Subgroups — C₂×#13116391 #15892803

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×#11718780	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718660	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718897	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718895	C₂	1	1	yes	maximal, characteristic
6	#13116391	C₂	1	8	yes	maximal, direct product factor
7	C₂×#11718123	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂×#88180	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂³×#1055	C₂²	1	1	yes	characteristic
16	C₁₃×#421	—	2	2	no	—
17	C₁₃×#421	C₂²	1	4	yes	—
18	C₂×C₁₃×#104	—	2	2	no	—
19	#11718897	—	2	2	no	—
20	#11718897	C₂²	1	4	yes	—
21	C₂×#88077	—	2	2	no	—
22	#11718895	—	2	2	no	—
23	#11718895	C₂²	1	4	yes	—
24	C₂×C₂²⋊#1055	—	2	2	no	—
25	#11718785	—	2	2	no	—
26	#11718785	C₂²	1	4	yes	complemented
27	C₂×#88062	—	2	2	no	—
28	#11718780	—	2	2	no	—
29	#11718780	C₂²	1	4	yes	complemented
30	C₂×#88054	—	2	2	no	—
31	#11718660	—	2	2	no	—
32	#11718660	C₂²	1	4	yes	complemented
33	C₂×C₄⋊#1055	—	2	2	no	—
34	#11718123	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#41	—	2	1	no	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	Q₈	1	2	yes	—
46	C₂×C₁₃×#41	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	C₂³	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	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	—	2	1	no	—
61	C₁₃×#117	D₄	1	2	yes	—
62	C₁₃×#117	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₄²×C₁₃	D₄	1	2	yes	—
66	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
67	#88180	—	2	1	no	—
68	#88180	—	2	1	no	—
69	#88180	D₄	1	2	yes	—
70	#88180	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₁₃	—	2	1	no	—
72	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
73	C₂×#6099	—	2	1	no	—
74	C₂×#6099	—	2	1	no	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	D₄	1	2	yes	—
83	C₂×#6099	C₂³	1	2	yes	—
84	C₂×#6099	C₂³	1	2	yes	—
85	C₂²×#1055	—	2	1	no	—
86	C₂²×#1055	—	2	1	no	—
87	C₂²×#1055	—	2	1	no	—
88	C₂²×#1055	—	2	1	no	—
89	C₂²×#1055	—	2	1	no	—
90	C₂²×#1055	—	2	1	no	—
91	C₂²×#1055	—	2	1	no	—
92	C₂²×#1055	D₄	1	2	yes	—
93	C₂²×#1055	C₂³	1	2	yes	—
94	C₁₃×#104	—	2	8	no	—
95	#88077	—	2	8	no	—
96	C₂²⋊#1055	—	2	8	no	—
97	#88062	—	2	8	no	—
98	#88054	—	2	8	no	—
99	C₄⋊#1055	—	2	8	no	—
100	C₂×#2098	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	—	2	1	no	—
102	C₂⁴×C₁₃	#41	1	1	yes	characteristic
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	—	2	2	no	—
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	—	4	1	no	—
112	C₁₃×#41	—	4	1	no	—
113	C₁₃×#41	—	4	1	no	—
114	C₁₃×#41	—	4	1	no	—
115	C₁₃×#41	—	4	1	no	—
116	C₁₃×#41	—	4	1	no	—
117	C₁₃×#41	—	4	1	no	—
118	C₁₃×#41	—	4	1	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	4	1	no	—
133	C₂×D₄×C₁₃	—	4	1	no	—
134	C₂×D₄×C₁₃	—	4	1	no	—
135	C₂×D₄×C₁₃	—	4	1	no	—
136	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	4	1	no	—
142	C₂²×C₄×C₁₃	—	4	1	no	—
143	C₂²×C₄×C₁₃	—	4	1	no	—
144	C₂²×C₄×C₁₃	—	4	1	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×Dic₁₃	—	2	2	no	—
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	—	4	1	no	—
166	C₂×C₈×C₁₃	—	4	1	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₂²⋊Dic₁₃	—	2	2	no	—
174	C₂²⋊Dic₁₃	—	2	2	no	—
175	C₄⋊Dic₁₃	—	2	2	no	—
176	C₄⋊Dic₁₃	—	2	2	no	—
177	C₄×Dic₁₃	—	2	2	no	—
178	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
179	#6099	—	2	2	no	—
180	#6099	—	2	2	no	—
181	#6099	—	2	2	no	—
182	#6099	—	2	2	no	—
183	#6099	—	2	2	no	—
184	#6099	—	2	2	no	—
185	#6099	—	4	1	no	—
186	#6099	—	4	1	no	—
187	C₂×#1055	—	2	2	no	—
188	C₂×#1055	—	2	2	no	—
189	C₂×#1055	—	2	2	no	—
190	C₂×#1055	—	2	2	no	—
191	C₂×#1055	—	2	2	no	—
192	C₂×#1055	—	2	2	no	—
193	C₂×#1055	—	4	1	no	—
194	C₂×#1055	—	4	1	no	—
195	C₂×#1055	—	4	1	no	—
196	C₂×#1055	—	4	1	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	—	13	1	no	—
203	C₂×#421	—	13	1	no	—
204	C₂×#421	D₁₃	1	1	yes	characteristic
205	C₂×#408	—	13	1	no	—
206	#2098	—	13	8	no	—
207	C₂×H(3,ℤ/4)	—	13	1	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	4	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
214	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
215	C₂³×C₁₃	#123	1	1	yes	characteristic
216	C₂³×C₁₃	#123	1	1	yes	characteristic
217	C₂³×C₁₃	#123	1	1	yes	characteristic
218	C₂³×C₁₃	#123	1	1	yes	characteristic
219	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	2	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	4	1	no	—
223	Q₈×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	4	2	no	—
227	D₄×C₁₃	—	4	2	no	—
228	D₄×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	1	no	—
231	D₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
254	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
255	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
256	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
257	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
258	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
259	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
260	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
261	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
262	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
269	C₂×Dic₁₃	—	2	4	no	—
270	C₂×Dic₁₃	—	4	4	no	—
271	C₈×C₁₃	—	4	2	no	—
272	#1055	—	2	4	no	—
273	#1055	—	4	2	no	—
274	#1055	—	4	2	no	—
275	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
276	C₂²×M₁₆	—	13	1	no	—
277	C₂²×M₁₆	—	13	1	no	—
278	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
279	C₂³×C₈	—	13	1	no	—
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	—	13	4	no	—
286	#424	—	13	4	no	—
287	#424	—	26	2	no	—
288	#424	—	26	2	no	—
289	C₂×C₄⋊C₈	—	26	2	no	—
290	C₂×C₄⋊C₈	—	26	2	no	—
291	#421	—	2	2	no	—
292	#421	—	13	4	no	—
293	#421	—	26	2	no	—
294	#421	C₂×D₁₃	1	4	yes	—
295	C₂×#104	—	2	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	—	4	4	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	8	2	no	—
311	C₂²×C₁₃	—	8	2	no	—
312	C₂²×C₁₃	#399	1	1	yes	characteristic
313	C₂²×C₁₃	#399	1	1	yes	characteristic
314	C₂²×C₁₃	#399	1	1	yes	characteristic
315	C₂²×C₁₃	#399	1	1	yes	characteristic
316	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
318	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	—	4	2	no	—
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	#399	1	1	yes	characteristic
325	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
328	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
329	Dic₁₃	—	4	4	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	Dic₂₆	1	2	yes	—
341	C₂×#41	C₂²×D₁₃	1	2	yes	—
342	C₂²×Q₈	Dic₂₆	1	1	yes	characteristic
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	Dic₂₆	1	1	yes	characteristic
345	C₂³×C₄	—	2	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	—	13	2	no	—
367	C₂²×C₈	—	13	2	no	—
368	C₂²×C₈	—	26	1	no	—
369	C₂²×C₈	—	26	1	no	—
370	C₂²×C₈	—	26	1	no	—
371	C₂²×C₈	—	26	1	no	—
372	C₂²×C₈	—	26	1	no	—
373	C₂²×C₈	—	26	1	no	—
374	C₂²×C₈	—	26	1	no	—
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	—	26	8	no	—
391	C₄⋊C₈	—	26	8	no	—
392	#104	—	2	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	—	8	2	no	—
402	C₂×C₁₃	#2098	1	2	yes	complemented
403	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
404	C₂⁴	—	2	1	no	—
405	C₂⁴	#6129	1	1	yes	characteristic
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	4	1	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	C₂×Dic₂₆	1	2	yes	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	C₂×Dic₂₆	1	2	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	26	2	no	—
449	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
450	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
451	C₂²×C₄	#6127	1	1	yes	characteristic
452	C₂²×C₄	#6127	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	D₄×D₁₃	1	1	yes	characteristic
457	C₂²×C₄	#6129	1	1	yes	characteristic
458	C₂²×C₄	#6129	1	1	yes	characteristic
459	C₂²×C₄	#6129	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	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	13	4	no	—
479	C₂×C₈	—	26	2	no	—
480	C₂×C₈	—	26	2	no	—
481	C₂×C₈	—	26	2	no	—
482	C₂×C₈	—	26	2	no	—
483	C₂×C₈	—	26	2	no	—
484	C₂×C₈	—	26	2	no	—
485	C₂×C₈	—	52	1	no	—
486	C₂×C₈	—	52	1	no	—
487	C₂×C₈	—	52	1	no	—
488	C₂×C₈	—	52	1	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	—	2	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	#88132	1	1	yes	characteristic
510	C₂³	#88132	1	1	yes	characteristic
511	C₂³	#88137	1	1	yes	characteristic
512	C₂³	#88137	1	1	yes	characteristic
513	C₂³	#88189	1	1	yes	characteristic
514	C₂³	#88189	1	1	yes	characteristic
515	C₂³	C₂×#6129	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	26	4	no	—
538	C₂×C₄	—	52	4	no	—
539	C₂×C₄	#88132	1	1	yes	characteristic
540	C₂×C₄	#88132	1	1	yes	characteristic
541	C₂×C₄	#88132	1	1	yes	characteristic
542	C₂×C₄	#88132	1	1	yes	characteristic
543	C₂×C₄	#88132	1	1	yes	characteristic
544	C₂×C₄	#88132	1	1	yes	characteristic
545	C₂×C₄	#88137	1	1	yes	characteristic
546	C₂×C₄	#88137	1	1	yes	characteristic
547	C₂×C₄	#88137	1	1	yes	characteristic
548	C₂×C₄	#88137	1	1	yes	characteristic
549	C₂×C₄	#88137	1	1	yes	characteristic
550	C₂×C₄	#88137	1	1	yes	characteristic
551	C₂×C₄	#88178	1	1	yes	characteristic
552	C₂×C₄	#88178	1	1	yes	characteristic
553	C₂×C₄	#88178	1	1	yes	characteristic
554	C₂×C₄	#88178	1	1	yes	characteristic
555	C₂×C₄	#88189	1	1	yes	characteristic
556	C₂×C₄	#88189	1	1	yes	characteristic
557	C₂×C₄	#88194	1	1	yes	characteristic
558	C₂×C₄	#88194	1	1	yes	characteristic
559	C₂×C₄	#88194	1	1	yes	characteristic
560	C₂×C₄	#88194	1	1	yes	characteristic
561	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
562	C₂×C₄	C₂×#6127	1	1	yes	characteristic
563	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂×#6129	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
567	C₈	—	4	2	no	—
568	C₈	—	26	4	no	—
569	C₈	—	52	2	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	—	4	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	—	8	2	no	—
582	C₂²	#11718610	1	1	yes	characteristic
583	C₂²	#11718610	1	1	yes	characteristic
584	C₂²	#11718610	1	1	yes	characteristic
585	C₂²	#11718610	1	1	yes	characteristic
586	C₂²	C₂×#88132	1	1	yes	characteristic
587	C₂²	C₂×#88137	1	1	yes	characteristic
588	C₂²	C₂×#88189	1	1	yes	characteristic
589	C₄	—	4	4	no	—
590	C₄	—	4	2	no	—
591	C₄	—	52	4	no	—
592	C₄	#11718610	1	1	yes	characteristic
593	C₄	#11718610	1	1	yes	characteristic
594	C₄	#11718610	1	1	yes	characteristic
595	C₄	#11718610	1	1	yes	characteristic
596	C₄	C₂×#88132	1	1	yes	characteristic
597	C₄	C₂×#88137	1	1	yes	characteristic
598	C₄	C₂×#88178	1	1	yes	characteristic
599	C₄	C₂×#88194	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	—	8	2	no	—
607	C₂	#13116391	1	2	yes	direct product factor
608	C₂	C₂×#11718610	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×#421	C₂
socle	C₂²×C₁₃	#399
prime radical	C₂²×C₁₃×#41	C₂²
hypercenter	C₂×#421	D₁₃
hypocenter	C₁₃	C₂×#2098
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
1. C₂×#11718785	C₂	semidirect
2. C₂×#11718780	C₂	semidirect
3. C₂×#11718660	C₂	semidirect
6. #13116391	C₂	direct (N × H)
7. C₂×#11718123	C₂	semidirect
26. #11718785	C₂²	semidirect
29. #11718780	C₂²	semidirect
32. #11718660	C₂²	semidirect
34. #11718123	C₂²	semidirect
402. C₂×C₁₃	#2098	semidirect
503. C₁₃	C₂×#2098	semidirect
607. C₂	#13116391	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×#11718780	2
C₂×#11718660	2
C₂×#11718897	2
C₂×#11718895	2
#13116391	2
C₂×#11718123	2
C₂×C₁₃×#421	2
C₂×#2098	13

Subgroups — C2×#13116391 #15892803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116391 #15892803