Subgroups — #34305878

Order 20224.

686 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772054	C₂	1	2	yes	maximal
2	#23771990	C₂	1	1	yes	maximal, characteristic
3	#23764153	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764148	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764000	C₂	1	2	yes	maximal, complemented
6	#23764000	C₂	1	2	yes	maximal, complemented
7	#23763500	C₂	1	2	yes	maximal
8	#23763442	C₂	1	1	yes	maximal, characteristic
9	#23763284	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763279	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579120	C₂²	1	2	yes	—
13	#19098621	—	2	2	no	—
14	#19098621	—	2	2	no	—
15	#19098617	—	2	2	no	—
16	#19098613	—	2	2	no	—
17	C₂×#14579097	C₂²	1	1	yes	characteristic
18	C₂×#14579097	C₂²	1	1	yes	characteristic
19	#19098605	C₄	1	2	yes	complemented
20	#19098605	C₄	1	2	yes	complemented
21	#19098605	C₄	1	2	yes	complemented
22	#19098605	C₄	1	2	yes	complemented
23	#19098601	C₂²	1	2	yes	—
24	#19098601	C₂²	1	1	yes	characteristic
25	#19098601	C₂²	1	1	yes	characteristic
26	#19098589	C₂²	1	2	yes	—
27	#19098589	C₂²	1	2	yes	—
28	#19098527	C₂²	1	2	yes	—
29	#19098518	C₂²	1	2	yes	—
30	#19098518	C₂²	1	2	yes	—
31	#19098328	C₂²	1	2	yes	—
32	#19098323	C₂²	1	2	yes	—
33	#19098323	C₂²	1	2	yes	—
34	#19098323	C₂²	1	2	yes	—
35	#19098323	C₂²	1	2	yes	—
36	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
41	#336×C₇₉	C₂²	1	1	yes	characteristic
42	#336×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#11929608	C₂³	1	2	yes	—
44	C₂×#11929608	C₂³	1	2	yes	—
45	#14579120	—	2	2	no	—
46	#14579120	—	2	2	no	—
47	#14579120	C₂×C₄	1	2	yes	—
48	#14579120	C₂×C₄	1	2	yes	—
49	#14579120	C₂³	1	2	yes	—
50	#14579120	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
54	C₂×C₄×Dic₇₉	—	2	2	no	—
55	#14579097	—	2	2	no	—
56	#14579097	—	2	2	no	—
57	#14579095	C₂×C₄	1	2	yes	—
58	#14579095	C₂×C₄	1	2	yes	—
59	#14579095	C₂×C₄	1	1	yes	characteristic
60	#14579095	C₂×C₄	1	1	yes	characteristic
61	#14579095	C₂×C₄	1	1	yes	characteristic
62	#14579095	C₂×C₄	1	1	yes	characteristic
63	#14579093	C₂×C₄	1	2	yes	—
64	#14579093	C₂×C₄	1	2	yes	—
65	#14579093	C₂×C₄	1	2	yes	—
66	#14579093	C₂×C₄	1	2	yes	—
67	Dic₇₉⋊C₈	—	2	2	no	—
68	Dic₇₉⋊C₈	—	2	2	no	—
69	Dic₇₉⋊C₈	—	2	2	no	—
70	Dic₇₉⋊C₈	—	2	2	no	—
71	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
72	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
73	#14579071	—	2	2	no	—
74	#14579071	—	2	2	no	—
75	C₈×Dic₇₉	—	2	2	no	—
76	C₈×Dic₇₉	—	2	2	no	—
77	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₇₉	—	2	2	no	—
79	C₂×M₁₆×C₇₉	—	2	2	no	—
80	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
81	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
87	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
89	C₂²⋊C₈×C₇₉	D₄	1	2	yes	—
90	C₂²⋊C₈×C₇₉	D₄	1	2	yes	—
91	#97×C₇₉	—	2	2	no	—
92	C₄×C₈×C₇₉	—	2	2	no	—
93	#95×C₇₉	—	2	1	no	—
94	C₂²×Dic₇₉	—	2	2	no	—
95	C₂²×Dic₇₉	—	2	2	no	—
96	#11929608	—	2	2	no	—
97	#11929608	—	2	2	no	—
98	#11929608	—	2	2	no	—
99	#11929608	—	2	2	no	—
100	C₂×C₇₉⋊C₈	—	2	2	no	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₄⋊Dic₇₉	—	2	2	no	—
103	C₄⋊Dic₇₉	—	2	2	no	—
104	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
105	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
106	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
107	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
108	C₂²⋊Dic₇₉	—	2	2	no	—
109	C₂²⋊Dic₇₉	—	2	2	no	—
110	C₂²⋊Dic₇₉	—	2	2	no	—
111	C₂²⋊Dic₇₉	—	2	2	no	—
112	C₄×Dic₇₉	—	2	2	no	—
113	C₄×Dic₇₉	—	2	2	no	—
114	C₄×Dic₇₉	—	2	2	no	—
115	C₄×Dic₇₉	—	2	2	no	—
116	C₂⁴×C₇₉	#41	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	—	2	1	no	—
118	C₂²×C₄×C₇₉	—	2	1	no	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	—	2	1	no	—
121	C₂²×C₄×C₇₉	—	2	1	no	—
122	C₂²×C₄×C₇₉	—	2	1	no	—
123	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₇₉	—	2	4	no	—
128	M₁₆×C₇₉	—	2	4	no	—
129	C₂×C₈×C₇₉	—	2	1	no	—
130	C₂×C₈×C₇₉	—	2	1	no	—
131	C₂×C₈×C₇₉	—	2	1	no	—
132	C₂×C₈×C₇₉	—	2	1	no	—
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₇₉	#41	1	2	yes	—
142	C₂×C₈×C₇₉	#41	1	2	yes	—
143	C₂²⋊C₄×C₇₉	—	4	2	no	—
144	C₄²×C₇₉	—	2	1	no	—
145	C₄²×C₇₉	—	2	1	no	—
146	C₄²×C₇₉	—	2	1	no	—
147	C₄²×C₇₉	—	2	1	no	—
148	C₂³×C₇₉	—	2	1	no	—
149	C₂³×C₇₉	—	2	1	no	—
150	C₂³×C₇₉	—	4	1	no	—
151	C₂³×C₇₉	—	4	1	no	—
152	C₂³×C₇₉	C₄×D₄	1	2	yes	—
153	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	2	2	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	4	1	no	—
162	C₂×C₄×C₇₉	—	4	1	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₇₉	—	2	2	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	2	2	no	—
176	C₂×Dic₇₉	—	2	2	no	—
177	C₂×Dic₇₉	—	4	4	no	—
178	C₂×Dic₇₉	—	8	2	no	—
179	C₈×C₇₉	—	2	2	no	—
180	C₈×C₇₉	—	2	1	no	—
181	C₈×C₇₉	—	2	1	no	—
182	C₈×C₇₉	—	2	2	no	—
183	C₈×C₇₉	#117	1	2	yes	—
184	C₈×C₇₉	#117	1	2	yes	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₇₉⋊C₈	—	4	2	no	—
187	C₂²×C₇₉	—	2	1	no	—
188	C₂²×C₇₉	—	2	1	no	—
189	C₂²×C₇₉	—	2	2	no	—
190	C₂²×C₇₉	—	2	2	no	—
191	C₂²×C₇₉	—	2	2	no	—
192	C₂²×C₇₉	—	8	1	no	—
193	C₂²×C₇₉	—	8	1	no	—
194	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂²×C₇₉	#552	1	1	yes	characteristic
196	C₂²×C₇₉	#552	1	1	yes	characteristic
197	C₄×C₇₉	—	2	2	no	—
198	C₄×C₇₉	—	4	2	no	—
199	C₄×C₇₉	—	8	1	no	—
200	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
201	C₄×C₇₉	#519	1	1	yes	characteristic
202	C₄×C₇₉	#547	1	1	yes	characteristic
203	C₄×C₇₉	#547	1	1	yes	characteristic
204	Dic₇₉	—	4	2	no	—
205	Dic₇₉	—	4	2	no	—
206	Dic₇₉	—	4	2	no	—
207	Dic₇₉	—	4	2	no	—
208	#22608	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	—	2	1	no	—
210	C₂×C₇₉	—	2	1	no	—
211	C₂×C₇₉	—	4	2	no	—
212	C₂×C₇₉	#2344	1	1	yes	characteristic
213	C₂×C₇₉	#2955	1	1	yes	characteristic
214	C₂×C₇₉	#2956	1	1	yes	characteristic
215	#2924	—	79	2	no	—
216	#2911	—	79	1	no	—
217	#1946	—	79	1	no	—
218	#1945	—	79	1	no	—
219	#1922	—	79	2	no	—
220	#1922	—	79	2	no	—
221	#1826	—	79	2	no	—
222	#1811	—	79	1	no	—
223	#1773	—	79	1	no	—
224	#1772	—	79	1	no	—
225	#1753	D₇₉	1	1	yes	characteristic
226	C₇₉	#22608	1	1	yes	characteristic, complemented, Sylow
227	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
228	C₂×#117	—	79	2	no	—
229	#433	—	158	2	no	—
230	#433	—	158	2	no	—
231	#432	—	158	2	no	—
232	#431	—	158	2	no	—
233	C₂×#108	—	79	1	no	—
234	C₂×#108	—	79	1	no	—
235	#428	—	79	2	no	—
236	#428	—	79	2	no	—
237	#428	—	79	2	no	—
238	#428	—	79	2	no	—
239	#427	—	79	2	no	—
240	#427	—	79	1	no	—
241	#427	—	79	1	no	—
242	#424	—	79	2	no	—
243	#424	—	79	2	no	—
244	#407	—	79	2	no	—
245	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
246	#405	—	79	2	no	—
247	#405	—	79	2	no	—
248	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
251	#341	—	79	2	no	—
252	#339	—	79	2	no	—
253	#339	—	79	2	no	—
254	#339	—	79	2	no	—
255	#339	—	79	2	no	—
256	#336	C₂×D₇₉	1	1	yes	characteristic
257	#336	C₂×D₇₉	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	79	2	no	—
262	C₂×M₁₆	—	79	2	no	—
263	C₂×M₁₆	C₄×D₇₉	1	2	yes	—
264	C₂×M₁₆	C₄×D₇₉	1	2	yes	—
265	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
269	#117	—	79	2	no	—
270	#117	—	79	2	no	—
271	#117	—	79	2	no	—
272	#117	—	79	2	no	—
273	#117	—	158	2	no	—
274	#117	—	158	2	no	—
275	C₂×C₄⋊C₄	—	79	2	no	—
276	C₂×C₄⋊C₄	—	79	2	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	158	2	no	—
279	C₂×C₄²	—	158	2	no	—
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
282	#108	—	158	2	no	—
283	#108	—	158	2	no	—
284	#107	—	79	2	no	—
285	#107	—	79	2	no	—
286	#107	—	79	1	no	—
287	#107	—	79	1	no	—
288	#107	—	79	1	no	—
289	#107	—	79	1	no	—
290	#106	—	79	2	no	—
291	#106	—	79	2	no	—
292	#106	—	79	2	no	—
293	#106	—	79	2	no	—
294	C₄⋊C₈	—	158	2	no	—
295	C₄⋊C₈	—	158	2	no	—
296	C₄⋊C₈	—	158	2	no	—
297	C₄⋊C₈	—	158	2	no	—
298	C₂²⋊C₈	—	158	2	no	—
299	C₂²⋊C₈	—	158	2	no	—
300	C₂²⋊C₈	D₃₁₆	1	2	yes	—
301	C₂²⋊C₈	D₃₁₆	1	2	yes	—
302	#97	—	2	2	no	—
303	#97	—	158	2	no	—
304	#97	—	158	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	158	2	no	—
307	C₄×C₈	—	158	2	no	—
308	#95	—	2	1	no	—
309	C₂⁴	#11929624	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	158	2	no	—
317	C₂²×C₄	—	158	2	no	—
318	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
319	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
320	C₂²×C₄	#11929624	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	158	2	no	—
325	M₁₆	—	158	2	no	—
326	M₁₆	—	158	2	no	—
327	M₁₆	—	158	2	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	—	2	1	no	—
334	C₂×C₈	—	158	2	no	—
335	C₂×C₈	—	158	2	no	—
336	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
337	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
339	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
340	C₂×C₈	C₂×D₃₁₆	1	2	yes	—
341	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
342	C₂×C₈	#11929623	1	2	yes	—
343	C₂×C₈	#11929623	1	2	yes	—
344	C₄⋊C₄	—	79	2	no	—
345	C₄⋊C₄	—	79	2	no	—
346	C₄⋊C₄	—	79	2	no	—
347	C₄⋊C₄	—	79	2	no	—
348	C₄⋊C₄	—	158	2	no	—
349	C₄⋊C₄	—	158	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	158	2	no	—
352	C₂²⋊C₄	—	158	2	no	—
353	C₂²⋊C₄	—	158	2	no	—
354	C₂²⋊C₄	—	158	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	158	2	no	—
360	C₄²	—	158	2	no	—
361	C₄²	—	158	2	no	—
362	C₄²	—	158	2	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₄×D₃₁₆	1	2	yes	—
368	C₂³	C₂×#11929624	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	316	4	no	—
382	C₂×C₄	—	632	2	no	—
383	C₂×C₄	—	158	2	no	—
384	C₂×C₄	—	158	2	no	—
385	C₂×C₄	—	158	2	no	—
386	C₂×C₄	—	158	2	no	—
387	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
388	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
390	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
391	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
392	C₂×C₄	#14579208	1	1	yes	characteristic
393	C₂×C₄	#14579208	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	316	2	no	—
399	C₈	—	316	2	no	—
400	C₈	#14579117	1	2	yes	—
401	C₈	#14579117	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
410	C₂²	#19099253	1	1	yes	characteristic
411	C₂²	#19099253	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	316	2	no	—
416	C₄	—	316	2	no	—
417	C₄	—	316	2	no	—
418	C₄	—	316	2	no	—
419	C₄	C₂×#14579117	1	1	yes	characteristic
420	C₄	#19099040	1	1	yes	characteristic
421	C₄	#19099217	1	1	yes	characteristic
422	C₄	#19099217	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#23766267	1	1	yes	characteristic
427	C₂	#23772304	1	1	yes	characteristic
428	C₂	#23772311	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1753	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂⁴×C₇₉	#41
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1753	D₇₉
hypocenter	C₇₉	#22608
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈ ◁ #1753

Complements

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

N	H ≅ G/N	type
3. #23764153	C₂	semidirect
4. #23764148	C₂	semidirect
5. #23764000	C₂	semidirect
6. #23764000	C₂	semidirect
9. #23763284	C₂	semidirect
10. #23763279	C₂	semidirect
19. #19098605	C₄	semidirect
20. #19098605	C₄	semidirect
21. #19098605	C₄	semidirect
22. #19098605	C₄	semidirect
226. C₇₉	#22608	semidirect

Maximal subgroups

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

subgroup	index
#23772054	2
#23771990	2
#23764153	2
#23764148	2
#23764000	2
#23763500	2
#23763442	2
#23763284	2
#23763279	2
C₇₉×#1753	2
#22608	79