Subgroups — C₇₃×#20953 #32930357

Order 18688.

1974 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2896	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1887	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1885	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1733	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
11	#535×C₇₃	—	2	4	no	—
12	#535×C₇₃	C₄	1	8	yes	complemented
13	C₂×#127×C₇₃	C₂²	1	2	yes	—
14	C₂×#124×C₇₃	C₂²	1	2	yes	—
15	C₂×#121×C₇₃	—	2	2	no	—
16	C₂×#120×C₇₃	—	2	2	no	—
17	#518×C₇₃	—	2	2	no	—
18	#518×C₇₃	—	2	4	no	—
19	#518×C₇₃	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₇₃	—	2	4	no	—
21	C₂×#117×C₇₃	C₂²	1	2	yes	—
22	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₇₃	—	2	2	no	—
24	#419×C₇₃	C₂²	1	4	yes	complemented
25	#418×C₇₃	C₂²	1	4	yes	complemented
26	#417×C₇₃	—	2	4	no	—
27	#416×C₇₃	—	2	4	no	—
28	C₂×#100×C₇₃	—	2	4	no	—
29	C₂×#100×C₇₃	C₂²	1	4	yes	—
30	#339×C₇₃	C₂²	1	8	yes	complemented
31	C₂⁵×C₇₃	D₄	1	2	yes	—
32	C₂×#41×C₇₃	—	2	2	no	—
33	C₂×#41×C₇₃	—	2	2	no	—
34	C₂×#41×C₇₃	—	2	2	no	—
35	C₂×#41×C₇₃	—	2	4	no	—
36	C₂×#41×C₇₃	C₂×C₄	1	4	yes	complemented
37	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₇₃	—	2	1	no	—
39	C₂²×D₄×C₇₃	—	2	4	no	—
40	C₂²×D₄×C₇₃	—	2	2	no	—
41	C₂²×D₄×C₇₃	—	2	2	no	—
42	C₂²×D₄×C₇₃	—	2	4	no	—
43	C₂²×D₄×C₇₃	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₇₃	D₄	1	2	yes	—
45	C₂²×D₄×C₇₃	D₄	1	4	yes	—
46	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₇₃	—	2	4	no	—
49	C₂³×C₄×C₇₃	—	2	1	no	—
50	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₇₃	—	2	2	no	—
52	C₂×M₁₆×C₇₃	—	2	4	no	—
53	C₂×M₁₆×C₇₃	—	2	4	no	—
54	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
55	C₂²×C₈×C₇₃	—	2	2	no	—
56	#127×C₇₃	—	2	4	no	—
57	#127×C₇₃	C₂×C₄	1	8	yes	complemented
58	#124×C₇₃	—	2	4	no	—
59	#124×C₇₃	C₂×C₄	1	8	yes	complemented
60	#121×C₇₃	—	2	16	no	—
61	#120×C₇₃	—	2	16	no	—
62	C₄×D₄×C₇₃	—	2	16	no	—
63	C₄×D₄×C₇₃	—	2	16	no	—
64	#117×C₇₃	—	2	2	no	—
65	#117×C₇₃	—	2	2	no	—
66	#117×C₇₃	—	2	2	no	—
67	#117×C₇₃	C₂×C₄	1	4	yes	complemented
68	#117×C₇₃	D₄	1	4	yes	complemented
69	#117×C₇₃	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	complemented
72	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
78	C₂×C₄²×C₇₃	—	2	2	no	—
79	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
80	#103×C₇₃	—	2	8	no	—
81	#102×C₇₃	—	2	8	no	—
82	#100×C₇₃	—	2	8	no	—
83	C₂⁴×C₇₃	—	2	2	no	—
84	C₂⁴×C₇₃	—	2	2	no	—
85	C₂⁴×C₇₃	—	2	4	no	—
86	C₂⁴×C₇₃	—	2	1	no	—
87	C₂⁴×C₇₃	—	8	4	no	—
88	C₂⁴×C₇₃	C₂²⋊C₄	1	8	yes	—
89	C₂⁴×C₇₃	C₂×D₄	1	4	yes	—
90	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
91	#41×C₇₃	—	2	8	no	—
92	#41×C₇₃	—	2	8	no	—
93	#41×C₇₃	—	4	4	no	—
94	#41×C₇₃	—	4	4	no	—
95	C₂×Q₈×C₇₃	—	2	1	no	—
96	C₂×Q₈×C₇₃	—	2	2	no	—
97	C₂×Q₈×C₇₃	—	2	2	no	—
98	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	complemented
99	C₂×D₄×C₇₃	—	2	4	no	—
100	C₂×D₄×C₇₃	—	2	16	no	—
101	C₂×D₄×C₇₃	—	2	8	no	—
102	C₂×D₄×C₇₃	—	2	8	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	8	no	—
105	C₂×D₄×C₇₃	—	2	8	no	—
106	C₂×D₄×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	1	no	—
110	C₂×D₄×C₇₃	—	2	4	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	4	1	no	—
113	C₂×D₄×C₇₃	—	4	1	no	—
114	C₂×D₄×C₇₃	—	4	2	no	—
115	C₂×D₄×C₇₃	—	8	8	no	—
116	C₂×D₄×C₇₃	C₂²⋊C₄	1	8	yes	—
117	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
118	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	complemented
119	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	16	no	—
124	C₂²×C₄×C₇₃	—	2	4	no	—
125	C₂²×C₄×C₇₃	—	4	2	no	—
126	C₂²×C₄×C₇₃	—	4	2	no	—
127	C₂²×C₄×C₇₃	—	8	8	no	—
128	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇₃	#41	1	4	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	—	4	4	no	—
138	C₂×C₈×C₇₃	—	2	4	no	—
139	C₂×C₈×C₇₃	—	4	4	no	—
140	C₄⋊C₄×C₇₃	—	2	4	no	—
141	C₄⋊C₄×C₇₃	—	2	4	no	—
142	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
143	C₂²⋊C₄×C₇₃	—	2	16	no	—
144	C₂²⋊C₄×C₇₃	—	2	4	no	—
145	C₂²⋊C₄×C₇₃	—	2	16	no	—
146	C₂²⋊C₄×C₇₃	—	2	4	no	—
147	C₂²⋊C₄×C₇₃	—	2	4	no	—
148	C₄²×C₇₃	—	2	4	no	—
149	C₄²×C₇₃	—	2	4	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₄²×C₇₃	C₂²×C₄	1	4	yes	complemented
152	C₂³×C₇₃	—	2	4	no	—
153	C₂³×C₇₃	—	2	8	no	—
154	C₂³×C₇₃	—	2	4	no	—
155	C₂³×C₇₃	—	2	8	no	—
156	C₂³×C₇₃	—	2	2	no	—
157	C₂³×C₇₃	—	4	2	no	—
158	C₂³×C₇₃	—	4	8	no	—
159	C₂³×C₇₃	—	4	8	no	—
160	C₂³×C₇₃	—	4	4	no	—
161	C₂³×C₇₃	—	4	1	no	—
162	C₂³×C₇₃	—	4	1	no	—
163	C₂³×C₇₃	—	8	4	no	—
164	C₂³×C₇₃	—	8	8	no	—
165	C₂³×C₇₃	—	8	8	no	—
166	C₂³×C₇₃	C₂×C₂²⋊C₄	1	8	yes	—
167	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂³×C₇₃	#120	1	1	yes	characteristic
169	C₂³×C₇₃	#120	1	1	yes	characteristic
170	C₂³×C₇₃	#123	1	2	yes	—
171	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₇₃	—	2	4	no	—
173	Q₈×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	2	8	no	—
175	D₄×C₇₃	—	2	4	no	—
176	D₄×C₇₃	—	2	8	no	—
177	D₄×C₇₃	—	2	16	no	—
178	D₄×C₇₃	—	4	4	no	—
179	D₄×C₇₃	—	4	4	no	—
180	D₄×C₇₃	—	4	2	no	—
181	D₄×C₇₃	—	8	16	no	—
182	C₂×C₄×C₇₃	—	2	4	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	2	8	no	—
185	C₂×C₄×C₇₃	—	4	8	no	—
186	C₂×C₄×C₇₃	—	4	4	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	—	4	1	no	—
189	C₂×C₄×C₇₃	—	4	8	no	—
190	C₂×C₄×C₇₃	—	8	16	no	—
191	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
193	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
194	C₂×C₄×C₇₃	#120	1	2	yes	—
195	C₂×C₄×C₇₃	#121	1	4	yes	—
196	C₂×C₄×C₇₃	#121	1	4	yes	—
197	C₂×C₄×C₇₃	#123	1	2	yes	—
198	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
202	C₈×C₇₃	—	4	4	no	—
203	C₂²×C₇₃	—	2	2	no	—
204	C₂²×C₇₃	—	2	2	no	—
205	C₂²×C₇₃	—	2	2	no	—
206	C₂²×C₇₃	—	2	8	no	—
207	C₂²×C₇₃	—	4	2	no	—
208	C₂²×C₇₃	—	4	2	no	—
209	C₂²×C₇₃	—	4	8	no	—
210	C₂²×C₇₃	—	4	16	no	—
211	C₂²×C₇₃	—	4	4	no	—
212	C₂²×C₇₃	—	4	8	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	8	4	no	—
215	C₂²×C₇₃	—	8	8	no	—
216	C₂²×C₇₃	—	8	2	no	—
217	C₂²×C₇₃	—	8	2	no	—
218	C₂²×C₇₃	#386	1	2	yes	—
219	C₂²×C₇₃	#386	1	2	yes	—
220	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
222	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
223	C₄×C₇₃	—	4	4	no	—
224	C₄×C₇₃	—	4	8	no	—
225	C₄×C₇₃	—	4	2	no	—
226	C₄×C₇₃	#386	1	4	yes	—
227	C₄×C₇₃	C₂×C₄×D₄	1	2	yes	—
228	C₄×C₇₃	C₂×#121	1	2	yes	—
229	#20953	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₇₃	—	2	1	no	—
231	C₂×C₇₃	—	2	2	no	—
232	C₂×C₇₃	—	2	1	no	—
233	C₂×C₇₃	—	2	2	no	—
234	C₂×C₇₃	—	4	8	no	—
235	C₂×C₇₃	—	8	2	no	—
236	C₂×C₇₃	C₂×#386	1	1	yes	characteristic
237	C₂×C₇₃	#3019	1	2	yes	—
238	C₂×#535	C₂×C₇₃	1	1	yes	characteristic
239	C₂×#518	C₂×C₇₃	1	1	yes	characteristic, complemented
240	#2896	C₂×C₇₃	1	2	yes	complemented
241	C₂²×#100	C₂×C₇₃	1	1	yes	characteristic, complemented
242	#1887	C₂×C₇₃	1	4	yes	complemented
243	#1885	C₂×C₇₃	1	4	yes	complemented
244	#1733	C₂×C₇₃	1	2	yes	complemented
245	C₇₃	#20953	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
247	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
249	#535	—	2	4	no	—
250	#535	C₄×C₇₃	1	8	yes	complemented
251	C₂×#127	C₂²×C₇₃	1	2	yes	—
252	C₂×#124	C₂²×C₇₃	1	2	yes	—
253	C₂×#121	—	2	2	no	—
254	C₂×#120	—	2	2	no	—
255	#518	—	2	2	no	—
256	#518	—	2	4	no	—
257	#518	C₂²×C₇₃	1	4	yes	—
258	C₂×C₄×D₄	—	2	4	no	—
259	C₂×#117	C₂²×C₇₃	1	2	yes	—
260	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	—	2	2	no	—
262	#419	C₂²×C₇₃	1	4	yes	complemented
263	#418	C₂²×C₇₃	1	4	yes	complemented
264	#417	—	2	4	no	—
265	#416	—	2	4	no	—
266	C₂×#100	—	2	4	no	—
267	C₂×#100	C₂²×C₇₃	1	4	yes	—
268	#339	C₂²×C₇₃	1	8	yes	complemented
269	C₂⁵	D₄×C₇₃	1	2	yes	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	C₂×C₄×C₇₃	1	4	yes	complemented
275	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	4	no	—
281	C₂²×D₄	C₂×C₄×C₇₃	1	4	yes	—
282	C₂²×D₄	D₄×C₇₃	1	2	yes	—
283	C₂²×D₄	D₄×C₇₃	1	4	yes	—
284	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
286	C₂³×C₄	—	2	4	no	—
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	4	no	—
291	C₂×M₁₆	—	2	4	no	—
292	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
293	C₂²×C₈	—	2	2	no	—
294	#127	—	2	4	no	—
295	#127	C₂×C₄×C₇₃	1	8	yes	complemented
296	#124	—	2	4	no	—
297	#124	C₂×C₄×C₇₃	1	8	yes	complemented
298	#121	—	2	16	no	—
299	#120	—	2	16	no	—
300	C₄×D₄	—	2	16	no	—
301	C₄×D₄	—	2	16	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	C₂×C₄×C₇₃	1	4	yes	complemented
306	#117	D₄×C₇₃	1	4	yes	complemented
307	#117	C₂³×C₇₃	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	complemented
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	C₂×C₂²⋊C₄	—	2	8	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	8	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	4	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
318	#103	—	2	8	no	—
319	#102	—	2	8	no	—
320	#100	—	2	8	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	2	2	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	1	no	—
325	C₂⁴	—	8	4	no	—
326	C₂⁴	C₂²⋊C₄×C₇₃	1	8	yes	—
327	C₂⁴	C₂×D₄×C₇₃	1	4	yes	—
328	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
329	#41	—	2	8	no	—
330	#41	—	2	8	no	—
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	complemented
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	16	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	8	8	no	—
354	C₂×D₄	C₂²⋊C₄×C₇₃	1	8	yes	—
355	C₂×D₄	C₂²×C₄×C₇₃	1	4	yes	—
356	C₂×D₄	C₂²×C₄×C₇₃	1	2	yes	complemented
357	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	16	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	8	8	no	—
366	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
371	C₂²×C₄	#41×C₇₃	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
373	M₁₆	—	2	4	no	—
374	M₁₆	—	2	4	no	—
375	M₁₆	—	4	4	no	—
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	4	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
381	C₂²⋊C₄	—	2	16	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	16	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂²×C₄×C₇₃	1	4	yes	complemented
390	C₂³	—	2	8	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	8	no	—
397	C₂³	—	4	8	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	8	4	no	—
402	C₂³	—	8	8	no	—
403	C₂³	—	8	8	no	—
404	C₂³	C₂×C₂²⋊C₄×C₇₃	1	8	yes	—
405	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
406	C₂³	#120×C₇₃	1	1	yes	characteristic
407	C₂³	#120×C₇₃	1	1	yes	characteristic
408	C₂³	#123×C₇₃	1	2	yes	—
409	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
410	Q₈	—	2	4	no	—
411	Q₈	—	4	2	no	—
412	D₄	—	2	16	no	—
413	D₄	—	2	8	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	8	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	16	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	8	16	no	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
430	C₂×C₄	C₄×D₄×C₇₃	1	4	yes	—
431	C₂×C₄	C₄×D₄×C₇₃	1	4	yes	—
432	C₂×C₄	#120×C₇₃	1	2	yes	—
433	C₂×C₄	#121×C₇₃	1	4	yes	—
434	C₂×C₄	#121×C₇₃	1	4	yes	—
435	C₂×C₄	#123×C₇₃	1	2	yes	—
436	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
440	C₈	—	4	4	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	8	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	8	no	—
448	C₂²	—	4	16	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	8	4	no	—
453	C₂²	—	8	8	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	#386×C₇₃	1	2	yes	—
457	C₂²	#386×C₇₃	1	2	yes	—
458	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
459	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
460	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
461	C₄	—	4	4	no	—
462	C₄	—	4	8	no	—
463	C₄	—	4	2	no	—
464	C₄	#386×C₇₃	1	4	yes	—
465	C₄	C₂×C₄×D₄×C₇₃	1	2	yes	—
466	C₄	C₂×#121×C₇₃	1	2	yes	—
467	C₂	—	2	1	no	—
468	C₂	—	2	2	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	2	no	—
471	C₂	—	4	8	no	—
472	C₂	—	8	2	no	—
473	C₂	C₂×#386×C₇₃	1	1	yes	characteristic
474	C₂	C₇₃×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#535×C₇₃	C₂
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
2. C₂×#518×C₇₃	C₂	semidirect
3. C₇₃×#2896	C₂	semidirect
4. C₂²×#100×C₇₃	C₂	semidirect
5. C₇₃×#1887	C₂	semidirect
6. C₇₃×#1885	C₂	semidirect
7. C₇₃×#1733	C₂	semidirect
12. #535×C₇₃	C₄	semidirect
24. #419×C₇₃	C₂²	semidirect
25. #418×C₇₃	C₂²	semidirect
30. #339×C₇₃	C₂²	semidirect
36. C₂×#41×C₇₃	C₂×C₄	semidirect
57. #127×C₇₃	C₂×C₄	semidirect
59. #124×C₇₃	C₂×C₄	semidirect
67. #117×C₇₃	C₂×C₄	semidirect
68. #117×C₇₃	D₄	semidirect
71. C₂×C₄⋊C₄×C₇₃	D₄	semidirect
98. C₂×Q₈×C₇₃	C₂²×C₄	semidirect
118. C₂×D₄×C₇₃	C₂²×C₄	semidirect
151. C₄²×C₇₃	C₂²×C₄	semidirect
229. #20953	C₇₃	direct (N × H)
239. C₂×#518	C₂×C₇₃	semidirect
240. #2896	C₂×C₇₃	semidirect
241. C₂²×#100	C₂×C₇₃	semidirect
242. #1887	C₂×C₇₃	semidirect
243. #1885	C₂×C₇₃	semidirect
244. #1733	C₂×C₇₃	semidirect
245. C₇₃	#20953	direct (N × H)
250. #535	C₄×C₇₃	semidirect
262. #419	C₂²×C₇₃	semidirect
263. #418	C₂²×C₇₃	semidirect
268. #339	C₂²×C₇₃	semidirect
274. C₂×#41	C₂×C₄×C₇₃	semidirect
295. #127	C₂×C₄×C₇₃	semidirect
297. #124	C₂×C₄×C₇₃	semidirect
305. #117	C₂×C₄×C₇₃	semidirect
306. #117	D₄×C₇₃	semidirect
309. C₂×C₄⋊C₄	D₄×C₇₃	semidirect
336. C₂×Q₈	C₂²×C₄×C₇₃	semidirect
356. C₂×D₄	C₂²×C₄×C₇₃	semidirect
389. C₄²	C₂²×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×#535×C₇₃	2
C₂×#518×C₇₃	2
C₇₃×#2896	2
C₂²×#100×C₇₃	2
C₇₃×#1887	2
C₇₃×#1885	2
C₇₃×#1733	2
#20953	73

Subgroups — C73×#20953 #32930357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#20953 #32930357