Subgroups — #34257435

Order 20224.

684 conjugacy classes of subgroups.

The subgroup lattice has 428 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×#19098614	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23762190	C₂	1	4	yes	maximal, complemented
5	#23762184	C₂	1	4	yes	maximal, complemented
6	#23762158	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762156	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₇₉	—	2	1	no	—
11	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
12	#19098619	—	2	1	no	—
13	#19098619	C₂²	1	2	yes	—
14	#19098615	—	2	1	no	—
15	#19098615	C₂²	1	2	yes	—
16	#19098614	C₄	1	2	yes	—
17	#19098614	C₄	1	2	yes	—
18	#19098614	C₂²	1	2	yes	—
19	#19098614	C₂²	1	2	yes	—
20	#19098587	C₂²	1	1	yes	characteristic
21	#19098587	C₂²	1	1	yes	characteristic
22	#19098586	—	2	1	no	—
23	#19098585	—	2	1	no	—
24	#19098585	C₂²	1	2	yes	—
25	C₂×Dic₇₉⋊C₈	C₄	1	2	yes	—
26	C₄⋊C₈×D₇₉	—	2	1	no	—
27	C₄⋊C₈×D₇₉	C₂²	1	2	yes	—
28	#19098526	—	2	1	no	—
29	C₂×(C₂×D₇₉)⋊C₈	C₄	1	2	yes	—
30	M₁₆×Dic₇₉	—	2	1	no	—
31	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
32	#19098315	C₂²	1	4	yes	complemented
33	#19098314	C₂²	1	4	yes	complemented
34	#19098313	C₂²	1	4	yes	complemented
35	#423×C₇₉	C₂²	1	1	yes	characteristic
36	#423×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
38	#335×C₇₉	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
42	C₂×#11929608	—	2	1	no	—
43	C₂×#11929608	—	2	1	no	—
44	C₂×#11929607	—	2	2	no	—
45	M₁₆×D₇₉	—	4	4	no	—
46	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₇₉	—	2	2	no	—
48	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₇₉	Q₈	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	D₄	1	1	yes	characteristic
54	C₄²×D₇₉	D₄	1	1	yes	characteristic
55	C₄²×D₇₉	Q₈	1	1	yes	characteristic
56	C₄²×D₇₉	Q₈	1	1	yes	characteristic
57	C₄²×D₇₉	C₂³	1	1	yes	characteristic
58	C₄²×D₇₉	C₂³	1	1	yes	characteristic
59	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
63	Dic₇₉⋊C₈	—	2	2	no	—
64	Dic₇₉⋊C₈	—	2	2	no	—
65	Dic₇₉⋊C₈	C₂×C₄	1	4	yes	—
66	Dic₇₉⋊C₈	C₂×C₄	1	4	yes	—
67	(C₂×D₇₉)⋊C₈	—	2	2	no	—
68	(C₂×D₇₉)⋊C₈	—	2	2	no	—
69	(C₂×D₇₉)⋊C₈	C₂×C₄	1	4	yes	—
70	(C₂×D₇₉)⋊C₈	C₂×C₄	1	4	yes	—
71	#14579071	—	2	2	no	—
72	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
73	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
74	C₈×Dic₇₉	—	2	2	no	—
75	C₂×M₁₆×C₇₉	—	2	1	no	—
76	C₂×M₁₆×C₇₉	—	2	1	no	—
77	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₇₉	—	2	1	no	—
80	C₄⋊C₈×C₇₉	—	2	1	no	—
81	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
82	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
83	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
84	C₄×C₈×C₇₉	C₂³	1	2	yes	—
85	C₂³×D₇₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₇₉	—	2	4	no	—
90	C₂×C₄×D₇₉	—	2	2	no	—
91	C₂×C₄×D₇₉	—	2	2	no	—
92	C₂×C₄×D₇₉	—	4	2	no	—
93	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₇₉	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₇₉	C₂×Q₈	1	1	yes	characteristic
105	#11929608	—	4	2	no	—
106	#11929608	—	4	2	no	—
107	#11929607	—	4	4	no	—
108	C₂×C₇₉⋊C₈	—	2	2	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	4	2	no	—
111	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
112	C₈×D₇₉	—	4	4	no	—
113	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
123	C₄×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
124	C₄×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
128	M₁₆×C₇₉	—	4	2	no	—
129	M₁₆×C₇₉	—	4	2	no	—
130	C₂×C₈×C₇₉	—	2	2	no	—
131	C₂×C₈×C₇₉	—	2	2	no	—
132	C₂×C₈×C₇₉	—	4	2	no	—
133	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
134	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
137	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
138	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₇₉	—	2	2	no	—
140	C₂²×D₇₉	—	2	2	no	—
141	C₂²×D₇₉	—	4	1	no	—
142	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₇₉	#137	1	2	yes	—
151	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×Dic₇₉	—	2	2	no	—
155	C₂×Dic₇₉	—	2	2	no	—
156	C₂×Dic₇₉	—	4	1	no	—
157	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₄×D₇₉	—	2	2	no	—
164	C₄×D₇₉	—	2	2	no	—
165	C₄×D₇₉	—	2	2	no	—
166	C₄×D₇₉	—	2	1	no	—
167	C₄×D₇₉	—	2	1	no	—
168	C₄×D₇₉	—	2	1	no	—
169	C₄×D₇₉	—	2	1	no	—
170	C₄×D₇₉	—	2	2	no	—
171	C₄×D₇₉	—	2	2	no	—
172	C₄×D₇₉	—	2	2	no	—
173	C₄×D₇₉	—	2	2	no	—
174	C₄×D₇₉	—	4	1	no	—
175	C₄×D₇₉	—	4	1	no	—
176	C₄×D₇₉	#108	1	4	yes	—
177	C₈×C₇₉	—	2	4	no	—
178	C₈×C₇₉	—	4	2	no	—
179	C₈×C₇₉	—	4	2	no	—
180	C₇₉⋊C₈	—	2	4	no	—
181	C₇₉⋊C₈	—	4	2	no	—
182	C₇₉⋊C₈	—	4	2	no	—
183	C₂²×C₇₉	—	2	1	no	—
184	C₂²×C₇₉	—	2	1	no	—
185	C₂²×C₇₉	#428	1	2	yes	—
186	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂×D₇₉	—	2	1	no	—
188	C₂×D₇₉	—	2	1	no	—
189	C₂×D₇₉	—	2	1	no	—
190	C₂×D₇₉	—	2	1	no	—
191	C₂×D₇₉	—	2	1	no	—
192	C₂×D₇₉	—	4	4	no	—
193	C₂×D₇₉	C₂×#108	1	2	yes	—
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	#428	1	2	yes	—
197	C₄×C₇₉	C₂×#108	1	2	yes	—
198	C₄×C₇₉	#568	1	2	yes	—
199	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
201	Dic₇₉	—	2	1	no	—
202	Dic₇₉	—	2	1	no	—
203	Dic₇₉	—	2	1	no	—
204	Dic₇₉	—	2	1	no	—
205	Dic₇₉	—	2	1	no	—
206	Dic₇₉	C₂×#108	1	2	yes	—
207	#17817	—	79	1	no	maximal, Sylow
208	C₂×C₇₉	—	2	2	no	—
209	C₂×C₇₉	#2905	1	1	yes	characteristic
210	C₂×C₇₉	C₂×#428	1	1	yes	characteristic
211	C₂×C₇₉	C₂²×#108	1	1	yes	characteristic
212	D₇₉	—	2	2	no	—
213	D₇₉	—	4	1	no	—
214	#2920	—	79	1	no	—
215	C₂×#431	—	79	1	no	—
216	C₂×#423	—	79	1	no	—
217	#1574	—	79	4	no	—
218	#1573	—	79	4	no	—
219	#1567	—	79	1	no	—
220	#1567	D₇₉	1	1	yes	characteristic, complemented
221	#1566	—	79	1	no	—
222	#1566	—	79	1	no	—
223	C₇₉	#17817	1	1	yes	characteristic, complemented, Sylow
224	C₂²×M₁₆	—	158	1	no	—
225	C₂²×C₄²	—	79	1	no	—
226	#432	—	79	2	no	—
227	#432	—	158	1	no	—
228	#431	—	79	2	no	—
229	#431	—	79	2	no	—
230	#431	—	79	2	no	—
231	#431	—	79	2	no	—
232	#431	—	79	2	no	—
233	#431	—	158	1	no	—
234	#423	—	79	1	no	—
235	#423	—	79	1	no	—
236	#423	—	79	2	no	—
237	#423	—	158	1	no	—
238	#423	—	158	1	no	—
239	#423	C₂×D₇₉	1	1	yes	characteristic
240	#423	C₂×D₇₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	—	79	2	no	—
242	C₂×C₄⋊C₈	—	79	2	no	—
243	C₂×C₄⋊C₈	—	158	1	no	—
244	#407	—	158	1	no	—
245	C₂×C₂²⋊C₈	—	79	2	no	—
246	C₄×M₁₆	—	158	1	no	—
247	C₂×C₄×C₈	—	79	1	no	—
248	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
249	#335	—	79	4	no	—
250	#335	C₂×D₇₉	1	4	yes	complemented
251	#334	—	79	4	no	—
252	#334	—	79	4	no	—
253	C₂³×C₄	—	79	1	no	—
254	C₂³×C₄	—	79	1	no	—
255	C₂³×C₄	—	79	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	316	4	no	—
259	C₂×M₁₆	—	158	2	no	—
260	C₂×M₁₆	—	158	1	no	—
261	C₂×M₁₆	—	158	1	no	—
262	C₂²×C₈	—	79	2	no	—
263	C₂²×C₈	—	158	2	no	—
264	C₂²×C₈	C₄×D₇₉	1	2	yes	—
265	C₂×C₄²	—	79	1	no	—
266	C₂×C₄²	—	79	1	no	—
267	C₂×C₄²	—	79	1	no	—
268	C₂×C₄²	—	79	1	no	—
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	C₂²×D₇₉	1	1	yes	characteristic
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	79	4	no	—
280	C₄⋊C₈	—	79	4	no	—
281	C₄⋊C₈	—	79	2	no	—
282	C₄⋊C₈	—	79	2	no	—
283	C₄⋊C₈	—	158	2	no	—
284	C₄⋊C₈	—	158	2	no	—
285	C₄⋊C₈	—	158	1	no	—
286	C₄⋊C₈	—	158	1	no	—
287	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
288	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
289	C₂²⋊C₈	—	79	4	no	—
290	C₂²⋊C₈	—	79	4	no	—
291	C₂²⋊C₈	—	158	2	no	—
292	C₂²⋊C₈	—	158	2	no	—
293	#97	—	158	2	no	—
294	C₄×C₈	—	79	2	no	—
295	C₄×C₈	—	79	2	no	—
296	C₄×C₈	—	158	2	no	—
297	C₄×C₈	C₄×D₇₉	1	2	yes	—
298	C₄×C₈	C₂²×D₇₉	1	2	yes	—
299	C₂⁴	—	79	1	no	—
300	C₂²×C₄	—	316	2	no	—
301	C₂²×C₄	—	79	1	no	—
302	C₂²×C₄	—	79	1	no	—
303	C₂²×C₄	—	79	1	no	—
304	C₂²×C₄	—	79	1	no	—
305	C₂²×C₄	—	79	1	no	—
306	C₂²×C₄	—	79	1	no	—
307	C₂²×C₄	—	79	1	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	—	158	4	no	—
317	C₂²×C₄	—	158	2	no	—
318	C₂²×C₄	—	158	2	no	—
319	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
321	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
322	M₁₆	—	4	2	no	—
323	M₁₆	—	4	2	no	—
324	M₁₆	—	316	4	no	—
325	M₁₆	—	316	2	no	—
326	M₁₆	—	316	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	316	4	no	—
331	C₂×C₈	—	316	2	no	—
332	C₂×C₈	—	79	4	no	—
333	C₂×C₈	—	158	2	no	—
334	C₂×C₈	—	158	2	no	—
335	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
336	C₄²	—	79	1	no	—
337	C₄²	—	79	1	no	—
338	C₄²	—	79	1	no	—
339	C₄²	—	79	1	no	—
340	C₄²	—	79	1	no	—
341	C₄²	—	79	1	no	—
342	C₄²	—	79	1	no	—
343	C₄²	—	79	1	no	—
344	C₄²	—	79	1	no	—
345	C₄²	—	79	1	no	—
346	C₄²	—	79	1	no	—
347	C₄²	—	79	1	no	—
348	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
349	C₄²	D₄×D₇₉	1	1	yes	characteristic
350	C₄²	Q₈×D₇₉	1	1	yes	characteristic
351	C₄²	C₂³×D₇₉	1	1	yes	characteristic
352	C₂³	—	316	1	no	—
353	C₂³	—	79	1	no	—
354	C₂³	—	79	1	no	—
355	C₂³	—	158	2	no	—
356	C₂³	—	158	2	no	—
357	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	316	1	no	—
361	C₂×C₄	—	316	1	no	—
362	C₂×C₄	—	316	1	no	—
363	C₂×C₄	—	79	1	no	—
364	C₂×C₄	—	79	4	no	—
365	C₂×C₄	—	79	1	no	—
366	C₂×C₄	—	79	1	no	—
367	C₂×C₄	—	79	1	no	—
368	C₂×C₄	—	79	1	no	—
369	C₂×C₄	—	79	1	no	—
370	C₂×C₄	—	158	2	no	—
371	C₂×C₄	—	158	2	no	—
372	C₂×C₄	—	158	2	no	—
373	C₂×C₄	—	158	2	no	—
374	C₂×C₄	—	158	2	no	—
375	C₂×C₄	—	158	2	no	—
376	C₂×C₄	—	158	1	no	—
377	C₂×C₄	—	158	1	no	—
378	C₂×C₄	—	158	1	no	—
379	C₂×C₄	—	158	1	no	—
380	C₂×C₄	—	158	2	no	—
381	C₂×C₄	—	158	2	no	—
382	C₂×C₄	—	158	2	no	—
383	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
384	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
385	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
386	C₂×C₄	#14579185	1	2	yes	—
387	C₂×C₄	#14579193	1	2	yes	—
388	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
390	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	316	2	no	—
395	C₈	—	316	2	no	—
396	C₈	—	158	4	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	316	4	no	—
400	C₂²	—	79	2	no	—
401	C₂²	—	158	1	no	—
402	C₂²	—	158	1	no	—
403	C₂²	—	158	1	no	—
404	C₂²	—	158	1	no	—
405	C₂²	—	158	1	no	—
406	C₂²	#19098604	1	2	yes	—
407	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	79	2	no	—
411	C₄	—	158	1	no	—
412	C₄	—	158	1	no	—
413	C₄	—	158	1	no	—
414	C₄	—	158	1	no	—
415	C₄	—	158	1	no	—
416	C₄	#19098604	1	2	yes	—
417	C₄	#108×D₇₉	1	2	yes	—
418	C₄	#19099329	1	2	yes	—
419	C₄	C₂×#14579185	1	1	yes	characteristic
420	C₄	C₂×#14579193	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	316	1	no	—
423	C₂	—	158	2	no	—
424	C₂	#23771962	1	1	yes	characteristic
425	C₂	C₂×#19098604	1	1	yes	characteristic
426	C₂	C₂×#108×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1567	C₂
socle	C₂²×C₇₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₉	C₄⋊C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1567	D₇₉
hypocenter	C₇₉	#17817
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
4. #23762190	C₂	semidirect
5. #23762184	C₂	semidirect
6. #23762158	C₂	semidirect
7. #23762156	C₂	semidirect
8. #23762155	C₂	semidirect
9. C₇₉×#1567	C₂	semidirect
32. #19098315	C₂²	semidirect
33. #19098314	C₂²	semidirect
34. #19098313	C₂²	semidirect
38. #335×C₇₉	C₂²	semidirect
220. #1567	D₇₉	semidirect
223. C₇₉	#17817	semidirect
250. #335	C₂×D₇₉	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×#19098614	2
#423×D₇₉	2
#23762190	2
#23762184	2
#23762158	2
#23762156	2
#23762155	2
C₇₉×#1567	2
#17817	79