Subgroups — #34182829

Order 20224.

620 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11929613	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₃₁₆	C₂	1	1	yes	maximal, characteristic
3	#23764336	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19098292	C₂	1	1	yes	maximal, characteristic
6	#23761235	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929613	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₇₉	—	2	1	no	—
10	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
12	C₄×#11929613	—	2	2	no	—
13	C₄×#11929613	—	2	2	no	—
14	C₈×D₃₁₆	—	2	2	no	—
15	C₈×D₃₁₆	—	2	2	no	—
16	C₂×#14579093	C₄	1	1	yes	characteristic
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#14579086	C₄	1	1	yes	characteristic
20	C₂×#14579083	C₄	1	1	yes	characteristic
21	C₂×(C₂×D₇₉)⋊C₈	—	2	1	no	—
22	#19098317	—	2	1	no	—
23	#19098317	—	2	1	no	—
24	#19098295	—	2	2	no	—
25	#19098292	—	2	2	no	—
26	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₃₁₆	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₉	—	2	1	no	—
32	C₂×#11929613	—	2	2	no	—
33	C₂×#11929613	—	2	2	no	—
34	C₂×#11929613	C₈	1	4	yes	complemented
35	C₂²×C₇₉⋊C₈	—	2	1	no	—
36	C₂²×C₇₉⋊C₈	—	2	1	no	—
37	C₂×C₈×D₇₉	—	2	4	no	—
38	C₂×C₈×D₇₉	—	4	2	no	—
39	C₂×C₈×D₇₉	—	4	2	no	—
40	C₄×Dic₁₅₈	—	2	1	no	—
41	C₄×Dic₁₅₈	—	2	1	no	—
42	C₄×Dic₁₅₈	—	2	1	no	—
43	C₄×Dic₁₅₈	—	2	1	no	—
44	C₄×D₃₁₆	—	2	1	no	—
45	C₄×D₃₁₆	—	2	1	no	—
46	C₄×D₃₁₆	D₄	1	2	yes	—
47	C₄×D₃₁₆	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₇₉⋊C₄	—	2	1	no	—
51	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
52	C₂×C₄×Dic₇₉	—	2	1	no	—
53	#14579093	—	2	2	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
58	#14579086	—	2	2	no	—
59	#14579083	—	2	2	no	—
60	(C₂×D₇₉)⋊C₈	—	2	4	no	—
61	C₂²×C₈×C₇₉	—	2	1	no	—
62	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
67	C₄×C₈×C₇₉	—	2	1	no	—
68	C₄×C₈×C₇₉	—	2	1	no	—
69	C₄×C₈×C₇₉	—	2	1	no	—
70	C₄×C₈×C₇₉	—	2	1	no	—
71	C₄×C₈×C₇₉	—	2	1	no	—
72	C₄×C₈×C₇₉	—	2	1	no	—
73	C₂³×D₇₉	—	2	1	no	—
74	C₂×Dic₁₅₈	—	2	1	no	—
75	C₂×Dic₁₅₈	—	2	1	no	—
76	C₂×Dic₁₅₈	—	2	1	no	—
77	C₂×Dic₁₅₈	—	2	1	no	—
78	C₂×Dic₁₅₈	—	2	1	no	—
79	C₂×Dic₁₅₈	C₂×C₈	1	2	yes	complemented
80	C₂×D₃₁₆	—	2	1	no	—
81	C₂×D₃₁₆	—	2	1	no	—
82	C₂×D₃₁₆	—	2	1	no	—
83	C₂×D₃₁₆	C₂²⋊C₄	1	2	yes	—
84	C₂×D₃₁₆	C₂×C₈	1	2	yes	—
85	C₂×D₃₁₆	M₁₆	1	2	yes	—
86	C₂²×Dic₇₉	—	2	1	no	—
87	C₂²×Dic₇₉	—	2	1	no	—
88	C₂²×Dic₇₉	—	2	1	no	—
89	C₂×C₄×D₇₉	—	2	2	no	—
90	C₂×C₄×D₇₉	—	2	2	no	—
91	C₂×C₄×D₇₉	—	4	1	no	—
92	C₂×C₄×D₇₉	—	4	1	no	—
93	C₂×C₄×D₇₉	—	4	1	no	—
94	C₂×C₄×D₇₉	—	4	1	no	—
95	#11929613	—	2	8	no	—
96	C₂×C₇₉⋊C₈	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	4	1	no	—
98	C₂×C₇₉⋊C₈	—	4	1	no	—
99	C₂×C₇₉⋊C₈	—	4	1	no	—
100	C₂×C₇₉⋊C₈	—	4	1	no	—
101	C₂×C₇₉⋊C₈	—	4	1	no	—
102	C₈×D₇₉	—	4	8	no	—
103	C₄⋊Dic₇₉	—	2	1	no	—
104	C₄⋊Dic₇₉	—	2	1	no	—
105	C₄⋊Dic₇₉	—	2	1	no	—
106	C₄⋊Dic₇₉	C₂²⋊C₄	1	2	yes	—
107	Dic₇₉⋊C₄	—	4	1	no	—
108	Dic₇₉⋊C₄	—	4	1	no	—
109	(C₂×D₇₉)⋊C₄	—	2	2	no	—
110	(C₂×D₇₉)⋊C₄	—	2	2	no	—
111	C₄×Dic₇₉	—	4	1	no	—
112	C₄×Dic₇₉	—	4	1	no	—
113	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
116	C₂×C₈×C₇₉	—	2	2	no	—
117	C₂×C₈×C₇₉	—	2	1	no	—
118	C₂×C₈×C₇₉	—	2	1	no	—
119	C₂×C₈×C₇₉	—	2	1	no	—
120	C₂×C₈×C₇₉	—	2	1	no	—
121	C₂×C₈×C₇₉	—	2	1	no	—
122	C₂×C₈×C₇₉	—	2	1	no	—
123	C₂×C₈×C₇₉	—	2	1	no	—
124	C₂×C₈×C₇₉	—	2	1	no	—
125	C₂×C₈×C₇₉	—	2	1	no	—
126	C₂×C₈×C₇₉	—	2	1	no	—
127	C₂×C₈×C₇₉	—	4	1	no	—
128	C₂×C₈×C₇₉	—	4	1	no	—
129	C₂×C₈×C₇₉	C₂×C₈	1	2	yes	complemented
130	C₂×C₈×C₇₉	SD₁₆	1	2	yes	complemented
131	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₇₉	#41	1	1	yes	characteristic
135	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
136	C₂²×D₇₉	—	2	2	no	—
137	C₂²×D₇₉	—	2	2	no	—
138	C₂²×D₇₉	—	2	2	no	—
139	C₂²×D₇₉	—	4	1	no	—
140	C₂²×D₇₉	—	4	1	no	—
141	C₂²×D₇₉	—	4	1	no	—
142	C₂²×D₇₉	—	4	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
148	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#131	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
159	C₂×Dic₇₉	—	2	2	no	—
160	C₂×Dic₇₉	—	2	2	no	—
161	C₂×Dic₇₉	—	4	1	no	—
162	C₂×Dic₇₉	—	4	1	no	—
163	C₂×Dic₇₉	—	4	1	no	—
164	C₂×Dic₇₉	—	4	1	no	—
165	C₂×Dic₇₉	—	4	1	no	—
166	C₂×Dic₇₉	—	4	1	no	—
167	C₂×Dic₇₉	—	4	1	no	—
168	D₃₁₆	—	2	2	no	—
169	D₃₁₆	—	2	2	no	—
170	D₃₁₆	—	2	2	no	—
171	D₃₁₆	C₂²⋊C₈	1	4	yes	—
172	C₄×D₇₉	—	4	2	no	—
173	C₄×D₇₉	—	4	2	no	—
174	C₄×D₇₉	—	4	2	no	—
175	C₄×D₇₉	—	4	2	no	—
176	Dic₁₅₈	—	2	2	no	—
177	Dic₁₅₈	—	2	2	no	—
178	Dic₁₅₈	—	4	1	no	—
179	Dic₁₅₈	—	4	1	no	—
180	C₈×C₇₉	—	2	2	no	—
181	C₈×C₇₉	—	2	2	no	—
182	C₈×C₇₉	—	4	2	no	—
183	C₈×C₇₉	—	4	1	no	—
184	C₈×C₇₉	—	4	1	no	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₇₉⋊C₈	—	8	1	no	—
187	C₂²×C₇₉	#386	1	1	yes	characteristic
188	C₂²×C₇₉	C₈×D₄	1	1	yes	characteristic
189	C₂²×C₇₉	#435	1	1	yes	characteristic
190	C₂²×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
191	C₂²×C₇₉	#440	1	1	yes	characteristic
192	C₂²×C₇₉	#443	1	1	yes	characteristic
193	C₂²×C₇₉	#444	1	1	yes	characteristic
194	C₂×D₇₉	—	2	4	no	—
195	C₂×D₇₉	—	4	2	no	—
196	C₂×D₇₉	—	4	2	no	—
197	C₂×D₇₉	—	4	2	no	—
198	C₂×D₇₉	—	4	2	no	—
199	C₂×D₇₉	—	4	2	no	—
200	C₂×D₇₉	—	4	2	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	2	1	no	—
203	C₄×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
204	C₄×C₇₉	#408	1	1	yes	characteristic
205	C₄×C₇₉	C₈×D₄	1	1	yes	characteristic
206	C₄×C₇₉	#435	1	1	yes	characteristic
207	C₄×C₇₉	#450	1	1	yes	characteristic
208	C₄×C₇₉	#452	1	1	yes	characteristic
209	C₄×C₇₉	#461	1	1	yes	characteristic
210	C₄×C₇₉	#463	1	1	yes	characteristic
211	Dic₇₉	—	4	2	no	—
212	Dic₇₉	—	4	2	no	—
213	Dic₇₉	—	8	1	no	—
214	#8945	—	79	1	no	maximal, Sylow
215	C₂×C₇₉	C₈×SD₁₆	1	1	yes	characteristic
216	C₂×C₇₉	SD₁₆⋊C₈	1	1	yes	characteristic
217	C₂×C₇₉	#1582	1	1	yes	characteristic
218	C₂×C₇₉	#1585	1	1	yes	characteristic
219	C₂×C₇₉	#1869	1	1	yes	characteristic
220	C₂×C₇₉	#1876	1	1	yes	characteristic
221	C₂×C₇₉	#1877	1	1	yes	characteristic
222	D₇₉	—	4	4	no	—
223	C₂×C₄×SD₁₆	—	79	1	no	—
224	C₂×C₈×D₄	—	79	1	no	—
225	#1984	—	79	1	no	—
226	C₂×Q₈⋊C₈	—	79	1	no	—
227	C₂×D₄⋊C₈	—	79	1	no	—
228	#1277	—	79	1	no	—
229	#1273	D₇₉	1	1	yes	characteristic, complemented
230	C₇₉	#8945	1	1	yes	characteristic, complemented, Sylow
231	C₂²×SD₁₆	—	79	1	no	—
232	C₂³×C₈	—	158	1	no	—
233	C₂×C₄×Q₈	—	79	1	no	—
234	C₂×C₄×D₄	—	79	1	no	—
235	C₄×SD₁₆	—	158	2	no	—
236	C₄×SD₁₆	—	158	2	no	—
237	C₈×D₄	—	158	2	no	—
238	C₈×D₄	—	158	2	no	—
239	C₂×#106	—	79	1	no	—
240	C₂×C₄⋊C₈	—	79	1	no	—
241	C₂×C₄⋊C₈	—	79	1	no	—
242	C₂×#103	—	79	1	no	—
243	C₂×#102	—	79	1	no	—
244	C₂×C₂²⋊C₈	—	158	1	no	—
245	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
248	#336	—	158	1	no	—
249	#336	—	158	1	no	—
250	Q₈⋊C₈	—	158	2	no	—
251	D₄⋊C₈	—	158	2	no	—
252	C₂²×Q₈	—	79	1	no	—
253	C₂²×D₄	—	79	1	no	—
254	C₂³×C₄	—	158	1	no	—
255	C₂×SD₁₆	—	79	4	no	—
256	C₂×SD₁₆	—	158	2	no	—
257	C₂×SD₁₆	—	158	2	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	316	2	no	—
260	C₂²×C₈	—	316	2	no	—
261	C₂²×C₈	—	158	4	no	—
262	C₂²×C₈	—	158	1	no	—
263	C₂²×C₈	—	158	1	no	—
264	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
266	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
267	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
268	C₄×Q₈	—	158	1	no	—
269	C₄×Q₈	—	158	1	no	—
270	C₄×Q₈	—	158	1	no	—
271	C₄×Q₈	—	158	1	no	—
272	C₄×D₄	—	79	2	no	—
273	C₄×D₄	—	79	2	no	—
274	C₄×D₄	—	158	1	no	—
275	C₄×D₄	—	158	1	no	—
276	C₂×C₄⋊C₄	—	79	1	no	—
277	C₂×C₄⋊C₄	—	79	1	no	—
278	C₂×C₄⋊C₄	—	158	1	no	—
279	C₂×C₂²⋊C₄	—	158	1	no	—
280	C₂×C₄²	—	158	1	no	—
281	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
282	#106	—	158	2	no	—
283	C₄⋊C₈	—	79	2	no	—
284	C₄⋊C₈	—	158	1	no	—
285	C₄⋊C₈	—	158	1	no	—
286	C₄⋊C₈	—	158	1	no	—
287	#103	—	158	2	no	—
288	#102	—	158	2	no	—
289	C₂²⋊C₈	—	158	4	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₂⁴	—	158	1	no	—
297	C₂×Q₈	—	79	2	no	—
298	C₂×Q₈	—	158	1	no	—
299	C₂×Q₈	—	158	1	no	—
300	C₂×Q₈	—	158	1	no	—
301	C₂×Q₈	—	158	1	no	—
302	C₂×Q₈	—	158	1	no	—
303	C₂×D₄	—	79	2	no	—
304	C₂×D₄	—	79	2	no	—
305	C₂×D₄	—	79	2	no	—
306	C₂×D₄	—	158	1	no	—
307	C₂×D₄	—	158	1	no	—
308	C₂×D₄	—	158	1	no	—
309	C₂²×C₄	—	316	1	no	—
310	C₂²×C₄	—	316	1	no	—
311	C₂²×C₄	—	316	1	no	—
312	C₂²×C₄	—	316	1	no	—
313	C₂²×C₄	—	158	1	no	—
314	C₂²×C₄	—	158	1	no	—
315	C₂²×C₄	—	158	1	no	—
316	C₂²×C₄	—	158	2	no	—
317	C₂²×C₄	—	158	2	no	—
318	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
320	C₂²×C₄	#11929624	1	1	yes	characteristic
321	SD₁₆	—	158	8	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	316	8	no	—
336	C₂×C₈	—	316	1	no	—
337	C₂×C₈	—	316	1	no	—
338	C₂×C₈	—	316	1	no	—
339	C₂×C₈	—	316	1	no	—
340	C₂×C₈	—	316	1	no	—
341	C₂×C₈	—	158	2	no	—
342	C₂×C₈	C₈×D₇₉	1	2	yes	complemented
343	C₂×C₈	#11929613	1	2	yes	complemented
344	C₄⋊C₄	—	316	1	no	—
345	C₄⋊C₄	—	316	1	no	—
346	C₄⋊C₄	—	79	2	no	—
347	C₄⋊C₄	—	158	1	no	—
348	C₄⋊C₄	—	158	1	no	—
349	C₄⋊C₄	—	158	1	no	—
350	C₂²⋊C₄	—	158	2	no	—
351	C₂²⋊C₄	—	158	2	no	—
352	C₄²	—	316	1	no	—
353	C₄²	—	316	1	no	—
354	C₄²	D₄×D₇₉	1	1	yes	characteristic
355	C₄²	D₄×D₇₉	1	1	yes	characteristic
356	C₄²	D₄×D₇₉	1	1	yes	characteristic
357	C₄²	#11929625	1	1	yes	characteristic
358	C₂³	—	316	1	no	—
359	C₂³	—	316	1	no	—
360	C₂³	—	316	1	no	—
361	C₂³	—	316	1	no	—
362	C₂³	—	158	2	no	—
363	C₂³	—	158	2	no	—
364	C₂³	—	158	2	no	—
365	C₂³	C₄×D₃₁₆	1	1	yes	characteristic
366	Q₈	—	316	1	no	—
367	Q₈	—	316	1	no	—
368	Q₈	—	158	2	no	—
369	Q₈	—	158	2	no	—
370	D₄	—	79	4	no	—
371	D₄	—	158	2	no	—
372	D₄	—	158	2	no	—
373	D₄	—	158	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	316	1	no	—
377	C₂×C₄	—	316	1	no	—
378	C₂×C₄	—	316	1	no	—
379	C₂×C₄	—	316	1	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	316	2	no	—
382	C₂×C₄	—	316	2	no	—
383	C₂×C₄	—	316	2	no	—
384	C₂×C₄	—	316	1	no	—
385	C₂×C₄	—	316	1	no	—
386	C₂×C₄	—	316	1	no	—
387	C₂×C₄	—	158	2	no	—
388	C₂×C₄	—	158	2	no	—
389	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
390	C₂×C₄	#14579123	1	1	yes	characteristic
391	C₂×C₄	#14579131	1	1	yes	characteristic
392	C₂×C₄	#14579134	1	1	yes	characteristic
393	C₂×C₄	#14579136	1	1	yes	characteristic
394	C₂×C₄	#14579146	1	1	yes	characteristic
395	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
396	C₂×C₄	M₁₆×D₇₉	1	1	yes	characteristic
397	C₂×C₄	#14579167	1	1	yes	characteristic
398	C₂×C₄	#14579169	1	1	yes	characteristic
399	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
400	C₂×C₄	#14579183	1	1	yes	characteristic
401	C₂×C₄	#14579189	1	1	yes	characteristic
402	C₂×C₄	#14579194	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	1	no	—
408	C₈	—	316	2	no	—
409	C₈	—	632	1	no	—
410	C₂²	—	316	2	no	—
411	C₂²	—	316	2	no	—
412	C₂²	—	316	2	no	—
413	C₂²	—	316	2	no	—
414	C₂²	—	316	2	no	—
415	C₂²	—	316	2	no	—
416	C₂²	—	158	4	no	—
417	C₂²	#19098441	1	1	yes	characteristic
418	C₂²	C₈×D₃₁₆	1	1	yes	characteristic
419	C₂²	#19098636	1	1	yes	characteristic
420	C₂²	C₄×#11929613	1	1	yes	characteristic
421	C₂²	#19098665	1	1	yes	characteristic
422	C₂²	#19098681	1	1	yes	characteristic
423	C₂²	#19098686	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	316	2	no	—
427	C₄	—	316	2	no	—
428	C₄	—	632	1	no	—
429	C₄	C₂²⋊C₈×D₇₉	1	1	yes	characteristic
430	C₄	#19098528	1	1	yes	characteristic
431	C₄	#19098628	1	1	yes	characteristic
432	C₄	#19098633	1	1	yes	characteristic
433	C₄	#19098716	1	1	yes	characteristic
434	C₄	#19098727	1	1	yes	characteristic
435	C₄	#19098769	1	1	yes	characteristic
436	C₄	#19098779	1	1	yes	characteristic
437	C₂	—	316	4	no	—
438	C₂	C₈×#11929613	1	1	yes	characteristic
439	C₂	#23762214	1	1	yes	characteristic
440	C₂	#23762238	1	1	yes	characteristic
441	C₂	#23762259	1	1	yes	characteristic
442	C₂	#23763691	1	1	yes	characteristic
443	C₂	#23763726	1	1	yes	characteristic
444	C₂	#23763733	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1273	C₂
socle	C₂³×C₇₉	C₄×D₄
prime radical	C₂²×D₃₁₆	C₂×C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1273	D₇₉
hypocenter	C₇₉	#8945
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1273

Complements

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

N	H ≅ G/N	type
3. #23764336	C₂	semidirect
4. C₂×#19098295	C₂	semidirect
6. #23761235	C₂	semidirect
7. C₇₉×#1273	C₂	semidirect
34. C₂×#11929613	C₈	semidirect
79. C₂×Dic₁₅₈	C₂×C₈	semidirect
129. C₂×C₈×C₇₉	C₂×C₈	semidirect
130. C₂×C₈×C₇₉	SD₁₆	semidirect
229. #1273	D₇₉	semidirect
230. C₇₉	#8945	semidirect
342. C₂×C₈	C₈×D₇₉	semidirect
343. C₂×C₈	#11929613	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11929613	2
C₂×C₈×D₃₁₆	2
#23764336	2
C₂×#19098295	2
C₂×#19098292	2
#23761235	2
C₇₉×#1273	2
#8945	79