Subgroups — C₂×#13130954 #16799087

Order 3328.

918 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719098	C₂	1	2	yes	maximal
2	C₂²×#88102	C₂	1	1	yes	maximal, characteristic
3	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
4	#13130954	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718271	C₂	1	2	yes	maximal
6	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊#261	C₂²	1	2	yes	—
9	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#11719098	—	2	4	no	—
13	#11719098	C₂²	1	8	yes	—
14	C₂×#88102	—	2	2	no	—
15	C₂×#88102	—	2	1	no	—
16	C₂×#88102	—	2	1	no	—
17	C₂×#88102	—	2	2	no	—
18	C₂×#88102	C₂²	1	4	yes	—
19	C₂×#88101	—	2	2	no	—
20	#11719089	—	2	2	no	—
21	#11719089	C₂²	1	4	yes	—
22	C₂×#88100	—	2	1	no	—
23	C₂×C₈×#261	—	2	1	no	—
24	C₂×C₁₃×#108	C₄	1	1	yes	characteristic, complemented
25	C₂×#88062	C₄	1	2	yes	complemented
26	C₂×#88059	C₄	1	1	yes	characteristic, complemented
27	D₁₃×#108	C₄	1	4	yes	complemented
28	D₁₃×#108	C₂²	1	4	yes	—
29	#11718271	C₂²	1	8	yes	—
30	C₂³×#261	—	2	2	no	—
31	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₂²⋊#261	—	2	1	no	—
33	C₂×#6122	Q₈	1	2	yes	—
34	#88237	—	2	1	no	—
35	#88237	—	2	1	no	—
36	#88237	D₄	1	2	yes	—
37	#88237	C₂³	1	2	yes	—
38	C₂×C₄⋊#261	—	2	2	no	—
39	C₂×C₄⋊#261	—	2	2	no	—
40	C₂×C₄⋊#261	—	2	2	no	—
41	C₂×C₄⋊#261	—	2	2	no	—
42	C₂×C₄⋊#261	—	2	2	no	—
43	C₂×C₄⋊#261	D₄	1	1	yes	characteristic
44	C₂×C₄⋊#261	D₄	1	1	yes	characteristic
45	C₂×C₄⋊#261	C₂³	1	4	yes	—
46	C₂×C₄×#261	—	2	1	no	—
47	D₁₃⋊M₁₆	—	2	1	no	—
48	D₁₃⋊M₁₆	—	2	1	no	—
49	D₁₃⋊M₁₆	Q₈	1	2	yes	—
50	D₁₃⋊M₁₆	C₂³	1	2	yes	—
51	C₂×#6118	—	2	1	no	—
52	C₂×D₁₃⋊C₈	—	2	1	no	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×#6099	C₂×C₄	1	2	yes	—
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	M₁₆×D₁₃	—	2	2	no	—
58	M₁₆×D₁₃	—	2	2	no	—
59	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
60	M₁₆×D₁₃	C₂³	1	4	yes	—
61	C₂×#6094	—	2	2	no	—
62	C₂×C₈×D₁₃	—	2	2	no	—
63	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	D₄	1	2	yes	—
67	C₂×C₈×D₁₃	Q₈	1	2	yes	—
68	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂³	1	2	yes	—
71	#88102	—	2	8	no	—
72	#88102	—	2	4	no	—
73	#88102	—	2	4	no	—
74	#88101	—	2	8	no	—
75	#88100	—	2	4	no	—
76	C₈×#261	—	2	4	no	—
77	C₁₃×#108	C₂×C₄	1	4	yes	complemented
78	#88062	C₂×C₄	1	8	yes	complemented
79	#88059	C₂×C₄	1	4	yes	complemented
80	C₂×#1952	—	13	1	no	maximal, Sylow
81	C₂³×D₁₃	#41	1	1	yes	characteristic
82	C₂²×#261	—	2	1	no	—
83	C₂²×#261	—	2	1	no	—
84	C₂²×#261	—	2	4	no	—
85	C₂²×#261	—	4	2	no	—
86	C₂²×#261	—	4	2	no	—
87	C₂²×#261	—	8	4	no	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
99	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
102	C₂²⋊#261	—	2	2	no	—
103	C₂²⋊#261	—	2	2	no	—
104	#6122	—	2	2	no	—
105	#6122	C₂×Q₈	1	4	yes	—
106	C₂×#1057	—	2	2	no	—
107	C₄⋊#261	—	2	1	no	—
108	C₄⋊#261	—	2	1	no	—
109	C₄⋊#261	—	2	4	no	—
110	C₄⋊#261	—	2	4	no	—
111	C₄⋊#261	—	4	2	no	—
112	C₄⋊#261	—	4	2	no	—
113	C₄⋊#261	C₂×D₄	1	2	yes	—
114	C₄⋊#261	C₂×D₄	1	2	yes	—
115	C₄×#261	—	2	2	no	—
116	C₄×#261	—	2	2	no	—
117	#6118	—	2	2	no	—
118	#6118	—	2	2	no	—
119	D₁₃⋊C₈	—	2	2	no	—
120	D₁₃⋊C₈	—	2	2	no	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	#6099	—	2	2	no	—
129	#6099	C₂²×C₄	1	4	yes	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
132	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
133	C₂×#1055	C₄⋊C₄	1	2	yes	—
134	C₂×#1055	C₂²×C₄	1	2	yes	—
135	#6094	—	2	4	no	—
136	#6094	—	2	4	no	—
137	C₈×D₁₃	—	2	4	no	—
138	C₈×D₁₃	—	2	4	no	—
139	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
140	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
141	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
142	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
143	C₈×D₁₃	C₂×D₄	1	2	yes	—
144	C₈×D₁₃	C₂×D₄	1	2	yes	—
145	C₈×D₁₃	C₂×Q₈	1	2	yes	—
146	C₈×D₁₃	C₂×Q₈	1	2	yes	—
147	C₂²×#108	—	13	1	no	—
148	C₂×#428	—	13	2	no	—
149	C₂²×#107	—	13	1	no	—
150	C₂×#405	—	13	1	no	—
151	#1952	—	13	8	no	—
152	C₂×#343	—	13	2	no	—
153	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
154	C₂²×D₁₃	—	2	2	no	—
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
157	C₂²×D₁₃	#121	1	1	yes	characteristic
158	C₂²×D₁₃	#121	1	1	yes	characteristic
159	C₂²×D₁₃	#125	1	1	yes	characteristic
160	C₂²×D₁₃	#125	1	1	yes	characteristic
161	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
162	C₂×#261	—	2	2	no	—
163	C₂×#261	—	2	2	no	—
164	C₂×#261	—	4	2	no	—
165	C₂×#261	—	4	2	no	—
166	C₂×#261	—	4	4	no	—
167	C₂×#261	—	8	4	no	—
168	C₂×#261	—	8	4	no	—
169	C₂×#261	—	8	4	no	—
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
180	C₂×Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
185	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
186	C₄×D₁₃	#121	1	1	yes	characteristic
187	C₄×D₁₃	#121	1	1	yes	characteristic
188	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
189	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
190	C₄×D₁₃	#125	1	1	yes	characteristic
191	C₄×D₁₃	#125	1	1	yes	characteristic
192	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
193	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
194	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
197	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
198	#1057	—	2	4	no	—
199	C₈×C₁₃	—	2	4	no	—
200	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
201	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
202	#1055	—	2	4	no	—
203	#1055	C₂×C₄⋊C₄	1	2	yes	—
204	#1055	C₂×C₄⋊C₄	1	2	yes	—
205	C₂²×M₁₆	—	13	1	no	—
206	C₂²×M₁₆	—	13	2	no	—
207	C₂³×C₈	—	13	1	no	—
208	C₂×#117	—	13	1	no	—
209	C₂²×C₄⋊C₄	—	13	2	no	—
210	C₂×#108	—	13	2	no	—
211	C₂×#108	—	13	1	no	—
212	C₂×#108	—	13	4	no	—
213	C₂×#108	—	13	4	no	—
214	C₂×#108	#261	1	1	yes	characteristic, complemented
215	#428	—	13	8	no	—
216	#428	—	26	4	no	—
217	C₂×#107	—	13	4	no	—
218	C₂×#107	—	26	2	no	—
219	C₂×#107	—	26	1	no	—
220	C₂×#107	—	26	1	no	—
221	C₂×#107	—	26	2	no	—
222	C₂×#106	—	26	2	no	—
223	#405	—	13	4	no	—
224	#405	—	26	2	no	—
225	C₂×#97	—	26	1	no	—
226	C₂×C₄×C₈	—	26	1	no	—
227	#343	—	13	8	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	#389	1	1	yes	characteristic
230	C₂²×C₁₃	#389	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
232	C₂×D₁₃	—	2	2	no	—
233	C₂×D₁₃	—	2	2	no	—
234	C₂×D₁₃	—	2	2	no	—
235	C₂×D₁₃	—	2	1	no	—
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	#389	1	1	yes	characteristic
240	C₂×D₁₃	#389	1	1	yes	characteristic
241	C₂×D₁₃	#472	1	2	yes	—
242	C₂×D₁₃	#473	1	2	yes	—
243	C₂×D₁₃	C₂×#121	1	1	yes	characteristic
244	C₂×D₁₃	C₂×#125	1	1	yes	characteristic
245	#261	—	4	2	no	—
246	#261	—	4	2	no	—
247	#261	—	8	4	no	—
248	C₄×C₁₃	#389	1	1	yes	characteristic
249	C₄×C₁₃	#389	1	1	yes	characteristic
250	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
251	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
252	Dic₁₃	#389	1	1	yes	characteristic
253	Dic₁₃	#389	1	1	yes	characteristic
254	Dic₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
255	Dic₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	—	26	2	no	—
258	C₂×M₁₆	—	13	2	no	—
259	C₂×M₁₆	—	13	2	no	—
260	C₂×M₁₆	—	13	2	no	—
261	C₂×M₁₆	—	13	2	no	—
262	C₂×M₁₆	—	13	4	no	—
263	C₂×M₁₆	—	13	4	no	—
264	C₂×M₁₆	—	26	2	no	—
265	C₂×M₁₆	—	26	2	no	—
266	C₂×M₁₆	—	26	2	no	—
267	C₂×M₁₆	—	26	1	no	—
268	C₂×M₁₆	—	26	1	no	—
269	C₂×M₁₆	—	26	1	no	—
270	C₂×M₁₆	C₂×#261	1	2	yes	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	13	2	no	—
275	C₂²×C₈	—	13	2	no	—
276	C₂²×C₈	—	13	1	no	—
277	C₂²×C₈	—	13	1	no	—
278	C₂²×C₈	—	13	2	no	—
279	C₂²×C₈	—	13	2	no	—
280	C₂²×C₈	—	26	2	no	—
281	C₂²×C₈	—	26	1	no	—
282	C₂²×C₈	C₂×#261	1	1	yes	characteristic
283	#117	—	13	2	no	—
284	#117	—	13	2	no	—
285	#117	—	26	1	no	—
286	#117	—	26	1	no	—
287	C₂×C₄⋊C₄	—	13	1	no	—
288	C₂×C₄⋊C₄	—	13	1	no	—
289	C₂×C₄⋊C₄	—	13	4	no	—
290	C₂×C₄⋊C₄	—	26	2	no	—
291	C₂×C₄⋊C₄	—	26	2	no	—
292	C₂×C₄⋊C₄	—	26	2	no	—
293	C₂×C₄⋊C₄	—	26	2	no	—
294	C₂×C₄⋊C₄	—	26	2	no	—
295	C₂×C₂²⋊C₄	—	26	1	no	—
296	C₂×C₄²	—	26	1	no	—
297	#108	—	13	8	no	—
298	#108	—	13	4	no	—
299	#108	C₂×#261	1	4	yes	complemented
300	#107	—	26	8	no	—
301	#107	—	26	4	no	—
302	#107	—	26	4	no	—
303	#106	—	26	8	no	—
304	#97	—	26	4	no	—
305	C₄×C₈	—	26	4	no	—
306	C₂×C₁₃	—	2	1	no	—
307	C₂×C₁₃	—	2	1	no	—
308	C₂×C₁₃	#1952	1	2	yes	complemented
309	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
310	D₁₃	—	2	1	no	—
311	D₁₃	—	2	1	no	—
312	D₁₃	#1952	1	2	yes	complemented
313	D₁₃	C₂×#472	1	1	yes	characteristic
314	D₁₃	C₂×#473	1	1	yes	characteristic
315	C₂⁴	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	26	1	no	—
330	C₂²×C₄	—	26	1	no	—
331	C₂²×C₄	—	26	4	no	—
332	C₂²×C₄	—	52	2	no	—
333	C₂²×C₄	—	52	2	no	—
334	C₂²×C₄	—	104	4	no	—
335	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
336	M₁₆	—	2	2	no	—
337	M₁₆	—	13	4	no	—
338	M₁₆	—	13	4	no	—
339	M₁₆	—	26	4	no	—
340	M₁₆	—	26	4	no	—
341	M₁₆	—	26	2	no	—
342	M₁₆	—	26	2	no	—
343	M₁₆	—	26	2	no	—
344	M₁₆	—	26	2	no	—
345	M₁₆	C₂²×#261	1	4	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	13	2	no	—
356	C₂×C₈	—	13	2	no	—
357	C₂×C₈	—	13	2	no	—
358	C₂×C₈	—	13	2	no	—
359	C₂×C₈	—	26	4	no	—
360	C₂×C₈	—	26	4	no	—
361	C₂×C₈	—	26	2	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	—	26	2	no	—
364	C₂×C₈	—	26	2	no	—
365	C₂×C₈	C₄⋊#261	1	2	yes	—
366	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
367	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
368	C₂×C₈	C₂²×#261	1	2	yes	—
369	C₄⋊C₄	—	13	2	no	—
370	C₄⋊C₄	—	13	2	no	—
371	C₄⋊C₄	—	26	1	no	—
372	C₄⋊C₄	—	26	1	no	—
373	C₄⋊C₄	—	26	4	no	—
374	C₄⋊C₄	—	26	4	no	—
375	C₄⋊C₄	—	52	2	no	—
376	C₄⋊C₄	—	52	2	no	—
377	C₂²⋊C₄	—	26	2	no	—
378	C₂²⋊C₄	—	26	2	no	—
379	C₄²	—	26	2	no	—
380	C₄²	—	26	2	no	—
381	C₁₃	C₂×#1952	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	13	1	no	—
383	C₂³	—	13	1	no	—
384	C₂³	—	13	1	no	—
385	C₂³	—	13	1	no	—
386	C₂³	—	13	1	no	—
387	C₂³	—	13	1	no	—
388	C₂³	—	26	2	no	—
389	C₂³	—	26	2	no	—
390	C₂³	Q₈×#261	1	1	yes	characteristic
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	1	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	13	1	no	—
412	C₂×C₄	—	13	1	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	52	2	no	—
416	C₂×C₄	—	52	2	no	—
417	C₂×C₄	—	52	4	no	—
418	C₂×C₄	—	104	4	no	—
419	C₂×C₄	—	104	4	no	—
420	C₂×C₄	—	104	4	no	—
421	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
422	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
423	C₂×C₄	D₄×#261	1	1	yes	characteristic
424	C₂×C₄	D₄×#261	1	1	yes	characteristic
425	C₂×C₄	Q₈×#261	1	1	yes	characteristic
426	C₂×C₄	C₂³×#261	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	—	13	2	no	—
429	C₈	—	13	2	no	—
430	C₈	—	26	4	no	—
431	C₈	—	26	4	no	—
432	C₈	C₂×C₄⋊#261	1	2	yes	—
433	C₈	C₂×C₄⋊#261	1	2	yes	—
434	C₂²	—	2	2	no	—
435	C₂²	—	13	1	no	—
436	C₂²	—	13	1	no	—
437	C₂²	—	13	2	no	—
438	C₂²	—	13	2	no	—
439	C₂²	—	13	1	no	—
440	C₂²	—	13	1	no	—
441	C₂²	—	26	1	no	—
442	C₂²	—	26	1	no	—
443	C₂²	—	26	1	no	—
444	C₂²	—	26	2	no	—
445	C₂²	—	26	1	no	—
446	C₂²	—	26	2	no	—
447	C₂²	—	26	2	no	—
448	C₂²	#11719083	1	1	yes	characteristic
449	C₂²	#11719083	1	1	yes	characteristic
450	C₂²	C₂×Q₈×#261	1	1	yes	characteristic
451	C₄	—	13	1	no	—
452	C₄	—	13	1	no	—
453	C₄	—	13	1	no	—
454	C₄	—	13	1	no	—
455	C₄	—	52	2	no	—
456	C₄	—	52	2	no	—
457	C₄	—	104	4	no	—
458	C₄	#11719083	1	1	yes	characteristic
459	C₄	#11719083	1	1	yes	characteristic
460	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
461	C₄	C₂×D₄×#261	1	1	yes	characteristic
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	13	1	no	—
465	C₂	—	13	1	no	—
466	C₂	—	13	2	no	—
467	C₂	—	26	1	no	—
468	C₂	—	26	1	no	—
469	C₂	#13130954	1	2	yes	direct product factor
470	C₂	C₂×#11719083	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11719083
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#108	C₄
socle	C₂²×C₁₃	#389
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×#108	#261
hypocenter	C₁₃	C₂×#1952
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #13130954	C₂	direct (N × H)
24. C₂×C₁₃×#108	C₄	semidirect
25. C₂×#88062	C₄	semidirect
26. C₂×#88059	C₄	semidirect
27. D₁₃×#108	C₄	semidirect
77. C₁₃×#108	C₂×C₄	semidirect
78. #88062	C₂×C₄	semidirect
79. #88059	C₂×C₄	semidirect
214. C₂×#108	#261	semidirect
299. #108	C₂×#261	semidirect
308. C₂×C₁₃	#1952	semidirect
312. D₁₃	#1952	semidirect
381. C₁₃	C₂×#1952	semidirect
469. C₂	#13130954	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×#11719098	2
C₂²×#88102	2
C₂×#11719089	2
#13130954	2
C₂×#11718271	2
C₂×D₁₃×#108	2
C₂×#1952	13

Subgroups — C2×#13130954 #16799087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130954 #16799087