Subgroups — #34298897

Order 20224.

704 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772032	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098618	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23764172	C₂	1	4	yes	maximal, complemented
5	#23763603	C₂	1	4	yes	maximal
6	#23763574	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763541	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1849	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₇₉	C₂²	1	2	yes	—
11	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
12	#19098619	—	2	1	no	—
13	#19098619	—	2	1	no	—
14	#19098618	C₄	1	2	yes	—
15	#19098618	C₄	1	2	yes	—
16	#19098618	C₄	1	2	yes	—
17	#19098618	C₄	1	2	yes	—
18	#19098615	—	2	1	no	—
19	#19098615	—	2	1	no	—
20	C₂×#14579096	C₂²	1	4	yes	—
21	#19098587	C₂²	1	1	yes	characteristic
22	#19098587	C₂²	1	1	yes	characteristic
23	#19098586	C₂²	1	2	yes	—
24	#19098585	—	2	1	no	—
25	#19098585	—	2	1	no	—
26	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
27	C₄⋊C₈×D₇₉	—	2	1	no	—
28	C₄⋊C₈×D₇₉	—	2	1	no	—
29	#19098526	C₂²	1	2	yes	—
30	C₂×(C₂×D₇₉)⋊C₈	C₂²	1	2	yes	—
31	M₁₆×Dic₇₉	C₂²	1	2	yes	—
32	C₂×#14579072	C₂²	1	1	yes	characteristic
33	#19098328	C₂²	1	4	yes	—
34	#19098327	C₂²	1	4	yes	—
35	C₂×#108×C₇₉	C₂²	1	4	yes	—
36	#423×C₇₉	C₂²	1	1	yes	characteristic
37	#423×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
40	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
41	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
42	C₂×#11929608	C₂³	1	2	yes	—
43	C₂×#11929608	C₂³	1	2	yes	—
44	C₂×#11929607	—	2	2	no	—
45	M₁₆×D₇₉	—	4	4	no	—
46	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
47	C₂×C₈×D₇₉	—	2	2	no	—
48	C₂×C₄×Dic₇₉	Q₈	1	1	yes	characteristic
49	C₂×C₄×Dic₇₉	Q₈	1	1	yes	characteristic
50	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
51	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₇₉	D₄	1	1	yes	characteristic
56	C₄²×D₇₉	D₄	1	1	yes	characteristic
57	C₄²×D₇₉	D₄	1	1	yes	characteristic
58	C₄²×D₇₉	D₄	1	1	yes	characteristic
59	#14579096	—	4	4	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
64	Dic₇₉⋊C₈	—	2	2	no	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	Dic₇₉⋊C₈	C₂×C₄	1	4	yes	—
67	Dic₇₉⋊C₈	C₂×C₄	1	4	yes	—
68	(C₂×D₇₉)⋊C₈	—	2	2	no	—
69	(C₂×D₇₉)⋊C₈	—	2	2	no	—
70	(C₂×D₇₉)⋊C₈	C₂×C₄	1	4	yes	—
71	(C₂×D₇₉)⋊C₈	C₂×C₄	1	4	yes	—
72	#14579072	C₂×C₄	1	2	yes	—
73	#14579072	C₂×C₄	1	2	yes	—
74	#14579071	—	2	2	no	—
75	C₈×Dic₇₉	—	2	2	no	—
76	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
77	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
78	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
80	#108×C₇₉	—	4	4	no	—
81	C₄⋊C₈×C₇₉	—	2	1	no	—
82	C₄⋊C₈×C₇₉	—	2	1	no	—
83	C₄⋊C₈×C₇₉	—	2	1	no	—
84	C₄⋊C₈×C₇₉	—	2	1	no	—
85	#97×C₇₉	C₂×C₄	1	2	yes	—
86	#97×C₇₉	C₂×C₄	1	2	yes	—
87	C₂³×D₇₉	C₂×Q₈	1	1	yes	characteristic
88	C₂²×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
89	C₂²×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
90	C₂²×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₄×D₇₉	—	2	2	no	—
92	C₂×C₄×D₇₉	—	2	2	no	—
93	C₂×C₄×D₇₉	—	4	2	no	—
94	C₂×C₄×D₇₉	—	4	2	no	—
95	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
107	#11929608	—	2	4	no	—
108	#11929608	—	2	4	no	—
109	#11929607	—	4	4	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	—	2	2	no	—
114	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
115	C₈×D₇₉	—	4	4	no	—
116	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₇₉	—	2	4	no	—
132	M₁₆×C₇₉	—	2	4	no	—
133	C₂×C₈×C₇₉	—	2	2	no	—
134	C₂×C₈×C₇₉	—	2	2	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
138	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂³×C₇₉	C₂²×Q₈	1	1	yes	characteristic
143	C₂²×D₇₉	—	2	2	no	—
144	C₂²×D₇₉	—	2	2	no	—
145	C₂²×D₇₉	—	4	1	no	—
146	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	—	4	1	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
157	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
158	C₂×Dic₇₉	—	2	2	no	—
159	C₂×Dic₇₉	—	2	2	no	—
160	C₂×Dic₇₉	—	4	1	no	—
161	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₄×D₇₉	—	2	2	no	—
168	C₄×D₇₉	—	2	2	no	—
169	C₄×D₇₉	—	2	2	no	—
170	C₄×D₇₉	—	2	2	no	—
171	C₄×D₇₉	—	2	1	no	—
172	C₄×D₇₉	—	2	1	no	—
173	C₄×D₇₉	—	2	1	no	—
174	C₄×D₇₉	—	2	1	no	—
175	C₄×D₇₉	—	2	2	no	—
176	C₄×D₇₉	—	2	2	no	—
177	C₄×D₇₉	—	4	1	no	—
178	C₄×D₇₉	—	4	1	no	—
179	C₄×D₇₉	—	4	1	no	—
180	C₄×D₇₉	—	4	1	no	—
181	C₈×C₇₉	—	2	4	no	—
182	C₈×C₇₉	—	4	2	no	—
183	C₈×C₇₉	—	4	2	no	—
184	C₇₉⋊C₈	—	2	4	no	—
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	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₇₉	#544	1	2	yes	—
191	C₂×D₇₉	—	2	1	no	—
192	C₂×D₇₉	—	2	1	no	—
193	C₂×D₇₉	—	2	1	no	—
194	C₂×D₇₉	—	2	1	no	—
195	C₂×D₇₉	—	2	1	no	—
196	C₂×D₇₉	—	4	4	no	—
197	C₂×D₇₉	#430	1	2	yes	—
198	C₄×C₇₉	—	2	1	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	#520	1	2	yes	—
203	C₄×C₇₉	#535	1	1	yes	characteristic
204	C₄×C₇₉	#536	1	1	yes	characteristic
205	Dic₇₉	—	2	1	no	—
206	Dic₇₉	—	2	1	no	—
207	Dic₇₉	—	2	1	no	—
208	Dic₇₉	—	2	1	no	—
209	Dic₇₉	—	2	1	no	—
210	Dic₇₉	#430	1	2	yes	—
211	#21994	—	79	1	no	maximal, Sylow
212	C₂×C₇₉	—	2	2	no	—
213	C₂×C₇₉	#2317	1	1	yes	characteristic
214	C₂×C₇₉	C₂×#430	1	1	yes	characteristic
215	C₂×C₇₉	C₂×#430	1	1	yes	characteristic
216	D₇₉	—	2	2	no	—
217	D₇₉	—	4	1	no	—
218	#2920	—	79	1	no	—
219	C₂×#432	—	79	1	no	—
220	C₂×#423	—	79	1	no	—
221	#1950	—	79	4	no	—
222	#1855	—	79	4	no	—
223	#1849	—	79	1	no	—
224	#1849	D₇₉	1	1	yes	characteristic, complemented
225	#1838	—	79	1	no	—
226	#1838	—	79	1	no	—
227	C₇₉	#21994	1	1	yes	characteristic, complemented, Sylow
228	C₂²×M₁₆	—	79	2	no	—
229	C₂²×C₄²	—	79	1	no	—
230	#432	—	79	2	no	—
231	#432	—	79	2	no	—
232	#432	—	79	2	no	—
233	#432	—	79	2	no	—
234	#432	—	158	1	no	—
235	#432	—	158	1	no	—
236	#431	—	158	1	no	—
237	#431	—	158	1	no	—
238	C₂×#108	—	79	4	no	—
239	C₂×#108	C₂×D₇₉	1	4	yes	—
240	#423	—	79	2	no	—
241	#423	—	79	1	no	—
242	#423	—	79	1	no	—
243	#423	—	158	1	no	—
244	#423	—	158	1	no	—
245	#423	C₂×D₇₉	1	1	yes	characteristic
246	#423	C₂×D₇₉	1	1	yes	characteristic
247	C₂×C₄⋊C₈	—	79	2	no	—
248	C₂×C₄⋊C₈	—	158	1	no	—
249	C₂×C₄⋊C₈	—	158	1	no	—
250	#407	—	79	2	no	—
251	C₂×C₂²⋊C₈	—	79	2	no	—
252	C₄×M₁₆	—	79	2	no	—
253	C₂×#97	—	79	1	no	—
254	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
255	#341	—	79	4	no	—
256	#341	—	79	4	no	—
257	C₂³×C₄	—	79	1	no	—
258	C₂³×C₄	—	79	1	no	—
259	C₂³×C₄	—	79	1	no	—
260	C₂×M₁₆	—	316	4	no	—
261	C₂×M₁₆	—	79	2	no	—
262	C₂×M₁₆	—	79	2	no	—
263	C₂×M₁₆	—	158	2	no	—
264	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
265	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
266	C₂²×C₈	—	79	2	no	—
267	C₂²×C₈	—	158	2	no	—
268	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
269	C₂×C₄²	—	79	1	no	—
270	C₂×C₄²	—	79	1	no	—
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	1	no	—
273	C₂×C₄²	—	79	1	no	—
274	C₂×C₄²	—	79	1	no	—
275	C₂×C₄²	—	79	1	no	—
276	C₂×C₄²	—	79	1	no	—
277	C₂×C₄²	—	79	1	no	—
278	C₂×C₄²	—	79	1	no	—
279	C₂×C₄²	—	79	1	no	—
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	#108	—	4	4	no	—
282	#108	—	316	4	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	79	4	no	—
288	C₄⋊C₈	—	79	4	no	—
289	C₄⋊C₈	—	158	2	no	—
290	C₄⋊C₈	—	158	2	no	—
291	C₄⋊C₈	—	158	1	no	—
292	C₄⋊C₈	—	158	1	no	—
293	C₄⋊C₈	—	158	1	no	—
294	C₄⋊C₈	—	158	1	no	—
295	C₂²⋊C₈	—	79	4	no	—
296	C₂²⋊C₈	—	79	4	no	—
297	C₂²⋊C₈	—	158	2	no	—
298	C₂²⋊C₈	—	158	2	no	—
299	#97	—	79	2	no	—
300	#97	—	79	2	no	—
301	#97	—	158	2	no	—
302	#97	C₄×D₇₉	1	2	yes	—
303	#97	C₄×D₇₉	1	2	yes	—
304	C₄×C₈	—	158	2	no	—
305	C₂⁴	—	79	1	no	—
306	C₂²×C₄	—	316	2	no	—
307	C₂²×C₄	—	316	2	no	—
308	C₂²×C₄	—	79	1	no	—
309	C₂²×C₄	—	79	1	no	—
310	C₂²×C₄	—	79	1	no	—
311	C₂²×C₄	—	79	1	no	—
312	C₂²×C₄	—	79	1	no	—
313	C₂²×C₄	—	79	1	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	1	no	—
317	C₂²×C₄	—	79	1	no	—
318	C₂²×C₄	—	79	1	no	—
319	C₂²×C₄	—	79	1	no	—
320	C₂²×C₄	—	79	1	no	—
321	C₂²×C₄	—	79	1	no	—
322	C₂²×C₄	—	79	1	no	—
323	C₂²×C₄	—	158	2	no	—
324	C₂²×C₄	—	158	2	no	—
325	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
326	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	316	4	no	—
331	M₁₆	—	158	4	no	—
332	M₁₆	—	158	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	316	4	no	—
338	C₂×C₈	—	79	4	no	—
339	C₂×C₈	—	158	2	no	—
340	C₂×C₈	—	158	2	no	—
341	C₂×C₈	—	158	2	no	—
342	C₂×C₈	—	158	2	no	—
343	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
344	C₄²	—	79	1	no	—
345	C₄²	—	79	1	no	—
346	C₄²	—	79	1	no	—
347	C₄²	—	79	1	no	—
348	C₄²	—	79	1	no	—
349	C₄²	—	79	1	no	—
350	C₄²	—	79	1	no	—
351	C₄²	—	79	1	no	—
352	C₄²	—	79	1	no	—
353	C₄²	—	79	1	no	—
354	C₄²	—	79	1	no	—
355	C₄²	—	79	1	no	—
356	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
358	C₄²	D₄×D₇₉	1	1	yes	characteristic
359	C₄²	D₄×D₇₉	1	1	yes	characteristic
360	C₂³	—	316	1	no	—
361	C₂³	—	79	1	no	—
362	C₂³	—	79	1	no	—
363	C₂³	—	158	2	no	—
364	C₂³	—	158	2	no	—
365	C₂³	C₂×Q₈×D₇₉	1	1	yes	characteristic
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	316	1	no	—
369	C₂×C₄	—	316	1	no	—
370	C₂×C₄	—	316	1	no	—
371	C₂×C₄	—	316	1	no	—
372	C₂×C₄	—	316	1	no	—
373	C₂×C₄	—	79	1	no	—
374	C₂×C₄	—	79	1	no	—
375	C₂×C₄	—	79	1	no	—
376	C₂×C₄	—	79	1	no	—
377	C₂×C₄	—	79	1	no	—
378	C₂×C₄	—	79	1	no	—
379	C₂×C₄	—	158	2	no	—
380	C₂×C₄	—	158	2	no	—
381	C₂×C₄	—	158	2	no	—
382	C₂×C₄	—	158	2	no	—
383	C₂×C₄	—	158	2	no	—
384	C₂×C₄	—	158	2	no	—
385	C₂×C₄	—	158	1	no	—
386	C₂×C₄	—	158	1	no	—
387	C₂×C₄	—	158	2	no	—
388	C₂×C₄	—	158	2	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	1	no	—
391	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
392	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
393	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
397	C₂×C₄	#14579206	1	2	yes	—
398	C₂×C₄	#14579209	1	2	yes	—
399	C₈	—	2	4	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	316	2	no	—
403	C₈	—	316	2	no	—
404	C₈	—	158	4	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	316	4	no	—
408	C₂²	—	79	2	no	—
409	C₂²	—	158	1	no	—
410	C₂²	—	158	1	no	—
411	C₂²	—	158	1	no	—
412	C₂²	—	158	1	no	—
413	C₂²	—	158	1	no	—
414	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
415	C₂²	#19099190	1	2	yes	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	79	2	no	—
421	C₄	—	158	1	no	—
422	C₄	—	158	1	no	—
423	C₄	—	158	1	no	—
424	C₄	—	158	1	no	—
425	C₄	—	158	1	no	—
426	C₄	#19099044	1	2	yes	—
427	C₄	#19099126	1	1	yes	characteristic
428	C₄	#19099138	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	316	1	no	—
431	C₂	—	158	2	no	—
432	C₂	#23766021	1	1	yes	characteristic
433	C₂	#430×D₇₉	1	1	yes	characteristic
434	C₂	#430×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1849	C₂
socle	C₂²×C₇₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₉	C₂×Q₈
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1849	D₇₉
hypocenter	C₇₉	#21994
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

Complements

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

N	H ≅ G/N	type
4. #23764172	C₂	semidirect
6. #23763574	C₂	semidirect
7. #23763541	C₂	semidirect
8. #23763540	C₂	semidirect
9. C₇₉×#1849	C₂	semidirect
224. #1849	D₇₉	semidirect
227. C₇₉	#21994	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
C₂×#19098618	2
#423×D₇₉	2
#23764172	2
#23763603	2
#23763574	2
#23763541	2
#23763540	2
C₇₉×#1849	2
#21994	79