Subgroups — C₇₃×#10785 #32920189

Order 18688.

1394 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#418×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#418×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1740	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×H(3,ℤ/4)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	#518×C₇₃	—	2	2	no	—
12	#518×C₇₃	—	2	2	no	—
13	#518×C₇₃	—	2	2	no	—
14	#518×C₇₃	C₄	1	4	yes	complemented
15	C₂×C₄×D₄×C₇₃	—	2	2	no	—
16	C₂×C₄×D₄×C₇₃	—	2	2	no	—
17	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₇₃	—	2	2	no	—
22	#418×C₇₃	—	2	2	no	—
23	#418×C₇₃	—	2	2	no	—
24	#418×C₇₃	—	2	2	no	—
25	#418×C₇₃	C₄	1	4	yes	complemented
26	C₂×#102×C₇₃	—	2	2	no	—
27	C₂×#102×C₇₃	C₄	1	4	yes	complemented
28	#344×C₇₃	—	2	2	no	—
29	#342×C₇₃	—	2	2	no	—
30	#339×C₇₃	—	2	2	no	—
31	H(3,ℤ/4)×C₇₃	—	2	2	no	—
32	C₂⁵×C₇₃	—	2	1	no	—
33	C₂²×D₄×C₇₃	—	2	1	no	—
34	C₂²×D₄×C₇₃	—	2	1	no	—
35	C₂²×D₄×C₇₃	—	2	1	no	—
36	C₂²×D₄×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	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
42	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₇₃	D₄	1	2	yes	—
44	C₂²×D₄×C₇₃	D₄	1	2	yes	—
45	C₂²×D₄×C₇₃	D₄	1	2	yes	—
46	C₂²×D₄×C₇₃	Q₈	1	2	yes	—
47	C₂³×C₄×C₇₃	—	2	4	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	1	no	—
52	C₂×M₁₆×C₇₃	—	2	1	no	—
53	C₂×M₁₆×C₇₃	—	2	1	no	—
54	C₂×M₁₆×C₇₃	—	2	1	no	—
55	C₂×M₁₆×C₇₃	—	2	1	no	—
56	C₂×M₁₆×C₇₃	—	2	1	no	—
57	C₂×M₁₆×C₇₃	—	2	1	no	—
58	C₂×M₁₆×C₇₃	—	2	1	no	—
59	C₂×M₁₆×C₇₃	—	2	1	no	—
60	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
61	C₂²×C₈×C₇₃	—	2	1	no	—
62	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
63	C₄×D₄×C₇₃	—	2	8	no	—
64	C₄×D₄×C₇₃	—	2	8	no	—
65	C₄×D₄×C₇₃	—	2	8	no	—
66	C₄×D₄×C₇₃	—	2	8	no	—
67	#117×C₇₃	—	2	1	no	—
68	#117×C₇₃	—	2	1	no	—
69	#117×C₇₃	—	2	1	no	—
70	#117×C₇₃	—	2	1	no	—
71	#117×C₇₃	—	2	1	no	—
72	#117×C₇₃	—	2	1	no	—
73	#117×C₇₃	—	2	1	no	—
74	#117×C₇₃	—	2	1	no	—
75	#117×C₇₃	—	2	1	no	—
76	#117×C₇₃	—	2	1	no	—
77	#117×C₇₃	—	2	1	no	—
78	#117×C₇₃	C₂×C₄	1	2	yes	—
79	#117×C₇₃	C₂×C₄	1	2	yes	—
80	#117×C₇₃	C₂×C₄	1	2	yes	complemented
81	#117×C₇₃	D₄	1	2	yes	—
82	#117×C₇₃	D₄	1	2	yes	—
83	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	complemented
87	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
94	C₂×C₄²×C₇₃	—	2	1	no	—
95	C₂×C₄²×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	—	2	1	no	—
97	C₂×C₄²×C₇₃	D₄	1	2	yes	—
98	#102×C₇₃	—	2	8	no	—
99	#102×C₇₃	—	2	8	no	—
100	C₂⁴×C₇₃	—	2	2	no	—
101	C₂⁴×C₇₃	—	2	2	no	—
102	C₂⁴×C₇₃	—	2	2	no	—
103	C₂⁴×C₇₃	—	2	2	no	—
104	C₂⁴×C₇₃	—	2	2	no	—
105	C₂⁴×C₇₃	—	2	2	no	—
106	C₂⁴×C₇₃	—	2	2	no	—
107	C₂⁴×C₇₃	—	8	4	no	—
108	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	2	2	no	—
118	C₂×D₄×C₇₃	—	2	2	no	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	2	2	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	—	2	2	no	—
130	C₂×D₄×C₇₃	C₄²	1	4	yes	—
131	C₂×D₄×C₇₃	C₂²⋊C₄	1	4	yes	—
132	C₂×D₄×C₇₃	C₂²⋊C₄	1	4	yes	—
133	C₂×D₄×C₇₃	C₂²⋊C₄	1	4	yes	—
134	C₂×D₄×C₇₃	C₄⋊C₄	1	4	yes	—
135	C₂×D₄×C₇₃	C₄⋊C₄	1	4	yes	—
136	C₂×D₄×C₇₃	C₄⋊C₄	1	4	yes	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	2	16	no	—
140	C₂²×C₄×C₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	—	4	1	no	—
142	C₂²×C₄×C₇₃	—	8	8	no	—
143	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
155	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
157	M₁₆×C₇₃	—	2	2	no	—
158	M₁₆×C₇₃	—	2	2	no	—
159	M₁₆×C₇₃	—	4	1	no	—
160	M₁₆×C₇₃	—	4	1	no	—
161	M₁₆×C₇₃	—	4	1	no	—
162	M₁₆×C₇₃	—	4	1	no	—
163	M₁₆×C₇₃	—	4	1	no	—
164	M₁₆×C₇₃	—	4	1	no	—
165	C₂×C₈×C₇₃	—	2	2	no	—
166	C₂×C₈×C₇₃	—	2	2	no	—
167	C₂×C₈×C₇₃	—	2	2	no	—
168	C₂×C₈×C₇₃	—	2	2	no	—
169	C₂×C₈×C₇₃	—	4	1	no	—
170	C₂×C₈×C₇₃	—	4	1	no	—
171	C₄⋊C₄×C₇₃	—	2	2	no	—
172	C₄⋊C₄×C₇₃	—	2	2	no	—
173	C₄⋊C₄×C₇₃	—	2	2	no	—
174	C₄⋊C₄×C₇₃	—	2	2	no	—
175	C₄⋊C₄×C₇₃	—	2	2	no	—
176	C₄⋊C₄×C₇₃	—	2	2	no	—
177	C₄⋊C₄×C₇₃	—	2	2	no	—
178	C₄⋊C₄×C₇₃	—	4	1	no	—
179	C₂²⋊C₄×C₇₃	—	2	16	no	—
180	C₂²⋊C₄×C₇₃	—	2	2	no	—
181	C₂²⋊C₄×C₇₃	—	2	2	no	—
182	C₂²⋊C₄×C₇₃	—	2	2	no	—
183	C₂²⋊C₄×C₇₃	—	2	2	no	—
184	C₂²⋊C₄×C₇₃	—	4	1	no	—
185	C₂²⋊C₄×C₇₃	—	4	1	no	—
186	C₂²⋊C₄×C₇₃	—	4	1	no	—
187	C₂²⋊C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
188	C₄²×C₇₃	—	2	2	no	—
189	C₄²×C₇₃	—	2	2	no	—
190	C₄²×C₇₃	—	2	2	no	—
191	C₄²×C₇₃	—	2	2	no	—
192	C₄²×C₇₃	—	4	1	no	—
193	C₄²×C₇₃	—	4	1	no	—
194	C₄²×C₇₃	—	4	1	no	—
195	C₄²×C₇₃	C₂²⋊C₄	1	4	yes	—
196	C₂³×C₇₃	—	2	4	no	—
197	C₂³×C₇₃	—	2	4	no	—
198	C₂³×C₇₃	—	2	4	no	—
199	C₂³×C₇₃	—	2	4	no	—
200	C₂³×C₇₃	—	2	4	no	—
201	C₂³×C₇₃	—	2	4	no	—
202	C₂³×C₇₃	—	2	4	no	—
203	C₂³×C₇₃	—	4	2	no	—
204	C₂³×C₇₃	—	4	8	no	—
205	C₂³×C₇₃	—	8	4	no	—
206	C₂³×C₇₃	—	8	4	no	—
207	C₂³×C₇₃	—	8	4	no	—
208	C₂³×C₇₃	—	8	4	no	—
209	C₂³×C₇₃	—	8	4	no	—
210	C₂³×C₇₃	—	8	4	no	—
211	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₇₃	#120	1	1	yes	characteristic
215	C₂³×C₇₃	#120	1	1	yes	characteristic
216	C₂³×C₇₃	#121	1	1	yes	characteristic
217	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
218	D₄×C₇₃	—	2	4	no	—
219	D₄×C₇₃	—	2	4	no	—
220	D₄×C₇₃	—	2	4	no	—
221	D₄×C₇₃	—	2	4	no	—
222	D₄×C₇₃	—	2	4	no	—
223	D₄×C₇₃	—	2	4	no	—
224	D₄×C₇₃	—	2	4	no	—
225	D₄×C₇₃	#95	1	8	yes	—
226	C₂×C₄×C₇₃	—	2	4	no	—
227	C₂×C₄×C₇₃	—	2	4	no	—
228	C₂×C₄×C₇₃	—	4	4	no	—
229	C₂×C₄×C₇₃	—	4	4	no	—
230	C₂×C₄×C₇₃	—	4	2	no	—
231	C₂×C₄×C₇₃	—	4	2	no	—
232	C₂×C₄×C₇₃	—	8	16	no	—
233	C₂×C₄×C₇₃	—	8	2	no	—
234	C₂×C₄×C₇₃	—	8	2	no	—
235	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
244	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
245	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
253	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
254	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
256	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
258	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
259	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
260	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
261	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
262	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
263	C₈×C₇₃	—	4	2	no	—
264	C₈×C₇₃	—	4	2	no	—
265	C₂²×C₇₃	—	2	2	no	—
266	C₂²×C₇₃	—	2	2	no	—
267	C₂²×C₇₃	—	2	2	no	—
268	C₂²×C₇₃	—	2	8	no	—
269	C₂²×C₇₃	—	4	1	no	—
270	C₂²×C₇₃	—	4	1	no	—
271	C₂²×C₇₃	—	4	1	no	—
272	C₂²×C₇₃	—	4	1	no	—
273	C₂²×C₇₃	—	4	8	no	—
274	C₂²×C₇₃	—	4	8	no	—
275	C₂²×C₇₃	—	4	8	no	—
276	C₂²×C₇₃	—	8	4	no	—
277	C₂²×C₇₃	—	8	4	no	—
278	C₂²×C₇₃	—	8	4	no	—
279	C₂²×C₇₃	—	8	4	no	—
280	C₂²×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
281	C₂²×C₇₃	#379	1	1	yes	characteristic
282	C₂²×C₇₃	#380	1	1	yes	characteristic
283	C₂²×C₇₃	#385	1	1	yes	characteristic
284	C₂²×C₇₃	#385	1	1	yes	characteristic
285	C₂²×C₇₃	#386	1	1	yes	characteristic
286	C₂²×C₇₃	#386	1	1	yes	characteristic
287	C₄×C₇₃	—	4	4	no	—
288	C₄×C₇₃	—	4	4	no	—
289	C₄×C₇₃	—	8	2	no	—
290	C₄×C₇₃	—	8	2	no	—
291	C₄×C₇₃	C₂×#95	1	1	yes	characteristic
292	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
293	C₄×C₇₃	#380	1	1	yes	characteristic
294	C₄×C₇₃	#381	1	1	yes	characteristic
295	C₄×C₇₃	#385	1	1	yes	characteristic
296	C₄×C₇₃	#385	1	1	yes	characteristic
297	C₄×C₇₃	#386	1	1	yes	characteristic
298	C₄×C₇₃	#386	1	1	yes	characteristic
299	#10785	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂×C₇₃	—	2	1	no	—
301	C₂×C₇₃	—	2	1	no	—
302	C₂×C₇₃	—	2	1	no	—
303	C₂×C₇₃	—	2	1	no	—
304	C₂×C₇₃	—	2	1	no	—
305	C₂×C₇₃	—	2	1	no	—
306	C₂×C₇₃	—	4	8	no	—
307	C₂×C₇₃	C₂²⋊#95	1	1	yes	characteristic
308	C₂×C₇₃	#1904	1	2	yes	—
309	C₂×#518	C₂×C₇₃	1	1	yes	characteristic
310	C₂×#418	C₂×C₇₃	1	1	yes	characteristic
311	C₂×#418	C₂×C₇₃	1	1	yes	characteristic
312	C₂×#344	C₂×C₇₃	1	1	yes	characteristic, complemented
313	#1740	C₂×C₇₃	1	1	yes	characteristic, complemented
314	#1733	C₂×C₇₃	1	1	yes	characteristic, complemented
315	C₂×H(3,ℤ/4)	C₂×C₇₃	1	1	yes	characteristic, complemented
316	C₇₃	#10785	1	1	yes	characteristic, direct product factor, Sylow
317	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
320	#518	—	2	2	no	—
321	#518	—	2	2	no	—
322	#518	—	2	2	no	—
323	#518	C₄×C₇₃	1	4	yes	complemented
324	C₂×C₄×D₄	—	2	2	no	—
325	C₂×C₄×D₄	—	2	2	no	—
326	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
327	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
328	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
329	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	—	2	2	no	—
331	#418	—	2	2	no	—
332	#418	—	2	2	no	—
333	#418	—	2	2	no	—
334	#418	C₄×C₇₃	1	4	yes	complemented
335	C₂×#102	—	2	2	no	—
336	C₂×#102	C₄×C₇₃	1	4	yes	complemented
337	#344	—	2	2	no	—
338	#342	—	2	2	no	—
339	#339	—	2	2	no	—
340	H(3,ℤ/4)	—	2	2	no	—
341	C₂⁵	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
350	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
351	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
352	C₂²×D₄	D₄×C₇₃	1	2	yes	—
353	C₂²×D₄	D₄×C₇₃	1	2	yes	—
354	C₂²×D₄	D₄×C₇₃	1	2	yes	—
355	C₂²×D₄	Q₈×C₇₃	1	2	yes	—
356	C₂³×C₄	—	2	4	no	—
357	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	C₂×C₄×C₇₃	1	2	yes	complemented
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	C₂×C₄×C₇₃	1	2	yes	complemented
372	C₄×D₄	—	2	8	no	—
373	C₄×D₄	—	2	8	no	—
374	C₄×D₄	—	2	8	no	—
375	C₄×D₄	—	2	8	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	C₂×C₄×C₇₃	1	2	yes	—
388	#117	C₂×C₄×C₇₃	1	2	yes	—
389	#117	C₂×C₄×C₇₃	1	2	yes	complemented
390	#117	D₄×C₇₃	1	2	yes	—
391	#117	D₄×C₇₃	1	2	yes	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	complemented
396	C₂×C₂²⋊C₄	—	2	4	no	—
397	C₂×C₂²⋊C₄	—	2	8	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	8	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	D₄×C₇₃	1	2	yes	—
407	#102	—	2	8	no	—
408	#102	—	2	8	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	8	4	no	—
417	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	C₄²×C₇₃	1	4	yes	—
440	C₂×D₄	C₂²⋊C₄×C₇₃	1	4	yes	—
441	C₂×D₄	C₂²⋊C₄×C₇₃	1	4	yes	—
442	C₂×D₄	C₂²⋊C₄×C₇₃	1	4	yes	—
443	C₂×D₄	C₄⋊C₄×C₇₃	1	4	yes	—
444	C₂×D₄	C₄⋊C₄×C₇₃	1	4	yes	—
445	C₂×D₄	C₄⋊C₄×C₇₃	1	4	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	16	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	8	8	no	—
452	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×Q₈×C₇₃	1	1	yes	characteristic
462	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
463	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
464	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
465	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	1	no	—
473	M₁₆	—	4	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	2	16	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	C₂²⋊C₄×C₇₃	1	4	yes	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	C₂²⋊C₄×C₇₃	1	4	yes	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	8	4	no	—
515	C₂³	—	8	4	no	—
516	C₂³	—	8	4	no	—
517	C₂³	—	8	4	no	—
518	C₂³	—	8	4	no	—
519	C₂³	—	8	4	no	—
520	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
521	C₂³	C₄×D₄×C₇₃	1	1	yes	characteristic
522	C₂³	C₄×D₄×C₇₃	1	1	yes	characteristic
523	C₂³	#120×C₇₃	1	1	yes	characteristic
524	C₂³	#120×C₇₃	1	1	yes	characteristic
525	C₂³	#121×C₇₃	1	1	yes	characteristic
526	C₂³	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	2	4	no	—
531	D₄	—	2	4	no	—
532	D₄	—	2	4	no	—
533	D₄	—	2	4	no	—
534	D₄	#95×C₇₃	1	8	yes	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	16	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	C₂×C₄²×C₇₃	1	1	yes	characteristic
545	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
546	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
547	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
548	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
549	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
550	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
551	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
552	C₂×C₄	#117×C₇₃	1	1	yes	characteristic
553	C₂×C₄	#117×C₇₃	1	1	yes	characteristic
554	C₂×C₄	C₄×D₄×C₇₃	1	1	yes	characteristic
555	C₂×C₄	C₄×D₄×C₇₃	1	1	yes	characteristic
556	C₂×C₄	C₄×D₄×C₇₃	1	1	yes	characteristic
557	C₂×C₄	C₄×D₄×C₇₃	1	1	yes	characteristic
558	C₂×C₄	C₄×D₄×C₇₃	1	1	yes	characteristic
559	C₂×C₄	C₄×D₄×C₇₃	1	1	yes	characteristic
560	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
561	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
562	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
563	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
564	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
565	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
567	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
568	C₂×C₄	#123×C₇₃	1	1	yes	characteristic
569	C₂×C₄	#123×C₇₃	1	1	yes	characteristic
570	C₂×C₄	#123×C₇₃	1	1	yes	characteristic
571	C₂×C₄	#123×C₇₃	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	8	no	—
585	C₂²	—	8	4	no	—
586	C₂²	—	8	4	no	—
587	C₂²	—	8	4	no	—
588	C₂²	—	8	4	no	—
589	C₂²	C₄×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
590	C₂²	#379×C₇₃	1	1	yes	characteristic
591	C₂²	#380×C₇₃	1	1	yes	characteristic
592	C₂²	#385×C₇₃	1	1	yes	characteristic
593	C₂²	#385×C₇₃	1	1	yes	characteristic
594	C₂²	#386×C₇₃	1	1	yes	characteristic
595	C₂²	#386×C₇₃	1	1	yes	characteristic
596	C₄	—	4	4	no	—
597	C₄	—	4	4	no	—
598	C₄	—	8	2	no	—
599	C₄	—	8	2	no	—
600	C₄	C₂×#95×C₇₃	1	1	yes	characteristic
601	C₄	C₄×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
602	C₄	#380×C₇₃	1	1	yes	characteristic
603	C₄	#381×C₇₃	1	1	yes	characteristic
604	C₄	#385×C₇₃	1	1	yes	characteristic
605	C₄	#385×C₇₃	1	1	yes	characteristic
606	C₄	#386×C₇₃	1	1	yes	characteristic
607	C₄	#386×C₇₃	1	1	yes	characteristic
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	4	8	no	—
615	C₂	C₇₃×C₂²⋊#95	1	1	yes	characteristic
616	C₂	C₇₃×#1904	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	#386
commutator	C₂×C₄	C₂×C₄²×C₇₃
Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
prime radical	C₂³×D₄×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#344×C₇₃	C₂	semidirect
5. C₇₃×#1740	C₂	semidirect
6. C₇₃×#1733	C₂	semidirect
7. C₂×H(3,ℤ/4)×C₇₃	C₂	semidirect
14. #518×C₇₃	C₄	semidirect
25. #418×C₇₃	C₄	semidirect
27. C₂×#102×C₇₃	C₄	semidirect
60. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
62. C₂²×C₈×C₇₃	C₂×C₄	semidirect
80. #117×C₇₃	C₂×C₄	semidirect
86. C₂×C₄⋊C₄×C₇₃	C₂×C₄	semidirect
299. #10785	C₇₃	direct (N × H)
312. C₂×#344	C₂×C₇₃	semidirect
313. #1740	C₂×C₇₃	semidirect
314. #1733	C₂×C₇₃	semidirect
315. C₂×H(3,ℤ/4)	C₂×C₇₃	semidirect
316. C₇₃	#10785	direct (N × H)
323. #518	C₄×C₇₃	semidirect
334. #418	C₄×C₇₃	semidirect
336. C₂×#102	C₄×C₇₃	semidirect
369. C₂×M₁₆	C₂×C₄×C₇₃	semidirect
371. C₂²×C₈	C₂×C₄×C₇₃	semidirect
389. #117	C₂×C₄×C₇₃	semidirect
395. C₂×C₄⋊C₄	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518×C₇₃	2
C₂×#418×C₇₃	2
C₂×#344×C₇₃	2
C₇₃×#1740	2
C₇₃×#1733	2
C₂×H(3,ℤ/4)×C₇₃	2
#10785	73

Subgroups — C73×#10785 #32920189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#10785 #32920189