Subgroups — C₇₃×#25784 #32935188

Order 18688.

1618 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#497×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#467×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#451×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#450×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2435	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2013	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1973	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
16	C₂²×SD₁₆×C₇₃	—	2	8	no	—
17	C₂²×SD₁₆×C₇₃	—	2	4	no	—
18	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
21	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
23	C₂×#124×C₇₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	#497×C₇₃	—	2	8	no	—
27	#467×C₇₃	—	2	4	no	—
28	#451×C₇₃	—	2	4	no	—
29	#450×C₇₃	—	2	4	no	—
30	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
32	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
37	#395×C₇₃	—	2	2	no	—
38	#394×C₇₃	—	2	2	no	—
39	#391×C₇₃	C₂²	1	2	yes	complemented
40	#390×C₇₃	C₂²	1	2	yes	—
41	#385×C₇₃	—	2	2	no	—
42	#379×C₇₃	—	2	2	no	—
43	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#336×C₇₃	C₂²	1	2	yes	complemented
45	C₂⁵×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	—	2	1	no	—
47	C₂²×Q₈×C₇₃	—	2	4	no	—
48	C₂²×Q₈×C₇₃	—	2	2	no	—
49	C₂²×Q₈×C₇₃	—	2	2	no	—
50	C₂²×Q₈×C₇₃	—	4	2	no	—
51	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₇₃	—	2	4	no	—
55	C₂²×D₄×C₇₃	—	2	2	no	—
56	C₂²×D₄×C₇₃	—	2	2	no	—
57	C₂²×D₄×C₇₃	—	2	1	no	—
58	C₂²×D₄×C₇₃	—	4	2	no	—
59	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₇₃	—	2	1	no	—
61	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₇₃	—	2	4	no	—
63	C₂×Q₁₆×C₇₃	—	2	4	no	—
64	C₂×Q₁₆×C₇₃	—	2	2	no	—
65	C₂×Q₁₆×C₇₃	—	2	4	no	—
66	C₂×Q₁₆×C₇₃	—	4	2	no	—
67	C₂×SD₁₆×C₇₃	—	2	32	no	—
68	C₂×SD₁₆×C₇₃	—	2	4	no	—
69	C₂×SD₁₆×C₇₃	—	2	4	no	—
70	C₂×SD₁₆×C₇₃	—	2	4	no	—
71	C₂×SD₁₆×C₇₃	—	2	4	no	—
72	C₂×SD₁₆×C₇₃	—	2	4	no	—
73	C₂×SD₁₆×C₇₃	—	2	4	no	—
74	C₂×SD₁₆×C₇₃	—	2	4	no	—
75	C₂×SD₁₆×C₇₃	—	4	2	no	—
76	C₂×SD₁₆×C₇₃	D₄	1	8	yes	—
77	C₂²×C₈×C₇₃	—	2	4	no	—
78	C₂²×C₈×C₇₃	D₄	1	4	yes	—
79	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₇₃	—	2	4	no	—
83	C₄⋊Q₈×C₇₃	—	4	2	no	—
84	#124×C₇₃	—	2	4	no	—
85	#124×C₇₃	—	4	2	no	—
86	C₂²⋊Q₈×C₇₃	—	2	2	no	—
87	C₂²⋊Q₈×C₇₃	—	2	2	no	—
88	C₂²⋊Q₈×C₇₃	—	2	2	no	—
89	C₂²⋊Q₈×C₇₃	—	2	2	no	—
90	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
91	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
100	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
101	#107×C₇₃	—	2	2	no	—
102	#103×C₇₃	—	2	4	no	—
103	#103×C₇₃	—	2	2	no	—
104	#103×C₇₃	—	2	2	no	—
105	#102×C₇₃	—	2	4	no	—
106	C₂²⋊C₈×C₇₃	D₄	1	4	yes	—
107	#97×C₇₃	—	2	4	no	—
108	#95×C₇₃	—	2	4	no	—
109	#95×C₇₃	D₄	1	2	yes	—
110	C₂⁴×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	—	4	4	no	—
112	C₂⁴×C₇₃	—	4	2	no	—
113	C₂⁴×C₇₃	—	4	4	no	—
114	C₂⁴×C₇₃	—	8	2	no	—
115	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	8	no	—
118	C₂×Q₈×C₇₃	—	2	2	no	—
119	C₂×Q₈×C₇₃	—	2	2	no	—
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	1	no	—
122	C₂×Q₈×C₇₃	—	2	1	no	—
123	C₂×Q₈×C₇₃	—	2	1	no	—
124	C₂×Q₈×C₇₃	—	2	1	no	—
125	C₂×Q₈×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	2	2	no	—
129	C₂×Q₈×C₇₃	—	2	2	no	—
130	C₂×Q₈×C₇₃	—	4	4	no	—
131	C₂×Q₈×C₇₃	—	4	8	no	—
132	C₂×Q₈×C₇₃	—	4	4	no	—
133	C₂×Q₈×C₇₃	—	4	2	no	—
134	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
135	C₂×D₄×C₇₃	—	2	8	no	—
136	C₂×D₄×C₇₃	—	2	2	no	—
137	C₂×D₄×C₇₃	—	2	2	no	—
138	C₂×D₄×C₇₃	—	2	2	no	—
139	C₂×D₄×C₇₃	—	2	2	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	4	8	no	—
142	C₂×D₄×C₇₃	—	4	4	no	—
143	C₂×D₄×C₇₃	—	4	4	no	—
144	C₂×D₄×C₇₃	—	4	2	no	—
145	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	2	no	—
148	C₂²×C₄×C₇₃	—	2	2	no	—
149	C₂²×C₄×C₇₃	—	2	1	no	—
150	C₂²×C₄×C₇₃	—	2	1	no	—
151	C₂²×C₄×C₇₃	—	2	1	no	—
152	C₂²×C₄×C₇₃	—	2	1	no	—
153	C₂²×C₄×C₇₃	—	4	4	no	—
154	C₂²×C₄×C₇₃	—	4	2	no	—
155	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₇₃	—	4	8	no	—
161	Q₁₆×C₇₃	—	4	4	no	—
162	SD₁₆×C₇₃	—	2	16	no	—
163	SD₁₆×C₇₃	—	2	16	no	—
164	SD₁₆×C₇₃	—	4	8	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	8	no	—
169	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
170	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
173	C₄⋊C₄×C₇₃	—	2	1	no	—
174	C₄⋊C₄×C₇₃	—	2	1	no	—
175	C₄⋊C₄×C₇₃	—	2	1	no	—
176	C₄⋊C₄×C₇₃	—	2	1	no	—
177	C₄⋊C₄×C₇₃	—	4	8	no	—
178	C₄⋊C₄×C₇₃	—	4	2	no	—
179	C₄⋊C₄×C₇₃	—	4	2	no	—
180	C₂²⋊C₄×C₇₃	—	2	4	no	—
181	C₂²⋊C₄×C₇₃	—	4	8	no	—
182	C₂²⋊C₄×C₇₃	—	4	2	no	—
183	C₂²⋊C₄×C₇₃	—	4	2	no	—
184	C₂²⋊C₄×C₇₃	—	8	4	no	—
185	C₄²×C₇₃	—	2	2	no	—
186	C₄²×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	2	2	no	—
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	—	2	4	no	—
190	C₂³×C₇₃	—	4	8	no	—
191	C₂³×C₇₃	—	4	2	no	—
192	C₂³×C₇₃	—	4	2	no	—
193	C₂³×C₇₃	—	4	4	no	—
194	C₂³×C₇₃	—	4	4	no	—
195	C₂³×C₇₃	—	8	16	no	—
196	C₂³×C₇₃	—	8	4	no	—
197	C₂³×C₇₃	—	8	4	no	—
198	C₂³×C₇₃	#127	1	2	yes	—
199	C₂³×C₇₃	#137	1	4	yes	—
200	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₇₃	—	2	4	no	—
202	Q₈×C₇₃	—	2	4	no	—
203	Q₈×C₇₃	—	4	8	no	—
204	Q₈×C₇₃	—	4	2	no	—
205	Q₈×C₇₃	—	4	2	no	—
206	Q₈×C₇₃	—	4	1	no	—
207	Q₈×C₇₃	—	4	1	no	—
208	Q₈×C₇₃	—	4	1	no	—
209	Q₈×C₇₃	—	4	1	no	—
210	Q₈×C₇₃	—	4	2	no	—
211	Q₈×C₇₃	—	4	2	no	—
212	D₄×C₇₃	—	2	4	no	—
213	D₄×C₇₃	—	2	4	no	—
214	D₄×C₇₃	—	4	8	no	—
215	D₄×C₇₃	—	4	2	no	—
216	D₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	2	2	no	—
218	C₂×C₄×C₇₃	—	2	2	no	—
219	C₂×C₄×C₇₃	—	2	2	no	—
220	C₂×C₄×C₇₃	—	2	4	no	—
221	C₂×C₄×C₇₃	—	2	4	no	—
222	C₂×C₄×C₇₃	—	2	4	no	—
223	C₂×C₄×C₇₃	—	2	4	no	—
224	C₂×C₄×C₇₃	—	2	4	no	—
225	C₂×C₄×C₇₃	—	4	8	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	—	4	2	no	—
228	C₂×C₄×C₇₃	—	4	1	no	—
229	C₂×C₄×C₇₃	—	4	1	no	—
230	C₂×C₄×C₇₃	—	4	1	no	—
231	C₂×C₄×C₇₃	—	4	1	no	—
232	C₂×C₄×C₇₃	—	4	2	no	—
233	C₂×C₄×C₇₃	—	4	2	no	—
234	C₂×C₄×C₇₃	—	4	2	no	—
235	C₂×C₄×C₇₃	—	4	2	no	—
236	C₂×C₄×C₇₃	#127	1	2	yes	—
237	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₇₃	—	2	2	no	—
242	C₈×C₇₃	—	2	4	no	—
243	C₈×C₇₃	#120	1	4	yes	—
244	C₂²×C₇₃	—	2	2	no	—
245	C₂²×C₇₃	—	2	2	no	—
246	C₂²×C₇₃	—	2	8	no	—
247	C₂²×C₇₃	—	4	4	no	—
248	C₂²×C₇₃	—	4	8	no	—
249	C₂²×C₇₃	—	8	16	no	—
250	C₂²×C₇₃	—	8	2	no	—
251	C₂²×C₇₃	—	8	2	no	—
252	C₂²×C₇₃	—	8	4	no	—
253	C₂²×C₇₃	#497	1	4	yes	complemented
254	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
255	C₂²×C₇₃	D₄²	1	2	yes	—
256	C₂²×C₇₃	C₂×#137	1	2	yes	—
257	C₂²×C₇₃	#577	1	2	yes	—
258	C₄×C₇₃	—	2	2	no	—
259	C₄×C₇₃	—	4	4	no	—
260	C₄×C₇₃	—	4	4	no	—
261	C₄×C₇₃	—	8	1	no	—
262	C₄×C₇₃	—	8	1	no	—
263	C₄×C₇₃	—	8	1	no	—
264	C₄×C₇₃	—	8	1	no	—
265	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
266	C₄×C₇₃	#535	1	1	yes	characteristic
267	C₄×C₇₃	D₄²	1	2	yes	—
268	#25784	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂×C₇₃	—	2	4	no	—
270	C₂×C₇₃	—	8	4	no	—
271	C₂×C₇₃	#2433	1	1	yes	characteristic
272	C₂×C₇₃	C₂×#497	1	1	yes	characteristic
273	C₂×C₇₃	#3154	1	1	yes	characteristic
274	C₂×C₇₃	#3266	1	4	yes	—
275	C₂³×SD₁₆	C₂×C₇₃	1	1	yes	characteristic
276	C₂×#497	C₂×C₇₃	1	2	yes	complemented
277	C₂×#467	C₂×C₇₃	1	1	yes	characteristic, complemented
278	C₂×#451	C₂×C₇₃	1	1	yes	characteristic, complemented
279	C₂×#450	C₂×C₇₃	1	1	yes	characteristic
280	#2435	C₂×C₇₃	1	1	yes	characteristic
281	#2434	C₂×C₇₃	1	1	yes	characteristic, complemented
282	#2015	C₂×C₇₃	1	2	yes	complemented
283	#2013	C₂×C₇₃	1	2	yes	complemented
284	#1973	C₂×C₇₃	1	2	yes	complemented
285	#1752	C₂×C₇₃	1	1	yes	characteristic, complemented
286	C₇₃	#25784	1	1	yes	characteristic, direct product factor, Sylow
287	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
288	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
289	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
290	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
291	C₂²×SD₁₆	—	2	8	no	—
292	C₂²×SD₁₆	—	2	4	no	—
293	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
294	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
295	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
296	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
297	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	complemented
298	C₂×#124	C₂²×C₇₃	1	2	yes	—
299	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
301	#497	—	2	8	no	—
302	#467	—	2	4	no	—
303	#451	—	2	4	no	—
304	#450	—	2	4	no	—
305	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
306	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
307	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
308	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
309	C₂×#102	C₂²×C₇₃	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
311	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
312	#395	—	2	2	no	—
313	#394	—	2	2	no	—
314	#391	C₂²×C₇₃	1	2	yes	complemented
315	#390	C₂²×C₇₃	1	2	yes	—
316	#385	—	2	2	no	—
317	#379	—	2	2	no	—
318	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
319	#336	C₂²×C₇₃	1	2	yes	complemented
320	C₂⁵	—	2	1	no	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×Q₈	—	2	4	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	4	2	no	—
326	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
328	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
329	C₂²×D₄	—	2	4	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	4	2	no	—
334	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
337	C₂×Q₁₆	—	2	4	no	—
338	C₂×Q₁₆	—	2	4	no	—
339	C₂×Q₁₆	—	2	2	no	—
340	C₂×Q₁₆	—	2	4	no	—
341	C₂×Q₁₆	—	4	2	no	—
342	C₂×SD₁₆	—	2	32	no	—
343	C₂×SD₁₆	—	2	4	no	—
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×SD₁₆	—	2	4	no	—
346	C₂×SD₁₆	—	2	4	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	4	2	no	—
351	C₂×SD₁₆	D₄×C₇₃	1	8	yes	—
352	C₂²×C₈	—	2	4	no	—
353	C₂²×C₈	D₄×C₇₃	1	4	yes	—
354	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
356	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
357	C₄⋊Q₈	—	2	4	no	—
358	C₄⋊Q₈	—	4	2	no	—
359	#124	—	2	4	no	—
360	#124	—	4	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	4	no	—
368	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
375	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
376	#107	—	2	2	no	—
377	#103	—	2	4	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#102	—	2	4	no	—
381	C₂²⋊C₈	D₄×C₇₃	1	4	yes	—
382	#97	—	2	4	no	—
383	#95	—	2	4	no	—
384	#95	D₄×C₇₃	1	2	yes	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	—	4	2	no	—
388	C₂⁴	—	4	4	no	—
389	C₂⁴	—	8	2	no	—
390	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	4	4	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	2	no	—
409	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
431	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
435	Q₁₆	—	4	8	no	—
436	Q₁₆	—	4	4	no	—
437	SD₁₆	—	2	16	no	—
438	SD₁₆	—	2	16	no	—
439	SD₁₆	—	4	8	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	8	no	—
444	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
445	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
446	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
447	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	4	8	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	4	8	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	8	4	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	8	16	no	—
471	C₂³	—	8	4	no	—
472	C₂³	—	8	4	no	—
473	C₂³	#127×C₇₃	1	2	yes	—
474	C₂³	#137×C₇₃	1	4	yes	—
475	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
476	Q₈	—	2	4	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	4	8	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	4	8	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	#127×C₇₃	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
514	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
515	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
516	C₈	—	2	2	no	—
517	C₈	—	2	4	no	—
518	C₈	#120×C₇₃	1	4	yes	—
519	C₂²	—	2	8	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	4	8	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	8	16	no	—
525	C₂²	—	8	4	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	#497×C₇₃	1	4	yes	complemented
529	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
530	C₂²	D₄²×C₇₃	1	2	yes	—
531	C₂²	C₂×#137×C₇₃	1	2	yes	—
532	C₂²	#577×C₇₃	1	2	yes	—
533	C₄	—	2	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	4	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
541	C₄	#535×C₇₃	1	1	yes	characteristic
542	C₄	D₄²×C₇₃	1	2	yes	—
543	C₂	—	2	4	no	—
544	C₂	—	8	4	no	—
545	C₂	C₇₃×#2433	1	1	yes	characteristic
546	C₂	C₂×#497×C₇₃	1	1	yes	characteristic
547	C₂	C₇₃×#3154	1	1	yes	characteristic
548	C₂	C₇₃×#3266	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#497×C₇₃	C₂	semidirect
3. C₂×#467×C₇₃	C₂	semidirect
4. C₂×#451×C₇₃	C₂	semidirect
7. C₇₃×#2434	C₂	semidirect
8. C₇₃×#2015	C₂	semidirect
9. C₇₃×#2013	C₂	semidirect
10. C₇₃×#1973	C₂	semidirect
11. C₇₃×#1752	C₂	semidirect
14. C₂²×Q₁₆×C₇₃	C₂²	semidirect
15. C₂²×Q₁₆×C₇₃	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
30. C₂×#107×C₇₃	C₂²	semidirect
31. C₂×#103×C₇₃	C₂²	semidirect
32. C₂×#103×C₇₃	C₂²	semidirect
33. C₂×#103×C₇₃	C₂²	semidirect
36. C₂×#97×C₇₃	C₂²	semidirect
39. #391×C₇₃	C₂²	semidirect
44. #336×C₇₃	C₂²	semidirect
253. C₂²×C₇₃	#497	semidirect
268. #25784	C₇₃	direct (N × H)
276. C₂×#497	C₂×C₇₃	semidirect
277. C₂×#467	C₂×C₇₃	semidirect
278. C₂×#451	C₂×C₇₃	semidirect
281. #2434	C₂×C₇₃	semidirect
282. #2015	C₂×C₇₃	semidirect
283. #2013	C₂×C₇₃	semidirect
284. #1973	C₂×C₇₃	semidirect
285. #1752	C₂×C₇₃	semidirect
286. C₇₃	#25784	direct (N × H)
289. C₂²×Q₁₆	C₂²×C₇₃	semidirect
290. C₂²×Q₁₆	C₂²×C₇₃	semidirect
297. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
305. C₂×#107	C₂²×C₇₃	semidirect
306. C₂×#103	C₂²×C₇₃	semidirect
307. C₂×#103	C₂²×C₇₃	semidirect
308. C₂×#103	C₂²×C₇₃	semidirect
311. C₂×#97	C₂²×C₇₃	semidirect
314. #391	C₂²×C₇₃	semidirect
319. #336	C₂²×C₇₃	semidirect
528. C₂²	#497×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₇₃	2
C₂×#497×C₇₃	2
C₂×#467×C₇₃	2
C₂×#451×C₇₃	2
C₂×#450×C₇₃	2
C₇₃×#2435	2
C₇₃×#2434	2
C₇₃×#2015	2
C₇₃×#2013	2
C₇₃×#1973	2
C₇₃×#1752	2
#25784	73

Subgroups — C73×#25784 #32935188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25784 #32935188