Subgroups — C₆₇×#60270 #30739521

Order 17152.

1786 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2994	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2993	C₂	1	4	yes	maximal, complemented
5	C₆₇×#2992	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2925	C₂	1	2	yes	maximal, complemented
13	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2906	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#131×C₆₇	C₂²	1	2	yes	—
17	C₂×#131×C₆₇	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
19	#542×C₆₇	C₄	1	2	yes	—
20	#542×C₆₇	C₄	1	2	yes	—
21	#541×C₆₇	C₄	1	2	yes	—
22	#540×C₆₇	C₄	1	2	yes	—
23	#539×C₆₇	C₄	1	2	yes	—
24	#539×C₆₇	C₄	1	2	yes	—
25	#538×C₆₇	C₄	1	2	yes	—
26	#538×C₆₇	C₄	1	2	yes	—
27	#533×C₆₇	C₂²	1	1	yes	characteristic
28	#532×C₆₇	C₂²	1	1	yes	characteristic
29	#529×C₆₇	C₂²	1	4	yes	—
30	#529×C₆₇	C₂²	1	4	yes	—
31	#525×C₆₇	C₂²	1	2	yes	—
32	C₄×#41×C₆₇	C₂²	1	2	yes	—
33	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
34	#446×C₆₇	C₂²	1	2	yes	complemented
35	#446×C₆₇	C₂²	1	2	yes	complemented
36	#446×C₆₇	C₂²	1	4	yes	complemented
37	#446×C₆₇	C₂²	1	4	yes	complemented
38	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
39	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
40	#436×C₆₇	C₂²	1	4	yes	—
41	#436×C₆₇	C₂²	1	4	yes	—
42	#436×C₆₇	C₂²	1	2	yes	complemented
43	#436×C₆₇	C₂²	1	2	yes	complemented
44	#435×C₆₇	C₂²	1	4	yes	—
45	#435×C₆₇	C₂²	1	4	yes	—
46	#435×C₆₇	C₂²	1	4	yes	—
47	#435×C₆₇	C₂²	1	4	yes	—
48	#435×C₆₇	C₂²	1	4	yes	complemented
49	#435×C₆₇	C₂²	1	4	yes	complemented
50	C₈×D₄×C₆₇	C₂²	1	4	yes	—
51	C₈×D₄×C₆₇	C₂²	1	4	yes	—
52	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
53	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
54	#433×C₆₇	C₂²	1	2	yes	—
55	#433×C₆₇	C₂²	1	2	yes	—
56	#433×C₆₇	C₂²	1	2	yes	—
57	#433×C₆₇	C₂²	1	2	yes	—
58	#433×C₆₇	C₂²	1	4	yes	complemented
59	#433×C₆₇	C₂²	1	4	yes	complemented
60	#432×C₆₇	C₂²	1	4	yes	complemented
61	#431×C₆₇	C₂²	1	4	yes	complemented
62	#424×C₆₇	C₂²	1	4	yes	—
63	#424×C₆₇	C₂²	1	4	yes	—
64	#424×C₆₇	C₂²	1	2	yes	—
65	#424×C₆₇	C₂²	1	2	yes	—
66	#424×C₆₇	C₂²	1	4	yes	complemented
67	#424×C₆₇	C₂²	1	4	yes	complemented
68	#423×C₆₇	C₂²	1	2	yes	—
69	#423×C₆₇	C₂²	1	1	yes	characteristic
70	#423×C₆₇	C₂²	1	1	yes	characteristic
71	#423×C₆₇	C₂²	1	4	yes	complemented
72	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	complemented
75	#408×C₆₇	C₂²	1	2	yes	—
76	#408×C₆₇	C₂²	1	2	yes	—
77	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
78	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
79	#405×C₆₇	C₂²	1	2	yes	—
80	#405×C₆₇	C₂²	1	2	yes	—
81	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×#41×C₆₇	C₂³	1	2	yes	—
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	#131×C₆₇	—	4	4	no	—
86	#131×C₆₇	—	4	4	no	—
87	C₂×M₁₆×C₆₇	—	4	4	no	—
88	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
89	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
90	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
91	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
92	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
93	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
98	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
99	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
100	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
103	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
104	#126×C₆₇	C₂×C₄	1	4	yes	—
105	#126×C₆₇	C₂×C₄	1	4	yes	—
106	#126×C₆₇	C₂×C₄	1	4	yes	—
107	#126×C₆₇	C₂×C₄	1	4	yes	—
108	#125×C₆₇	C₂×C₄	1	4	yes	—
109	#125×C₆₇	C₂×C₄	1	4	yes	—
110	#125×C₆₇	C₂×C₄	1	2	yes	—
111	#124×C₆₇	C₂×C₄	1	4	yes	—
112	#124×C₆₇	C₂×C₄	1	4	yes	—
113	#124×C₆₇	C₂×C₄	1	2	yes	—
114	#123×C₆₇	C₂×C₄	1	4	yes	—
115	#123×C₆₇	C₂×C₄	1	4	yes	—
116	#123×C₆₇	C₂×C₄	1	4	yes	—
117	#123×C₆₇	C₂×C₄	1	4	yes	—
118	#123×C₆₇	C₂×C₄	1	4	yes	—
119	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
120	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
121	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
122	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
123	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
124	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
125	#121×C₆₇	C₂×C₄	1	2	yes	—
126	#121×C₆₇	C₂×C₄	1	2	yes	—
127	#121×C₆₇	C₂×C₄	1	4	yes	—
128	#121×C₆₇	C₂×C₄	1	4	yes	—
129	#121×C₆₇	C₂×C₄	1	2	yes	—
130	#121×C₆₇	C₂×C₄	1	2	yes	—
131	#120×C₆₇	C₂×C₄	1	4	yes	—
132	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
133	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
134	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
135	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
136	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
137	C₄×D₄×C₆₇	C₂×C₄	1	4	yes	—
138	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
139	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
140	C₄×D₄×C₆₇	C₂³	1	4	yes	—
141	C₄×D₄×C₆₇	C₂³	1	4	yes	—
142	C₄×D₄×C₆₇	C₂³	1	2	yes	—
143	C₄×D₄×C₆₇	C₂³	1	2	yes	—
144	#117×C₆₇	C₂×C₄	1	2	yes	—
145	#117×C₆₇	C₂×C₄	1	2	yes	—
146	#117×C₆₇	C₂³	1	2	yes	—
147	#117×C₆₇	C₂³	1	2	yes	—
148	#117×C₆₇	C₂³	1	2	yes	—
149	#117×C₆₇	C₂³	1	4	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
157	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
158	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
159	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
160	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
161	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
162	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
163	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
164	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
165	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
166	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
167	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
168	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
169	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
170	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
171	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
172	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
173	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
174	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
175	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
177	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
179	#97×C₆₇	C₂³	1	2	yes	—
180	#97×C₆₇	C₂³	1	2	yes	—
181	#97×C₆₇	C₂³	1	4	yes	—
182	#97×C₆₇	C₂³	1	4	yes	—
183	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
184	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
185	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
186	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
187	C₄×C₈×C₆₇	C₂³	1	4	yes	—
188	C₄×C₈×C₆₇	C₂³	1	4	yes	—
189	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
190	#41×C₆₇	—	2	4	no	—
191	#41×C₆₇	—	2	4	no	—
192	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
193	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
194	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
195	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
196	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
197	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
198	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
199	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
200	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₆₇	—	2	2	no	—
202	C₂²×C₄×C₆₇	—	2	2	no	—
203	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
205	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
210	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
211	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
214	M₁₆×C₆₇	—	2	4	no	—
215	M₁₆×C₆₇	—	2	4	no	—
216	M₁₆×C₆₇	—	4	4	no	—
217	M₁₆×C₆₇	—	4	4	no	—
218	M₁₆×C₆₇	—	4	4	no	—
219	C₂×C₈×C₆₇	—	2	2	no	—
220	C₂×C₈×C₆₇	—	2	2	no	—
221	C₂×C₈×C₆₇	—	2	2	no	—
222	C₂×C₈×C₆₇	—	2	2	no	—
223	C₂×C₈×C₆₇	—	4	4	no	—
224	C₂×C₈×C₆₇	—	4	4	no	—
225	C₂×C₈×C₆₇	—	4	4	no	—
226	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
228	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
229	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
230	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
233	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
235	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
236	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
237	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
238	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
239	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
240	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
241	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
242	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
243	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
244	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
245	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
246	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
247	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
248	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
249	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
250	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
251	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
252	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
253	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
254	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
255	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
256	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
257	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
258	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
259	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
260	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
261	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
262	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
263	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
264	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
265	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
266	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
267	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
268	C₄²×C₆₇	C₂⁴	1	2	yes	—
269	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
270	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₄²×C₆₇	C₂⁴	1	4	yes	—
272	C₂³×C₆₇	—	2	2	no	—
273	C₂³×C₆₇	—	4	1	no	—
274	C₂³×C₆₇	—	4	1	no	—
275	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
276	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
277	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
278	Q₈×C₆₇	—	2	4	no	—
279	Q₈×C₆₇	—	4	2	no	—
280	Q₈×C₆₇	—	4	2	no	—
281	D₄×C₆₇	—	2	8	no	—
282	D₄×C₆₇	—	2	4	no	—
283	D₄×C₆₇	—	4	2	no	—
284	D₄×C₆₇	—	4	2	no	—
285	D₄×C₆₇	—	4	4	no	—
286	D₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	4	no	—
293	C₂×C₄×C₆₇	—	4	1	no	—
294	C₂×C₄×C₆₇	—	4	1	no	—
295	C₂×C₄×C₆₇	—	4	4	no	—
296	C₂×C₄×C₆₇	—	4	4	no	—
297	C₂×C₄×C₆₇	—	4	1	no	—
298	C₂×C₄×C₆₇	—	4	1	no	—
299	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
303	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
305	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
306	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
308	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
311	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
312	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
313	C₈×C₆₇	—	2	1	no	—
314	C₈×C₆₇	—	2	2	no	—
315	C₈×C₆₇	—	2	1	no	—
316	C₈×C₆₇	—	2	4	no	—
317	C₈×C₆₇	—	2	4	no	—
318	C₈×C₆₇	—	2	1	no	—
319	C₈×C₆₇	—	2	1	no	—
320	C₈×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	1	no	—
322	C₂²×C₆₇	—	2	1	no	—
323	C₂²×C₆₇	—	2	2	no	—
324	C₂²×C₆₇	—	2	4	no	—
325	C₂²×C₆₇	—	2	4	no	—
326	C₂²×C₆₇	—	2	4	no	—
327	C₂²×C₆₇	—	2	2	no	—
328	C₂²×C₆₇	—	2	2	no	—
329	C₂²×C₆₇	—	8	2	no	—
330	C₂²×C₆₇	#520	1	2	yes	—
331	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
332	C₄×C₆₇	—	2	2	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	2	2	no	—
335	C₄×C₆₇	—	2	2	no	—
336	C₄×C₆₇	—	2	1	no	—
337	C₄×C₆₇	—	2	1	no	—
338	C₄×C₆₇	—	2	4	no	—
339	C₄×C₆₇	—	2	4	no	—
340	C₄×C₆₇	—	2	1	no	—
341	C₄×C₆₇	—	2	1	no	—
342	C₄×C₆₇	#520	1	2	yes	—
343	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	#60270	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂×C₆₇	—	2	2	no	—
347	C₂×C₆₇	—	4	4	no	—
348	C₂×C₆₇	—	4	2	no	—
349	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
350	C₂×C₆₇	#3573	1	1	yes	characteristic
351	C₂×C₆₇	#3573	1	1	yes	characteristic
352	#3455	C₂×C₆₇	1	1	yes	characteristic
353	#2995	C₂×C₆₇	1	4	yes	complemented
354	#2994	C₂×C₆₇	1	4	yes	complemented
355	#2993	C₂×C₆₇	1	4	yes	complemented
356	#2992	C₂×C₆₇	1	4	yes	complemented
357	#2961	C₂×C₆₇	1	1	yes	characteristic, complemented
358	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
359	#2933	C₂×C₆₇	1	2	yes	complemented
360	#2933	C₂×C₆₇	1	2	yes	complemented
361	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
362	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
363	#2925	C₂×C₆₇	1	2	yes	complemented
364	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
365	#2906	C₂×C₆₇	1	2	yes	complemented
366	#2905	C₂×C₆₇	1	1	yes	characteristic, complemented
367	C₆₇	#60270	1	1	yes	characteristic, direct product factor, Sylow
368	C₂×#131	C₂²×C₆₇	1	2	yes	—
369	C₂×#131	C₂²×C₆₇	1	2	yes	—
370	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
371	#542	C₄×C₆₇	1	2	yes	—
372	#542	C₄×C₆₇	1	2	yes	—
373	#541	C₄×C₆₇	1	2	yes	—
374	#540	C₄×C₆₇	1	2	yes	—
375	#539	C₄×C₆₇	1	2	yes	—
376	#539	C₄×C₆₇	1	2	yes	—
377	#538	C₄×C₆₇	1	2	yes	—
378	#538	C₄×C₆₇	1	2	yes	—
379	#533	C₂²×C₆₇	1	1	yes	characteristic
380	#532	C₂²×C₆₇	1	1	yes	characteristic
381	#529	C₂²×C₆₇	1	4	yes	—
382	#529	C₂²×C₆₇	1	4	yes	—
383	#525	C₂²×C₆₇	1	2	yes	—
384	C₄×#41	C₂²×C₆₇	1	2	yes	—
385	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
386	#446	C₂²×C₆₇	1	2	yes	complemented
387	#446	C₂²×C₆₇	1	2	yes	complemented
388	#446	C₂²×C₆₇	1	4	yes	complemented
389	#446	C₂²×C₆₇	1	4	yes	complemented
390	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
391	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
392	#436	C₂²×C₆₇	1	4	yes	—
393	#436	C₂²×C₆₇	1	4	yes	—
394	#436	C₂²×C₆₇	1	2	yes	complemented
395	#436	C₂²×C₆₇	1	2	yes	complemented
396	#435	C₂²×C₆₇	1	4	yes	—
397	#435	C₂²×C₆₇	1	4	yes	—
398	#435	C₂²×C₆₇	1	4	yes	—
399	#435	C₂²×C₆₇	1	4	yes	—
400	#435	C₂²×C₆₇	1	4	yes	complemented
401	#435	C₂²×C₆₇	1	4	yes	complemented
402	C₈×D₄	C₂²×C₆₇	1	4	yes	—
403	C₈×D₄	C₂²×C₆₇	1	4	yes	—
404	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
405	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
406	#433	C₂²×C₆₇	1	2	yes	—
407	#433	C₂²×C₆₇	1	2	yes	—
408	#433	C₂²×C₆₇	1	2	yes	—
409	#433	C₂²×C₆₇	1	2	yes	—
410	#433	C₂²×C₆₇	1	4	yes	complemented
411	#433	C₂²×C₆₇	1	4	yes	complemented
412	#432	C₂²×C₆₇	1	4	yes	complemented
413	#431	C₂²×C₆₇	1	4	yes	complemented
414	#424	C₂²×C₆₇	1	4	yes	—
415	#424	C₂²×C₆₇	1	4	yes	—
416	#424	C₂²×C₆₇	1	2	yes	—
417	#424	C₂²×C₆₇	1	2	yes	—
418	#424	C₂²×C₆₇	1	4	yes	complemented
419	#424	C₂²×C₆₇	1	4	yes	complemented
420	#423	C₂²×C₆₇	1	2	yes	—
421	#423	C₂²×C₆₇	1	1	yes	characteristic
422	#423	C₂²×C₆₇	1	1	yes	characteristic
423	#423	C₂²×C₆₇	1	4	yes	complemented
424	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
425	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
426	C₂×C₄⋊C₈	C₂²×C₆₇	1	4	yes	complemented
427	#408	C₂²×C₆₇	1	2	yes	—
428	#408	C₂²×C₆₇	1	2	yes	—
429	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
431	#405	C₂²×C₆₇	1	2	yes	—
432	#405	C₂²×C₆₇	1	2	yes	—
433	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×#41	C₂³×C₆₇	1	2	yes	—
436	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
437	#131	—	4	4	no	—
438	#131	—	4	4	no	—
439	C₂×M₁₆	—	4	4	no	—
440	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
441	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
442	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
443	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
444	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
445	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
450	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
451	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
452	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
453	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
454	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
455	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
456	#126	C₂×C₄×C₆₇	1	4	yes	—
457	#126	C₂×C₄×C₆₇	1	4	yes	—
458	#126	C₂×C₄×C₆₇	1	4	yes	—
459	#126	C₂×C₄×C₆₇	1	4	yes	—
460	#125	C₂×C₄×C₆₇	1	4	yes	—
461	#125	C₂×C₄×C₆₇	1	4	yes	—
462	#125	C₂×C₄×C₆₇	1	2	yes	—
463	#124	C₂×C₄×C₆₇	1	4	yes	—
464	#124	C₂×C₄×C₆₇	1	4	yes	—
465	#124	C₂×C₄×C₆₇	1	2	yes	—
466	#123	C₂×C₄×C₆₇	1	4	yes	—
467	#123	C₂×C₄×C₆₇	1	4	yes	—
468	#123	C₂×C₄×C₆₇	1	4	yes	—
469	#123	C₂×C₄×C₆₇	1	4	yes	—
470	#123	C₂×C₄×C₆₇	1	4	yes	—
471	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
472	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
473	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
474	C₂²⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
475	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
476	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
477	#121	C₂×C₄×C₆₇	1	2	yes	—
478	#121	C₂×C₄×C₆₇	1	2	yes	—
479	#121	C₂×C₄×C₆₇	1	4	yes	—
480	#121	C₂×C₄×C₆₇	1	4	yes	—
481	#121	C₂×C₄×C₆₇	1	2	yes	—
482	#121	C₂×C₄×C₆₇	1	2	yes	—
483	#120	C₂×C₄×C₆₇	1	4	yes	—
484	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
485	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
486	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
487	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
488	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
489	C₄×D₄	C₂×C₄×C₆₇	1	4	yes	—
490	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
491	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
492	C₄×D₄	C₂³×C₆₇	1	4	yes	—
493	C₄×D₄	C₂³×C₆₇	1	4	yes	—
494	C₄×D₄	C₂³×C₆₇	1	2	yes	—
495	C₄×D₄	C₂³×C₆₇	1	2	yes	—
496	#117	C₂×C₄×C₆₇	1	2	yes	—
497	#117	C₂×C₄×C₆₇	1	2	yes	—
498	#117	C₂³×C₆₇	1	2	yes	—
499	#117	C₂³×C₆₇	1	2	yes	—
500	#117	C₂³×C₆₇	1	2	yes	—
501	#117	C₂³×C₆₇	1	4	yes	—
502	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
509	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
510	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
511	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
512	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
513	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
514	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
515	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
516	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
517	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
518	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
519	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
520	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
521	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
522	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
523	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
524	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
525	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
526	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
527	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
528	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
529	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
530	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
531	#97	C₂³×C₆₇	1	2	yes	—
532	#97	C₂³×C₆₇	1	2	yes	—
533	#97	C₂³×C₆₇	1	4	yes	—
534	#97	C₂³×C₆₇	1	4	yes	—
535	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
536	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
537	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
538	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
539	C₄×C₈	C₂³×C₆₇	1	4	yes	—
540	C₄×C₈	C₂³×C₆₇	1	4	yes	—
541	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
542	#41	—	2	4	no	—
543	#41	—	2	4	no	—
544	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
545	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
546	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
547	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
548	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
549	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
550	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
551	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
552	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
557	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
558	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
559	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
560	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
561	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
562	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
563	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
566	M₁₆	—	2	4	no	—
567	M₁₆	—	2	4	no	—
568	M₁₆	—	4	4	no	—
569	M₁₆	—	4	4	no	—
570	M₁₆	—	4	4	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	—	2	2	no	—
575	C₂×C₈	—	4	4	no	—
576	C₂×C₈	—	4	4	no	—
577	C₂×C₈	—	4	4	no	—
578	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
579	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
580	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
581	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
582	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
583	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
584	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
585	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
586	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
587	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
588	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
589	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
590	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
591	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
592	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
593	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
594	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
595	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
596	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
597	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
598	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
599	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
600	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
601	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
602	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
603	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
604	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
605	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
606	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
607	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
608	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
609	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
610	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
611	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
612	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
613	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
614	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
615	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
616	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
617	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
618	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
619	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
620	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
622	C₄²	C₂⁴×C₆₇	1	4	yes	—
623	C₄²	C₂⁴×C₆₇	1	2	yes	—
624	C₂³	—	2	2	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
628	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
629	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
630	Q₈	—	2	4	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	2	no	—
633	D₄	—	2	8	no	—
634	D₄	—	2	4	no	—
635	D₄	—	4	2	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	4	no	—
638	D₄	—	4	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
652	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
655	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
657	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
658	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
659	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
660	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
661	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
662	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
663	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
664	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
665	C₈	—	2	1	no	—
666	C₈	—	2	2	no	—
667	C₈	—	2	1	no	—
668	C₈	—	2	4	no	—
669	C₈	—	2	4	no	—
670	C₈	—	2	1	no	—
671	C₈	—	2	1	no	—
672	C₈	—	2	2	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	8	2	no	—
682	C₂²	#520×C₆₇	1	2	yes	—
683	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	4	no	—
694	C₄	#520×C₆₇	1	2	yes	—
695	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
696	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
697	C₂	—	2	2	no	—
698	C₂	—	4	2	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
701	C₂	C₆₇×#3573	1	1	yes	characteristic
702	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3455	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2994	C₂	semidirect
4. C₆₇×#2993	C₂	semidirect
5. C₆₇×#2992	C₂	semidirect
6. C₆₇×#2961	C₂	semidirect
7. C₆₇×#2960	C₂	semidirect
8. C₆₇×#2933	C₂	semidirect
9. C₆₇×#2933	C₂	semidirect
10. C₆₇×#2932	C₂	semidirect
11. C₆₇×#2931	C₂	semidirect
12. C₆₇×#2925	C₂	semidirect
13. C₂×#433×C₆₇	C₂	semidirect
14. C₆₇×#2906	C₂	semidirect
15. C₆₇×#2905	C₂	semidirect
34. #446×C₆₇	C₂²	semidirect
35. #446×C₆₇	C₂²	semidirect
36. #446×C₆₇	C₂²	semidirect
37. #446×C₆₇	C₂²	semidirect
38. C₈×Q₈×C₆₇	C₂²	semidirect
39. C₈×Q₈×C₆₇	C₂²	semidirect
42. #436×C₆₇	C₂²	semidirect
43. #436×C₆₇	C₂²	semidirect
48. #435×C₆₇	C₂²	semidirect
49. #435×C₆₇	C₂²	semidirect
52. C₈×D₄×C₆₇	C₂²	semidirect
53. C₈×D₄×C₆₇	C₂²	semidirect
58. #433×C₆₇	C₂²	semidirect
59. #433×C₆₇	C₂²	semidirect
60. #432×C₆₇	C₂²	semidirect
61. #431×C₆₇	C₂²	semidirect
66. #424×C₆₇	C₂²	semidirect
67. #424×C₆₇	C₂²	semidirect
71. #423×C₆₇	C₂²	semidirect
74. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
345. #60270	C₆₇	direct (N × H)
353. #2995	C₂×C₆₇	semidirect
354. #2994	C₂×C₆₇	semidirect
355. #2993	C₂×C₆₇	semidirect
356. #2992	C₂×C₆₇	semidirect
357. #2961	C₂×C₆₇	semidirect
358. #2960	C₂×C₆₇	semidirect
359. #2933	C₂×C₆₇	semidirect
360. #2933	C₂×C₆₇	semidirect
361. #2932	C₂×C₆₇	semidirect
362. #2931	C₂×C₆₇	semidirect
363. #2925	C₂×C₆₇	semidirect
364. C₂×#433	C₂×C₆₇	semidirect
365. #2906	C₂×C₆₇	semidirect
366. #2905	C₂×C₆₇	semidirect
367. C₆₇	#60270	direct (N × H)
386. #446	C₂²×C₆₇	semidirect
387. #446	C₂²×C₆₇	semidirect
388. #446	C₂²×C₆₇	semidirect
389. #446	C₂²×C₆₇	semidirect
390. C₈×Q₈	C₂²×C₆₇	semidirect
391. C₈×Q₈	C₂²×C₆₇	semidirect
394. #436	C₂²×C₆₇	semidirect
395. #436	C₂²×C₆₇	semidirect
400. #435	C₂²×C₆₇	semidirect
401. #435	C₂²×C₆₇	semidirect
404. C₈×D₄	C₂²×C₆₇	semidirect
405. C₈×D₄	C₂²×C₆₇	semidirect
410. #433	C₂²×C₆₇	semidirect
411. #433	C₂²×C₆₇	semidirect
412. #432	C₂²×C₆₇	semidirect
413. #431	C₂²×C₆₇	semidirect
418. #424	C₂²×C₆₇	semidirect
419. #424	C₂²×C₆₇	semidirect
423. #423	C₂²×C₆₇	semidirect
426. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3455	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2961	2
C₆₇×#2960	2
C₆₇×#2933	2
C₆₇×#2932	2
C₆₇×#2931	2
C₆₇×#2925	2
C₂×#433×C₆₇	2
C₆₇×#2906	2
C₆₇×#2905	2
#60270	67

Subgroups — C67×#60270 #30739521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60270 #30739521