Subgroups — C₂×C₇₃×#1931 #32930478

Order 18688.

1154 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#418×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#100×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#405×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#1931	C₂	1	8	yes	maximal, direct product factor
7	C₂×#343×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#341×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
16	#428×C₇₃	—	2	2	no	—
17	#428×C₇₃	C₂²	1	4	yes	complemented
18	C₂×#107×C₇₃	—	2	1	no	—
19	C₂×#106×C₇₃	—	2	1	no	—
20	#418×C₇₃	—	2	2	no	—
21	#418×C₇₃	C₂²	1	4	yes	—
22	C₂×#102×C₇₃	—	2	1	no	—
23	C₂×#102×C₇₃	—	2	1	no	—
24	C₂×#102×C₇₃	—	2	2	no	—
25	C₂×#102×C₇₃	—	2	1	no	—
26	C₂×#102×C₇₃	—	2	1	no	—
27	C₂×#102×C₇₃	C₂²	1	4	yes	—
28	C₂×#100×C₇₃	C₄	1	8	yes	complemented
29	C₂×#100×C₇₃	C₂²	1	4	yes	—
30	#405×C₇₃	—	2	2	no	—
31	#405×C₇₃	C₂²	1	4	yes	complemented
32	C₂×#97×C₇₃	—	2	1	no	—
33	C₂×C₄×C₈×C₇₃	—	2	1	no	—
34	#343×C₇₃	C₂²	1	4	yes	complemented
35	#341×C₇₃	C₂²	1	4	yes	complemented
36	C₂⁵×C₇₃	—	2	1	no	—
37	C₂²×D₄×C₇₃	—	2	1	no	—
38	C₂²×D₄×C₇₃	—	2	1	no	—
39	C₂²×D₄×C₇₃	—	2	1	no	—
40	C₂²×D₄×C₇₃	—	2	1	no	—
41	C₂²×D₄×C₇₃	—	2	2	no	—
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	C₂×C₄	1	4	yes	—
46	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₇₃	—	2	1	no	—
48	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₇₃	—	2	1	no	—
50	C₂×M₁₆×C₇₃	—	2	1	no	—
51	C₂×M₁₆×C₇₃	—	2	2	no	—
52	C₂×M₁₆×C₇₃	—	2	2	no	—
53	C₂×M₁₆×C₇₃	—	2	1	no	—
54	C₂×M₁₆×C₇₃	—	2	2	no	—
55	C₂×M₁₆×C₇₃	—	2	2	no	—
56	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	—
57	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	—
58	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
59	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
60	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₇₃	—	2	1	no	—
62	C₂²×C₈×C₇₃	—	2	1	no	—
63	C₂²×C₈×C₇₃	—	2	2	no	—
64	C₂²×C₈×C₇₃	—	2	2	no	—
65	C₂²×C₈×C₇₃	—	2	1	no	—
66	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₇₃	D₄	1	2	yes	—
69	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
70	#117×C₇₃	—	2	1	no	—
71	#117×C₇₃	—	2	1	no	—
72	#117×C₇₃	D₄	1	2	yes	—
73	#117×C₇₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
83	C₂×C₄²×C₇₃	—	2	1	no	—
84	#107×C₇₃	—	2	4	no	—
85	#106×C₇₃	—	2	4	no	—
86	#102×C₇₃	—	2	4	no	—
87	#102×C₇₃	—	2	4	no	—
88	#102×C₇₃	—	2	4	no	—
89	#102×C₇₃	—	2	4	no	—
90	#100×C₇₃	C₂×C₄	1	16	yes	complemented
91	#97×C₇₃	—	2	4	no	—
92	C₄×C₈×C₇₃	—	2	4	no	—
93	C₂⁴×C₇₃	—	2	4	no	—
94	C₂⁴×C₇₃	—	2	2	no	—
95	C₂⁴×C₇₃	—	4	1	no	—
96	C₂⁴×C₇₃	—	4	1	no	—
97	C₂⁴×C₇₃	—	4	2	no	—
98	C₂⁴×C₇₃	—	8	2	no	—
99	C₂⁴×C₇₃	—	8	2	no	—
100	C₂⁴×C₇₃	#41	1	1	yes	characteristic
101	C₂×D₄×C₇₃	—	2	4	no	—
102	C₂×D₄×C₇₃	—	2	4	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	4	no	—
105	C₂×D₄×C₇₃	—	2	4	no	—
106	C₂×D₄×C₇₃	—	2	2	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	4	1	no	—
112	C₂×D₄×C₇₃	—	4	1	no	—
113	C₂×D₄×C₇₃	—	4	2	no	—
114	C₂×D₄×C₇₃	—	4	2	no	—
115	C₂×D₄×C₇₃	—	4	2	no	—
116	C₂×D₄×C₇₃	—	4	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₇₃	—	2	1	no	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	4	1	no	—
123	C₂²×C₄×C₇₃	—	4	1	no	—
124	C₂²×C₄×C₇₃	—	8	2	no	—
125	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	#41	1	2	yes	—
132	C₂²×C₄×C₇₃	#41	1	2	yes	—
133	C₂²×C₄×C₇₃	#41	1	2	yes	—
134	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₇₃	—	2	4	no	—
136	M₁₆×C₇₃	—	2	4	no	—
137	M₁₆×C₇₃	—	2	2	no	—
138	M₁₆×C₇₃	—	2	2	no	—
139	M₁₆×C₇₃	—	2	2	no	—
140	M₁₆×C₇₃	—	2	2	no	—
141	M₁₆×C₇₃	—	4	2	no	—
142	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
143	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
144	C₂×C₈×C₇₃	—	2	4	no	—
145	C₂×C₈×C₇₃	—	2	4	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	4	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	4	2	no	—
155	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₇₃	—	2	1	no	—
158	C₄⋊C₄×C₇₃	—	2	1	no	—
159	C₄⋊C₄×C₇₃	—	2	2	no	—
160	C₄⋊C₄×C₇₃	—	2	2	no	—
161	C₄⋊C₄×C₇₃	—	4	1	no	—
162	C₄⋊C₄×C₇₃	—	4	1	no	—
163	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₇₃	—	2	2	no	—
166	C₂²⋊C₄×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	2	no	—
168	C₄²×C₇₃	—	2	2	no	—
169	C₂³×C₇₃	—	2	2	no	—
170	C₂³×C₇₃	—	2	2	no	—
171	C₂³×C₇₃	—	2	4	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	4	no	—
175	C₂³×C₇₃	—	4	4	no	—
176	C₂³×C₇₃	—	8	8	no	—
177	C₂³×C₇₃	—	8	2	no	—
178	C₂³×C₇₃	—	8	2	no	—
179	C₂³×C₇₃	—	8	8	no	—
180	C₂³×C₇₃	—	8	2	no	—
181	C₂³×C₇₃	—	8	2	no	—
182	C₂³×C₇₃	—	8	2	no	—
183	C₂³×C₇₃	—	8	2	no	—
184	C₂³×C₇₃	#117	1	2	yes	—
185	C₂³×C₇₃	#121	1	1	yes	characteristic
186	C₂³×C₇₃	#121	1	1	yes	characteristic
187	C₂³×C₇₃	#126	1	2	yes	—
188	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
189	D₄×C₇₃	—	2	4	no	—
190	D₄×C₇₃	—	2	4	no	—
191	D₄×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	4	2	no	—
193	D₄×C₇₃	—	4	4	no	—
194	D₄×C₇₃	—	4	4	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	4	2	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	8	2	no	—
201	C₂×C₄×C₇₃	—	8	2	no	—
202	C₂×C₄×C₇₃	—	8	2	no	—
203	C₂×C₄×C₇₃	#117	1	2	yes	—
204	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
209	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
210	C₂×C₄×C₇₃	#123	1	2	yes	—
211	C₂×C₄×C₇₃	#123	1	2	yes	—
212	C₂×C₄×C₇₃	#124	1	2	yes	—
213	C₂×C₄×C₇₃	#124	1	2	yes	—
214	C₂×C₄×C₇₃	#126	1	2	yes	—
215	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
221	C₈×C₇₃	—	2	4	no	—
222	C₈×C₇₃	—	2	4	no	—
223	C₈×C₇₃	—	2	2	no	—
224	C₈×C₇₃	—	2	2	no	—
225	C₈×C₇₃	—	4	2	no	—
226	C₂²×C₇₃	—	2	4	no	—
227	C₂²×C₇₃	—	2	4	no	—
228	C₂²×C₇₃	—	2	1	no	—
229	C₂²×C₇₃	—	2	1	no	—
230	C₂²×C₇₃	—	2	1	no	—
231	C₂²×C₇₃	—	2	1	no	—
232	C₂²×C₇₃	—	4	4	no	—
233	C₂²×C₇₃	—	8	4	no	—
234	C₂²×C₇₃	—	8	4	no	—
235	C₂²×C₇₃	—	8	8	no	—
236	C₂²×C₇₃	—	8	8	no	—
237	C₂²×C₇₃	—	8	2	no	—
238	C₂²×C₇₃	—	8	2	no	—
239	C₂²×C₇₃	#388	1	2	yes	—
240	C₂²×C₇₃	#388	1	2	yes	—
241	C₂²×C₇₃	#471	1	2	yes	—
242	C₂²×C₇₃	#472	1	2	yes	—
243	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
244	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₇₃	C₂×#126	1	1	yes	characteristic
246	C₄×C₇₃	—	4	2	no	—
247	C₄×C₇₃	—	4	2	no	—
248	C₄×C₇₃	—	8	2	no	—
249	C₄×C₇₃	#388	1	2	yes	—
250	C₄×C₇₃	#388	1	2	yes	—
251	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
254	C₄×C₇₃	C₂×#124	1	1	yes	characteristic
255	C₂×#1931	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂×C₇₃	—	2	1	no	—
257	C₂×C₇₃	—	2	1	no	—
258	C₂×C₇₃	—	2	2	no	—
259	C₂×C₇₃	—	8	4	no	—
260	C₂×C₇₃	#1931	1	4	yes	direct product factor
261	C₂×C₇₃	C₂×#388	1	1	yes	characteristic
262	C₂×C₇₃	C₂×#471	1	1	yes	characteristic
263	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
264	C₂×#428	C₂×C₇₃	1	1	yes	characteristic, complemented
265	C₂×#418	C₂×C₇₃	1	1	yes	characteristic
266	C₂²×#102	C₂×C₇₃	1	1	yes	characteristic
267	C₂²×#100	C₂×C₇₃	1	1	yes	characteristic
268	C₂×#405	C₂×C₇₃	1	1	yes	characteristic, complemented
269	#1931	C₂×C₇₃	1	8	yes	direct product factor
270	C₂×#343	C₂×C₇₃	1	1	yes	characteristic, complemented
271	C₂×#341	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₇₃	C₂×#1931	1	1	yes	characteristic, direct product factor, Sylow
273	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
274	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
276	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
277	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
278	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
280	#428	—	2	2	no	—
281	#428	C₂²×C₇₃	1	4	yes	complemented
282	C₂×#107	—	2	1	no	—
283	C₂×#106	—	2	1	no	—
284	#418	—	2	2	no	—
285	#418	C₂²×C₇₃	1	4	yes	—
286	C₂×#102	—	2	1	no	—
287	C₂×#102	—	2	1	no	—
288	C₂×#102	—	2	2	no	—
289	C₂×#102	—	2	1	no	—
290	C₂×#102	—	2	1	no	—
291	C₂×#102	C₂²×C₇₃	1	4	yes	—
292	C₂×#100	C₄×C₇₃	1	8	yes	complemented
293	C₂×#100	C₂²×C₇₃	1	4	yes	—
294	#405	—	2	2	no	—
295	#405	C₂²×C₇₃	1	4	yes	complemented
296	C₂×#97	—	2	1	no	—
297	C₂×C₄×C₈	—	2	1	no	—
298	#343	C₂²×C₇₃	1	4	yes	complemented
299	#341	C₂²×C₇₃	1	4	yes	complemented
300	C₂⁵	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	C₂×C₄×C₇₃	1	4	yes	—
310	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	2	2	no	—
320	C₂×M₁₆	C₂×C₄×C₇₃	1	4	yes	—
321	C₂×M₁₆	C₂×C₄×C₇₃	1	4	yes	—
322	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
323	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
324	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
331	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
332	C₂²×C₈	D₄×C₇₃	1	2	yes	—
333	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
334	#117	—	2	1	no	—
335	#117	—	2	1	no	—
336	#117	D₄×C₇₃	1	2	yes	—
337	#117	C₂³×C₇₃	1	2	yes	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	#107	—	2	4	no	—
349	#106	—	2	4	no	—
350	#102	—	2	4	no	—
351	#102	—	2	4	no	—
352	#102	—	2	4	no	—
353	#102	—	2	4	no	—
354	#100	C₂×C₄×C₇₃	1	16	yes	complemented
355	#97	—	2	4	no	—
356	C₄×C₈	—	2	4	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	4	1	no	—
360	C₂⁴	—	4	1	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	8	2	no	—
363	C₂⁴	—	8	2	no	—
364	C₂⁴	#41×C₇₃	1	1	yes	characteristic
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	C₂²×C₄×C₇₃	1	4	yes	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	8	2	no	—
389	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
394	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
395	C₂²×C₄	#41×C₇₃	1	2	yes	—
396	C₂²×C₄	#41×C₇₃	1	2	yes	—
397	C₂²×C₄	#41×C₇₃	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
399	M₁₆	—	2	4	no	—
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	4	2	no	—
406	M₁₆	C₂²×C₄×C₇₃	1	4	yes	—
407	M₁₆	C₂²×C₄×C₇₃	1	4	yes	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	4	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	8	8	no	—
441	C₂³	—	8	2	no	—
442	C₂³	—	8	2	no	—
443	C₂³	—	8	8	no	—
444	C₂³	—	8	2	no	—
445	C₂³	—	8	2	no	—
446	C₂³	—	8	2	no	—
447	C₂³	—	8	2	no	—
448	C₂³	#117×C₇₃	1	2	yes	—
449	C₂³	#121×C₇₃	1	1	yes	characteristic
450	C₂³	#121×C₇₃	1	1	yes	characteristic
451	C₂³	#126×C₇₃	1	2	yes	—
452	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
453	D₄	—	2	4	no	—
454	D₄	—	2	4	no	—
455	D₄	—	4	4	no	—
456	D₄	—	4	4	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	—	8	2	no	—
467	C₂×C₄	#117×C₇₃	1	2	yes	—
468	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
469	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
470	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
471	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
472	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
473	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
474	C₂×C₄	#123×C₇₃	1	2	yes	—
475	C₂×C₄	#123×C₇₃	1	2	yes	—
476	C₂×C₄	#124×C₇₃	1	2	yes	—
477	C₂×C₄	#124×C₇₃	1	2	yes	—
478	C₂×C₄	#126×C₇₃	1	2	yes	—
479	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	2	4	no	—
487	C₈	—	2	2	no	—
488	C₈	—	2	2	no	—
489	C₈	—	4	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	4	no	—
498	C₂²	—	8	8	no	—
499	C₂²	—	8	4	no	—
500	C₂²	—	8	8	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	#388×C₇₃	1	2	yes	—
504	C₂²	#388×C₇₃	1	2	yes	—
505	C₂²	#471×C₇₃	1	2	yes	—
506	C₂²	#472×C₇₃	1	2	yes	—
507	C₂²	C₂×#117×C₇₃	1	1	yes	characteristic
508	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
509	C₂²	C₂×#126×C₇₃	1	1	yes	characteristic
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	8	2	no	—
513	C₄	#388×C₇₃	1	2	yes	—
514	C₄	#388×C₇₃	1	2	yes	—
515	C₄	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
516	C₄	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
517	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
518	C₄	C₂×#124×C₇₃	1	1	yes	characteristic
519	C₂	—	2	2	no	—
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	8	4	no	—
523	C₂	C₇₃×#1931	1	4	yes	direct product factor
524	C₂	C₂×#388×C₇₃	1	1	yes	characteristic
525	C₂	C₂×#471×C₇₃	1	1	yes	characteristic
526	C₂	C₂×#472×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	#121
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂³×D₄×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₇₃	C₂	semidirect
5. C₂×#405×C₇₃	C₂	semidirect
6. C₇₃×#1931	C₂	direct (N × H)
7. C₂×#343×C₇₃	C₂	semidirect
8. C₂×#341×C₇₃	C₂	semidirect
17. #428×C₇₃	C₂²	semidirect
28. C₂×#100×C₇₃	C₄	semidirect
31. #405×C₇₃	C₂²	semidirect
34. #343×C₇₃	C₂²	semidirect
35. #341×C₇₃	C₂²	semidirect
90. #100×C₇₃	C₂×C₄	semidirect
255. C₂×#1931	C₇₃	direct (N × H)
260. C₂×C₇₃	#1931	direct (N × H)
264. C₂×#428	C₂×C₇₃	semidirect
268. C₂×#405	C₂×C₇₃	semidirect
269. #1931	C₂×C₇₃	direct (N × H)
270. C₂×#343	C₂×C₇₃	semidirect
271. C₂×#341	C₂×C₇₃	semidirect
272. C₇₃	C₂×#1931	direct (N × H)
281. #428	C₂²×C₇₃	semidirect
292. C₂×#100	C₄×C₇₃	semidirect
295. #405	C₂²×C₇₃	semidirect
298. #343	C₂²×C₇₃	semidirect
299. #341	C₂²×C₇₃	semidirect
354. #100	C₂×C₄×C₇₃	semidirect
523. C₂	C₇₃×#1931	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#428×C₇₃	2
C₂×#418×C₇₃	2
C₂²×#102×C₇₃	2
C₂²×#100×C₇₃	2
C₂×#405×C₇₃	2
C₇₃×#1931	2
C₂×#343×C₇₃	2
C₂×#341×C₇₃	2
C₂×#1931	73

Subgroups — C2×C73×#1931 #32930478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#1931 #32930478