Subgroups — C₆₇×#59914 #30739165

Order 17152.

2156 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2807	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2780	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2763	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2587	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2583	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2505	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2505	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2487	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2449	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2437	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2437	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2360	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2358	C₂	1	2	yes	maximal
17	C₆₇×#2349	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	1	yes	maximal, characteristic
19	C₂×#385×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
34	#400×C₆₇	C₂²	1	2	yes	complemented
35	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#400×C₆₇	C₂²	1	2	yes	complemented
37	#400×C₆₇	C₂²	1	2	yes	complemented
38	#400×C₆₇	C₂²	1	2	yes	complemented
39	#399×C₆₇	C₂²	1	1	yes	characteristic
40	#399×C₆₇	C₂²	1	1	yes	characteristic
41	#399×C₆₇	C₂²	1	2	yes	complemented
42	#399×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#398×C₆₇	C₂²	1	2	yes	complemented
44	#398×C₆₇	C₂²	1	2	yes	complemented
45	#398×C₆₇	C₂²	1	2	yes	complemented
46	#396×C₆₇	C₂²	1	2	yes	—
47	#396×C₆₇	C₂²	1	2	yes	—
48	#396×C₆₇	C₂²	1	2	yes	complemented
49	#395×C₆₇	C₂²	1	2	yes	complemented
50	#395×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#393×C₆₇	C₂²	1	1	yes	characteristic
52	#393×C₆₇	C₂²	1	1	yes	characteristic
53	#393×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#391×C₆₇	C₂²	1	2	yes	complemented
55	#390×C₆₇	C₂²	1	2	yes	—
56	#389×C₆₇	C₂²	1	2	yes	complemented
57	#389×C₆₇	C₂²	1	2	yes	complemented
58	#389×C₆₇	C₂²	1	2	yes	complemented
59	#389×C₆₇	C₂²	1	2	yes	complemented
60	#389×C₆₇	C₂²	1	2	yes	complemented
61	#389×C₆₇	C₂²	1	2	yes	complemented
62	#389×C₆₇	C₂²	1	2	yes	complemented
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	—
65	#387×C₆₇	C₂²	1	2	yes	complemented
66	#387×C₆₇	C₂²	1	2	yes	complemented
67	#387×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#386×C₆₇	C₂²	1	1	yes	characteristic
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	2	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#385×C₆₇	C₂²	1	2	yes	—
75	#385×C₆₇	C₂²	1	2	yes	—
76	#385×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	—
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	1	yes	characteristic
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	—
85	#385×C₆₇	C₂²	1	2	yes	—
86	#385×C₆₇	C₂²	1	2	yes	—
87	#385×C₆₇	C₂²	1	2	yes	—
88	#385×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#385×C₆₇	C₂²	1	2	yes	complemented
91	#385×C₆₇	C₂²	1	2	yes	complemented
92	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#382×C₆₇	C₂²	1	2	yes	complemented
94	#380×C₆₇	C₂²	1	2	yes	—
95	#380×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	2	yes	complemented
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₂×#95×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₇	—	4	2	no	—
113	C₂³×C₄×C₆₇	—	4	4	no	—
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²⋊Q₈×C₆₇	—	2	8	no	—
125	C₂²⋊Q₈×C₆₇	—	4	4	no	—
126	C₂²⋊Q₈×C₆₇	—	4	2	no	—
127	#120×C₆₇	Q₈	1	8	yes	complemented
128	C₄×Q₈×C₆₇	—	4	2	no	—
129	C₄×D₄×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	4	2	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	C₄×D₄×C₆₇	—	4	4	no	—
133	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
134	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
159	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	1	yes	characteristic
193	#95×C₆₇	C₂³	1	1	yes	characteristic
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	1	yes	characteristic
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	1	yes	characteristic
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	C₂⁴×C₆₇	—	2	4	no	—
210	C₂⁴×C₆₇	—	2	4	no	—
211	C₂⁴×C₆₇	—	4	1	no	—
212	C₂⁴×C₆₇	—	4	1	no	—
213	C₂⁴×C₆₇	C₂×Q₈	1	4	yes	—
214	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
216	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
217	C₂×Q₈×C₆₇	—	2	4	no	—
218	C₂×Q₈×C₆₇	—	4	1	no	—
219	C₂×Q₈×C₆₇	—	4	2	no	—
220	C₂×Q₈×C₆₇	—	4	1	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	4	1	no	—
224	C₂×D₄×C₆₇	—	4	1	no	—
225	C₂×D₄×C₆₇	C₂×Q₈	1	8	yes	—
226	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
227	C₂²×C₄×C₆₇	—	2	4	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	2	4	no	—
230	C₂²×C₄×C₆₇	—	2	4	no	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	2	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	—	4	2	no	—
241	C₂²×C₄×C₆₇	—	4	2	no	—
242	C₂²×C₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	1	no	—
246	C₂²×C₄×C₆₇	—	4	2	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	2	no	—
251	C₂²×C₄×C₆₇	—	4	2	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	16	no	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	4	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	—	4	2	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	2	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	2	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	—	4	1	no	—
287	C₄⋊C₄×C₆₇	—	4	2	no	—
288	C₄⋊C₄×C₆₇	—	4	2	no	—
289	C₄⋊C₄×C₆₇	—	4	1	no	—
290	C₄⋊C₄×C₆₇	—	4	2	no	—
291	C₄⋊C₄×C₆₇	—	4	2	no	—
292	C₄⋊C₄×C₆₇	—	4	2	no	—
293	C₄⋊C₄×C₆₇	—	4	1	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	2	4	no	—
298	C₂²⋊C₄×C₆₇	—	2	4	no	—
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	4	2	no	—
303	C₂²⋊C₄×C₆₇	—	4	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	1	no	—
305	C₂²⋊C₄×C₆₇	—	4	1	no	—
306	C₂²⋊C₄×C₆₇	—	4	1	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
311	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
312	C₂²⋊C₄×C₆₇	#41	1	8	yes	—
313	C₄²×C₆₇	—	2	4	no	—
314	C₄²×C₆₇	—	2	2	no	—
315	C₄²×C₆₇	—	4	2	no	—
316	C₄²×C₆₇	—	4	2	no	—
317	C₄²×C₆₇	—	4	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	16	no	—
323	C₂³×C₆₇	—	2	2	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	1	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	1	no	—
329	C₂³×C₆₇	—	2	1	no	—
330	C₂³×C₆₇	—	2	1	no	—
331	C₂³×C₆₇	—	4	4	no	—
332	C₂³×C₆₇	—	4	4	no	—
333	C₂³×C₆₇	—	4	4	no	—
334	C₂³×C₆₇	—	4	8	no	—
335	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
336	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
337	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
338	C₂³×C₆₇	C₂×#41	1	4	yes	—
339	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
340	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
341	Q₈×C₆₇	—	4	4	no	—
342	Q₈×C₆₇	—	8	2	no	—
343	D₄×C₆₇	—	2	16	no	—
344	D₄×C₆₇	—	4	4	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	4	8	no	—
385	C₂×C₄×C₆₇	—	4	8	no	—
386	C₂×C₄×C₆₇	—	4	8	no	—
387	C₂×C₄×C₆₇	—	4	4	no	—
388	C₂×C₄×C₆₇	—	4	8	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	8	4	no	—
391	C₂×C₄×C₆₇	—	8	2	no	—
392	C₂×C₄×C₆₇	—	8	4	no	—
393	C₂×C₄×C₆₇	—	8	4	no	—
394	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
395	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
396	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
397	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
398	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
399	C₂²×C₆₇	—	2	4	no	—
400	C₂²×C₆₇	—	2	4	no	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	4	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	2	4	no	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	4	no	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	4	16	no	—
410	C₂²×C₆₇	—	4	1	no	—
411	C₂²×C₆₇	—	4	1	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	1	no	—
416	C₂²×C₆₇	#554	1	8	yes	—
417	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
418	C₂²×C₆₇	C₂²×#41	1	2	yes	—
419	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
420	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₆₇	#585	1	1	yes	characteristic
422	C₄×C₆₇	—	2	4	no	—
423	C₄×C₆₇	—	2	4	no	—
424	C₄×C₆₇	—	2	2	no	—
425	C₄×C₆₇	—	2	4	no	—
426	C₄×C₆₇	—	2	2	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	2	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	—	4	1	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	2	no	—
437	C₄×C₆₇	—	4	1	no	—
438	#59914	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂×C₆₇	—	2	8	no	—
440	C₂×C₆₇	—	4	2	no	—
441	C₂×C₆₇	—	4	2	no	—
442	C₂×C₆₇	C₂×#554	1	2	yes	—
443	C₂×C₆₇	#3481	1	1	yes	characteristic
444	C₂×C₆₇	#3501	1	1	yes	characteristic
445	C₂×C₆₇	#3513	1	2	yes	—
446	C₂×C₆₇	#3532	1	1	yes	characteristic
447	#2807	C₂×C₆₇	1	1	yes	characteristic, complemented
448	#2780	C₂×C₆₇	1	2	yes	complemented
449	#2763	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2587	C₂×C₆₇	1	2	yes	complemented
451	#2583	C₂×C₆₇	1	2	yes	complemented
452	#2580	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#2564	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#2505	C₂×C₆₇	1	2	yes	complemented
455	#2505	C₂×C₆₇	1	2	yes	complemented
456	#2487	C₂×C₆₇	1	2	yes	complemented
457	#2450	C₂×C₆₇	1	2	yes	complemented
458	#2449	C₂×C₆₇	1	2	yes	complemented
459	#2437	C₂×C₆₇	1	1	yes	characteristic, complemented
460	#2437	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2360	C₂×C₆₇	1	2	yes	complemented
462	#2358	C₂×C₆₇	1	2	yes	—
463	#2349	C₂×C₆₇	1	2	yes	complemented
464	C₄×#120	C₂×C₆₇	1	1	yes	characteristic
465	C₂×#385	C₂×C₆₇	1	2	yes	complemented
466	C₆₇	#59914	1	1	yes	characteristic, direct product factor, Sylow
467	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
470	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
473	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
476	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
477	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
478	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
479	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
480	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
481	#400	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	#400	C₂²×C₆₇	1	2	yes	complemented
483	#400	C₂²×C₆₇	1	2	yes	complemented
484	#400	C₂²×C₆₇	1	2	yes	complemented
485	#400	C₂²×C₆₇	1	2	yes	complemented
486	#399	C₂²×C₆₇	1	1	yes	characteristic
487	#399	C₂²×C₆₇	1	1	yes	characteristic
488	#399	C₂²×C₆₇	1	1	yes	characteristic, complemented
489	#399	C₂²×C₆₇	1	2	yes	complemented
490	#398	C₂²×C₆₇	1	2	yes	complemented
491	#398	C₂²×C₆₇	1	2	yes	complemented
492	#398	C₂²×C₆₇	1	2	yes	complemented
493	#396	C₂²×C₆₇	1	2	yes	—
494	#396	C₂²×C₆₇	1	2	yes	—
495	#396	C₂²×C₆₇	1	2	yes	complemented
496	#395	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	#395	C₂²×C₆₇	1	2	yes	complemented
498	#393	C₂²×C₆₇	1	1	yes	characteristic
499	#393	C₂²×C₆₇	1	1	yes	characteristic
500	#393	C₂²×C₆₇	1	1	yes	characteristic, complemented
501	#391	C₂²×C₆₇	1	2	yes	complemented
502	#390	C₂²×C₆₇	1	2	yes	—
503	#389	C₂²×C₆₇	1	2	yes	complemented
504	#389	C₂²×C₆₇	1	2	yes	complemented
505	#389	C₂²×C₆₇	1	2	yes	complemented
506	#389	C₂²×C₆₇	1	2	yes	complemented
507	#389	C₂²×C₆₇	1	2	yes	complemented
508	#389	C₂²×C₆₇	1	2	yes	complemented
509	#389	C₂²×C₆₇	1	2	yes	complemented
510	#388	C₂²×C₆₇	1	2	yes	—
511	#388	C₂²×C₆₇	1	2	yes	—
512	#387	C₂²×C₆₇	1	2	yes	complemented
513	#387	C₂²×C₆₇	1	2	yes	complemented
514	#387	C₂²×C₆₇	1	2	yes	complemented
515	#387	C₂²×C₆₇	1	2	yes	complemented
516	#386	C₂²×C₆₇	1	2	yes	—
517	#386	C₂²×C₆₇	1	2	yes	—
518	#386	C₂²×C₆₇	1	2	yes	—
519	#386	C₂²×C₆₇	1	2	yes	—
520	#386	C₂²×C₆₇	1	1	yes	characteristic
521	#385	C₂²×C₆₇	1	2	yes	—
522	#385	C₂²×C₆₇	1	2	yes	—
523	#385	C₂²×C₆₇	1	2	yes	—
524	#385	C₂²×C₆₇	1	2	yes	—
525	#385	C₂²×C₆₇	1	2	yes	—
526	#385	C₂²×C₆₇	1	2	yes	—
527	#385	C₂²×C₆₇	1	2	yes	—
528	#385	C₂²×C₆₇	1	2	yes	—
529	#385	C₂²×C₆₇	1	2	yes	—
530	#385	C₂²×C₆₇	1	2	yes	—
531	#385	C₂²×C₆₇	1	2	yes	—
532	#385	C₂²×C₆₇	1	2	yes	—
533	#385	C₂²×C₆₇	1	2	yes	—
534	#385	C₂²×C₆₇	1	2	yes	—
535	#385	C₂²×C₆₇	1	1	yes	characteristic
536	#385	C₂²×C₆₇	1	2	yes	—
537	#385	C₂²×C₆₇	1	2	yes	complemented
538	#385	C₂²×C₆₇	1	2	yes	complemented
539	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
540	#382	C₂²×C₆₇	1	2	yes	complemented
541	#380	C₂²×C₆₇	1	2	yes	—
542	#380	C₂²×C₆₇	1	2	yes	—
543	#380	C₂²×C₆₇	1	2	yes	complemented
544	#380	C₂²×C₆₇	1	2	yes	complemented
545	#379	C₂²×C₆₇	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
547	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
549	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
551	C₂×#95	C₂²×C₆₇	1	2	yes	—
552	C₂×#95	C₂²×C₆₇	1	2	yes	—
553	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
558	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
559	C₂³×C₄	—	4	2	no	—
560	C₂³×C₄	—	4	4	no	—
561	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
562	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
563	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
564	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
565	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
566	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
567	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
569	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₂²⋊Q₈	—	2	8	no	—
572	C₂²⋊Q₈	—	4	4	no	—
573	C₂²⋊Q₈	—	4	2	no	—
574	#120	Q₈×C₆₇	1	8	yes	complemented
575	C₄×Q₈	—	4	2	no	—
576	C₄×D₄	—	2	8	no	—
577	C₄×D₄	—	4	2	no	—
578	C₄×D₄	—	4	4	no	—
579	C₄×D₄	—	4	4	no	—
580	C₂×C₄⋊C₄	—	4	4	no	—
581	C₂×C₄⋊C₄	—	4	4	no	—
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	—	2	8	no	—
606	C₂×C₂²⋊C₄	—	4	4	no	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	1	yes	characteristic
640	#95	C₂³×C₆₇	1	1	yes	characteristic
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	2	yes	—
649	#95	C₂³×C₆₇	1	1	yes	characteristic
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	1	yes	characteristic
654	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	C₂⁴	—	2	4	no	—
657	C₂⁴	—	2	4	no	—
658	C₂⁴	—	4	1	no	—
659	C₂⁴	—	4	1	no	—
660	C₂⁴	C₂×Q₈×C₆₇	1	4	yes	—
661	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
663	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	4	1	no	—
666	C₂×Q₈	—	4	2	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	4	1	no	—
671	C₂×D₄	—	4	1	no	—
672	C₂×D₄	C₂×Q₈×C₆₇	1	8	yes	—
673	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	16	no	—
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
758	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
759	C₂²⋊C₄	#41×C₆₇	1	8	yes	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	4	2	no	—
763	C₄²	—	4	2	no	—
764	C₄²	—	4	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	16	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	8	no	—
782	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
783	C₂³	C₂²×Q₈×C₆₇	1	2	yes	—
784	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
785	C₂³	C₂×#41×C₆₇	1	4	yes	—
786	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
787	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
788	Q₈	—	4	4	no	—
789	Q₈	—	8	2	no	—
790	D₄	—	2	16	no	—
791	D₄	—	4	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	4	no	—
841	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
842	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
843	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
844	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
845	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	4	16	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	#554×C₆₇	1	8	yes	—
864	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
865	C₂²	C₂²×#41×C₆₇	1	2	yes	—
866	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
867	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
868	C₂²	#585×C₆₇	1	1	yes	characteristic
869	C₄	—	2	2	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₂	—	2	8	no	—
886	C₂	—	4	2	no	—
887	C₂	—	4	2	no	—
888	C₂	C₂×#554×C₆₇	1	2	yes	—
889	C₂	C₆₇×#3481	1	1	yes	characteristic
890	C₂	C₆₇×#3501	1	1	yes	characteristic
891	C₂	C₆₇×#3513	1	2	yes	—
892	C₂	C₆₇×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#120×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2807	C₂	semidirect
2. C₆₇×#2780	C₂	semidirect
3. C₆₇×#2763	C₂	semidirect
4. C₆₇×#2587	C₂	semidirect
5. C₆₇×#2583	C₂	semidirect
6. C₆₇×#2580	C₂	semidirect
7. C₆₇×#2564	C₂	semidirect
8. C₆₇×#2505	C₂	semidirect
9. C₆₇×#2505	C₂	semidirect
10. C₆₇×#2487	C₂	semidirect
11. C₆₇×#2450	C₂	semidirect
12. C₆₇×#2449	C₂	semidirect
13. C₆₇×#2437	C₂	semidirect
14. C₆₇×#2437	C₂	semidirect
15. C₆₇×#2360	C₂	semidirect
17. C₆₇×#2349	C₂	semidirect
19. C₂×#385×C₆₇	C₂	semidirect
23. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
25. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
35. #400×C₆₇	C₂²	semidirect
36. #400×C₆₇	C₂²	semidirect
37. #400×C₆₇	C₂²	semidirect
38. #400×C₆₇	C₂²	semidirect
41. #399×C₆₇	C₂²	semidirect
42. #399×C₆₇	C₂²	semidirect
43. #398×C₆₇	C₂²	semidirect
44. #398×C₆₇	C₂²	semidirect
45. #398×C₆₇	C₂²	semidirect
48. #396×C₆₇	C₂²	semidirect
49. #395×C₆₇	C₂²	semidirect
50. #395×C₆₇	C₂²	semidirect
53. #393×C₆₇	C₂²	semidirect
54. #391×C₆₇	C₂²	semidirect
56. #389×C₆₇	C₂²	semidirect
57. #389×C₆₇	C₂²	semidirect
58. #389×C₆₇	C₂²	semidirect
59. #389×C₆₇	C₂²	semidirect
60. #389×C₆₇	C₂²	semidirect
61. #389×C₆₇	C₂²	semidirect
62. #389×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
90. #385×C₆₇	C₂²	semidirect
91. #385×C₆₇	C₂²	semidirect
92. #382×C₆₇	C₂²	semidirect
93. #382×C₆₇	C₂²	semidirect
96. #380×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
99. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
127. #120×C₆₇	Q₈	semidirect
438. #59914	C₆₇	direct (N × H)
447. #2807	C₂×C₆₇	semidirect
448. #2780	C₂×C₆₇	semidirect
449. #2763	C₂×C₆₇	semidirect
450. #2587	C₂×C₆₇	semidirect
451. #2583	C₂×C₆₇	semidirect
452. #2580	C₂×C₆₇	semidirect
453. #2564	C₂×C₆₇	semidirect
454. #2505	C₂×C₆₇	semidirect
455. #2505	C₂×C₆₇	semidirect
456. #2487	C₂×C₆₇	semidirect
457. #2450	C₂×C₆₇	semidirect
458. #2449	C₂×C₆₇	semidirect
459. #2437	C₂×C₆₇	semidirect
460. #2437	C₂×C₆₇	semidirect
461. #2360	C₂×C₆₇	semidirect
463. #2349	C₂×C₆₇	semidirect
465. C₂×#385	C₂×C₆₇	semidirect
466. C₆₇	#59914	direct (N × H)
470. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
472. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
481. #400	C₂²×C₆₇	semidirect
482. #400	C₂²×C₆₇	semidirect
483. #400	C₂²×C₆₇	semidirect
484. #400	C₂²×C₆₇	semidirect
485. #400	C₂²×C₆₇	semidirect
488. #399	C₂²×C₆₇	semidirect
489. #399	C₂²×C₆₇	semidirect
490. #398	C₂²×C₆₇	semidirect
491. #398	C₂²×C₆₇	semidirect
492. #398	C₂²×C₆₇	semidirect
495. #396	C₂²×C₆₇	semidirect
496. #395	C₂²×C₆₇	semidirect
497. #395	C₂²×C₆₇	semidirect
500. #393	C₂²×C₆₇	semidirect
501. #391	C₂²×C₆₇	semidirect
503. #389	C₂²×C₆₇	semidirect
504. #389	C₂²×C₆₇	semidirect
505. #389	C₂²×C₆₇	semidirect
506. #389	C₂²×C₆₇	semidirect
507. #389	C₂²×C₆₇	semidirect
508. #389	C₂²×C₆₇	semidirect
509. #389	C₂²×C₆₇	semidirect
512. #387	C₂²×C₆₇	semidirect
513. #387	C₂²×C₆₇	semidirect
514. #387	C₂²×C₆₇	semidirect
515. #387	C₂²×C₆₇	semidirect
537. #385	C₂²×C₆₇	semidirect
538. #385	C₂²×C₆₇	semidirect
539. #382	C₂²×C₆₇	semidirect
540. #382	C₂²×C₆₇	semidirect
543. #380	C₂²×C₆₇	semidirect
544. #380	C₂²×C₆₇	semidirect
546. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
553. C₂×#95	C₂²×C₆₇	semidirect
574. #120	Q₈×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2807	2
C₆₇×#2780	2
C₆₇×#2763	2
C₆₇×#2587	2
C₆₇×#2583	2
C₆₇×#2580	2
C₆₇×#2564	2
C₆₇×#2505	2
C₆₇×#2487	2
C₆₇×#2450	2
C₆₇×#2449	2
C₆₇×#2437	2
C₆₇×#2360	2
C₆₇×#2358	2
C₆₇×#2349	2
C₄×#120×C₆₇	2
C₂×#385×C₆₇	2
#59914	67

Subgroups — C67×#59914 #30739165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59914 #30739165