	no	—
171	C₄×Q₈×C₁₃	—	2	1	no	—
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×D₄×C₁₃	—	2	4	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₃	D₄	1	2	yes	—
186	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×#106	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	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	4	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₁₃	C₂³	1	2	yes	—
231	#61602	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
233	C₁₃×#41	—	4	4	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₂×Q₈×C₁₃	—	2	4	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	4	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	8	no	—
243	C₂×Q₈×C₁₃	—	2	8	no	—
244	C₂×Q₈×C₁₃	—	4	4	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	—	4	4	no	—
247	C₂×Q₈×C₁₃	—	4	8	no	—
248	C₂×Q₈×C₁₃	—	4	4	no	—
249	C₂×Q₈×C₁₃	—	4	8	no	—
250	C₂×Q₈×C₁₃	—	4	8	no	—
251	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
252	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
254	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	4	4	no	—
273	C₂²×C₄×C₁₃	—	4	8	no	—
274	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₁₃×Q₁₆	—	2	4	no	—
283	C₁₃×Q₁₆	—	2	8	no	—
284	C₁₃×Q₁₆	—	4	4	no	—
285	C₁₃×Q₁₆	—	4	4	no	—
286	C₁₃×Q₁₆	—	4	4	no	—
287	C₁₃×SD₁₆	—	2	4	no	—
288	C₁₃×SD₁₆	—	4	4	no	—
289	C₁₃×M₁₆	—	4	4	no	—
290	C₂×C₈×C₁₃	—	4	4	no	—
291	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
293	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
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	—	2	1	no	—
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	1	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	1	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	1	no	—
316	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
317	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
318	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
321	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	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	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	1	no	—
332	C₁₃×C₂²⋊C₄	—	2	1	no	—
333	C₁₃×C₂²⋊C₄	—	2	1	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	—	2	2	no	—
341	C₄²×C₁₃	—	2	2	no	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	1	no	—
345	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
349	#3520	C₂×C₁₃	1	1	yes	characteristic
350	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3328	C₂×C₁₃	1	2	yes	complemented
352	#3312	C₂×C₁₃	1	4	yes	complemented
353	#3298	C₂×C₁₃	1	2	yes	complemented
354	D₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
355	#3276	C₂×C₁₃	1	2	yes	complemented
356	#3270	C₂×C₁₃	1	4	yes	complemented
357	#3218	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3195	C₂×C₁₃	1	2	yes	complemented
360	#3190	C₂×C₁₃	1	2	yes	complemented
361	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3004	C₂×C₁₃	1	2	yes	complemented
364	C₂×#451	C₂×C₁₃	1	2	yes	complemented
365	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₂³×C₁₃	—	2	4	no	—
367	C₂³×C₁₃	—	2	4	no	—
368	C₂³×C₁₃	—	2	1	no	—
369	C₂³×C₁₃	—	4	2	no	—
370	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	Q₈×C₁₃	—	2	4	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	4	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	2	4	no	—
378	Q₈×C₁₃	—	2	4	no	—
379	Q₈×C₁₃	—	4	8	no	—
380	Q₈×C₁₃	—	4	8	no	—
381	Q₈×C₁₃	—	4	4	no	—
382	Q₈×C₁₃	—	4	2	no	—
383	Q₈×C₁₃	—	8	2	no	—
384	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
385	D₄×C₁₃	—	2	4	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	4	4	no	—
389	D₄×C₁₃	—	4	2	no	—
390	D₄×C₁₃	—	8	2	no	—
391	D₄×C₁₃	#137	1	4	yes	complemented
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	2	4	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	4	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	4	8	no	—
410	C₂×C₄×C₁₃	—	4	8	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	8	2	no	—
416	C₂×C₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
425	C₈×C₁₃	—	2	2	no	—
426	C₈×C₁₃	—	2	4	no	—
427	C₈×C₁₃	—	2	2	no	—
428	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
429	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
430	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
431	#556	C₂²×C₁₃	1	1	yes	characteristic
432	#554	—	2	1	no	—
433	#552	C₂²×C₁₃	1	2	yes	—
434	#551	—	2	2	no	—
435	D₄×Q₈	—	2	1	no	—
436	D₄×Q₈	—	2	2	no	—
437	D₄×Q₈	—	2	1	no	—
438	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
439	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
440	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
441	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	#548	C₂²×C₁₃	1	2	yes	—
443	#547	C₂²×C₁₃	1	1	yes	characteristic
444	#547	C₂²×C₁₃	1	1	yes	characteristic
445	#546	—	2	1	no	—
446	#542	—	2	1	no	—
447	#539	—	2	2	no	—
448	#533	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	—	2	1	no	—
450	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	#529	C₂²×C₁₃	1	1	yes	characteristic
452	#525	C₂²×C₁₃	1	2	yes	—
453	C₂×C₂²⋊Q₈	—	2	2	no	—
454	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
455	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
456	#520	—	2	1	no	—
457	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×D₄	—	2	1	no	—
459	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
460	#497	C₂²×C₁₃	1	2	yes	complemented
461	#494	C₂²×C₁₃	1	2	yes	complemented
462	#491	C₂²×C₁₃	1	2	yes	complemented
463	#487	C₂²×C₁₃	1	2	yes	complemented
464	#485	C₂²×C₁₃	1	4	yes	complemented
465	#483	C₂²×C₁₃	1	1	yes	characteristic
466	#483	C₂²×C₁₃	1	2	yes	—
467	#483	C₂²×C₁₃	1	4	yes	complemented
468	#480	C₂²×C₁₃	1	1	yes	characteristic
469	#479	C₂²×C₁₃	1	2	yes	complemented
470	#475	C₂²×C₁₃	1	2	yes	complemented
471	#470	C₂²×C₁₃	1	4	yes	complemented
472	#470	C₂²×C₁₃	1	4	yes	complemented
473	#467	C₂²×C₁₃	1	4	yes	complemented
474	#465	C₂²×C₁₃	1	4	yes	complemented
475	#464	C₂²×C₁₃	1	2	yes	complemented
476	#462	C₂²×C₁₃	1	2	yes	complemented
477	#462	C₂²×C₁₃	1	2	yes	complemented
478	#462	C₂²×C₁₃	1	4	yes	complemented
479	#461	C₂²×C₁₃	1	2	yes	complemented
480	#452	C₂²×C₁₃	1	4	yes	complemented
481	#451	C₂²×C₁₃	1	1	yes	characteristic
482	#451	C₂²×C₁₃	1	2	yes	—
483	#451	C₂²×C₁₃	1	2	yes	—
484	#451	C₂²×C₁₃	1	2	yes	—
485	#451	C₂²×C₁₃	1	2	yes	—
486	#451	C₂²×C₁₃	1	4	yes	complemented
487	#451	C₂²×C₁₃	1	4	yes	complemented
488	#451	C₂²×C₁₃	1	4	yes	complemented
489	#451	C₂²×C₁₃	1	4	yes	complemented
490	#448	C₂²×C₁₃	1	1	yes	characteristic
491	#448	C₂²×C₁₃	1	2	yes	—
492	#448	C₂²×C₁₃	1	4	yes	complemented
493	#441	C₂²×C₁₃	1	4	yes	complemented
494	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
495	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
496	#436	C₂²×C₁₃	1	2	yes	—
497	#435	C₂²×C₁₃	1	4	yes	—
498	C₈×D₄	C₂²×C₁₃	1	2	yes	—
499	#432	C₂²×C₁₃	1	1	yes	characteristic
500	#431	C₂²×C₁₃	1	1	yes	characteristic
501	#419	C₂²×C₁₃	1	4	yes	complemented
502	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
503	#407	C₂²×C₁₃	1	2	yes	—
504	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	2	2	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	4	8	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	1	no	—
515	C₂²×C₁₃	—	4	1	no	—
516	C₂²×C₁₃	C₂×#137	1	4	yes	—
517	C₂²×C₁₃	#578	1	2	yes	—
518	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₁₃	—	2	4	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	4	4	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	—	4	2	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	C₂×#137	1	2	yes	—
534	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
535	C₂×#41	—	2	1	no	—
536	C₂×#41	C₂³×C₁₃	1	2	yes	—
537	C₂²×Q₈	—	2	2	no	—
538	C₂²×Q₈	—	2	2	no	—
539	C₂²×Q₈	—	2	2	no	—
540	C₂²×Q₈	—	4	8	no	—
541	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
543	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
544	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
545	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
547	C₂³×C₄	—	2	2	no	—
548	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
549	#137	—	4	8	no	—
550	C₂×Q₁₆	—	4	8	no	—
551	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
552	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
553	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
554	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
555	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
556	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
559	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
560	C₄⋊Q₈	—	2	2	no	—
561	C₄⋊Q₈	—	2	4	no	—
562	C₄⋊Q₈	—	2	2	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#126	—	2	1	no	—
573	#125	—	2	2	no	—
574	#125	—	2	1	no	—
575	#125	C₂³×C₁₃	1	1	yes	characteristic
576	#124	—	2	1	no	—
577	#124	—	2	2	no	—
578	#124	C₂³×C₁₃	1	1	yes	characteristic
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	1	no	—
582	#123	—	2	2	no	—
583	#123	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	1	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	C₂²⋊Q₈	—	2	4	no	—
593	C₂²⋊Q₈	—	2	4	no	—
594	C₂²⋊Q₈	—	2	4	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
601	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
603	#121	—	2	2	no	—
604	#121	—	2	1	no	—
605	#121	C₂³×C₁₃	1	1	yes	characteristic
606	#121	C₂³×C₁₃	1	2	yes	—
607	#120	—	2	2	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
613	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
614	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
625	C₄×D₄	D₄×C₁₃	1	2	yes	—
626	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₁₃	1	2	yes	—
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	—	2	1	no	—
634	#117	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₂²⋊C₄	—	2	2	no	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	#107	C₂³×C₁₃	1	2	yes	—
650	#106	C₂³×C₁₃	1	2	yes	—
651	#106	C₂³×C₁₃	1	4	yes	—
652	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
654	#103	C₂³×C₁₃	1	2	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	2	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#103	C₂³×C₁₃	1	4	yes	—
661	#103	C₂³×C₁₃	1	2	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
665	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
667	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
668	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
669	#97	C₂³×C₁₃	1	2	yes	—
670	C₄×C₈	C₂³×C₁₃	1	2	yes	—
671	C₂×C₁₃	—	2	2	no	—
672	C₂×C₁₃	—	2	4	no	—
673	C₂×C₁₃	—	4	2	no	—
674	C₂×C₁₃	—	8	1	no	—
675	C₂×C₁₃	#3484	1	1	yes	characteristic
676	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
677	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
678	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	8	no	—
689	C₂×Q₈	—	2	8	no	—
690	C₂×Q₈	—	4	4	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	4	no	—
693	C₂×Q₈	—	4	8	no	—
694	C₂×Q₈	—	4	4	no	—
695	C₂×Q₈	—	4	8	no	—
696	C₂×Q₈	—	4	8	no	—
697	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
698	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
708	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	4	4	no	—
719	C₂²×C₄	—	4	8	no	—
720	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
728	Q₁₆	—	2	4	no	—
729	Q₁₆	—	2	8	no	—
730	Q₁₆	—	4	4	no	—
731	Q₁₆	—	4	4	no	—
732	Q₁₆	—	4	4	no	—
733	SD₁₆	—	2	4	no	—
734	SD₁₆	—	4	4	no	—
735	M₁₆	—	4	4	no	—
736	C₂×C₈	—	4	4	no	—
737	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
738	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
739	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
783	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	1	no	—
791	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
792	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
793	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₁₃	#61602	1	1	yes	characteristic, direct product factor, Sylow
796	C₂³	—	2	4	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	4	2	no	—
800	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
801	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
802	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	4	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	2	4	no	—
808	Q₈	—	2	4	no	—
809	Q₈	—	4	8	no	—
810	Q₈	—	4	8	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	4	2	no	—
813	Q₈	—	8	2	no	—
814	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
815	D₄	—	2	4	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	2	no	—
820	D₄	—	8	2	no	—
821	D₄	C₁₃×#137	1	4	yes	complemented
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	4	8	no	—
840	C₂×C₄	—	4	8	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	8	2	no	—
846	C₂×C₄	—	8	2	no	—
847	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
850	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
854	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
855	C₈	—	2	2	no	—
856	C₈	—	2	4	no	—
857	C₈	—	2	2	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	4	8	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	C₂×C₁₃×#137	1	4	yes	—
870	C₂²	C₁₃×#578	1	2	yes	—
871	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	2	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	4	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	1	no	—
886	C₄	C₂×C₁₃×#137	1	2	yes	—
887	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
888	C₂	—	2	2	no	—
889	C₂	—	2	4	no	—
890	C₂	—	4	2	no	—
891	C₂	—	8	1	no	—
892	C₂	C₁₃×#3484	1	1	yes	characteristic
893	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
894	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3520	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×#3328	C₂	semidirect
4. C₁₃×#3312	C₂	semidirect
5. C₁₃×#3298	C₂	semidirect
6. D₄×C₁₃×Q₁₆	C₂	semidirect
7. C₁₃×#3276	C₂	semidirect
8. C₁₃×#3270	C₂	semidirect
9. C₁₃×#3218	C₂	semidirect
10. C₁₃×#3209	C₂	semidirect
11. C₁₃×#3195	C₂	semidirect
12. C₁₃×#3190	C₂	semidirect
13. C₁₃×#3113	C₂	semidirect
14. C₁₃×#3108	C₂	semidirect
15. C₁₃×#3004	C₂	semidirect
16. C₂×C₁₃×#451	C₂	semidirect
17. C₁₃×#2974	C₂	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂²×C₁₃×Q₁₆	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
51. C₁₃×#494	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
53. C₁₃×#487	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
57. C₁₃×#483	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#470	C₂²	semidirect
62. C₁₃×#470	C₂²	semidirect
63. C₁₃×#467	C₂²	semidirect
64. C₁₃×#465	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#461	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
76. C₁₃×#451	C₂²	semidirect
77. C₁₃×#451	C₂²	semidirect
78. C₁₃×#451	C₂²	semidirect
79. C₁₃×#451	C₂²	semidirect
82. C₁₃×#448	C₂²	semidirect
83. C₁₃×#441	C₂²	semidirect
84. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
91. C₁₃×#419	C₂²	semidirect
92. C₂×C₁₃×#103	C₂²	semidirect
231. #61602	C₁₃	direct (N × H)
350. C₂×D₄×Q₈	C₂×C₁₃	semidirect
351. #3328	C₂×C₁₃	semidirect
352. #3312	C₂×C₁₃	semidirect
353. #3298	C₂×C₁₃	semidirect
354. D₄×Q₁₆	C₂×C₁₃	semidirect
355. #3276	C₂×C₁₃	semidirect
356. #3270	C₂×C₁₃	semidirect
357. #3218	C₂×C₁₃	semidirect
358. #3209	C₂×C₁₃	semidirect
359. #3195	C₂×C₁₃	semidirect
360. #3190	C₂×C₁₃	semidirect
361. #3113	C₂×C₁₃	semidirect
362. #3108	C₂×C₁₃	semidirect
363. #3004	C₂×C₁₃	semidirect
364. C₂×#451	C₂×C₁₃	semidirect
365. #2974	C₂×C₁₃	semidirect
391. D₄×C₁₃	#137	semidirect
429. C₂×#137	C₂²×C₁₃	semidirect
430. C₂²×Q₁₆	C₂²×C₁₃	semidirect
460. #497	C₂²×C₁₃	semidirect
461. #494	C₂²×C₁₃	semidirect
462. #491	C₂²×C₁₃	semidirect
463. #487	C₂²×C₁₃	semidirect
464. #485	C₂²×C₁₃	semidirect
467. #483	C₂²×C₁₃	semidirect
469. #479	C₂²×C₁₃	semidirect
470. #475	C₂²×C₁₃	semidirect
471. #470	C₂²×C₁₃	semidirect
472. #470	C₂²×C₁₃	semidirect
473. #467	C₂²×C₁₃	semidirect
474. #465	C₂²×C₁₃	semidirect
475. #464	C₂²×C₁₃	semidirect
476. #462	C₂²×C₁₃	semidirect
477. #462	C₂²×C₁₃	semidirect
478. #462	C₂²×C₁₃	semidirect
479. #461	C₂²×C₁₃	semidirect
480. #452	C₂²×C₁₃	semidirect
486. #451	C₂²×C₁₃	semidirect
487. #451	C₂²×C₁₃	semidirect
488. #451	C₂²×C₁₃	semidirect
489. #451	C₂²×C₁₃	semidirect
492. #448	C₂²×C₁₃	semidirect
493. #441	C₂²×C₁₃	semidirect
494. C₄×Q₁₆	C₂²×C₁₃	semidirect
495. C₄×SD₁₆	C₂²×C₁₃	semidirect
501. #419	C₂²×C₁₃	semidirect
502. C₂×#103	C₂²×C₁₃	semidirect
795. C₁₃	#61602	direct (N × H)
821. 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×#3520	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3328	2
C₁₃×#3312	2
C₁₃×#3298	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3276	2
C₁₃×#3270	2
C₁₃×#3218	2
C₁₃×#3209	2
C₁₃×#3195	2
C₁₃×#3190	2
C₁₃×#3113	2
C₁₃×#3108	2
C₁₃×#3004	2
C₂×C₁₃×#451	2
C₁₃×#2974	2
#61602	13

Subgroups — C13×#61602 #15747941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61602 #15747941