Subgroups — #34288633

Order 20224.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14579167	C₂	1	1	yes	maximal, characteristic
2	#23763546	C₂	1	2	yes	maximal, complemented
3	#23763525	C₂	1	1	yes	maximal, characteristic, complemented
4	#23763523	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763503	C₂	1	2	yes	maximal
6	#23763447	C₂	1	1	yes	maximal, characteristic
7	#23763443	C₂	1	1	yes	maximal, characteristic
8	#23763279	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763201	C₂	1	2	yes	maximal
10	#23763155	C₂	1	2	yes	maximal, complemented
11	C₇₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	C₂²	1	1	yes	characteristic
13	C₂×#14579167	C₂²	1	1	yes	characteristic
14	C₄×#11929624	C₂²	1	1	yes	characteristic
15	C₂×#14579097	C₂²	1	1	yes	characteristic
16	#19098601	C₂²	1	1	yes	characteristic
17	#19098545	C₂²	1	2	yes	—
18	#19098536	C₂²	1	2	yes	—
19	#19098518	C₂²	1	2	yes	—
20	#19098518	C₂²	1	1	yes	characteristic
21	#19098518	C₂²	1	1	yes	characteristic
22	#19098517	C₄	1	2	yes	complemented
23	#19098517	C₄	1	2	yes	complemented
24	C₄×#11929608	C₂²	1	1	yes	characteristic
25	C₄×#11929607	C₄	1	2	yes	complemented
26	C₄×C₈×D₇₉	C₄	1	2	yes	complemented
27	#19098335	C₂²	1	2	yes	—
28	#19098333	C₂²	1	2	yes	—
29	#19098323	C₂²	1	2	yes	—
30	C₇₉⋊#338	C₂²	1	2	yes	—
31	#19098320	C₂²	1	2	yes	—
32	#19098319	C₂²	1	2	yes	—
33	#19098319	C₂²	1	2	yes	—
34	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
35	#427×C₇₉	C₂²	1	1	yes	characteristic
36	#405×C₇₉	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
38	#339×C₇₉	C₂²	1	2	yes	—
39	C₂×#11929624	C₂³	1	1	yes	characteristic
40	#14579167	—	2	1	no	—
41	#14579167	—	2	1	no	—
42	#14579167	—	2	1	no	—
43	#14579167	—	2	1	no	—
44	#14579167	—	2	1	no	—
45	#14579167	—	2	1	no	—
46	#14579167	—	2	1	no	—
47	#14579167	—	2	1	no	—
48	C₂×#11929608	C₂³	1	2	yes	—
49	C₂×#11929608	C₂³	1	1	yes	characteristic
50	C₂×#11929608	C₂³	1	1	yes	characteristic
51	C₂×#11929607	C₂×C₄	1	2	yes	—
52	C₂×#11929607	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₇₉	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₇₉	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₅₈	—	2	1	no	—
56	C₄×D₃₁₆	—	2	1	no	—
57	C₄×C₂²⋊D₇₉	—	2	2	no	—
58	#14579120	C₂³	1	2	yes	—
59	#14579120	C₂³	1	1	yes	characteristic
60	#14579118	C₂×C₄	1	2	yes	—
61	C₄²×D₇₉	C₂×C₄	1	2	yes	—
62	#14579097	—	2	1	no	—
63	#14579097	—	2	1	no	—
64	#14579095	—	2	1	no	—
65	#14579093	—	2	1	no	—
66	#14579079	—	2	2	no	—
67	#14579077	—	2	2	no	—
68	#14579075	—	2	4	no	—
69	#14579072	C₂×C₄	1	2	yes	—
70	#14579071	—	2	2	no	—
71	#14579071	C₂×C₄	1	2	yes	—
72	#14579071	C₂×C₄	1	2	yes	—
73	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₈×Dic₇₉	—	2	2	no	—
75	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
76	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
77	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
78	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	#117×C₇₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
82	#108×C₇₉	—	2	1	no	—
83	#108×C₇₉	—	2	1	no	—
84	#107×C₇₉	—	2	1	no	—
85	#106×C₇₉	—	2	1	no	—
86	#97×C₇₉	—	2	2	no	—
87	C₄×C₈×C₇₉	—	2	2	no	—
88	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
92	#11929624	—	2	1	no	—
93	#11929624	—	2	1	no	—
94	#11929624	—	2	1	no	—
95	#11929624	—	2	1	no	—
96	C₂×Dic₁₅₈	#41	1	1	yes	characteristic
97	C₂×D₃₁₆	#41	1	1	yes	characteristic
98	C₂×C₂²⋊D₇₉	#41	1	2	yes	—
99	C₂×C₄×D₇₉	—	2	2	no	—
100	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
101	#11929608	—	2	1	no	—
102	#11929608	—	2	1	no	—
103	#11929608	—	2	1	no	—
104	#11929608	—	2	1	no	—
105	#11929608	—	2	2	no	—
106	#11929608	—	2	2	no	—
107	#11929607	—	2	2	no	—
108	#11929607	—	2	2	no	—
109	#11929607	—	2	2	no	—
110	#11929607	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
114	C₈×D₇₉	—	2	2	no	—
115	C₈×D₇₉	—	2	2	no	—
116	C₈×D₇₉	—	2	2	no	—
117	C₈×D₇₉	—	2	2	no	—
118	C₄⋊Dic₇₉	—	2	1	no	—
119	C₄⋊Dic₇₉	—	2	2	no	—
120	Dic₇₉⋊C₄	—	2	2	no	—
121	C₂²⋊Dic₇₉	—	2	1	no	—
122	C₂²⋊Dic₇₉	—	2	2	no	—
123	(C₂×D₇₉)⋊C₄	—	2	2	no	—
124	C₄×Dic₇₉	—	2	2	no	—
125	C₄×Dic₇₉	—	2	2	no	—
126	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇₉	—	2	1	no	—
128	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₇₉	—	2	2	no	—
130	M₁₆×C₇₉	—	2	2	no	—
131	C₂×C₈×C₇₉	—	2	2	no	—
132	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
137	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
138	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
139	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
141	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
142	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
143	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
144	C₄⋊C₄×C₇₉	—	2	2	no	—
145	C₂²⋊C₄×C₇₉	—	2	2	no	—
146	C₄²×C₇₉	—	2	1	no	—
147	C₄²×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
150	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
151	C₂²×D₇₉	#117	1	2	yes	—
152	C₂×C₄×C₇₉	—	2	1	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	4	2	no	—
155	C₂×C₄×C₇₉	—	4	2	no	—
156	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₇₉	—	2	2	no	—
163	C₂²⋊D₇₉	—	2	2	no	—
164	C₂×Dic₇₉	—	2	2	no	—
165	C₂×Dic₇₉	—	4	2	no	—
166	C₂×Dic₇₉	#117	1	2	yes	—
167	D₃₁₆	—	2	1	no	—
168	D₃₁₆	—	2	1	no	—
169	C₄×D₇₉	—	2	2	no	—
170	C₄×D₇₉	—	2	2	no	—
171	C₄×D₇₉	—	4	4	no	—
172	Dic₁₅₈	—	2	1	no	—
173	Dic₁₅₈	—	2	1	no	—
174	C₈×C₇₉	—	4	2	no	—
175	C₈×C₇₉	#117	1	1	yes	characteristic
176	C₈×C₇₉	#117	1	1	yes	characteristic
177	C₈×C₇₉	#117	1	1	yes	characteristic
178	C₈×C₇₉	#117	1	1	yes	characteristic
179	C₈×C₇₉	#117	1	1	yes	characteristic
180	C₈×C₇₉	#117	1	1	yes	characteristic
181	C₈×C₇₉	#117	1	1	yes	characteristic
182	C₈×C₇₉	#117	1	1	yes	characteristic
183	C₇₉⋊C₈	—	2	2	no	—
184	C₇₉⋊C₈	—	2	2	no	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₂²×C₇₉	—	4	1	no	—
187	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
188	C₂²×C₇₉	#529	1	1	yes	characteristic
189	C₂²×C₇₉	#529	1	1	yes	characteristic
190	C₂×D₇₉	—	2	2	no	—
191	C₂×D₇₉	—	4	2	no	—
192	C₄×C₇₉	—	2	2	no	—
193	C₄×C₇₉	—	4	1	no	—
194	C₄×C₇₉	—	8	2	no	—
195	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
196	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
197	C₄×C₇₉	#529	1	1	yes	characteristic
198	C₄×C₇₉	#529	1	1	yes	characteristic
199	Dic₇₉	—	2	2	no	—
200	Dic₇₉	—	4	2	no	—
201	Dic₇₉	—	8	2	no	—
202	#20787	—	79	1	no	maximal, Sylow
203	C₂×C₇₉	—	2	1	no	—
204	C₂×C₇₉	—	2	1	no	—
205	C₂×C₇₉	—	2	1	no	—
206	C₂×C₇₉	#2283	1	1	yes	characteristic
207	D₇₉	—	4	2	no	—
208	C₄×#131	—	79	1	no	—
209	#1841	—	79	2	no	—
210	#1833	—	79	1	no	—
211	#1833	—	79	1	no	—
212	#1827	—	79	2	no	—
213	#1813	—	79	1	no	—
214	#1812	—	79	1	no	—
215	#1772	—	79	1	no	—
216	#1772	D₇₉	1	1	yes	characteristic, complemented
217	#1757	—	79	2	no	—
218	#1747	—	79	2	no	—
219	C₇₉	#20787	1	1	yes	characteristic, complemented, Sylow
220	C₂×#131	—	79	1	no	—
221	C₂×#131	—	79	1	no	—
222	C₄×#41	—	79	1	no	—
223	C₂×#108	—	79	1	no	—
224	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
225	#427	—	79	1	no	—
226	#427	C₂×D₇₉	1	1	yes	characteristic
227	#413	—	79	2	no	—
228	#410	—	79	2	no	—
229	#405	—	79	1	no	—
230	#405	—	79	1	no	—
231	#405	—	79	2	no	—
232	#405	—	79	2	no	—
233	#405	—	79	2	no	—
234	#405	C₂×D₇₉	1	2	yes	—
235	C₄×M₁₆	—	79	1	no	—
236	C₄×M₁₆	—	79	2	no	—
237	C₂×C₄×C₈	—	79	2	no	—
238	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
239	#344	—	79	2	no	—
240	#344	—	79	2	no	—
241	#339	—	79	2	no	—
242	#339	C₂×D₇₉	1	2	yes	—
243	#338	—	79	2	no	—
244	H(3,ℤ/4)	—	79	2	no	—
245	H(3,ℤ/4)	—	79	2	no	—
246	H(3,ℤ/4)	—	79	2	no	—
247	C₂×#41	—	79	1	no	—
248	#131	—	158	1	no	—
249	#131	—	158	1	no	—
250	#131	—	158	1	no	—
251	#131	—	158	1	no	—
252	#131	—	158	1	no	—
253	#131	—	158	1	no	—
254	#131	—	158	1	no	—
255	#131	—	158	1	no	—
256	C₂×M₁₆	—	79	1	no	—
257	C₂×M₁₆	—	79	1	no	—
258	C₂×M₁₆	—	79	2	no	—
259	C₂×M₁₆	—	79	2	no	—
260	C₂×M₁₆	—	79	2	no	—
261	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
262	C₂²×C₈	—	79	2	no	—
263	C₂²×C₈	—	79	2	no	—
264	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
266	C₄×Q₈	—	158	1	no	—
267	C₄×D₄	—	158	1	no	—
268	C₄×D₄	—	158	2	no	—
269	#117	—	79	1	no	—
270	#117	—	79	2	no	—
271	#117	—	79	2	no	—
272	#117	C₂²×D₇₉	1	2	yes	—
273	C₂×C₄²	—	79	2	no	—
274	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
275	#108	—	2	1	no	—
276	#108	—	2	1	no	—
277	#108	—	158	1	no	—
278	#108	—	158	1	no	—
279	#107	—	2	1	no	—
280	#107	—	158	1	no	—
281	#106	—	2	1	no	—
282	#106	—	158	1	no	—
283	#101	—	158	2	no	—
284	#100	—	158	2	no	—
285	#99	—	158	4	no	—
286	#97	—	2	2	no	—
287	#97	—	79	2	no	—
288	#97	—	79	2	no	—
289	#97	—	79	2	no	—
290	#97	—	158	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	79	2	no	—
293	C₄×C₈	—	79	2	no	—
294	C₄×C₈	—	79	2	no	—
295	C₄×C₈	—	158	2	no	—
296	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
297	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
298	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
299	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
300	#41	—	158	1	no	—
301	#41	—	158	1	no	—
302	#41	—	158	1	no	—
303	#41	—	158	1	no	—
304	C₂×Q₈	—	79	1	no	—
305	C₂×D₄	—	79	2	no	—
306	C₂×D₄	—	79	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	79	2	no	—
309	C₂²×C₄	—	158	2	no	—
310	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	158	2	no	—
314	M₁₆	—	158	2	no	—
315	M₁₆	—	158	1	no	—
316	M₁₆	—	158	1	no	—
317	M₁₆	—	158	1	no	—
318	M₁₆	—	158	1	no	—
319	M₁₆	—	158	2	no	—
320	M₁₆	—	158	2	no	—
321	M₁₆	—	158	2	no	—
322	M₁₆	—	158	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	79	2	no	—
325	C₂×C₈	—	79	2	no	—
326	C₂×C₈	—	158	2	no	—
327	C₂×C₈	—	158	2	no	—
328	C₂×C₈	—	158	2	no	—
329	C₂×C₈	—	158	2	no	—
330	C₂×C₈	—	158	2	no	—
331	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
335	C₂×C₈	#11929623	1	1	yes	characteristic
336	C₂×C₈	#11929623	1	1	yes	characteristic
337	C₂×C₈	#11929624	1	1	yes	characteristic
338	C₂×C₈	#11929624	1	1	yes	characteristic
339	C₂×C₈	#11929624	1	1	yes	characteristic
340	C₂×C₈	#11929624	1	1	yes	characteristic
341	C₂×C₈	#11929625	1	1	yes	characteristic
342	C₂×C₈	#11929625	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	158	2	no	—
345	C₄⋊C₄	—	158	2	no	—
346	C₄⋊C₄	—	158	1	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	158	2	no	—
349	C₂²⋊C₄	—	158	2	no	—
350	C₂²⋊C₄	—	158	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	79	2	no	—
354	C₄²	—	158	2	no	—
355	C₄²	—	158	2	no	—
356	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
358	C₂³	—	79	2	no	—
359	C₂³	#41×D₇₉	1	1	yes	characteristic
360	Q₈	—	158	1	no	—
361	Q₈	—	158	1	no	—
362	D₄	—	158	2	no	—
363	D₄	—	158	2	no	—
364	D₄	—	158	1	no	—
365	D₄	—	158	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	316	4	no	—
371	C₂×C₄	—	316	2	no	—
372	C₂×C₄	—	79	2	no	—
373	C₂×C₄	—	158	2	no	—
374	C₂×C₄	—	158	2	no	—
375	C₂×C₄	—	158	2	no	—
376	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
377	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
379	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
380	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
381	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	316	2	no	—
384	C₈	—	158	2	no	—
385	C₈	—	158	2	no	—
386	C₈	#14579118	1	1	yes	characteristic
387	C₈	#14579118	1	1	yes	characteristic
388	C₈	#14579118	1	1	yes	characteristic
389	C₈	#14579118	1	1	yes	characteristic
390	C₈	#14579119	1	1	yes	characteristic
391	C₈	#14579119	1	1	yes	characteristic
392	C₈	#14579119	1	1	yes	characteristic
393	C₈	#14579119	1	1	yes	characteristic
394	C₂²	—	4	1	no	—
395	C₂²	—	316	2	no	—
396	C₂²	—	158	2	no	—
397	C₂²	#117×D₇₉	1	1	yes	characteristic
398	C₂²	#19099095	1	1	yes	characteristic
399	C₂²	#19099100	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	316	2	no	—
404	C₄	—	632	2	no	—
405	C₄	—	158	2	no	—
406	C₄	C₂×#14579118	1	1	yes	characteristic
407	C₄	C₂×#14579119	1	1	yes	characteristic
408	C₄	#19099095	1	1	yes	characteristic
409	C₄	#19099100	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	316	2	no	—
414	C₂	#23765796	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#14579119
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1772	C₂
socle	C₂×C₇₉	#2283
prime radical	C₂×#11929624	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1772	D₇₉
hypocenter	C₇₉	#20787
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. #23763546	C₂	semidirect
3. #23763525	C₂	semidirect
4. #23763523	C₂	semidirect
8. #23763279	C₂	semidirect
10. #23763155	C₂	semidirect
11. C₇₉×#1772	C₂	semidirect
22. #19098517	C₄	semidirect
23. #19098517	C₄	semidirect
25. C₄×#11929607	C₄	semidirect
26. C₄×C₈×D₇₉	C₄	semidirect
216. #1772	D₇₉	semidirect
219. C₇₉	#20787	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579167	2
#23763546	2
#23763525	2
#23763523	2
#23763503	2
#23763447	2
#23763443	2
#23763279	2
#23763201	2
#23763155	2
C₇₉×#1772	2
#20787	79