Subgroups — C₂×#13116392 #15892804

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718763	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718666	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718800	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718771	C₂	1	1	yes	maximal, characteristic
6	#13116392	C₂	1	8	yes	maximal, direct product factor
7	C₂×#11718123	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂×#88180	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	C₁₃×#424	—	2	2	no	—
17	C₁₃×#424	C₂²	1	4	yes	complemented
18	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
19	#11718800	—	2	2	no	—
20	#11718800	C₂²	1	4	yes	—
21	C₂×#88065	—	2	2	no	—
22	#11718785	—	2	2	no	—
23	#11718785	C₂²	1	4	yes	complemented
24	C₂×#88062	—	2	2	no	—
25	#11718771	—	2	2	no	—
26	#11718771	C₂²	1	4	yes	—
27	C₂×#88060	—	2	2	no	—
28	#11718763	—	2	2	no	—
29	#11718763	C₂²	1	4	yes	complemented
30	C₂×#88054	—	2	2	no	—
31	#11718666	—	2	2	no	—
32	#11718666	C₂²	1	4	yes	—
33	C₂×#88045	—	2	2	no	—
34	#11718123	C₂²	1	4	yes	complemented
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₂²⋊D₁₃	—	2	1	no	—
37	C₂×#6127	—	2	1	no	—
38	C₂×#6127	—	2	1	no	—
39	C₂×#6127	—	2	1	no	—
40	C₂×#6127	—	2	1	no	—
41	C₂×#6127	—	2	1	no	—
42	C₂×#6127	—	2	1	no	—
43	C₂×#6127	—	2	1	no	—
44	C₂×#6127	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×#6127	—	2	1	no	—
47	C₂×#6127	Q₈	1	2	yes	—
48	C₂×#6127	C₂³	1	2	yes	—
49	C₂²×D₅₂	Q₈	1	1	yes	characteristic
50	C₂²×C₄×D₁₃	—	2	1	no	—
51	C₂²×Dic₂₆	Q₈	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	1	no	—
62	C₂²×C₈×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	—	2	1	no	—
65	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₁₃×#117	—	2	1	no	—
68	C₁₃×#117	D₄	1	2	yes	—
69	C₁₃×#117	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₁₃	D₄	1	2	yes	—
73	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
74	#88180	—	2	1	no	—
75	#88180	—	2	1	no	—
76	#88180	D₄	1	2	yes	—
77	#88180	C₂³	1	2	yes	—
78	C₂×C₄⋊Dic₁₃	—	2	1	no	—
79	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	—	2	1	no	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	—	2	1	no	—
87	C₂×#6099	—	2	1	no	—
88	C₂×#6099	—	2	1	no	—
89	C₂×#6099	D₄	1	2	yes	—
90	C₂×#6099	C₂³	1	2	yes	—
91	C₂×#6099	C₂³	1	2	yes	—
92	C₂²×#1055	—	2	1	no	—
93	C₂²×#1055	D₄	1	2	yes	—
94	C₁₃×C₄⋊C₈	—	2	8	no	—
95	#88065	—	2	8	no	—
96	#88062	—	2	8	no	—
97	#88060	—	2	8	no	—
98	#88054	—	2	8	no	—
99	#88045	—	2	8	no	—
100	C₂×#2098	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	#41	1	1	yes	characteristic
102	C₂³×D₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₃	—	2	2	no	—
119	C₂×C₂²⋊D₁₃	—	2	2	no	—
120	C₂×C₂²⋊D₁₃	—	4	1	no	—
121	C₂×C₂²⋊D₁₃	—	4	1	no	—
122	C₂×C₂²⋊D₁₃	—	4	1	no	—
123	C₂×C₂²⋊D₁₃	—	4	1	no	—
124	C₂²×Dic₁₃	—	2	1	no	—
125	C₂²×Dic₁₃	—	2	2	no	—
126	#6127	—	2	2	no	—
127	#6127	—	2	2	no	—
128	#6127	—	2	2	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	4	1	no	—
135	#6127	—	4	1	no	—
136	#6127	—	4	1	no	—
137	#6127	—	4	1	no	—
138	#6127	—	4	1	no	—
139	#6127	—	4	1	no	—
140	#6127	—	4	1	no	—
141	#6127	—	4	1	no	—
142	C₂×D₅₂	—	2	1	no	—
143	C₂×D₅₂	—	2	1	no	—
144	C₂×D₅₂	—	2	1	no	—
145	C₂×D₅₂	—	2	1	no	—
146	C₂×D₅₂	—	2	1	no	—
147	C₂×D₅₂	C₂×Q₈	1	2	yes	—
148	C₂×C₄×D₁₃	—	2	2	no	—
149	C₂×C₄×D₁₃	—	2	2	no	—
150	C₂×C₄×D₁₃	—	4	1	no	—
151	C₂×C₄×D₁₃	—	4	1	no	—
152	C₂×C₄×D₁₃	—	4	1	no	—
153	C₂×C₄×D₁₃	—	4	1	no	—
154	C₂×Dic₂₆	—	2	1	no	—
155	C₂×Dic₂₆	—	2	1	no	—
156	C₂×Dic₂₆	—	2	1	no	—
157	C₂×Dic₂₆	—	2	1	no	—
158	C₂×Dic₂₆	—	2	1	no	—
159	C₂×Dic₂₆	C₂×Q₈	1	2	yes	—
160	C₁₃×M₁₆	—	2	2	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	4	1	no	—
163	C₁₃×M₁₆	—	4	1	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	4	1	no	—
169	C₂×C₈×C₁₃	—	4	1	no	—
170	C₂×C₈×C₁₃	—	4	1	no	—
171	C₂×C₈×C₁₃	—	4	1	no	—
172	C₂×C₈×C₁₃	—	4	1	no	—
173	C₂×C₈×C₁₃	—	4	1	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₄²×C₁₃	—	2	2	no	—
179	C₄²×C₁₃	C₂×D₄	1	4	yes	—
180	C₂²⋊Dic₁₃	—	2	2	no	—
181	C₂²⋊Dic₁₃	—	2	2	no	—
182	C₄⋊Dic₁₃	—	2	2	no	—
183	C₄⋊Dic₁₃	—	2	2	no	—
184	C₄×Dic₁₃	—	2	2	no	—
185	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
186	#6099	—	2	2	no	—
187	#6099	—	2	2	no	—
188	#6099	—	2	2	no	—
189	#6099	—	2	2	no	—
190	#6099	—	2	2	no	—
191	#6099	—	2	2	no	—
192	#6099	—	4	1	no	—
193	#6099	—	4	1	no	—
194	C₂×#1055	—	2	2	no	—
195	C₂×#1055	—	2	2	no	—
196	C₂×#1055	—	2	2	no	—
197	C₂×#1055	—	4	1	no	—
198	C₂×#1055	—	4	1	no	—
199	C₂×#1055	C₂×D₄	1	4	yes	—
200	C₂×#430	—	13	1	no	—
201	C₂×#424	—	13	1	no	—
202	C₂×#424	D₁₃	1	1	yes	characteristic, complemented
203	C₂×#421	—	13	1	no	—
204	C₂×#421	—	13	1	no	—
205	C₂×#408	—	13	1	no	—
206	#2098	—	13	8	no	—
207	C₂×H(3,ℤ/4)	—	13	1	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
210	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂³×C₁₃	#123	1	1	yes	characteristic
212	C₂³×C₁₃	#123	1	1	yes	characteristic
213	C₂³×C₁₃	#123	1	1	yes	characteristic
214	C₂³×C₁₃	#123	1	1	yes	characteristic
215	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂²×D₁₃	—	2	2	no	—
217	C₂²×D₁₃	—	4	4	no	—
218	C₂²×D₁₃	—	4	1	no	—
219	C₂²×D₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
233	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
234	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
235	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
236	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
237	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
238	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
250	C₂²⋊D₁₃	—	4	2	no	—
251	C₂²⋊D₁₃	—	4	2	no	—
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂×Dic₁₃	—	2	2	no	—
255	C₂×Dic₁₃	—	2	4	no	—
256	C₂×Dic₁₃	—	4	4	no	—
257	C₂×Dic₁₃	—	4	1	no	—
258	C₂×Dic₁₃	—	4	1	no	—
259	D₅₂	—	2	2	no	—
260	D₅₂	—	2	2	no	—
261	D₅₂	—	4	1	no	—
262	D₅₂	—	4	1	no	—
263	C₄×D₁₃	—	4	2	no	—
264	C₄×D₁₃	—	4	2	no	—
265	C₄×D₁₃	—	4	2	no	—
266	C₄×D₁₃	—	4	2	no	—
267	Dic₂₆	—	2	2	no	—
268	Dic₂₆	—	2	2	no	—
269	Dic₂₆	—	4	1	no	—
270	Dic₂₆	—	4	1	no	—
271	C₈×C₁₃	—	4	2	no	—
272	C₈×C₁₃	—	4	2	no	—
273	#1055	—	2	4	no	—
274	#1055	—	4	2	no	—
275	C₂²×#41	—	13	1	no	—
276	C₂²×M₁₆	—	13	1	no	—
277	C₂²×M₁₆	—	13	1	no	—
278	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
279	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
280	C₂×#117	—	13	1	no	—
281	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
282	#430	—	13	4	no	—
283	#430	—	26	2	no	—
284	C₂×#108	—	26	2	no	—
285	#424	—	2	2	no	—
286	#424	—	13	4	no	—
287	#424	—	26	2	no	—
288	#424	C₂×D₁₃	1	4	yes	complemented
289	C₂×C₄⋊C₈	—	2	2	no	—
290	C₂×C₄⋊C₈	—	26	2	no	—
291	#421	—	13	4	no	—
292	#421	—	13	4	no	—
293	#421	—	26	2	no	—
294	#421	—	26	2	no	—
295	C₂×#104	—	26	2	no	—
296	C₂×#104	—	26	2	no	—
297	#408	—	13	4	no	—
298	#408	—	26	2	no	—
299	C₂×C₂²⋊C₈	—	26	2	no	—
300	H(3,ℤ/4)	—	13	4	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	4	1	no	—
306	C₂²×C₁₃	—	4	1	no	—
307	C₂²×C₁₃	—	4	1	no	—
308	C₂²×C₁₃	#399	1	1	yes	characteristic
309	C₂²×C₁₃	#399	1	1	yes	characteristic
310	C₂²×C₁₃	#399	1	1	yes	characteristic
311	C₂²×C₁₃	#399	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
314	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
315	C₂×D₁₃	—	4	4	no	—
316	C₂×D₁₃	—	4	2	no	—
317	C₂×D₁₃	—	8	2	no	—
318	C₂×D₁₃	—	8	2	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	#399	1	1	yes	characteristic
321	C₄×C₁₃	#399	1	1	yes	characteristic
322	C₄×C₁₃	#399	1	1	yes	characteristic
323	C₄×C₁₃	#399	1	1	yes	characteristic
324	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
325	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
327	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
328	Dic₁₃	—	4	4	no	—
329	Dic₁₃	—	4	2	no	—
330	C₂×#41	—	13	2	no	—
331	C₂×#41	—	13	2	no	—
332	C₂×#41	—	26	1	no	—
333	C₂×#41	—	26	1	no	—
334	C₂×#41	—	26	1	no	—
335	C₂×#41	—	26	1	no	—
336	C₂×#41	—	26	1	no	—
337	C₂×#41	—	26	1	no	—
338	C₂×#41	—	26	1	no	—
339	C₂×#41	—	26	1	no	—
340	C₂×#41	—	26	1	no	—
341	C₂×#41	—	26	1	no	—
342	C₂²×Q₈	—	13	1	no	—
343	C₂²×D₄	—	13	1	no	—
344	C₂²×D₄	—	26	1	no	—
345	C₂³×C₄	—	26	1	no	—
346	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	13	2	no	—
353	C₂×M₁₆	—	13	2	no	—
354	C₂×M₁₆	—	13	2	no	—
355	C₂×M₁₆	—	26	1	no	—
356	C₂×M₁₆	—	26	1	no	—
357	C₂×M₁₆	—	26	1	no	—
358	C₂×M₁₆	—	26	1	no	—
359	C₂×M₁₆	—	26	1	no	—
360	C₂×M₁₆	—	26	1	no	—
361	C₂×M₁₆	—	26	1	no	—
362	C₂×M₁₆	—	26	1	no	—
363	C₂×M₁₆	—	26	1	no	—
364	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	13	2	no	—
373	C₂²×C₈	—	26	1	no	—
374	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	13	2	no	—
378	#117	—	13	2	no	—
379	#117	—	26	1	no	—
380	#117	—	26	1	no	—
381	#117	C₂²⋊D₁₃	1	2	yes	—
382	#117	C₂²×D₁₃	1	2	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	26	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	26	1	no	—
387	C₂×C₄²	—	13	2	no	—
388	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
389	#108	—	26	8	no	—
390	C₄⋊C₈	—	2	8	no	—
391	C₄⋊C₈	—	26	8	no	—
392	#104	—	26	8	no	—
393	#104	—	26	8	no	—
394	C₂²⋊C₈	—	26	8	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	2	1	no	—
398	C₂×C₁₃	—	2	1	no	—
399	C₂×C₁₃	—	2	1	no	—
400	C₂×C₁₃	—	2	1	no	—
401	C₂×C₁₃	#2098	1	2	yes	complemented
402	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
403	D₁₃	—	8	2	no	—
404	C₂⁴	—	26	1	no	—
405	C₂⁴	#6127	1	1	yes	characteristic
406	#41	—	26	2	no	—
407	#41	—	26	2	no	—
408	#41	—	26	2	no	—
409	#41	—	26	2	no	—
410	#41	—	26	2	no	—
411	#41	—	26	2	no	—
412	#41	—	26	2	no	—
413	#41	—	26	2	no	—
414	#41	—	52	1	no	—
415	#41	—	52	1	no	—
416	#41	—	52	1	no	—
417	#41	—	52	1	no	—
418	#41	—	52	1	no	—
419	#41	—	52	1	no	—
420	#41	—	52	1	no	—
421	#41	—	52	1	no	—
422	C₂×Q₈	—	13	2	no	—
423	C₂×Q₈	—	26	1	no	—
424	C₂×Q₈	—	26	1	no	—
425	C₂×Q₈	—	26	1	no	—
426	C₂×Q₈	—	26	1	no	—
427	C₂×Q₈	—	26	1	no	—
428	C₂×D₄	—	13	2	no	—
429	C₂×D₄	—	26	2	no	—
430	C₂×D₄	—	26	2	no	—
431	C₂×D₄	—	26	1	no	—
432	C₂×D₄	—	26	1	no	—
433	C₂×D₄	—	26	1	no	—
434	C₂×D₄	—	26	1	no	—
435	C₂×D₄	—	26	1	no	—
436	C₂×D₄	—	52	1	no	—
437	C₂×D₄	—	52	1	no	—
438	C₂×D₄	—	52	1	no	—
439	C₂×D₄	—	52	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	26	2	no	—
442	C₂²×C₄	—	26	1	no	—
443	C₂²×C₄	—	26	2	no	—
444	C₂²×C₄	—	26	2	no	—
445	C₂²×C₄	—	52	1	no	—
446	C₂²×C₄	—	52	1	no	—
447	C₂²×C₄	—	52	1	no	—
448	C₂²×C₄	—	52	1	no	—
449	C₂²×C₄	#6127	1	1	yes	characteristic
450	C₂²×C₄	#6127	1	1	yes	characteristic
451	C₂²×C₄	#6127	1	1	yes	characteristic
452	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
454	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
455	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
456	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
457	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
458	C₂²×C₄	#6131	1	1	yes	characteristic
459	C₂²×C₄	#6131	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	26	2	no	—
468	M₁₆	—	26	2	no	—
469	M₁₆	—	26	2	no	—
470	M₁₆	—	26	2	no	—
471	M₁₆	—	26	2	no	—
472	M₁₆	—	26	2	no	—
473	M₁₆	—	52	1	no	—
474	M₁₆	—	52	1	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	13	4	no	—
486	C₂×C₈	—	26	2	no	—
487	C₂×C₈	—	26	2	no	—
488	C₂×C₈	—	26	2	no	—
489	C₂×C₈	—	52	1	no	—
490	C₂×C₈	—	52	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	26	2	no	—
494	C₄⋊C₄	—	26	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	26	2	no	—
498	C₂²⋊C₄	—	26	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	13	4	no	—
501	C₄²	—	26	2	no	—
502	C₄²	C₂×C₂²⋊D₁₃	1	4	yes	—
503	C₁₃	C₂×#2098	1	1	yes	characteristic, complemented, Sylow
504	C₂³	—	4	2	no	—
505	C₂³	—	26	2	no	—
506	C₂³	—	52	4	no	—
507	C₂³	—	52	1	no	—
508	C₂³	—	52	1	no	—
509	C₂³	#88148	1	1	yes	characteristic
510	C₂³	#88148	1	1	yes	characteristic
511	C₂³	#88150	1	1	yes	characteristic
512	C₂³	#88150	1	1	yes	characteristic
513	C₂³	#88183	1	1	yes	characteristic
514	C₂³	#88183	1	1	yes	characteristic
515	C₂³	C₂×#6127	1	1	yes	characteristic
516	Q₈	—	26	2	no	—
517	Q₈	—	26	2	no	—
518	Q₈	—	52	1	no	—
519	Q₈	—	52	1	no	—
520	D₄	—	26	2	no	—
521	D₄	—	26	2	no	—
522	D₄	—	52	2	no	—
523	D₄	—	52	2	no	—
524	D₄	—	52	2	no	—
525	D₄	—	52	2	no	—
526	D₄	—	52	1	no	—
527	D₄	—	52	1	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	26	4	no	—
531	C₂×C₄	—	26	2	no	—
532	C₂×C₄	—	52	4	no	—
533	C₂×C₄	—	52	1	no	—
534	C₂×C₄	—	52	1	no	—
535	C₂×C₄	—	52	2	no	—
536	C₂×C₄	—	52	2	no	—
537	C₂×C₄	—	52	2	no	—
538	C₂×C₄	—	52	2	no	—
539	C₂×C₄	#88148	1	1	yes	characteristic
540	C₂×C₄	#88148	1	1	yes	characteristic
541	C₂×C₄	#88148	1	1	yes	characteristic
542	C₂×C₄	#88148	1	1	yes	characteristic
543	C₂×C₄	#88148	1	1	yes	characteristic
544	C₂×C₄	#88148	1	1	yes	characteristic
545	C₂×C₄	#88150	1	1	yes	characteristic
546	C₂×C₄	#88150	1	1	yes	characteristic
547	C₂×C₄	#88150	1	1	yes	characteristic
548	C₂×C₄	#88150	1	1	yes	characteristic
549	C₂×C₄	#88150	1	1	yes	characteristic
550	C₂×C₄	#88150	1	1	yes	characteristic
551	C₂×C₄	#88183	1	1	yes	characteristic
552	C₂×C₄	#88183	1	1	yes	characteristic
553	C₂×C₄	#88194	1	1	yes	characteristic
554	C₂×C₄	#88194	1	1	yes	characteristic
555	C₂×C₄	#88194	1	1	yes	characteristic
556	C₂×C₄	#88194	1	1	yes	characteristic
557	C₂×C₄	#88200	1	1	yes	characteristic
558	C₂×C₄	#88200	1	1	yes	characteristic
559	C₂×C₄	#88200	1	1	yes	characteristic
560	C₂×C₄	#88200	1	1	yes	characteristic
561	C₂×C₄	C₂×#6127	1	1	yes	characteristic
562	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂×#6131	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
567	C₈	—	4	2	no	—
568	C₈	—	4	2	no	—
569	C₈	—	26	4	no	—
570	C₈	—	52	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	52	4	no	—
579	C₂²	—	52	2	no	—
580	C₂²	—	104	2	no	—
581	C₂²	—	104	2	no	—
582	C₂²	#11718653	1	1	yes	characteristic
583	C₂²	#11718653	1	1	yes	characteristic
584	C₂²	#11718653	1	1	yes	characteristic
585	C₂²	#11718653	1	1	yes	characteristic
586	C₂²	C₂×#88148	1	1	yes	characteristic
587	C₂²	C₂×#88150	1	1	yes	characteristic
588	C₂²	C₂×#88183	1	1	yes	characteristic
589	C₄	—	4	4	no	—
590	C₄	—	52	4	no	—
591	C₄	—	52	2	no	—
592	C₄	#11718653	1	1	yes	characteristic
593	C₄	#11718653	1	1	yes	characteristic
594	C₄	#11718653	1	1	yes	characteristic
595	C₄	#11718653	1	1	yes	characteristic
596	C₄	C₂×#88148	1	1	yes	characteristic
597	C₄	C₂×#88150	1	1	yes	characteristic
598	C₄	C₂×#88194	1	1	yes	characteristic
599	C₄	C₂×#88200	1	1	yes	characteristic
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	104	2	no	—
607	C₂	#13116392	1	2	yes	direct product factor
608	C₂	C₂×#11718653	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88194
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#424	C₂
socle	C₂²×C₁₃	#399
prime radical	C₂²×#6127	C₂²
hypercenter	C₂×#424	D₁₃
hypocenter	C₁₃	C₂×#2098
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#424

Complements

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

N	H ≅ G/N	type
1. C₂×#11718785	C₂	semidirect
2. C₂×#11718763	C₂	semidirect
6. #13116392	C₂	direct (N × H)
7. C₂×#11718123	C₂	semidirect
8. C₂×C₁₃×#424	C₂	semidirect
17. C₁₃×#424	C₂²	semidirect
23. #11718785	C₂²	semidirect
29. #11718763	C₂²	semidirect
34. #11718123	C₂²	semidirect
202. C₂×#424	D₁₃	semidirect
288. #424	C₂×D₁₃	semidirect
401. C₂×C₁₃	#2098	semidirect
503. C₁₃	C₂×#2098	semidirect
607. C₂	#13116392	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11718785	2
C₂×#11718763	2
C₂×#11718666	2
C₂×#11718800	2
C₂×#11718771	2
#13116392	2
C₂×#11718123	2
C₂×C₁₃×#424	2
C₂×#2098	13

Subgroups — C2×#13116392 #15892804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116392 #15892804