Subgroups — C₇₃×#59420 #32968824

Order 18688.

3036 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2697	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2538	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2534	C₂	1	4	yes	maximal, complemented
6	C₇₃×#2435	C₂	1	4	yes	maximal, complemented
7	C₇₃×#2427	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2420	C₂	1	4	yes	maximal, complemented
9	D₄×C₂²⋊C₄×C₇₃	C₂	1	4	yes	maximal, complemented
10	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#124×C₇₃	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₇₃	C₂²	1	4	yes	—
13	#559×C₇₃	—	2	8	no	—
14	D₄²×C₇₃	—	2	8	no	—
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₇₃	C₂²	1	2	yes	—
17	C₂×#124×C₇₃	C₂²	1	4	yes	complemented
18	C₂×#123×C₇₃	C₂²	1	4	yes	complemented
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	complemented
20	C₂×#121×C₇₃	C₂²	1	4	yes	—
21	C₂×#120×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
23	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	complemented
27	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	complemented
28	#397×C₇₃	C₂²	1	8	yes	complemented
29	#396×C₇₃	C₂²	1	8	yes	complemented
30	#394×C₇₃	C₂²	1	8	yes	complemented
31	#394×C₇₃	C₂²	1	8	yes	complemented
32	#391×C₇₃	C₂²	1	2	yes	complemented
33	#390×C₇₃	C₂²	1	4	yes	—
34	#390×C₇₃	C₂²	1	2	yes	—
35	#390×C₇₃	C₂²	1	2	yes	complemented
36	#390×C₇₃	C₂²	1	4	yes	complemented
37	#389×C₇₃	C₂²	1	4	yes	complemented
38	#388×C₇₃	C₂²	1	4	yes	complemented
39	#388×C₇₃	C₂²	1	4	yes	complemented
40	#386×C₇₃	C₂²	1	8	yes	complemented
41	#386×C₇₃	C₂²	1	8	yes	complemented
42	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#382×C₇₃	C₂²	1	2	yes	complemented
44	#381×C₇₃	C₂²	1	4	yes	complemented
45	#380×C₇₃	C₂²	1	4	yes	complemented
46	#380×C₇₃	C₂²	1	4	yes	complemented
47	#379×C₇₃	C₂²	1	8	yes	complemented
48	#379×C₇₃	C₂²	1	4	yes	complemented
49	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	complemented
51	C₄³×C₇₃	C₂²	1	1	yes	characteristic, complemented
52	C₂⁵×C₇₃	C₂³	1	4	yes	—
53	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₇₃	—	2	16	no	—
55	C₂²×D₄×C₇₃	—	2	16	no	—
56	C₂²×D₄×C₇₃	—	4	8	no	—
57	C₂²×D₄×C₇₃	C₂³	1	8	yes	—
58	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
64	#127×C₇₃	D₄	1	8	yes	—
65	#124×C₇₃	—	2	16	no	—
66	#124×C₇₃	—	2	8	no	—
67	#123×C₇₃	—	2	16	no	—
68	C₂²⋊Q₈×C₇₃	—	4	8	no	—
69	#121×C₇₃	—	2	16	no	—
70	#120×C₇₃	—	2	16	no	—
71	C₄×Q₈×C₇₃	—	2	8	no	—
72	C₄×D₄×C₇₃	—	2	16	no	—
73	C₄×D₄×C₇₃	—	2	8	no	—
74	C₄×D₄×C₇₃	—	4	8	no	—
75	C₄×D₄×C₇₃	—	4	4	no	—
76	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₇₃	—	4	8	no	—
83	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
95	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
98	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
101	#95×C₇₃	C₂³	1	4	yes	—
102	#95×C₇₃	C₂³	1	4	yes	—
103	#95×C₇₃	C₂³	1	4	yes	—
104	#95×C₇₃	C₂³	1	4	yes	—
105	#95×C₇₃	C₂³	1	8	yes	—
106	C₂⁴×C₇₃	—	2	8	no	—
107	C₂⁴×C₇₃	—	2	16	no	—
108	C₂⁴×C₇₃	—	4	4	no	—
109	C₂⁴×C₇₃	—	4	8	no	—
110	C₂⁴×C₇₃	—	4	4	no	—
111	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
112	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
113	C₂×Q₈×C₇₃	—	2	4	no	—
114	C₂×Q₈×C₇₃	—	2	4	no	—
115	C₂×Q₈×C₇₃	—	2	4	no	—
116	C₂×D₄×C₇₃	—	2	16	no	—
117	C₂×D₄×C₇₃	—	2	16	no	—
118	C₂×D₄×C₇₃	—	2	4	no	—
119	C₂×D₄×C₇₃	—	2	8	no	—
120	C₂×D₄×C₇₃	—	2	8	no	—
121	C₂×D₄×C₇₃	—	2	4	no	—
122	C₂×D₄×C₇₃	—	4	2	no	—
123	C₂×D₄×C₇₃	—	4	8	no	—
124	C₂×D₄×C₇₃	—	4	2	no	—
125	C₂×D₄×C₇₃	—	4	64	no	—
126	C₂×D₄×C₇₃	C₂×D₄	1	16	yes	—
127	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
128	C₂×D₄×C₇₃	#41	1	8	yes	—
129	C₂²×C₄×C₇₃	—	2	8	no	—
130	C₂²×C₄×C₇₃	—	2	8	no	—
131	C₂²×C₄×C₇₃	—	2	8	no	—
132	C₂²×C₄×C₇₃	—	2	8	no	—
133	C₂²×C₄×C₇₃	—	2	8	no	—
134	C₂²×C₄×C₇₃	—	4	4	no	—
135	C₂²×C₄×C₇₃	—	4	8	no	—
136	C₂²×C₄×C₇₃	—	4	4	no	—
137	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
146	C₄⋊C₄×C₇₃	—	2	4	no	—
147	C₄⋊C₄×C₇₃	—	2	4	no	—
148	C₄⋊C₄×C₇₃	—	2	8	no	—
149	C₄⋊C₄×C₇₃	—	2	8	no	—
150	C₄⋊C₄×C₇₃	—	4	2	no	—
151	C₄⋊C₄×C₇₃	—	4	8	no	—
152	C₂²⋊C₄×C₇₃	—	2	16	no	—
153	C₂²⋊C₄×C₇₃	—	2	8	no	—
154	C₂²⋊C₄×C₇₃	—	2	8	no	—
155	C₂²⋊C₄×C₇₃	—	2	8	no	—
156	C₂²⋊C₄×C₇₃	—	2	8	no	—
157	C₂²⋊C₄×C₇₃	—	2	8	no	—
158	C₂²⋊C₄×C₇₃	—	2	8	no	—
159	C₂²⋊C₄×C₇₃	—	4	8	no	—
160	C₂²⋊C₄×C₇₃	—	4	4	no	—
161	C₂²⋊C₄×C₇₃	—	4	4	no	—
162	C₂²⋊C₄×C₇₃	—	4	8	no	—
163	C₂²⋊C₄×C₇₃	—	4	8	no	—
164	C₄²×C₇₃	—	2	8	no	—
165	C₄²×C₇₃	—	2	4	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	4	no	—
168	C₄²×C₇₃	—	4	1	no	—
169	C₄²×C₇₃	C₂×D₄	1	4	yes	—
170	C₂³×C₇₃	—	2	4	no	—
171	C₂³×C₇₃	—	2	4	no	—
172	C₂³×C₇₃	—	2	8	no	—
173	C₂³×C₇₃	—	2	4	no	—
174	C₂³×C₇₃	—	2	4	no	—
175	C₂³×C₇₃	—	2	4	no	—
176	C₂³×C₇₃	—	2	8	no	—
177	C₂³×C₇₃	—	2	4	no	—
178	C₂³×C₇₃	—	2	4	no	—
179	C₂³×C₇₃	—	2	4	no	—
180	C₂³×C₇₃	—	4	32	no	—
181	C₂³×C₇₃	—	4	16	no	—
182	C₂³×C₇₃	—	8	8	no	—
183	C₂³×C₇₃	—	8	16	no	—
184	C₂³×C₇₃	—	8	8	no	—
185	C₂³×C₇₃	C₂²×D₄	1	8	yes	—
186	C₂³×C₇₃	C₂×#41	1	8	yes	—
187	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
188	Q₈×C₇₃	—	4	8	no	—
189	D₄×C₇₃	—	2	16	no	—
190	D₄×C₇₃	—	2	32	no	—
191	D₄×C₇₃	—	4	8	no	—
192	D₄×C₇₃	—	4	32	no	—
193	C₂×C₄×C₇₃	—	2	1	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	4	no	—
197	C₂×C₄×C₇₃	—	2	4	no	—
198	C₂×C₄×C₇₃	—	2	4	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	4	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	8	no	—
208	C₂×C₄×C₇₃	—	2	4	no	—
209	C₂×C₄×C₇₃	—	2	4	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	4	no	—
212	C₂×C₄×C₇₃	—	4	16	no	—
213	C₂×C₄×C₇₃	—	8	8	no	—
214	C₂×C₄×C₇₃	—	8	8	no	—
215	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
218	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
219	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
220	C₂²×C₇₃	—	2	8	no	—
221	C₂²×C₇₃	—	2	16	no	—
222	C₂²×C₇₃	—	2	8	no	—
223	C₂²×C₇₃	—	2	8	no	—
224	C₂²×C₇₃	—	2	8	no	—
225	C₂²×C₇₃	—	4	4	no	—
226	C₂²×C₇₃	—	4	4	no	—
227	C₂²×C₇₃	—	4	4	no	—
228	C₂²×C₇₃	—	4	8	no	—
229	C₂²×C₇₃	—	4	4	no	—
230	C₂²×C₇₃	—	4	4	no	—
231	C₂²×C₇₃	—	4	4	no	—
232	C₂²×C₇₃	—	8	32	no	—
233	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
234	C₂²×C₇₃	C₂²×#41	1	2	yes	—
235	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
236	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₇₃	#585	1	1	yes	characteristic
238	C₄×C₇₃	—	2	2	no	—
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	4	4	no	—
241	C₄×C₇₃	—	4	4	no	—
242	C₄×C₇₃	—	4	1	no	—
243	C₄×C₇₃	—	4	4	no	—
244	C₄×C₇₃	—	4	2	no	—
245	C₄×C₇₃	—	4	4	no	—
246	C₄×C₇₃	#546	1	8	yes	—
247	#59420	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₇₃	—	4	8	no	—
249	C₂×C₇₃	—	4	8	no	—
250	C₂×C₇₃	C₂×#546	1	2	yes	—
251	C₂×C₇₃	#3481	1	1	yes	characteristic
252	C₂×C₇₃	#3496	1	1	yes	characteristic
253	C₂×C₇₃	#3514	1	2	yes	—
254	C₂×C₇₃	#3543	1	1	yes	characteristic
255	C₂×#559	C₂×C₇₃	1	1	yes	characteristic, complemented
256	C₂×D₄²	C₂×C₇₃	1	1	yes	characteristic
257	#2697	C₂×C₇₃	1	4	yes	complemented
258	#2538	C₂×C₇₃	1	2	yes	complemented
259	#2534	C₂×C₇₃	1	4	yes	complemented
260	#2435	C₂×C₇₃	1	4	yes	complemented
261	#2427	C₂×C₇₃	1	4	yes	complemented
262	#2420	C₂×C₇₃	1	4	yes	complemented
263	D₄×C₂²⋊C₄	C₂×C₇₃	1	4	yes	complemented
264	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
265	C₄×#124	C₂×C₇₃	1	2	yes	complemented
266	C₇₃	#59420	1	1	yes	characteristic, direct product factor, Sylow
267	C₂³×D₄	C₂²×C₇₃	1	4	yes	—
268	#559	—	2	8	no	—
269	D₄²	—	2	8	no	—
270	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
271	C₂×#124	C₂²×C₇₃	1	2	yes	—
272	C₂×#124	C₂²×C₇₃	1	4	yes	complemented
273	C₂×#123	C₂²×C₇₃	1	4	yes	complemented
274	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	complemented
275	C₂×#121	C₂²×C₇₃	1	4	yes	—
276	C₂×#120	C₂²×C₇₃	1	4	yes	—
277	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
278	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	complemented
280	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	complemented
281	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
282	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	complemented
283	#397	C₂²×C₇₃	1	8	yes	complemented
284	#396	C₂²×C₇₃	1	8	yes	complemented
285	#394	C₂²×C₇₃	1	8	yes	complemented
286	#394	C₂²×C₇₃	1	8	yes	complemented
287	#391	C₂²×C₇₃	1	2	yes	complemented
288	#390	C₂²×C₇₃	1	2	yes	—
289	#390	C₂²×C₇₃	1	4	yes	—
290	#390	C₂²×C₇₃	1	4	yes	complemented
291	#390	C₂²×C₇₃	1	2	yes	complemented
292	#389	C₂²×C₇₃	1	4	yes	complemented
293	#388	C₂²×C₇₃	1	4	yes	complemented
294	#388	C₂²×C₇₃	1	4	yes	complemented
295	#386	C₂²×C₇₃	1	8	yes	complemented
296	#386	C₂²×C₇₃	1	8	yes	complemented
297	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
298	#382	C₂²×C₇₃	1	2	yes	complemented
299	#381	C₂²×C₇₃	1	4	yes	complemented
300	#380	C₂²×C₇₃	1	4	yes	complemented
301	#380	C₂²×C₇₃	1	4	yes	complemented
302	#379	C₂²×C₇₃	1	8	yes	complemented
303	#379	C₂²×C₇₃	1	4	yes	complemented
304	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	complemented
305	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	complemented
306	C₄³	C₂²×C₇₃	1	1	yes	characteristic, complemented
307	C₂⁵	C₂³×C₇₃	1	4	yes	—
308	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
309	C₂²×D₄	—	2	16	no	—
310	C₂²×D₄	—	2	16	no	—
311	C₂²×D₄	—	4	8	no	—
312	C₂²×D₄	C₂³×C₇₃	1	8	yes	—
313	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
314	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
315	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
316	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
317	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
318	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
319	#127	D₄×C₇₃	1	8	yes	—
320	#124	—	2	16	no	—
321	#124	—	2	8	no	—
322	#123	—	2	16	no	—
323	C₂²⋊Q₈	—	4	8	no	—
324	#121	—	2	16	no	—
325	#120	—	2	16	no	—
326	C₄×Q₈	—	2	8	no	—
327	C₄×D₄	—	2	16	no	—
328	C₄×D₄	—	2	8	no	—
329	C₄×D₄	—	4	8	no	—
330	C₄×D₄	—	4	4	no	—
331	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
337	C₂×C₂²⋊C₄	—	4	8	no	—
338	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
350	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
351	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
353	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
354	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
356	#95	C₂³×C₇₃	1	4	yes	—
357	#95	C₂³×C₇₃	1	4	yes	—
358	#95	C₂³×C₇₃	1	4	yes	—
359	#95	C₂³×C₇₃	1	4	yes	—
360	#95	C₂³×C₇₃	1	8	yes	—
361	C₂⁴	—	2	8	no	—
362	C₂⁴	—	2	16	no	—
363	C₂⁴	—	4	4	no	—
364	C₂⁴	—	4	8	no	—
365	C₂⁴	—	4	4	no	—
366	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
367	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×D₄	—	2	16	no	—
372	C₂×D₄	—	2	16	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	64	no	—
381	C₂×D₄	C₂×D₄×C₇₃	1	16	yes	—
382	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
383	C₂×D₄	#41×C₇₃	1	8	yes	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	8	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	8	no	—
407	C₂²⋊C₄	—	2	16	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	4	8	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	8	no	—
418	C₂²⋊C₄	—	4	8	no	—
419	C₄²	—	2	8	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	4	1	no	—
424	C₄²	C₂×D₄×C₇₃	1	4	yes	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	4	32	no	—
436	C₂³	—	4	16	no	—
437	C₂³	—	8	8	no	—
438	C₂³	—	8	16	no	—
439	C₂³	—	8	8	no	—
440	C₂³	C₂²×D₄×C₇₃	1	8	yes	—
441	C₂³	C₂×#41×C₇₃	1	8	yes	—
442	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
443	Q₈	—	4	8	no	—
444	D₄	—	2	16	no	—
445	D₄	—	2	32	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	32	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	16	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	—	8	8	no	—
470	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
472	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
473	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
474	C₂×C₄	H(5,𝔽₂)×C₇₃	1	4	yes	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	16	no	—
477	C₂²	—	2	8	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	2	8	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	8	32	no	—
488	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
489	C₂²	C₂²×#41×C₇₃	1	2	yes	—
490	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	2	yes	—
491	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
492	C₂²	#585×C₇₃	1	1	yes	characteristic
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	4	no	—
501	C₄	#546×C₇₃	1	8	yes	—
502	C₂	—	4	8	no	—
503	C₂	—	4	8	no	—
504	C₂	C₂×#546×C₇₃	1	2	yes	—
505	C₂	C₇₃×#3481	1	1	yes	characteristic
506	C₂	C₇₃×#3496	1	1	yes	characteristic
507	C₂	C₇₃×#3514	1	2	yes	—
508	C₂	C₇₃×#3543	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×D₄²×C₇₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#559×C₇₃	C₂	semidirect
3. C₇₃×#2697	C₂	semidirect
4. C₇₃×#2538	C₂	semidirect
5. C₇₃×#2534	C₂	semidirect
6. C₇₃×#2435	C₂	semidirect
7. C₇₃×#2427	C₂	semidirect
8. C₇₃×#2420	C₂	semidirect
9. D₄×C₂²⋊C₄×C₇₃	C₂	semidirect
10. C₄×#127×C₇₃	C₂	semidirect
11. C₄×#124×C₇₃	C₂	semidirect
17. C₂×#124×C₇₃	C₂²	semidirect
18. C₂×#123×C₇₃	C₂²	semidirect
19. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
22. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
24. C₂×C₄×D₄×C₇₃	C₂²	semidirect
25. C₂×C₄×D₄×C₇₃	C₂²	semidirect
26. C₂×C₄×D₄×C₇₃	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
28. #397×C₇₃	C₂²	semidirect
29. #396×C₇₃	C₂²	semidirect
30. #394×C₇₃	C₂²	semidirect
31. #394×C₇₃	C₂²	semidirect
32. #391×C₇₃	C₂²	semidirect
35. #390×C₇₃	C₂²	semidirect
36. #390×C₇₃	C₂²	semidirect
37. #389×C₇₃	C₂²	semidirect
38. #388×C₇₃	C₂²	semidirect
39. #388×C₇₃	C₂²	semidirect
40. #386×C₇₃	C₂²	semidirect
41. #386×C₇₃	C₂²	semidirect
42. #384×C₇₃	C₂²	semidirect
43. #382×C₇₃	C₂²	semidirect
44. #381×C₇₃	C₂²	semidirect
45. #380×C₇₃	C₂²	semidirect
46. #380×C₇₃	C₂²	semidirect
47. #379×C₇₃	C₂²	semidirect
48. #379×C₇₃	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
50. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
51. C₄³×C₇₃	C₂²	semidirect
247. #59420	C₇₃	direct (N × H)
255. C₂×#559	C₂×C₇₃	semidirect
257. #2697	C₂×C₇₃	semidirect
258. #2538	C₂×C₇₃	semidirect
259. #2534	C₂×C₇₃	semidirect
260. #2435	C₂×C₇₃	semidirect
261. #2427	C₂×C₇₃	semidirect
262. #2420	C₂×C₇₃	semidirect
263. D₄×C₂²⋊C₄	C₂×C₇₃	semidirect
264. C₄×#127	C₂×C₇₃	semidirect
265. C₄×#124	C₂×C₇₃	semidirect
266. C₇₃	#59420	direct (N × H)
272. C₂×#124	C₂²×C₇₃	semidirect
273. C₂×#123	C₂²×C₇₃	semidirect
274. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
277. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
279. C₂×C₄×D₄	C₂²×C₇₃	semidirect
280. C₂×C₄×D₄	C₂²×C₇₃	semidirect
281. C₂×C₄×D₄	C₂²×C₇₃	semidirect
282. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
283. #397	C₂²×C₇₃	semidirect
284. #396	C₂²×C₇₃	semidirect
285. #394	C₂²×C₇₃	semidirect
286. #394	C₂²×C₇₃	semidirect
287. #391	C₂²×C₇₃	semidirect
290. #390	C₂²×C₇₃	semidirect
291. #390	C₂²×C₇₃	semidirect
292. #389	C₂²×C₇₃	semidirect
293. #388	C₂²×C₇₃	semidirect
294. #388	C₂²×C₇₃	semidirect
295. #386	C₂²×C₇₃	semidirect
296. #386	C₂²×C₇₃	semidirect
297. #384	C₂²×C₇₃	semidirect
298. #382	C₂²×C₇₃	semidirect
299. #381	C₂²×C₇₃	semidirect
300. #380	C₂²×C₇₃	semidirect
301. #380	C₂²×C₇₃	semidirect
302. #379	C₂²×C₇₃	semidirect
303. #379	C₂²×C₇₃	semidirect
304. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
305. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
306. C₄³	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₇₃	2
C₂×D₄²×C₇₃	2
C₇₃×#2697	2
C₇₃×#2538	2
C₇₃×#2534	2
C₇₃×#2435	2
C₇₃×#2427	2
C₇₃×#2420	2
D₄×C₂²⋊C₄×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
#59420	73

Subgroups — C73×#59420 #32968824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59420 #32968824