Subgroups — #34181055

Order 20224.

684 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14579158	C₂	1	1	yes	maximal, characteristic
2	#23763552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098306	C₂	1	2	yes	maximal
4	#23761284	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14579158	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₃₁₆	—	2	1	no	—
8	C₂×C₄×D₃₁₆	—	2	1	no	—
9	C₂×C₄×D₃₁₆	C₄	1	2	yes	—
10	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
13	#19098465	—	2	1	no	—
14	#19098465	—	2	1	no	—
15	#19098465	C₄	1	2	yes	—
16	#19098433	C₂²	1	1	yes	characteristic
17	#19098306	—	2	4	no	—
18	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
19	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	C₄³×C₇₉	C₂²	1	1	yes	characteristic
22	C₂²×D₃₁₆	—	2	1	no	—
23	C₂²×D₃₁₆	—	2	1	no	—
24	C₂²×D₃₁₆	C₂×C₄	1	2	yes	—
25	C₂²×C₄×D₇₉	—	2	2	no	—
26	C₂²×C₇₉⋊C₈	—	2	2	no	—
27	#14579158	—	2	1	no	—
28	#14579158	—	2	1	no	—
29	#14579158	D₄	1	2	yes	—
30	#14579158	Q₈	1	2	yes	—
31	C₄×D₃₁₆	—	4	2	no	—
32	C₄×D₃₁₆	—	4	2	no	—
33	C₄×D₃₁₆	—	4	2	no	—
34	C₄×D₃₁₆	—	4	2	no	—
35	C₄×D₃₁₆	—	4	4	no	—
36	C₂×C₄⋊Dic₇₉	—	2	1	no	—
37	C₂×C₄⋊Dic₇₉	—	2	1	no	—
38	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
39	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
40	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
41	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
42	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
45	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
46	C₂²×C₈×C₇₉	—	2	2	no	—
47	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₇₉	—	2	2	no	—
55	C₄⋊C₈×C₇₉	—	2	2	no	—
56	C₄⋊C₈×C₇₉	—	4	2	no	—
57	C₄⋊C₈×C₇₉	—	4	2	no	—
58	C₂³×D₇₉	—	2	2	no	—
59	C₂×D₃₁₆	—	2	2	no	—
60	C₂×D₃₁₆	—	2	2	no	—
61	C₂×D₃₁₆	—	2	2	no	—
62	C₂×D₃₁₆	—	2	2	no	—
63	C₂×D₃₁₆	—	2	2	no	—
64	C₂×D₃₁₆	—	4	2	no	—
65	C₂×D₃₁₆	—	4	2	no	—
66	C₂×D₃₁₆	—	4	1	no	—
67	C₂×D₃₁₆	—	4	1	no	—
68	C₂×D₃₁₆	—	4	1	no	—
69	C₂×D₃₁₆	—	4	1	no	—
70	C₂×D₃₁₆	—	4	1	no	—
71	C₂×D₃₁₆	—	4	1	no	—
72	C₂×D₃₁₆	—	4	1	no	—
73	C₂×D₃₁₆	—	4	1	no	—
74	C₂×D₃₁₆	C₄⋊C₄	1	4	yes	—
75	C₂²×Dic₇₉	—	2	2	no	—
76	C₂×C₄×D₇₉	—	4	4	no	—
77	C₂×C₄×D₇₉	—	4	4	no	—
78	C₂×C₄×D₇₉	—	4	4	no	—
79	C₂×C₇₉⋊C₈	—	4	2	no	—
80	C₂×C₇₉⋊C₈	—	4	2	no	—
81	C₂×C₇₉⋊C₈	—	4	2	no	—
82	C₄⋊Dic₇₉	—	4	2	no	—
83	C₄⋊Dic₇₉	—	4	1	no	—
84	C₄⋊Dic₇₉	—	4	1	no	—
85	C₄⋊Dic₇₉	—	4	1	no	—
86	C₄⋊Dic₇₉	—	4	1	no	—
87	(C₂×D₇₉)⋊C₄	—	4	4	no	—
88	(C₂×D₇₉)⋊C₄	—	4	4	no	—
89	(C₂×D₇₉)⋊C₄	—	4	4	no	—
90	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₇₉	—	4	2	no	—
98	C₂×C₈×C₇₉	—	4	2	no	—
99	C₂×C₈×C₇₉	—	4	2	no	—
100	C₄²×C₇₉	—	2	2	no	—
101	C₄²×C₇₉	—	2	1	no	—
102	C₄²×C₇₉	—	2	1	no	—
103	C₄²×C₇₉	—	2	1	no	—
104	C₄²×C₇₉	—	2	1	no	—
105	C₄²×C₇₉	—	4	1	no	—
106	C₄²×C₇₉	D₈	1	2	yes	—
107	C₄²×C₇₉	D₈	1	2	yes	—
108	C₄²×C₇₉	SD₁₆	1	2	yes	—
109	C₄²×C₇₉	SD₁₆	1	2	yes	—
110	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₇₉	#41	1	1	yes	characteristic
113	C₄²×C₇₉	#41	1	1	yes	characteristic
114	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×D₇₉	—	2	4	no	—
116	C₂²×D₇₉	—	4	2	no	—
117	C₂²×D₇₉	—	4	2	no	—
118	C₂²×D₇₉	—	4	2	no	—
119	C₂²×D₇₉	—	4	2	no	—
120	C₂²×D₇₉	—	4	2	no	—
121	C₂²×D₇₉	—	4	2	no	—
122	C₂×C₄×C₇₉	—	2	1	no	—
123	C₂×C₄×C₇₉	—	2	1	no	—
124	C₂×C₄×C₇₉	—	2	1	no	—
125	C₂×C₄×C₇₉	—	2	1	no	—
126	C₂×C₄×C₇₉	—	2	1	no	—
127	C₂×C₄×C₇₉	—	2	1	no	—
128	C₂×C₄×C₇₉	—	2	1	no	—
129	C₂×C₄×C₇₉	—	2	1	no	—
130	C₂×C₄×C₇₉	—	2	1	no	—
131	C₂×C₄×C₇₉	#100	1	2	yes	—
132	C₂×C₄×C₇₉	#102	1	2	yes	—
133	C₂×C₄×C₇₉	#102	1	2	yes	—
134	C₂×C₄×C₇₉	#102	1	2	yes	—
135	C₂×C₄×C₇₉	#102	1	2	yes	—
136	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
138	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
139	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
149	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
150	C₂×Dic₇₉	—	4	2	no	—
151	C₂×Dic₇₉	—	4	2	no	—
152	C₂×Dic₇₉	—	4	2	no	—
153	D₃₁₆	—	4	4	no	—
154	D₃₁₆	—	4	4	no	—
155	D₃₁₆	—	4	2	no	—
156	D₃₁₆	—	4	2	no	—
157	D₃₁₆	—	4	2	no	—
158	D₃₁₆	—	4	2	no	—
159	D₃₁₆	—	4	2	no	—
160	D₃₁₆	—	4	2	no	—
161	D₃₁₆	—	4	2	no	—
162	D₃₁₆	—	4	2	no	—
163	C₄×D₇₉	—	8	8	no	—
164	C₈×C₇₉	—	8	2	no	—
165	C₇₉⋊C₈	—	8	2	no	—
166	C₂²×C₇₉	#380	1	1	yes	characteristic
167	C₂²×C₇₉	C₂×#100	1	1	yes	characteristic
168	C₂²×C₇₉	#413	1	1	yes	characteristic
169	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
170	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
171	C₂²×C₇₉	#417	1	1	yes	characteristic
172	C₂²×C₇₉	#417	1	1	yes	characteristic
173	C₂×D₇₉	—	4	4	no	—
174	C₂×D₇₉	—	4	4	no	—
175	C₂×D₇₉	—	4	4	no	—
176	C₂×D₇₉	—	8	2	no	—
177	C₂×D₇₉	—	8	2	no	—
178	C₂×D₇₉	—	8	2	no	—
179	C₂×D₇₉	—	8	2	no	—
180	C₄×C₇₉	—	2	1	no	—
181	C₄×C₇₉	—	2	1	no	—
182	C₄×C₇₉	—	2	2	no	—
183	C₄×C₇₉	—	2	2	no	—
184	C₄×C₇₉	—	4	1	no	—
185	C₄×C₇₉	#331	1	4	yes	complemented
186	C₄×C₇₉	#459	1	1	yes	characteristic
187	C₄×C₇₉	#459	1	1	yes	characteristic
188	C₄×C₇₉	#461	1	1	yes	characteristic
189	C₄×C₇₉	#461	1	1	yes	characteristic
190	C₄×C₇₉	#474	1	1	yes	characteristic
191	C₄×C₇₉	#474	1	1	yes	characteristic
192	C₄×C₇₉	#476	1	1	yes	characteristic
193	C₄×C₇₉	#476	1	1	yes	characteristic
194	Dic₇₉	—	8	2	no	—
195	#8585	—	79	1	no	maximal, Sylow
196	C₂×C₇₉	C₂×#331	1	1	yes	characteristic
197	C₂×C₇₉	#1547	1	1	yes	characteristic
198	C₂×C₇₉	#1547	1	1	yes	characteristic
199	C₂×C₇₉	#1560	1	1	yes	characteristic
200	C₂×C₇₉	#1800	1	1	yes	characteristic
201	C₂×C₇₉	#1802	1	1	yes	characteristic
202	C₂×C₇₉	#1802	1	1	yes	characteristic
203	D₇₉	—	8	4	no	—
204	C₄×#127	—	79	1	no	—
205	#1842	—	79	1	no	—
206	#1842	D₇₉	1	1	yes	characteristic, complemented
207	C₂×#331	—	79	2	no	—
208	#1296	—	79	2	no	—
209	C₇₉	#8585	1	1	yes	characteristic, complemented, Sylow
210	C₂×#127	—	79	1	no	—
211	C₂×C₄×D₄	—	79	2	no	—
212	C₂×C₄×D₄	—	158	1	no	—
213	C₂×C₄×D₄	—	158	1	no	—
214	C₂×C₄⋊C₈	—	2	1	no	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	—	79	2	no	—
217	C₂×C₄⋊C₈	—	158	1	no	—
218	C₂×C₄⋊C₈	—	158	1	no	—
219	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
220	#390	—	79	2	no	—
221	#390	—	158	1	no	—
222	#390	—	158	1	no	—
223	#384	—	79	1	no	—
224	C₄³	C₂×D₇₉	1	1	yes	characteristic
225	#331	—	158	4	no	—
226	C₂²×D₄	—	79	2	no	—
227	C₂²×D₄	—	158	1	no	—
228	C₂²×D₄	—	158	1	no	—
229	C₂³×C₄	—	158	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	158	2	no	—
232	#127	—	79	2	no	—
233	#127	—	79	2	no	—
234	#127	—	158	1	no	—
235	#127	—	158	1	no	—
236	C₄×D₄	—	316	4	no	—
237	C₄×D₄	—	316	2	no	—
238	C₄×D₄	—	316	2	no	—
239	C₄×D₄	—	316	2	no	—
240	C₄×D₄	—	316	2	no	—
241	C₂×C₄⋊C₄	—	79	2	no	—
242	C₂×C₄⋊C₄	—	158	1	no	—
243	C₂×C₄⋊C₄	—	158	1	no	—
244	C₂×C₂²⋊C₄	—	158	2	no	—
245	C₂×C₂²⋊C₄	—	158	2	no	—
246	C₂×C₂²⋊C₄	—	158	2	no	—
247	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
249	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
250	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	4	2	no	—
257	C₄⋊C₈	—	4	2	no	—
258	C₄⋊C₈	—	316	2	no	—
259	C₄⋊C₈	—	316	2	no	—
260	C₄⋊C₈	—	158	2	no	—
261	C₄⋊C₈	—	158	2	no	—
262	C₂⁴	—	158	2	no	—
263	C₂×D₄	—	316	2	no	—
264	C₂×D₄	—	316	2	no	—
265	C₂×D₄	—	316	1	no	—
266	C₂×D₄	—	316	1	no	—
267	C₂×D₄	—	316	1	no	—
268	C₂×D₄	—	316	1	no	—
269	C₂×D₄	—	316	1	no	—
270	C₂×D₄	—	316	1	no	—
271	C₂×D₄	—	316	1	no	—
272	C₂×D₄	—	316	1	no	—
273	C₂×D₄	—	79	4	no	—
274	C₂×D₄	—	158	2	no	—
275	C₂×D₄	—	158	2	no	—
276	C₂×D₄	—	158	2	no	—
277	C₂×D₄	—	158	2	no	—
278	C₂×D₄	—	158	2	no	—
279	C₂²×C₄	—	316	4	no	—
280	C₂²×C₄	—	316	4	no	—
281	C₂²×C₄	—	316	4	no	—
282	C₂²×C₄	—	158	2	no	—
283	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	316	2	no	—
294	C₂×C₈	—	316	2	no	—
295	C₂×C₈	—	316	2	no	—
296	C₄⋊C₄	—	316	2	no	—
297	C₄⋊C₄	—	316	1	no	—
298	C₄⋊C₄	—	316	1	no	—
299	C₄⋊C₄	—	316	1	no	—
300	C₄⋊C₄	—	316	1	no	—
301	C₂²⋊C₄	—	316	4	no	—
302	C₂²⋊C₄	—	316	4	no	—
303	C₂²⋊C₄	—	316	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	4	1	no	—
310	C₄²	#11929609	1	2	yes	—
311	C₄²	D₆₃₂	1	2	yes	—
312	C₄²	#11929611	1	2	yes	—
313	C₄²	#11929613	1	2	yes	—
314	C₄²	D₄×D₇₉	1	1	yes	characteristic
315	C₄²	Q₈×D₇₉	1	1	yes	characteristic
316	C₄²	#11929623	1	1	yes	characteristic
317	C₄²	#11929625	1	1	yes	characteristic
318	C₂³	—	316	2	no	—
319	C₂³	—	316	2	no	—
320	C₂³	—	316	2	no	—
321	C₂³	—	316	2	no	—
322	C₂³	—	316	2	no	—
323	C₂³	—	316	2	no	—
324	C₂³	—	158	4	no	—
325	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
326	D₄	—	316	4	no	—
327	D₄	—	316	4	no	—
328	D₄	—	316	2	no	—
329	D₄	—	316	2	no	—
330	D₄	—	316	2	no	—
331	D₄	—	316	2	no	—
332	D₄	—	316	2	no	—
333	D₄	—	316	2	no	—
334	D₄	—	316	2	no	—
335	D₄	—	316	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	316	2	no	—
346	C₂×C₄	—	316	2	no	—
347	C₂×C₄	—	316	2	no	—
348	C₂×C₄	—	632	8	no	—
349	C₂×C₄	#14579077	1	2	yes	—
350	C₂×C₄	#14579081	1	2	yes	—
351	C₂×C₄	#14579081	1	2	yes	—
352	C₂×C₄	#14579083	1	2	yes	—
353	C₂×C₄	#14579083	1	2	yes	—
354	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
355	C₂×C₄	#14579119	1	1	yes	characteristic
356	C₂×C₄	#14579132	1	1	yes	characteristic
357	C₂×C₄	#14579136	1	1	yes	characteristic
358	C₂×C₄	#14579137	1	1	yes	characteristic
359	C₂×C₄	#14579141	1	1	yes	characteristic
360	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
361	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
362	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
363	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
364	C₂×C₄	#14579187	1	1	yes	characteristic
365	C₂×C₄	#14579189	1	1	yes	characteristic
366	C₂×C₄	#14579192	1	1	yes	characteristic
367	C₂×C₄	#14579194	1	1	yes	characteristic
368	C₈	—	8	2	no	—
369	C₈	—	632	2	no	—
370	C₂²	—	316	4	no	—
371	C₂²	—	316	4	no	—
372	C₂²	—	316	4	no	—
373	C₂²	—	632	2	no	—
374	C₂²	—	632	2	no	—
375	C₂²	—	632	2	no	—
376	C₂²	—	632	2	no	—
377	C₂²	#19098420	1	1	yes	characteristic
378	C₂²	C₂×#14579077	1	1	yes	characteristic
379	C₂²	#19098545	1	1	yes	characteristic
380	C₂²	C₂×#14579081	1	1	yes	characteristic
381	C₂²	C₂×#14579083	1	1	yes	characteristic
382	C₂²	#19098562	1	1	yes	characteristic
383	C₂²	#19098565	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	632	2	no	—
390	C₄	#19098306	1	4	yes	complemented
391	C₄	#19098755	1	1	yes	characteristic
392	C₄	#19098759	1	1	yes	characteristic
393	C₄	#19098765	1	1	yes	characteristic
394	C₄	#19098769	1	1	yes	characteristic
395	C₄	#19098840	1	1	yes	characteristic
396	C₄	#19098844	1	1	yes	characteristic
397	C₄	#19098850	1	1	yes	characteristic
398	C₄	#19098854	1	1	yes	characteristic
399	C₂	—	632	4	no	—
400	C₂	C₂×#19098306	1	1	yes	characteristic
401	C₂	#23762075	1	1	yes	characteristic
402	C₂	#23762078	1	1	yes	characteristic
403	C₂	#23762133	1	1	yes	characteristic
404	C₂	#23763389	1	1	yes	characteristic
405	C₂	#23763397	1	1	yes	characteristic
406	C₂	#23763401	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₇₉)⋊C₄
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1842	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂×#14579158	C₂²
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1842	D₇₉
hypocenter	C₇₉	#8585
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
2. #23763552	C₂	semidirect
4. #23761284	C₂	semidirect
5. C₇₉×#1842	C₂	semidirect
185. C₄×C₇₉	#331	semidirect
206. #1842	D₇₉	semidirect
209. C₇₉	#8585	semidirect
390. C₄	#19098306	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579158	2
#23763552	2
C₂×#19098306	2
#23761284	2
C₇₉×#1842	2
#8585	79