Subgroups — C₁₃×#61595 #15747934

Order 3328.

2116 conjugacy classes of subgroups.

The subgroup lattice has 914 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, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3330	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3315	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3283	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3269	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×#3196	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3189	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
21	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#552	C₂²	1	2	yes	complemented
24	C₁₃×#551	—	2	2	no	—
25	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#548	C₂²	1	2	yes	complemented
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#547	—	2	2	no	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#547	C₂²	1	4	yes	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#547	C₂²	1	2	yes	—
33	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic
40	C₁₃×#529	C₂²	1	1	yes	characteristic
41	C₁₃×#525	C₂²	1	2	yes	—
42	C₂×C₁₃×#123	—	2	2	no	—
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₁₃×#121	—	2	1	no	—
46	C₁₃×#520	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
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×#484	C₂²	1	1	yes	characteristic
56	C₁₃×#484	C₂²	1	2	yes	—
57	C₁₃×#484	C₂²	1	4	yes	complemented
58	C₁₃×#481	C₂²	1	1	yes	characteristic
59	C₁₃×#478	C₂²	1	2	yes	complemented
60	C₁₃×#474	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×#467	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#461	C₂²	1	2	yes	complemented
69	C₁₃×#461	C₂²	1	2	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#452	C₂²	1	4	yes	complemented
73	C₁₃×#452	C₂²	1	4	yes	complemented
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#451	C₂²	1	2	yes	—
76	C₁₃×#451	C₂²	1	2	yes	—
77	C₁₃×#451	C₂²	1	4	yes	complemented
78	C₁₃×#450	C₂²	1	1	yes	characteristic
79	C₁₃×#450	C₂²	1	2	yes	—
80	C₁₃×#449	C₂²	1	4	yes	complemented
81	C₁₃×#448	C₂²	1	2	yes	—
82	C₁₃×#447	C₂²	1	1	yes	characteristic
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
86	C₁₃×#436	C₂²	1	2	yes	complemented
87	C₁₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#417	C₂²	1	4	yes	complemented
92	C₁₃×#416	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	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	4	8	no	—
99	C₂×C₁₃×#41	C₂³	1	4	yes	—
100	C₂×C₁₃×#41	C₂³	1	4	yes	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	—	2	1	no	—
108	C₂³×C₄×C₁₃	—	2	2	no	—
109	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
110	C₁₃×#137	—	4	8	no	—
111	C₁₃×#135	—	4	8	no	—
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×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	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	1	no	—
122	C₁₃×C₄⋊Q₈	—	2	1	no	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#126	—	2	2	no	—
130	C₁₃×#126	—	2	1	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	—	2	1	no	—
133	C₁₃×#125	C₂³	1	1	yes	characteristic
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	C₂³	1	1	yes	characteristic
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	1	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
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	4	yes	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	2	no	—
163	C₁₃×#121	—	2	4	no	—
164	C₁₃×#121	—	2	2	no	—
165	C₁₃×#121	—	2	1	no	—
166	C₁₃×#121	C₂³	1	1	yes	characteristic
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₁₃×#120	—	2	2	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	1	no	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₁₃	D₄	1	2	yes	—
182	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	4	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	—	2	1	no	—
207	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	4	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×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	2	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	#61595	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	1	no	—
233	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
234	C₁₃×#41	—	2	8	no	—
235	C₁₃×#41	—	2	8	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	4	4	no	—
240	C₁₃×#41	—	4	8	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	—	4	4	no	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	8	no	—
259	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	4	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	4	4	no	—
275	C₂²×C₄×C₁₃	—	4	4	no	—
276	C₂²×C₄×C₁₃	—	4	8	no	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₁₃×Q₁₆	—	4	4	no	—
286	C₁₃×Q₁₆	—	4	4	no	—
287	C₁₃×Q₁₆	—	4	4	no	—
288	C₁₃×SD₁₆	—	2	8	no	—
289	C₁₃×SD₁₆	—	2	4	no	—
290	C₁₃×SD₁₆	—	4	4	no	—
291	C₁₃×D₈	—	2	4	no	—
292	C₁₃×M₁₆	—	4	4	no	—
293	C₂×C₈×C₁₃	—	4	4	no	—
294	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
295	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	1	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
321	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	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	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
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	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	1	no	—
346	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
350	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3330	C₂×C₁₃	1	2	yes	complemented
353	#3315	C₂×C₁₃	1	4	yes	complemented
354	#3302	C₂×C₁₃	1	2	yes	complemented
355	#3283	C₂×C₁₃	1	2	yes	complemented
356	#3276	C₂×C₁₃	1	2	yes	complemented
357	#3269	C₂×C₁₃	1	4	yes	complemented
358	#3218	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3196	C₂×C₁₃	1	2	yes	complemented
361	#3189	C₂×C₁₃	1	2	yes	complemented
362	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3105	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#3007	C₂×C₁₃	1	2	yes	complemented
365	#3002	C₂×C₁₃	1	2	yes	complemented
366	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
367	C₂³×C₁₃	—	2	4	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	4	no	—
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	4	2	no	—
372	C₂³×C₁₃	—	4	2	no	—
373	C₂³×C₁₃	—	4	2	no	—
374	C₂³×C₁₃	—	4	2	no	—
375	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	Q₈×C₁₃	—	2	2	no	—
379	Q₈×C₁₃	—	2	4	no	—
380	Q₈×C₁₃	—	2	4	no	—
381	Q₈×C₁₃	—	2	4	no	—
382	Q₈×C₁₃	—	4	4	no	—
383	Q₈×C₁₃	—	4	2	no	—
384	Q₈×C₁₃	—	8	2	no	—
385	D₄×C₁₃	—	2	4	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	2	no	—
389	D₄×C₁₃	—	2	2	no	—
390	D₄×C₁₃	—	4	2	no	—
391	D₄×C₁₃	—	4	8	no	—
392	D₄×C₁₃	—	4	8	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	8	2	no	—
396	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	2	4	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	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	4	no	—
409	C₂×C₄×C₁₃	—	4	2	no	—
410	C₂×C₄×C₁₃	—	4	2	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	8	no	—
413	C₂×C₄×C₁₃	—	4	8	no	—
414	C₂×C₄×C₁₃	—	4	4	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	8	2	no	—
421	C₂×C₄×C₁₃	—	8	2	no	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
430	C₈×C₁₃	—	2	2	no	—
431	C₈×C₁₃	—	2	4	no	—
432	C₈×C₁₃	—	2	2	no	—
433	C₂²×#41	C₂²×C₁₃	1	2	yes	—
434	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
435	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
436	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#554	—	2	1	no	—
438	#552	C₂²×C₁₃	1	2	yes	complemented
439	#551	—	2	2	no	—
440	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#548	C₂²×C₁₃	1	2	yes	complemented
442	#547	—	2	1	no	—
443	#547	—	2	2	no	—
444	#547	—	2	1	no	—
445	#547	C₂²×C₁₃	1	2	yes	—
446	#547	C₂²×C₁₃	1	4	yes	—
447	#547	C₂²×C₁₃	1	2	yes	—
448	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#546	—	2	1	no	—
451	#542	—	2	1	no	—
452	#539	—	2	2	no	—
453	#533	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
455	#529	C₂²×C₁₃	1	1	yes	characteristic
456	#525	C₂²×C₁₃	1	2	yes	—
457	C₂×#123	—	2	2	no	—
458	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
459	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
460	C₂×#121	—	2	1	no	—
461	#520	—	2	1	no	—
462	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
464	C₂²×C₄⋊C₄	—	2	1	no	—
465	#497	C₂²×C₁₃	1	2	yes	complemented
466	#494	C₂²×C₁₃	1	2	yes	complemented
467	#491	C₂²×C₁₃	1	2	yes	complemented
468	#487	C₂²×C₁₃	1	2	yes	complemented
469	#485	C₂²×C₁₃	1	4	yes	complemented
470	#484	C₂²×C₁₃	1	1	yes	characteristic
471	#484	C₂²×C₁₃	1	2	yes	—
472	#484	C₂²×C₁₃	1	4	yes	complemented
473	#481	C₂²×C₁₃	1	1	yes	characteristic
474	#478	C₂²×C₁₃	1	2	yes	complemented
475	#474	C₂²×C₁₃	1	2	yes	complemented
476	#470	C₂²×C₁₃	1	4	yes	complemented
477	#468	C₂²×C₁₃	1	4	yes	complemented
478	#467	C₂²×C₁₃	1	4	yes	complemented
479	#467	C₂²×C₁₃	1	4	yes	complemented
480	#463	C₂²×C₁₃	1	2	yes	complemented
481	#462	C₂²×C₁₃	1	4	yes	complemented
482	#462	C₂²×C₁₃	1	2	yes	complemented
483	#461	C₂²×C₁₃	1	2	yes	complemented
484	#461	C₂²×C₁₃	1	2	yes	complemented
485	#452	C₂²×C₁₃	1	4	yes	complemented
486	#452	C₂²×C₁₃	1	4	yes	complemented
487	#452	C₂²×C₁₃	1	4	yes	complemented
488	#452	C₂²×C₁₃	1	4	yes	complemented
489	#451	C₂²×C₁₃	1	2	yes	—
490	#451	C₂²×C₁₃	1	2	yes	—
491	#451	C₂²×C₁₃	1	2	yes	—
492	#451	C₂²×C₁₃	1	4	yes	complemented
493	#450	C₂²×C₁₃	1	1	yes	characteristic
494	#450	C₂²×C₁₃	1	2	yes	—
495	#449	C₂²×C₁₃	1	4	yes	complemented
496	#448	C₂²×C₁₃	1	2	yes	—
497	#447	C₂²×C₁₃	1	1	yes	characteristic
498	#440	C₂²×C₁₃	1	4	yes	complemented
499	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
500	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
501	#436	C₂²×C₁₃	1	2	yes	complemented
502	#435	C₂²×C₁₃	1	4	yes	complemented
503	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
504	#432	C₂²×C₁₃	1	1	yes	characteristic
505	#431	C₂²×C₁₃	1	1	yes	characteristic
506	#417	C₂²×C₁₃	1	4	yes	complemented
507	#416	C₂²×C₁₃	1	4	yes	complemented
508	#407	C₂²×C₁₃	1	2	yes	—
509	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
510	C₂²×C₁₃	—	2	1	no	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	4	no	—
515	C₂²×C₁₃	—	2	2	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	4	8	no	—
520	C₂²×C₁₃	—	4	2	no	—
521	C₂²×C₁₃	—	4	2	no	—
522	C₂²×C₁₃	—	4	1	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	1	no	—
525	C₂²×C₁₃	—	8	4	no	—
526	C₂²×C₁₃	#578	1	2	yes	—
527	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₁₃	—	2	2	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	1	no	—
532	C₄×C₁₃	—	2	1	no	—
533	C₄×C₁₃	—	2	1	no	—
534	C₄×C₁₃	—	4	4	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	1	no	—
539	C₄×C₁₃	—	4	2	no	—
540	C₄×C₁₃	—	4	1	no	—
541	C₄×C₁₃	#575	1	2	yes	—
542	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	4	8	no	—
547	C₂×#41	C₂³×C₁₃	1	4	yes	—
548	C₂×#41	C₂³×C₁₃	1	4	yes	—
549	C₂×#41	C₂³×C₁₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
551	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂³×C₄	—	2	1	no	—
556	C₂³×C₄	—	2	2	no	—
557	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
558	#137	—	4	8	no	—
559	#135	—	4	8	no	—
560	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
561	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
562	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
564	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
565	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×D₈	C₂³×C₁₃	1	2	yes	—
567	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
568	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
569	C₄⋊Q₈	—	2	1	no	—
570	C₄⋊Q₈	—	2	1	no	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
573	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
574	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	1	no	—
579	#125	—	2	2	no	—
580	#125	—	2	1	no	—
581	#125	C₂³×C₁₃	1	1	yes	characteristic
582	#124	—	2	1	no	—
583	#124	—	2	2	no	—
584	#124	C₂³×C₁₃	1	1	yes	characteristic
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	1	no	—
588	#123	—	2	4	no	—
589	#123	—	2	4	no	—
590	#123	—	2	4	no	—
591	#123	—	2	4	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
603	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
606	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
608	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	2	4	no	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	C₂³×C₁₃	1	1	yes	characteristic
615	#121	C₂³×C₁₃	1	2	yes	—
616	#120	—	2	2	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	1	no	—
619	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
620	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	—	2	1	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	D₄×C₁₃	1	1	yes	characteristic
629	C₄×D₄	D₄×C₁₃	1	2	yes	—
630	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₁₃	1	2	yes	—
632	C₄×D₄	C₂³×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	#117	—	2	1	no	—
638	#117	—	2	2	no	—
639	#117	—	2	1	no	—
640	#117	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	2	no	—
643	C₂×C₄⋊C₄	—	2	2	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	—	2	4	no	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	#107	C₂³×C₁₃	1	2	yes	—
658	#107	C₂³×C₁₃	1	4	yes	—
659	#106	C₂³×C₁₃	1	2	yes	—
660	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
661	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#103	C₂³×C₁₃	1	4	yes	—
664	#103	C₂³×C₁₃	1	4	yes	—
665	#103	C₂³×C₁₃	1	4	yes	—
666	#103	C₂³×C₁₃	1	2	yes	—
667	#103	C₂³×C₁₃	1	4	yes	—
668	#102	C₂³×C₁₃	1	2	yes	—
669	#102	C₂³×C₁₃	1	4	yes	—
670	#102	C₂³×C₁₃	1	2	yes	—
671	#102	C₂³×C₁₃	1	2	yes	—
672	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
673	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
675	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
676	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
677	#97	C₂³×C₁₃	1	2	yes	—
678	C₄×C₈	C₂³×C₁₃	1	2	yes	—
679	C₂×C₁₃	—	2	2	no	—
680	C₂×C₁₃	—	4	2	no	—
681	C₂×C₁₃	—	4	2	no	—
682	C₂×C₁₃	—	4	4	no	—
683	C₂×C₁₃	—	8	1	no	—
684	C₂×C₁₃	#3484	1	1	yes	characteristic
685	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
686	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
687	C₂⁴	—	2	1	no	—
688	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
689	#41	—	2	8	no	—
690	#41	—	2	8	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	4	8	no	—
695	#41	—	4	8	no	—
696	#41	—	4	4	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	4	4	no	—
701	C₂×Q₈	—	4	4	no	—
702	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
703	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
704	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	8	no	—
714	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
717	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	—	4	4	no	—
731	C₂²×C₄	—	4	8	no	—
732	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
740	Q₁₆	—	4	4	no	—
741	Q₁₆	—	4	4	no	—
742	Q₁₆	—	4	4	no	—
743	SD₁₆	—	2	8	no	—
744	SD₁₆	—	2	4	no	—
745	SD₁₆	—	4	4	no	—
746	D₈	—	2	4	no	—
747	M₁₆	—	4	4	no	—
748	C₂×C₈	—	4	4	no	—
749	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
750	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
751	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	1	no	—
801	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
803	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
805	C₁₃	#61595	1	1	yes	characteristic, direct product factor, Sylow
806	C₂³	—	2	4	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	4	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	4	2	no	—
814	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
815	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	Q₈	—	2	2	no	—
818	Q₈	—	2	4	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	2	4	no	—
821	Q₈	—	4	4	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	8	2	no	—
824	D₄	—	2	4	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	8	no	—
832	D₄	—	4	4	no	—
833	D₄	—	4	2	no	—
834	D₄	—	8	2	no	—
835	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	8	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
863	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
866	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
867	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
868	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
869	C₈	—	2	2	no	—
870	C₈	—	2	4	no	—
871	C₈	—	2	2	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	4	8	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	8	4	no	—
888	C₂²	C₁₃×#578	1	2	yes	—
889	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	4	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	C₁₃×#575	1	2	yes	—
904	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
905	C₂	—	2	2	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	4	no	—
909	C₂	—	8	1	no	—
910	C₂	C₁₃×#3484	1	1	yes	characteristic
911	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
912	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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
1. C₁₃×#3520	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3330	C₂	semidirect
4. C₁₃×#3315	C₂	semidirect
5. C₁₃×#3302	C₂	semidirect
6. C₁₃×#3283	C₂	semidirect
7. C₁₃×#3276	C₂	semidirect
8. C₁₃×#3269	C₂	semidirect
9. C₁₃×#3218	C₂	semidirect
10. C₁₃×#3209	C₂	semidirect
11. C₁₃×#3196	C₂	semidirect
12. C₁₃×#3189	C₂	semidirect
13. C₁₃×#3110	C₂	semidirect
14. C₁₃×#3105	C₂	semidirect
15. C₁₃×#3007	C₂	semidirect
16. C₁₃×#3002	C₂	semidirect
17. C₁₃×#2974	C₂	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×#135	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#548	C₂²	semidirect
33. C₁₃×#547	C₂²	semidirect
34. C₁₃×#547	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×#484	C₂²	semidirect
59. C₁₃×#478	C₂²	semidirect
60. C₁₃×#474	C₂²	semidirect
61. C₁₃×#470	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#467	C₂²	semidirect
64. C₁₃×#467	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#461	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#452	C₂²	semidirect
73. C₁₃×#452	C₂²	semidirect
77. C₁₃×#451	C₂²	semidirect
80. C₁₃×#449	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
86. C₁₃×#436	C₂²	semidirect
87. C₁₃×#435	C₂²	semidirect
88. C₈×D₄×C₁₃	C₂²	semidirect
91. C₁₃×#417	C₂²	semidirect
92. C₁₃×#416	C₂²	semidirect
231. #61595	C₁₃	direct (N × H)
350. #3520	C₂×C₁₃	semidirect
351. C₂×#547	C₂×C₁₃	semidirect
352. #3330	C₂×C₁₃	semidirect
353. #3315	C₂×C₁₃	semidirect
354. #3302	C₂×C₁₃	semidirect
355. #3283	C₂×C₁₃	semidirect
356. #3276	C₂×C₁₃	semidirect
357. #3269	C₂×C₁₃	semidirect
358. #3218	C₂×C₁₃	semidirect
359. #3209	C₂×C₁₃	semidirect
360. #3196	C₂×C₁₃	semidirect
361. #3189	C₂×C₁₃	semidirect
362. #3110	C₂×C₁₃	semidirect
363. #3105	C₂×C₁₃	semidirect
364. #3007	C₂×C₁₃	semidirect
365. #3002	C₂×C₁₃	semidirect
366. #2974	C₂×C₁₃	semidirect
434. C₂×#137	C₂²×C₁₃	semidirect
435. C₂×#135	C₂²×C₁₃	semidirect
436. #556	C₂²×C₁₃	semidirect
438. #552	C₂²×C₁₃	semidirect
440. D₄×Q₈	C₂²×C₁₃	semidirect
441. #548	C₂²×C₁₃	semidirect
448. #547	C₂²×C₁₃	semidirect
449. #547	C₂²×C₁₃	semidirect
465. #497	C₂²×C₁₃	semidirect
466. #494	C₂²×C₁₃	semidirect
467. #491	C₂²×C₁₃	semidirect
468. #487	C₂²×C₁₃	semidirect
469. #485	C₂²×C₁₃	semidirect
472. #484	C₂²×C₁₃	semidirect
474. #478	C₂²×C₁₃	semidirect
475. #474	C₂²×C₁₃	semidirect
476. #470	C₂²×C₁₃	semidirect
477. #468	C₂²×C₁₃	semidirect
478. #467	C₂²×C₁₃	semidirect
479. #467	C₂²×C₁₃	semidirect
480. #463	C₂²×C₁₃	semidirect
481. #462	C₂²×C₁₃	semidirect
482. #462	C₂²×C₁₃	semidirect
483. #461	C₂²×C₁₃	semidirect
484. #461	C₂²×C₁₃	semidirect
485. #452	C₂²×C₁₃	semidirect
486. #452	C₂²×C₁₃	semidirect
487. #452	C₂²×C₁₃	semidirect
488. #452	C₂²×C₁₃	semidirect
492. #451	C₂²×C₁₃	semidirect
495. #449	C₂²×C₁₃	semidirect
498. #440	C₂²×C₁₃	semidirect
499. C₄×SD₁₆	C₂²×C₁₃	semidirect
500. C₄×D₈	C₂²×C₁₃	semidirect
501. #436	C₂²×C₁₃	semidirect
502. #435	C₂²×C₁₃	semidirect
503. C₈×D₄	C₂²×C₁₃	semidirect
506. #417	C₂²×C₁₃	semidirect
507. #416	C₂²×C₁₃	semidirect
805. C₁₃	#61595	direct (N × H)

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×C₁₃×#547	2
C₁₃×#3330	2
C₁₃×#3315	2
C₁₃×#3302	2
C₁₃×#3283	2
C₁₃×#3276	2
C₁₃×#3269	2
C₁₃×#3218	2
C₁₃×#3209	2
C₁₃×#3196	2
C₁₃×#3189	2
C₁₃×#3110	2
C₁₃×#3105	2
C₁₃×#3007	2
C₁₃×#3002	2
C₁₃×#2974	2
#61595	13

Subgroups — C13×#61595 #15747934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61595 #15747934